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The Irish Bee Conservation Project is a charitable organisation in Ireland that seeks to conserve all native Irish bee species. It has four "pillars of support" in its work: providing habitats, increasing biodiversity, holding education events and performing research into the decline of bee species. [ 1 ] Species of bee in Ireland include the honeybee ( Apis mellifera ), 21 species of bumblebee and 78 species of solitary bee . [ 2 ]
The Irish Bee Conservation Project (IBCP) grew out of a research project looking at honeybees and the Varroa mite and was formed in 2019 as a not for profit private company limited by guarantee . That same year it designed and installed its first honeybee "lodges" in Fota Wildlife Park , County Cork. [ 1 ]
In 2021, the Irish Bee Conservation Project registered as a charity with the Charities Regulator of Ireland. [ 3 ]
The charity developed and installed a pollinator trail, in conjunction with the Office of Public Works , at Fota Gardens . [ 4 ] Opened in 2021, the walking trail consists of a series of 12 stations with QR codes which provide links to information about the gardens, bees and other pollinators. [ 5 ]
Other projects by the IBCP include the installation of 24 wild bee lodges at Lough Gur , County Limerick . These lodges are designed to replace lost natural habitats. [ 6 ] Since 2020, it has been helping Randal Plunkett, 21st Baron of Dunsany with the rewilding of the Dunsany estate in County Meath by advising him and supplying bee lodges. [ 7 ]
In 2022, the charity hosted a free educational event at the South East Technological University 's Bealtaine Living Earth Festival. [ 8 ] The charity also has an apiary holding native honeybees, where it performs breeding and an ongoing eight year research project into varroa mite tolerance, no research results have been published. [ 9 ] | https://en.wikipedia.org/wiki/Irish_Bee_Conservation_Project |
The Irish Council for Bioethics ( Irish : Comhairle Bitheitice na hÉireann ) was an independent body established by the Government of Ireland in 2002 to examine and respond to bioethical issues in science and medicine. [ 1 ] It provided independent advice to the government and those making policy, as well as promoting public understanding of contemporary bioethical issues. It ceased operations in 2010, due to withdrawal of state funding in the wake of the post-2008 Irish economic downturn . [ 1 ]
During its years of operation, the members of the council were nominated by the Royal Irish Academy , which also provided the body's secretariat. [ 2 ] It was funded by grants through Forfás . [ 2 ]
This article about an organisation in Ireland is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Irish_Council_for_Bioethics |
The Irish Federation of Astronomical Societies (IFAS) is an umbrella group comprising most of the National and Regional Astronomical Societies on the Island of Ireland.
IFAS was formed in October 1999 to provide an umbrella organisation for mutual benefit and co-operation for almost all Irish astronomical clubs and societies on the Island of Ireland, north and south.
Since its inception it has formed an on-line community for astronomers though its website.
Currently (July 2014) there are over 2,200 registered users from around the world taking part in over 12,000 different topics of astronomical interest. A monthly, sponsored astrophotography competition allows for people to pursue an added interest and better their skills, and perhaps win a prize.
The federation council is made up of 2 members from each club/society, regardless of the size of the society.
Out of the council, a Chairman, vice Chairman, Secretary and Treasurer are elected annually.
The IFAS Constitution details the running of IFAS. [ 1 ]
IFAS holds its Annual General Meeting September and October each year. [ 1 ]
According to the IFAS constitution, membership is open to any astronomical clubs or societies on the island of Ireland "which are governed by a democratically elected council or committee". [ 1 ]
The current members are: | https://en.wikipedia.org/wiki/Irish_Federation_of_Astronomical_Societies |
The Irish Steam Preservation Society is a voluntary organisation based in Stradbally, Co Laois whose aim is to preserve and maintain machinery connected to Ireland's industrial and social heritage. The society is responsible for the Irish National Steam Rally. Additionally, it curates the Stradbally Steam Museum and runs the traditional Irish 3 ft ( 914 mm ) narrow gauge Stradbally Woodland Railway .
The Irish Steam Preservation Society was formed by a group of Laois based enthusiasts who set out to preserve for the good of the country, a part of our national agricultural heritage, the steam traction engine and its many forms after a meeting of half a dozen members at Harold Condell’s farm in Whitefields Co. Laois in 1964. They visited the Lowton Park rally in Lancashire England to see how a rally was run in the summer of 1965. A small gathering of engines was held at the market house in Stradbally on St Stephen's day 1965 and thus with this being regarded as a success it was decided upon by the newly formed society to hold a larger rally in the grounds of Stradbally hall on the August Bank holiday weekend the following year.
The National Steam Rally began as a simple arena with engines taking part in various competitions such as a slow race, lining up to the threshing mill competitions and winching displays. Other attractions at the rally soon came about, notable was the addition of the steam railway in 1967 of a simple track laid out and a locomotive kindly donated by the Guinness Brewery was run with its passenger carriage in tow. In 1969 tracks were laid to run the preserved Bórd na Móna locomotive No.2. With this addition the National Steam Rally at Stradbally remains as the only rally in Ireland to have a steam railway.
The National Steam Rally has grown and for its 50th year gathered the most steam engines ever on the island of Ireland for that special anniversary year. With this prominence other heritage focused groups such as the Celtic steamers have used the National rally as a place to end their ‘road runs’ which they use to raise money for various charities around the country. The rally has grown again in recent years to establish itself as the premier event in the Irish Steam rally calendar and has gained international recognition with visitors travelling from as far as Germany to experience it.
The Stradbally Woodland Railway was the first volunteer-run heritage railway in Ireland, having been established in 1969. We've been running regular steam services every Bank Holiday weekend and selected other running days during the year ever since. The railway operates from a station through the woods, returning via a balloon loop . This line is home to former Bord na Móna steam locomotive No. 2 (later No. LM44) "Roisín" which had been built by Andrew Barclay Sons & Co. (2264 of 1949).
In June 1968 the “Steam Museum” was opened in Stradbally by P.J Lalor, parliamentary secretary to the Minister of Transport and Power. It has grown from its humble beginnings to the fine building it is today housing many fine exhibits and engines for the public to see. It is open by arrangement with the societies secretary. | https://en.wikipedia.org/wiki/Irish_Steam_Preservation_Society |
The Irish Stem Cell Foundation is Ireland's National Stem Cell Research Organisation. [ 1 ] A Member of the International Consortium of Stem Cell Networks, [ 2 ] the foundation is committed to the pursuit of international cooperation, collaboration and excellence in the stem cell field.
The Irish Stem Cell Foundation is a non-profit organization . It was established in Dublin [ 3 ] in October 2009, and is composed of doctors, researchers, patient advocates, science communicators, solicitors, teachers and students.
The foundation's objectives are described as:
The Chief Scientific Officer of the Foundation is Dr Stephen Sullivan [ 8 ] [ 9 ] [ 10 ] [ 11 ] The Chief Medical Officer of the Foundation is Professor Orla Hardiman .
The foundation has engaged the international and domestic media on the topic of stem cell tourism , where patients are scammed by unregulated clinics making medically and scientifically unsubstantiated claims to patients over the internet. [ 12 ] [ 13 ] Such experimental protocols endanger patients' lives and harm the reputation of legitimate stem cell research and clinical trials (which are tightly regulated).
The foundation agrees with the Irish Council Of Bioethics and the Irish Committee for Assisted Human Reproduction that Irish stem cell research needs a strong, transparent ethical and legislative structure. In 2010, the Foundation issued a public policy document on embryonic stem cell research .
In 2012 the Irish Stem Cell Foundation hosted its second conference, the Irish Stem Cell Summit, in Dublin. [ 14 ] The Summit focused on the underdevelopment of Irish policy and law pertaining to stem cells, and the detrimental effect this has on the quality of research in the area, as well as the damage this is doing to public trust, international investment and collaboration. [ 15 ]
In 2013, the Foundation led a campaign with other Irish medical research charities to question the wisdom of abolishing Ireland's independent Chief Scientific Adviser. [ 16 ] [ 17 ] [ 18 ] More recently, the Foundation joined with the Wellcome Trust and the Royal Society of Medicine in the UK to urge the European Parliament to maintain funding for European stem cell research. [ 19 ]
The Irish Stem Cell Foundation is not affiliated with the lobby group calling itself 'The Adult Stem Cell Foundation of Ireland'. [ 20 ] The Irish Stem Cell Foundation supports all types of stem cell research governed by an open and transparent ethics structure. This position is consistent with those formulated by several other Irish groups including The Commission for Assisted Human Reproduction, The Irish Council of Bioethics, and The Irish Patients Association. | https://en.wikipedia.org/wiki/Irish_Stem_Cell_Foundation |
The Irish defective block crisis affects several counties within the Republic of Ireland . To date the counties most severely impacted have been County Donegal and County Mayo , with other counties having fewer affected buildings. An expert committee established in 2016 by the then Minister of Housing and Urban Renewal investigated the causes in both County Donegal and County Mayo, and concluded that the principal cause of the damage was due to the use of defective concrete blocks. [ 1 ] Within county Donegal this was originally termed the Mica scandal in 2011, which is the point at which homes and other buildings began showing signs of cracking and decay. [ 2 ] The term "mica scandal" arose because the expert committee had observed that defective concrete blocks within County Donegal contained excessive quantities of the mineral mica liberated within the binder. Within County Mayo the expert committee concluded that the defective blocks were caused by internal sulphate attack sourced from framboidal pyrite within the aggregate, as evidenced from both presence of framboidal pyrite and elevated sulphate content. [ 1 ]
The scandal led to calls for, and then the establishment of, a scheme to fund affected homeowners of the fault to repair, or demolish and rebuild, their homes. [ 2 ] A similar issue with the presence of pyrite in the hardfill of properties was also identified in 2007, originating within quarries in the east of Ireland, [ 3 ] and legislation was enacted to address both of the issues similarly. During 2023, new theories were advanced as to the source of the problems with the blocks, specifically that within County Donegal elevated concentrations of pyrrhotite (above relevant EN 12620 guidance [ 4 ] ) was the principal cause of the problem, albeit with the elevated mica contributing to a weakened binder. [ 5 ] [ 6 ] At present the root cause in County Mayo and other counties is considered to be the presence of framboidal pyrite as highlighted by the original expert report.
More than five thousand houses and an unknown number of office and other buildings have been affected, with some owners moving out of their homes as they are no longer safe. [ 2 ] Damage generally manifests on properties as cracking of render and walls, expansion of concrete and the eventual loss of structural integrity. The majority of affected homes are in County Donegal, but there are also some in County Mayo , County Clare , County Limerick and elsewhere. [ 2 ] [ 7 ] Around the same time, the use of pyrite in construction caused similar issues for buildings in the East of Ireland. Cracking and bulging appeared in flooring concrete and other materials soon after construction. [ 7 ] [ 8 ] [ 3 ]
Muscovite (also known as common mica) can be found in rocks used to make concrete blocks. It is estimated that a presence of 1% of muscovite in concrete reduces the strength of the internal bonding by 5%, and further that such blocks bond poorly with cement paste. [ 2 ] Mica also absorbs water, and excess water can cause problems in cold winters as the process of freezing and thawing damages the blocks. [ 2 ] During 2023, additional scientific evidence as to the root cause possibilities emerged, suggesting that the issue may lie more with the iron compound pyrrhotite than with mica, [ 5 ] [ 6 ] although the high mica content of the binder may still be relevant due to its impact on binder quality, making it more susceptible to internal sulphate attack from the oxidising pyrrhotite.
An expert panel reported to government in 2017 that the problems in these counties add to "the legacy of building failures or severe non-compliance concerns following the downturn in economic and construction activity in 2008, which exposed vulnerabilities in the building control system that was in place at that time". [ 2 ] The report included information from the National Standards Authority of Ireland that mica and other harmful impurities are limited to 1% of concrete blocks and this is covered by a statutory instrument . [ 2 ] In some affected homes in Donegal, the amount of mica in samples was significantly above the limit, potentially up to 14%. [ 2 ] [ 9 ] Companies producing building materials must comply with regulations such as the Building Control Regulations. [ 2 ]
The report stated that building control authorities lacked the ability to test materials in-house and that all ability to enforce regulations was limited by local authority budgets. [ 2 ]
Campaigns seeking redress for the issue began in 2011. [ 10 ]
Partly as a result of homeowner campaigning, the Defective Block Scheme was opened in June 2020. [ 2 ] The scheme offers five options, from replacing an external wall, with a limit of €49,500, to demolition and rebuilding, with a limit of €247,500. [ 2 ] 433 people in Donegal had engaged with the scheme as of June 2021. [ 2 ] Campaigners pointed out that homeowners had to pay €5,000 for a mica test to apply to the scheme and that this was a barrier for those who were in financial difficulty. [ 2 ] They also wanted the scheme to cover 100% of costs, instead of the proposed 90% of costs. [ 2 ] The grant was updated in November 2021, with the limit increased to €420,000, and 100% cover for costs. [ 11 ] Houses in Clare and Limerick were added to the scheme, with estimates suggesting that over one thousand homes could be affected in those counties. In June 2022, ministers were advised that the cost of the scheme could reach €3.65 billion if inflation remained high. [ 7 ] A similar redress scheme was announced for those affected by pyrite usage in construction, similarly covering 100% of costs, but only for repair works. [ 11 ]
Protest marches were held in Dublin in June and October 2021, with thousands of people reported to have attended. [ 2 ] [ 12 ]
In 2023, the Donegal Mica Action Group founded 100% Redress , a political party registered to contest local and Dáil elections. [ 13 ] [ 14 ] [ 15 ] In the 2024 general election , Charles Ward was elected representing 100% Redress.
2,000 or more legal actions were initiated against suppliers of defective blocks, as well as local authorities and standards bodies for failing to detect the issue, doubts were expressed as to whether the suppliers, at least, had the resources or insurance cover to provide any significant compensation. Actions against developers for using or failing to test blocks were scarcer. [ 16 ] [ 17 ]
Cassidy Brothers, one of the companies that produced the blocks, was issued with an enforcement notice in October 2021 in relation to land in Cranford, County Donegal . [ 18 ] The company was ordered to shut a concrete batching plant and storage yard. [ 18 ] In November 2021, they were issued with an unauthorised development letter by Donegal County Council , as they did not have planning permission to develop blocks at their site in Gransha, Buncrana . [ 18 ] | https://en.wikipedia.org/wiki/Irish_defective_block_crisis |
Irma Goldberg (born 1871) was a Russian-born chemist. She was one of the first female organic chemists to have and sustain a successful career, her work even being quoted in her own name in standard textbooks. [ 1 ]
Born in Moscow to a Russian-Jewish family, she later traveled to Geneva in the 1890s to study chemistry at Geneva University. [ 2 ]
Her early research included the development of a process to remove sulfur and phosphorus from acetylene. Her first article on the derivatives of benzophenone , coauthored by German chemist Fritz Ullmann , was published in 1897. [ 1 ] [ 3 ] She also researched and wrote a paper (published in 1904) on using copper as a catalyst for the preparation of a phenyl derivative of thiosalicylic acid, a process known as the Ullmann reaction ; Goldberg is the only woman scientist unambiguously recognized for her own named reaction: the amidation (Goldberg) reaction . [ 4 ] This modification to previous forms of the method was a great improvement, and was extremely helpful for laboratory-scale preparations. She coordinated on other forms of chemistry research with her husband, Fritz Ullmann , in what they called the Ullmann-Goldberg collaborative. [ 1 ] [ 5 ]
In 1905, both Goldberg and Ullman moved to Technische Hochschule in Berlin. Goldberg's research, along with that of the Ullmann-Goldberg collaborative, was also a part of Germany's synthetic dye industry. Their research helped with the creation of the synthetic alizarin industry, or the process of replacing natural dye obtained from madder. In 1909, Goldberg also collaborated with Hermann Friedman to review German patents under BASF (Badische Anilin und Soda Fabrik) and Bayer & Co. Farbenfabriken, providing notes on preparation for 114 dyes. [ 1 ]
In 1910, Goldberg married Ullman. In 1923, they moved back to Geneva when Ullman accepted a faculty position at Geneva University. [ 1 ]
Her exact death date is not known, but her name does appear at the top of a list of people signing a memorial notice in a Geneva newspaper for her deceased husband, Fritz Ullmann in 1939. [ 1 ] | https://en.wikipedia.org/wiki/Irma_Goldberg |
Ferrous oxalate ( iron(II) oxalate ) refers to inorganic compounds with the formula FeC 2 O 4 (H 2 O) x where x is 0 or 2. These are yellow compounds. Characteristic of metal oxalate complexes , these compounds tend to be polymeric , hence their low solubility in water.
Like other iron oxalates, ferrous oxalates feature octahedral Fe centers. The dihydrate FeC 2 O 4 (H 2 O) x is a coordination polymer , consisting of chains of oxalate-bridged ferrous centers, each with two aquo ligands. [ 3 ]
When heated to 120 °C, the dihydrate dehydrates, and the anhydrous ferrous oxalate decomposes near 190 °C. [ 4 ] The products of thermal decomposition is a mixture of iron oxides and pyrophoric iron metal, as well as released carbon dioxide , carbon monoxide , and water. [ 5 ]
Ferrous oxalates are precursors to iron phosphates , which are of value in batteries. [ 6 ]
Anhydrous iron(II) oxalate is unknown among minerals as of 2020. However, the dihydrate is known as humboldtine . [ 7 ] [ 8 ] A related, although much more complex mineral is stepanovite . Na[Mg(H 2 O) 6 ][Fe(III)(C 2 O 4 ) 3 ]·3H 2 O is an unusual example of a naturally-occurring ferrioxalate . [ 9 ] [ 8 ] | https://en.wikipedia.org/wiki/Iron(II)_oxalate |
Iron(II) oxide or ferrous oxide is the inorganic compound with the formula FeO. Its mineral form is known as wüstite . [ 3 ] [ 4 ] One of several iron oxides , it is a black-colored powder that is sometimes confused with rust , the latter of which consists of hydrated iron(III) oxide (ferric oxide). Iron(II) oxide also refers to a family of related non-stoichiometric compounds , which are typically iron deficient with compositions ranging from Fe 0.84 O to Fe 0.95 O. [ 5 ]
FeO can be prepared by the thermal decomposition of iron(II) oxalate .
The procedure is conducted under an inert atmosphere to avoid the formation of iron(III) oxide ( Fe 2 O 3 ). A similar procedure can also be used for the synthesis of manganous oxide and stannous oxide . [ 6 ] [ 7 ]
Stoichiometric FeO can be prepared by heating Fe 0.95 O with metallic iron at 770 °C and 36 kbar. [ 8 ]
FeO is thermodynamically unstable below 575 °C, tending to disproportionate to metal and Fe 3 O 4 : [ 5 ]
Iron (II) oxide adopts the cubic, rock salt structure, where iron atoms are octahedrally coordinated by oxygen atoms and the oxygen atoms octahedrally coordinated by iron atoms. The non-stoichiometry occurs because of the ease of oxidation of Fe II to Fe III effectively replacing a small portion of Fe II with two-thirds their number of Fe III , which take up tetrahedral positions in the close packed oxide lattice. [ 8 ]
In contrast to the crystalline solid, in the molten state iron atoms are coordinated by predominantly 4 or 5 oxygen atoms. [ 9 ]
Below 200 K there is a minor change to the structure which changes the symmetry to rhombohedral and samples become antiferromagnetic . [ 8 ] [ 10 ]
Iron(II) oxide makes up approximately 9% of the Earth's mantle . Within the mantle, it may be electrically conductive, which is a possible explanation for perturbations in Earth's rotation not accounted for by accepted models of the mantle's properties. [ 11 ]
Iron(II) oxide is used as a pigment . It is FDA -approved for use in cosmetics and it is used in some tattoo inks. It can also be used as a phosphate remover from home aquaria. | https://en.wikipedia.org/wiki/Iron(II)_oxide |
Iron(II) selenide refers to a number of inorganic compounds of ferrous iron and selenide (Se 2− ). The phase diagram of the system Fe–Se [ 1 ] reveals the existence of several non-stoichiometric phases between ~49 at. % Se and ~53 at. % Fe, and temperatures up to ~450 °C. The low temperature stable phases are the tetragonal PbO -structure (P4/nmm) β-Fe 1− x Se and α-Fe 7 Se 8 . The high temperature phase is the hexagonal , NiAs structure (P6 3 /mmc) δ-Fe 1− x Se. Iron(II) selenide occurs naturally as the NiAs -structure mineral achavalite .
More selenium rich iron selenide phases are the γ phases (γ and γˈ), assigned the Fe 3 Se 4 stoichiometry , and FeSe 2 , which occurs as the marcasite -structure natural mineral ferroselite , or the rare pyrite -structure mineral dzharkenite .
It is used in electrical semiconductors . [ citation needed ]
β -FeSe is the simplest iron-based superconductor but with diverse properties. [ 2 ] It starts to superconduct at 8 K at normal pressure [ 3 ] but its critical temperature ( T c ) is dramatically increased to 38 K under pressure, [ 4 ] by means of intercalation , [ 2 ] or after quenching at high pressures. [ 5 ] The combination of both intercalation and pressure results in re-emerging superconductivity at 48 K. [ 2 ]
In 2013 it was reported that a single atomic layer of FeSe epitaxially grown on SrTiO 3 is superconductive with a then-record transition temperature for iron-based superconductors of 70 K. [ 6 ] This discovery has attracted significant attention and in 2014 a superconducting transition temperature of over 100K was reported for this system. [ 7 ] | https://en.wikipedia.org/wiki/Iron(II)_selenide |
Iron(II) sulfate ( British English : iron(II) sulphate ) or ferrous sulfate denotes a range of salts with the formula Fe SO 4 · x H 2 O. These compounds exist most commonly as the heptahydrate ( x = 7) but several values for x are known. The hydrated form is used medically to treat or prevent iron deficiency , and also for industrial applications. Known since ancient times as copperas and as green vitriol ( vitriol is an archaic name for hydrated sulfate minerals ), the blue-green heptahydrate ( hydrate with 7 molecules of water) is the most common form of this material. All the iron(II) sulfates dissolve in water to give the same aquo complex [Fe(H 2 O) 6 ] 2+ , which has octahedral molecular geometry and is paramagnetic . The name copperas dates from times when the copper(II) sulfate was known as blue copperas, and perhaps in analogy, iron(II) and zinc sulfate were known respectively as green and white copperas. [ 18 ]
It is on the World Health Organization's List of Essential Medicines . [ 19 ] In 2022, it was the 107th most commonly prescribed medication in the United States, with more than 6 million prescriptions. [ 20 ] [ 21 ]
Industrially, ferrous sulfate is mainly used as a precursor to other iron compounds. It is a reducing agent , and as such is useful for the reduction of chromate in cement to less toxic Cr(III) compounds. Historically ferrous sulfate was used in the textile industry for centuries as a dye fixative . It is used historically to blacken leather and as a constituent of iron gall ink . [ 22 ] The preparation of sulfuric acid ('oil of vitriol') by the distillation of green vitriol (iron(II) sulfate) has been known for at least 700 years.
Iron(II) sulfate is sold as ferrous sulfate, a soil amendment [ 23 ] for lowering the pH of a high alkaline soil so that plants can access the soil's nutrients. [ 24 ]
In horticulture it is used for treating iron chlorosis . [ 25 ] Although not as rapid-acting as ferric EDTA , its effects are longer-lasting. It can be mixed with compost and dug into the soil to create a store which can last for years. [ 26 ] Ferrous sulfate can be used as a lawn conditioner. [ 26 ] It can also be used to eliminate silvery thread moss in golf course putting greens. [ 27 ]
Ferrous sulfate can be used to stain concrete and some limestones and sandstones a yellowish rust color. [ 28 ]
Woodworkers use ferrous sulfate solutions to color maple wood a silvery hue.
Green vitriol is also a useful reagent in the identification of mushrooms. [ 29 ]
Ferrous sulfate was used in the manufacture of inks , most notably iron gall ink , which was used from the Middle Ages until the end of the 18th century. Chemical tests made on the Lachish letters ( c. 588–586 BCE ) showed the possible presence of iron. [ 30 ] It is thought that oak galls and copperas may have been used in making the ink on those letters. [ 31 ] It also finds use in wool dyeing as a mordant . Harewood , a material used in marquetry and parquetry since the 17th century, is also made using ferrous sulfate.
Two different methods for the direct application of indigo dye were developed in England in the 18th century and remained in use well into the 19th century. One of these, known as china blue , involved iron(II) sulfate. After printing an insoluble form of indigo onto the fabric, the indigo was reduced to leuco -indigo in a sequence of baths of ferrous sulfate (with reoxidation to indigo in air between immersions). The china blue process could make sharp designs, but it could not produce the dark hues of other methods.
In the second half of the 1850s ferrous sulfate was used as a photographic developer for collodion process images. [ 32 ]
Iron(II) sulfate can be found in various states of hydration , and several of these forms exist in nature or were created synthetically.
The tetrahydrate is stabilized when the temperature of aqueous solutions reaches 56.6 °C (133.9 °F). At 64.8 °C (148.6 °F) these solutions form both the tetrahydrate and monohydrate. [ 5 ]
Mineral forms are found in oxidation zones of iron-bearing ore beds, e.g. pyrite , marcasite , chalcopyrite , etc. They are also found in related environments, like coal fire sites. Many rapidly dehydrate and sometimes oxidize. Numerous other, more complex (either basic, hydrated, and/or containing additional cations) Fe(II)-bearing sulfates exist in such environments, with copiapite being a common example. [ 41 ]
In the finishing of steel prior to plating or coating, the steel sheet or rod is passed through pickling baths of sulfuric acid. This treatment produces large quantities of iron(II) sulfate as a by-product. [ 42 ]
Another source of large amounts results from the production of titanium dioxide from ilmenite via the sulfate process.
Ferrous sulfate is also prepared commercially by oxidation of pyrite : [ 43 ]
It can be produced by displacement of metals less reactive than Iron from solutions of their sulfate:
Upon dissolving in water, ferrous sulfates form the metal aquo complex [Fe(H 2 O) 6 ] 2+ , which is an almost colorless, paramagnetic ion.
On heating, iron(II) sulfate first loses its water of crystallization and the original green crystals are converted into a white anhydrous solid. When further heated, the anhydrous material decomposes into sulfur dioxide and sulfur trioxide , leaving a reddish-brown iron(III) oxide . Thermolysis of iron(II) sulfate begins at about 680 °C (1,256 °F).
Like other iron(II) salts, iron(II) sulfate is a reducing agent. For example, it reduces nitric acid to nitrogen monoxide and chlorine to chloride :
Its mild reducing power is of value in organic synthesis. [ 44 ] It is used as the iron catalyst component of Fenton's reagent .
Ferrous sulfate can be detected by the cerimetric method, which is the official method of the Indian Pharmacopoeia. This method includes the use of ferroin solution showing a red to light green colour change during titration. [ 45 ] | https://en.wikipedia.org/wiki/Iron(II)_sulfate |
Iron(II) sulfide or ferrous sulfide (Br.E. sulphide ) is one of a family of chemical compounds and minerals with the approximate formula Fe S . Iron sulfides are often iron-deficient non-stoichiometric . All are black, water-insoluble solids.
FeS can be obtained by the heating of iron and sulfur : [ 1 ]
FeS adopts the nickel arsenide structure, featuring octahedral Fe centers and trigonal prismatic sulfide sites.
Iron sulfide reacts with hydrochloric acid , releasing hydrogen sulfide : [ 2 ]
In moist air, iron sulfides oxidize to hydrated ferrous sulfate .
Iron sulfides occur widely in nature in the form of iron–sulfur proteins .
As organic matter decays under low-oxygen (or hypoxic ) conditions such as in swamps or dead zones of lakes and oceans, sulfate-reducing bacteria reduce various sulfates present in the water, producing hydrogen sulfide . Some of the hydrogen sulfide will react with metal ions in the water or solid to produce iron or metal sulfides, which are not water-soluble. These metal sulfides, such as iron(II) sulfide, are often black or brown, leading to the color of sludge.
Pyrrhotite is a waste product of the Desulfovibrio bacteria, a sulfate reducing bacteria.
When eggs are cooked for a long time, the yolk 's surface may turn green. This color change is due to iron(II) sulfide, which forms as iron from the yolk reacts with hydrogen sulfide released from the egg white by the heat. [ 3 ] This reaction occurs more rapidly in older eggs as the whites are more alkaline. [ 4 ]
The presence of ferrous sulfide as a visible black precipitate in the growth medium peptone iron agar can be used to distinguish between microorganisms that produce the cysteine metabolizing enzyme cysteine desulfhydrase and those that do not. Peptone iron agar contains the amino acid cysteine and a chemical indicator , ferric citrate . The degradation of cysteine releases hydrogen sulfide gas that reacts with the ferric citrate to produce ferrous sulfide. | https://en.wikipedia.org/wiki/Iron(II)_sulfide |
FeO.Fe 2 O 3
Iron(II,III) oxide , or black iron oxide, is the chemical compound with formula Fe 3 O 4 . It occurs in nature as the mineral magnetite . It is one of a number of iron oxides , the others being iron(II) oxide (FeO), which is rare, and iron(III) oxide (Fe 2 O 3 ) which also occurs naturally as the mineral hematite . It contains both Fe 2+ and Fe 3+ ions and is sometimes formulated as FeO ∙ Fe 2 O 3 . This iron oxide is encountered in the laboratory as a black powder. It exhibits permanent magnetism and is ferrimagnetic , but is sometimes incorrectly described as ferromagnetic . [ 5 ] Its most extensive use is as a black pigment (see: Mars Black ). For this purpose, it is synthesized rather than being extracted from the naturally occurring mineral as the particle size and shape can be varied by the method of production. [ 6 ]
Heated iron metal interacts with steam to form iron oxide and hydrogen gas.
Under anaerobic conditions, ferrous hydroxide (Fe(OH) 2 ) can be oxidized by water to form magnetite and molecular hydrogen . This process is described by the Schikorr reaction :
This works because crystalline magnetite (Fe 3 O 4 ) is thermodynamically more stable than amorphous ferrous hydroxide (Fe(OH) 2 ). [ 7 ]
The Massart method of preparation of magnetite as a ferrofluid , is convenient in the laboratory: mix iron(II) chloride and iron(III) chloride in the presence of sodium hydroxide . [ 8 ]
A more efficient method of preparing magnetite without troublesome residues of sodium, is to use ammonia to promote chemical co-precipitation from the iron chlorides: first mix solutions of 0.1 M FeCl 3 ·6H 2 O and FeCl 2 ·4H 2 O with vigorous stirring at about 2000 rpm. The molar ratio of the FeCl 3 :FeCl 2 should be about 2:1. Heat the mix to 70 °C, then raise the speed of stirring to about 7500 rpm and quickly add a solution of NH 4 OH (10 volume %). A dark precipitate of nanoparticles of magnetite forms immediately. [ 9 ]
In both methods, the precipitation reaction relies on rapid transformation of acidic iron ions into the spinel iron oxide structure at pH 10 or higher.
Controlling the formation of magnetite nanoparticles presents challenges: the reactions and phase transformations necessary for the creation of the magnetite spinel structure are complex. [ 10 ] The subject is of practical importance because magnetite particles are of interest in bioscience applications such as magnetic resonance imaging (MRI), in which iron oxide magnetite nanoparticles potentially present a non-toxic alternative to the gadolinium-based contrast agents currently in use. However, difficulties in controlling the formation of the particles, still frustrate the preparation of superparamagnetic magnetite particles, that is to say: magnetite nanoparticles with a coercivity of 0 A/m, meaning that they completely lose their permanent magnetisation in the absence of an external magnetic field. The smallest values currently reported for nanosized magnetite particles is Hc = 8.5 A m −1 , [ 11 ] whereas the largest reported magnetization value is 87 Am 2 kg −1 for synthetic magnetite. [ 12 ] [ 13 ]
Pigment quality Fe 3 O 4 , so called synthetic magnetite, can be prepared using processes that use industrial wastes, scrap iron or solutions containing iron salts (e.g. those produced as by-products in industrial processes such as the acid vat treatment ( pickling ) of steel):
Reduction of Fe 2 O 3 with hydrogen: [ 14 ] [ 15 ]
Reduction of Fe 2 O 3 with CO: [ 16 ]
Production of nano-particles can be performed chemically by taking for example mixtures of Fe II and Fe III salts and mixing them with alkali to precipitate colloidal Fe 3 O 4 . The reaction conditions are critical to the process and determine the particle size. [ 17 ]
Iron(II) carbonate can also be thermally decomposed into Iron(II,III): [ 18 ]
Reduction of magnetite ore by CO in a blast furnace is used to produce iron as part of steel production process: [ 5 ]
Controlled oxidation of Fe 3 O 4 is used to produce brown pigment quality γ-Fe 2 O 3 ( maghemite ): [ 19 ]
More vigorous calcining (roasting in air) gives red pigment quality α-Fe 2 O 3 ( hematite ): [ 19 ]
Fe 3 O 4 has a cubic inverse spinel group structure which consists of a cubic close packed array of oxide ions where all of the Fe 2+ ions occupy half of the octahedral sites and the Fe 3+ are split evenly across the remaining octahedral sites and the tetrahedral sites.
Both FeO and γ-Fe 2 O 3 have a similar cubic close packed array of oxide ions and this accounts for the ready interchangeability between the three compounds on oxidation and reduction as these reactions entail a relatively small change to the overall structure. [ 5 ] Fe 3 O 4 samples can be non-stoichiometric . [ 5 ]
The ferrimagnetism of Fe 3 O 4 arises because the electron spins of the Fe II and Fe III ions in the octahedral sites are coupled and the spins of the Fe III ions in the tetrahedral sites are coupled but anti-parallel to the former. The net effect is that the magnetic contributions of both sets are not balanced and there is a permanent magnetism. [ 5 ]
In the molten state, experimentally constrained models show that the iron ions are coordinated to 5 oxygen ions on average. [ 20 ] There is a distribution of coordination sites in the liquid state, with the majority of both Fe II and Fe III being 5-coordinated to oxygen and minority populations of both 4- and 6-fold coordinated iron.
Fe 3 O 4 is ferrimagnetic with a Curie temperature of 858 K (585 °C). There is a phase transition at 120 K (−153 °C), called Verwey transition where there is a discontinuity in the structure, conductivity and magnetic properties. [ 21 ] This effect has been extensively investigated and whilst various explanations have been proposed, it does not appear to be fully understood. [ 22 ]
While it has much higher electrical resistivity than iron metal (96.1 nΩ m), Fe 3 O 4 's electrical resistivity (0.3 mΩ m [ 23 ] ) is significantly lower than that of Fe 2 O 3 (approx kΩ m). This is ascribed to electron exchange between the Fe II and Fe III centres in Fe 3 O 4 . [ 5 ]
Fe 3 O 4 is used as a black pigment and is known as C.I pigment black 11 (C.I. No.77499) or Mars Black . [ 19 ]
Fe 3 O 4 is used as a catalyst in the Haber process and in the water-gas shift reaction . [ 27 ] The latter uses an HTS (high temperature shift catalyst) of iron oxide stabilised by chromium oxide . [ 27 ] This iron–chrome catalyst is reduced at reactor start up to generate Fe 3 O 4 from α-Fe 2 O 3 and Cr 2 O 3 to CrO 3 . [ 27 ]
Bluing is a passivation process that produces a layer of Fe 3 O 4 on the surface of steel to protect it from rust. Along with sulfur and aluminium, it is an ingredient in steel-cutting thermite . [ citation needed ]
Nano particles of Fe 3 O 4 are used as contrast agents in MRI scanning . [ 28 ]
Ferumoxytol, sold under the brand names Feraheme and Rienso, is an intravenous Fe 3 O 4 preparation for treatment of anemia resulting from chronic kidney disease . [ 24 ] [ 25 ] [ 29 ] [ 30 ] Ferumoxytol is manufactured and globally distributed by AMAG Pharmaceuticals . [ 24 ] [ 30 ]
Magnetite has been found as nano-crystals in magnetotactic bacteria (42–45 nm) [ 6 ] and in the beak tissue of homing pigeons . [ 31 ] | https://en.wikipedia.org/wiki/Iron(II,III)_oxide |
Iron(III) chromate is the iron (III) salt of chromic acid with the chemical formula Fe 2 (CrO 4 ) 3 .
Iron(III) chromate was discovered by Samuel Hibbert-Ware in 1817 while visiting Shetland . [ 2 ]
It may be formed by the salt metathesis reaction of potassium chromate and iron(III) nitrate , which gives potassium nitrate as byproduct .
It also can be formed by the oxidation by air of iron and chromium oxides in a basic environment:
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Iron(III)_chromate |
Iron(III) nitrate , or ferric nitrate , is the name used for a series of inorganic compounds with the formula Fe(NO 3 ) 3 . (H 2 O) n . Most common is the nonahydrate Fe(NO 3 ) 3 . (H 2 O) 9 . The hydrates are all pale colored, water-soluble paramagnetic salts.
Iron(III) nitrate is deliquescent , and it is commonly found as the nonahydrate Fe(NO 3 ) 3 · 9H 2 O , which forms colourless to pale violet crystals. This compound is the trinitrate salt of the aquo complex [Fe(H 2 O) 6 ] 3+ . [ 3 ] Other hydrates Fe(NO 3 ) 3 · x H 2 O , include:
Iron(III) nitrate is a useful precursor to other iron compounds because the nitrate is easily removed or decomposed. It is for example, a standard precursor to potassium ferrate K 2 FeO 4 . [ 5 ]
When dissolved, iron(III) nitrate forms yellow solutions. When this solution is heated to near boiling, nitric acid evaporates and a solid precipitate of iron(III) oxide Fe 2 O 3 appears. [ 6 ] Another method for producing iron oxides from this nitrate salt involves neutralizing its aqueous solutions. [ 7 ]
The compound can be prepared by treating iron metal powder with nitric acid , as summarized by the following idealized equation: [ 8 ]
Ferric nitrate has no large scale applications. It is a catalyst for the synthesis of sodium amide from a solution of sodium in ammonia : [ 9 ]
Certain clays impregnated with ferric nitrate have been shown to be useful oxidants in organic synthesis . For example, ferric nitrate on Montmorillonite —a reagent called Clayfen—has been employed for the oxidation of alcohols to aldehydes and thiols to disulfides . [ 10 ]
Ferric nitrate solutions are used by jewelers and metalsmiths to etch silver and silver alloys. | https://en.wikipedia.org/wiki/Iron(III)_nitrate |
Iron(III) sulfide , also known as ferric sulfide or sesquisulfide ( Fe 2 S 3 ), is one of the several binary iron sulfides . It is a solid, black powder that degrades at ambient temperature. [ 2 ]
Fe 2 S 3 precipitates from solutions containing its respective ions: [ 2 ]
The resulting solid decays at a temperature over 20 °C into iron(II) sulfide (FeS) and elemental sulfur : [ 3 ]
With hydrochloric acid it decays according to the following reaction equation: [ 4 ]
Greigite , with the chemical formula Fe 2+ Fe 3+ 2 S 4 , is a mixed valence compound containing both Fe(III) and Fe(II). It is the sulfur equivalent of the iron oxide magnetite (Fe 3 O 4 ). As established by X-ray crystallography , the S anions form a cubic close-packed lattice, and the Fe cations occupy both tetrahedral and octahedral sites. [ 5 ] | https://en.wikipedia.org/wiki/Iron(III)_sulfide |
Iron-based superconductors ( FeSC ) are iron -containing chemical compounds whose superconducting properties were discovered in 2006. [ 2 ] [ 3 ] The first of such superconducting compounds belong to the group of oxypnictides , which was known since 1995. [ 4 ] Until 2006, however, they were in the first stages of experimentation and implementation [ 5 ] and only the semiconductive properties of these compounds were known and patented. [ 6 ] Previously most high-temperature superconductors were cuprates containing copper - oxygen layers. Much of the interest in iron-based superconductors is precisely because of the differences from the cuprates, which may help lead to a theory of non- BCS-theory superconductivity. [ 7 ]
Iron-based superconductors of the group of oxypnictides were initially called ferropnictides . The crystal structure of these compounds displays conducting layers of iron and a pnictogen (typically arsenic (As) and phosphorus (P)) separated by a charge-reservoir block. [ 8 ] It has also been found that some iron chalcogens and crystallogens superconduct. [ 9 ] [ 10 ]
The crystalline material, known chemically as LaOFeAs, stacks iron and arsenic layers, where the electrons flow, between planes of lanthanum and oxygen . Replacing up to 11 percent of the oxygen with fluorine improved the compound – it became superconductive at 26 kelvin , the team reports in the March 19, 2008 Journal of the American Chemical Society. Subsequent research from other groups suggests that replacing the lanthanum in LaOFeAs with other rare earth elements such as cerium , samarium , neodymium and praseodymium leads to superconductors that work at 52 kelvin. [ 7 ]
Iron-based superconductors are classified according to their crystal structure and chemical formula into the following main families,
Superconductivity is obtained either in the parent phases of some of these systems (e.g. LaFePO, [ 2 ] LaFeSiH, [ 14 ] and LiFeAs [ 15 ] [ 16 ] [ 17 ] ) or by means of doping or applied pressure. [ 8 ] [ 26 ] [ 27 ]
Undoped β -FeSe is the simplest iron-based superconductor but with distinct properties. [ 22 ] It has a critical temperature ( T c ) of 8 K at normal pressure, and 36.7 K under high pressure [ 28 ] and by means of intercalation. The combination of both intercalation and higher pressure results in re-emerging superconductivity at T c of up to 48 K (see, [ 22 ] [ 29 ] and references therein).
Compared with other families, the synthesis of the 122 compounds is relatively easy which facilitates the investigation of these systems.
Compounds such as Sr 2 ScFePO 3 discovered in 2009 are referred to as the '42622' family, as FePSr 2 ScO 3 . [ 41 ] Noteworthy is the synthesis of (Ca 4 Al 2 O 6−y )(Fe 2 Pn 2 ) (or Al-42622(Pn); Pn = As and P) using high-pressure synthesis technique. Al-42622(Pn) exhibit superconductivity for both Pn = As and P with the transition temperatures of 28.3 K and 17.1 K, respectively. The a-lattice parameters of Al-42622(Pn) (a = 3.713 Å and 3.692 Å for Pn = As and P, respectively) are smallest among the iron-pnictide superconductors. Correspondingly, Al-42622(As) has the smallest As–Fe–As bond angle (102.1°) and the largest As distance from the Fe planes (1.5 Å). [ 34 ] High-pressure technique also yields (Ca 3 Al 2 O 5−y )(Fe 2 Pn 2 ) (Pn = As and P), the first reported iron-based superconductors with the perovskite-based '32522' structure. The transition temperature (T c ) is 30.2 K for Pn = As and 16.6 K for Pn = P. The emergence of superconductivity is ascribed to the small tetragonal a-axis lattice constant of these materials. From these results, an empirical relationship was established between the a-axis lattice constant and T c in iron-based superconductors. [ 33 ]
In 2009, it was shown that undoped iron pnictides had a magnetic quantum critical point deriving from competition between electronic localization and itinerancy. [ 42 ]
Similarly to superconducting cuprates, the properties of iron based superconductors change dramatically with doping. Parent compounds of FeSC are usually metals (unlike the cuprates) but, similarly to cuprates, are ordered antiferromagnetically that often termed as a spin-density wave (SDW). Some parent compounds superconduct. [ 2 ] [ 14 ] [ 15 ] [ 16 ] [ 17 ] Otherwise, superconductivity emerges upon either hole or electron doping. In general, the phase diagram is similar to the cuprates. [ 43 ]
Superconducting transition temperatures are listed in the tables (some at high pressure). BaFe 1.8 Co 0.2 As 2 is predicted to have an upper critical field of 43 tesla from the measured coherence length of 2.8 nm. [ 36 ]
In 2011, Japanese scientists made a discovery which increased a metal compound's superconductivity by immersing iron-based compounds in hot alcoholic beverages such as red wine. [ 49 ] [ 50 ] Earlier reports indicated that excess Fe is the cause of the bicollinear antiferromagnetic order and is not in favor of superconductivity. Further investigation revealed that weak acid has the ability to deintercalate the excess Fe from the interlayer sites. Therefore, weak acid annealing suppresses the antiferromagnetic correlation by deintercalating the excess Fe and, hence superconductivity is achieved. [ 51 ] [ 52 ]
There is an empirical correlation of the transition temperature with electronic band structure : the T c maximum is observed when some of the Fermi surface stays in proximity to Lifshitz topological transition. [ 43 ] Similar correlation has been later reported for high-T c cuprates that indicates possible similarity of the superconductivity mechanisms in these two families of high temperature superconductors . [ 53 ]
The critical temperature is increased further in thin-films of iron chalcogenides on suitable substrates. In 2015, a T c of around 105–111 K was observed in thin films of iron selenide grown on strontium titanate . [ 54 ] | https://en.wikipedia.org/wiki/Iron-based_superconductor |
Iron-oxidizing bacteria (or iron bacteria ) are chemotrophic bacteria that derive energy by oxidizing dissolved iron . They are known to grow and proliferate in waters containing iron concentrations as low as 0.1 mg/L. However, at least 0.3 ppm of dissolved oxygen is needed to carry out the oxidation. [ 1 ]
When de-oxygenated water reaches a source of oxygen, iron bacteria convert dissolved iron into an insoluble reddish-brown gelatinous slime that discolors stream beds and can stain plumbing fixtures, clothing, or utensils washed with the water carrying it. [ 2 ]
Organic material dissolved in water is often the underlying cause of an iron-oxidizing bacteria population. Groundwater may be naturally de-oxygenated by decaying vegetation in swamps . Useful mineral deposits of bog iron ore have formed where groundwater has historically emerged and been exposed to atmospheric oxygen. [ 3 ] Anthropogenic hazards like landfill leachate , septic drain fields , or leakage of light petroleum fuels like gasoline are other possible sources of organic materials allowing soil microbes to de-oxygenate groundwater. [ 4 ]
A similar reaction may form black deposits of manganese dioxide from dissolved manganese but is less common because of the relative abundance of iron (5.4%) in comparison to manganese (0.1%) in average soils. [ 5 ] The sulfurous smell of rot or decay sometimes associated with iron-oxidizing bacteria results from the enzymatic conversion of soil sulfates to volatile hydrogen sulfide as an alternative source of oxygen in anaerobic water. [ 6 ]
Iron is a very important chemical element required by living organisms to carry out numerous metabolic reactions such as the formation of proteins involved in biochemical reactions. Examples of these proteins include iron–sulfur proteins , hemoglobin , and coordination complexes . Iron has a widespread distribution globally and is considered one of the most abundant elements in the Earth's crust, soil, and sediments. Iron is a trace element in marine environments . [ 7 ] Its role as the electron donor of some chemolithotrophs is probably very ancient. [ 8 ]
The anoxygenic phototrophic iron oxidation was the first anaerobic metabolism to be described within the iron anaerobic oxidation metabolism. The photoferrotrophic bacteria use Fe 2+ as electron donor and the energy from light to assimilate CO 2 into biomass through the Calvin Benson-Bassam cycle (or rTCA cycle ) in a neutrophilic environment (pH 5.5-7.2), producing Fe 3+ oxides as a waste product that precipitates as a mineral, according to the following stoichiometry (4 mM of Fe(II) can yield 1 mM of CH 2 O):
HCO − 3 + 4Fe(II) + 10H 2 O → [CH 2 O] + 4Fe(OH) 3 + 7H + (∆G° > 0) [ 7 ] [ 9 ]
Nevertheless, some bacteria do not use the photoautotrophic Fe(II) oxidation metabolism for growth purposes. [ 10 ] Instead, it has been suggested that these groups are sensitive to Fe(II) and therefore oxidize Fe(II) into more insoluble Fe(III) oxide to reduce its toxicity, enabling them to grow in the presence of Fe(II). [ 10 ] On the other hand, based on experiments with R. capsulatus SB1003 (photoheterotrophic), it has been demonstrated that the oxidation of Fe(II) might be the mechanisms whereby the bacteria is enabled to access organic carbon sources (acetate, succinate) whose use depends on Fe(II) oxidation [ 11 ] Nonetheless, many iron-oxidizing bacteria can use other compounds as electron donors in addition to Fe(II), or even perform dissimilatory Fe(III) reduction as the Geobacter metallireducens . [ 10 ]
The dependence of photoferrotrophics on light as a crucial resource [ 12 ] [ 9 ] [ 13 ] can take the bacteria to a cumbersome situation, where due to their requirement for anoxic lighted regions (near the surface) [ 9 ] they could be faced with competition by abiotic reactions due to the presence of molecular oxygen. To avoid this problem, they tolerate microaerophilic surface conditions or perform the photoferrotrophic Fe(II) oxidation deeper in the sediment/water column, with low light availability. [ 9 ]
Light penetration can limit the Fe(II) oxidation in the water column. [ 12 ] However, nitrate dependent microbial Fe(II) oxidation is a light independent metabolism that has been shown to support microbial growth in various freshwater and marine sediments (paddy soil, stream, brackish lagoon, hydrothermal, deep-sea sediments) and later on demonstrated as a pronounced metabolism within the water column at the oxygen minimum zone . [ 14 ] [ 13 ] Microbes that perform this metabolism are successful in neutrophilic or alcaline environments, due to the high difference in between the redox potential of the couples Fe 2+ /Fe 3+ and NO 3 − /NO 2 − (+200 mV and +770 mV, respectively) releasing a lot of free energy when compared to other iron oxidation metabolisms. [ 10 ] [ 15 ]
2Fe 2+ + NO − 3 + 5H 2 O → 2Fe(OH) 3 + NO − 2 + 4H + (∆G°=-103.5 kJ/mol)
The microbial oxidation of ferrous iron coupled to denitrification (with nitrite or dinitrogen gas being the final product) [ 7 ] can be autotrophic using inorganic carbon or organic co-substrates (acetate, butyrate, pyruvate, ethanol) performing heterotrophic growth in the absence of inorganic carbon. [ 10 ] [ 15 ] It has been suggested that the heterotrophic nitrate-dependent ferrous iron oxidation using organic carbon might be the most favorable process. [ 16 ] This metabolism might be very important for carrying out an important step in the biogeochemical cycle within the OMZ. [ 17 ]
Despite being phylogenetically diverse, the microbial ferrous iron oxidation metabolic strategy (found in Archaea and Bacteria) is present in 7 phyla , being highly pronounced in the phylum Pseudomonadota (formerly Proteobacteria), particularly the Alpha , Beta , Gamma , and Zetaproteobacteria classes, [ 10 ] [ 18 ] and among the Archaea domain in the " Euryarchaeota " and Thermoproteota phyla, as well as in Actinomycetota , Bacillota , Chlorobiota , and Nitrospirota phyla. [ 18 ]
There are very well-studied iron-oxidizing bacterial species such as Thiobacillus ferrooxidans , and Leptospirillum ferrooxidans , and some like Gallionella ferruginea and Mariprofundis ferrooxydans are able to produce a particular extracellular stalk-ribbon structure rich in iron, known as a typical biosignature of microbial iron oxidation. These structures can be easily detected in a sample of water, indicating the presence iron-oxidizing bacteria. This biosignature has been a tool to understand the importance of iron metabolism in the Earth's past. [ 19 ]
Iron-oxidizing bacteria colonize the transition zone where de-oxygenated water from an anaerobic environment flows into an aerobic environment. Groundwater containing dissolved organic material may be de-oxygenated by microorganisms feeding on that dissolved organic material. In aerobic conditions, pH variation plays an important role in driving the oxidation reaction of Fe 2+ /Fe 3+ . [ 7 ] [ 13 ] At neutrophilic pHs (hydrothermal vents, deep ocean basalts, groundwater iron seeps) the oxidation of iron by microorganisms is highly competitive with the rapid abiotic reaction occurring in <1 min. [ 20 ] Therefore, the microbial community has to inhabit microaerophilic regions where the low oxygen concentration allows the cell to oxidize Fe(II) and produce energy to grow. [ 21 ] [ 22 ] However, under acidic conditions, where ferrous iron is more soluble and stable even in the presence of oxygen, only biological processes are responsible for the oxidation of iron, [ 9 ] thus making ferrous iron oxidation the major metabolic strategy in iron-rich acidic environments. [ 18 ] [ 7 ]
In the marine environment, the most well-known class of iron oxidizing-bacteria is zetaproteobacteria , [ 23 ] which are major players in marine ecosystems. Being generally microaerophilic they are adapted to live in transition zones where the oxic and anoxic waters mix. [ 21 ] The zetaproteobacteria are present in different Fe(II)-rich habitats, found in deep ocean sites associated with hydrothermal activity and in coastal and terrestrial habitats, and have been reported in the surface of shallow sediments, beach aquifer, and surface water.
Mariprofundus ferrooxydans is one of the most common and well-studied species of zetaproteobacteria. It was first isolated from the Kamaʻehuakanaloa Seamount (formerly Loihi) vent field, near Hawaii [ 18 ] at a depth between 1100 and 1325 meters, on the summit of this shield volcano . Vents can be found ranging from slightly above ambient (10 °C) to high temperature (167 °C). The vent waters are rich in CO 2 , Fe(II) and Mn. [ 24 ] Large, heavily encrusted mats with a gelatinous texture are created by iron-oxidizing bacteria as a by-product (iron-oxyhydroxide precipitation), and can be present around the vent orifices. The vents present at Kamaʻehuakanaloa seamount can be categorized into two types based on concentration and temperature of flow. Those with a focused and high-temperature flow (above 50 °C) can be expected to show higher flow rates as well. These vents are characterized by flocculent mats aggregated around the vent orifices. Mat depth at focused, high-temperature vents averages in the tens of centimeters, but can vary. In contrast, vents with cooler (10-30 °C) and diffuse flow can create mats up to one meter thick. These mats may cover hundreds of square meters of sea floor. [ 18 ] Either type of mat can be colonized by other bacterial communities, which can change the chemical composition and the flow of the local waters. [ 25 ]
Unlike most lithotrophic metabolisms, the oxidation of Fe 2+ to Fe 3+ yields very little energy to the cell (∆G° = 29 kJ/mol and ∆G° = -90 kJ/mol in acidic and neutral environments, respectively) compared to other chemolithotrophic metabolisms. [ 18 ] Therefore, the cell must oxidize large amounts of Fe 2+ to fulfill its metabolic requirements while contributing to the mineralization process (through the excretion of twisted stalks). [ 7 ] [ 26 ] The aerobic iron-oxidizing bacterial metabolism is thought to have made a remarkable contribution to the formation of the largest iron deposit ( banded iron formation (BIF) ) due to the advent of oxygen in the atmosphere 2.7 billion years ago (produced by cyanobacteria ). [ 13 ]
However, with the discovery of Fe(II) oxidation carried out under anoxic conditions in the late 1990s [ 16 ] using light as an energy source or chemolithotrophically, using a different terminal electron acceptor (mostly NO 3 − ), [ 9 ] the suggestion arose that anoxic Fe 2+ metabolism may pre-date aerobic Fe 2+ oxidation and that the age of the BIF pre-dates oxygenic photosynthesis. [ 7 ] This suggests that microbial anoxic phototrophic and anaerobic chemolithotrophic metabolism may have been present on the ancient earth, and together with Fe(III) reducers, they may have been responsible for the BIF in the Precambrian eon. [ 9 ]
In open ocean systems full of dissolved iron, iron-oxidizing bacterial metabolism is ubiquitous and influences the iron cycle. Nowadays, this biochemical cycle is undergoing modifications due to pollution and climate change; nonetheless, the normal distribution of ferrous iron in the ocean could be affected by global warming under the following conditions: acidification, shifting of ocean currents, and ocean water and groundwater hypoxia trend. [ 20 ]
These are all consequences of the substantial increase of CO 2 emissions into the atmosphere from anthropogenic sources. Currently the concentration of carbon dioxide in the atmosphere is around 420 ppm (120 ppm more than 20 million years ago), and about a quarter of the total CO 2 emission enters the oceans (2.2 pg C year −1 ). Reacting with seawater it produces bicarbonate ion (HCO 3 − ) and thus the ocean acidity increases. Furthermore, the temperature of the ocean has increased by almost one degree (0.74 °C) causing the melting of big quantities of glaciers contributing to the sea-level rise. This lowers the O 2 solubility by inhibiting the oxygen exchange between surface waters, where O 2 is very abundant, and anoxic deep waters. [ 27 ] [ 28 ]
All these changes in the marine parameters (temperature, acidity, and oxygenation) impact the iron biogeochemical cycle and could have several and critical implications on ferrous iron oxidizing microbes; hypoxic and acid conditions could improve primary productivity in the superficial and coastal waters because that would increase the availability of ferrous iron Fe(II) for microbial iron oxidation. Still, at the same time, this scenario could also disrupt the cascade effect to the sediment in deep water and cause the death of benthonic animals. Moreover it is very important to consider that iron and phosphate cycles are strictly interconnected and balanced, so that a small change in the first could have substantial consequences on the second. [ 29 ]
Iron-oxidizing bacteria can pose an issue for the management of water-supply wells , as they can produce insoluble ferric oxide , which appears as brown gelatinous slime that will stain plumbing fixtures, and clothing or utensils washed with the water carrying it.
The dramatic effects of iron bacteria are seen in surface waters as brown slimy masses on stream bottoms and lakeshores or as an oily sheen upon the water. More serious problems occur when bacteria build up in well systems. Iron bacteria in wells do not cause health problems, but they can reduce well yields by clogging screens and pipes.
Treatment techniques that may successfully remove or reduce iron bacteria include physical removal, pasteurization, and chemical treatment. Treatment of heavily infected wells may be difficult, expensive, and only partially successful. [ 30 ] Recent application of ultrasonic devices that destroy and prevent the formation of biofilm in wells has been proven to prevent iron bacteria infection and the associated clogging very successfully. [ 31 ] [ 32 ]
Physical removal is typically done as a first step. Small diameter pipes are sometimes cleaned with a wire brush, while larger lines can be scrubbed and flushed clean with a sewer jetter . [ 33 ] The pumping equipment in the well must also be removed and cleaned. [ 34 ]
Iron filters have been used to treat iron bacteria. Iron filters are similar in appearance and size to conventional water softeners but contain beds of media that have mild oxidizing power. As the iron-bearing water is passed through the bed, any soluble ferrous iron is converted to the insoluble ferric state and then filtered from the water. Any previously precipitated iron is removed by simple mechanical filtration. Several different filter media may be used in these iron filters, including manganese greensand, Birm, MTM, multi-media, sand, and other synthetic materials. In most cases, the higher oxides of manganese produce the desired oxidizing action. Iron filters do have limitations; since the oxidizing action is relatively mild, it will not work well when organic matter, either combined with the iron or completely separate, is present in the water. As a result, the iron bacteria will not be killed. Extremely high iron concentrations may require inconvenient frequent backwashing and/or regeneration. Finally, iron filter media requires high flow rates for proper backwashing, and such water flows are not always available.
Wildfires may release iron-containing compounds from the soil into small wildland streams and cause a rapid but usually temporary proliferation of iron-oxidizing bacteria complete with orange coloration, gelatinous mats, and sulfurous odors. Higher quality personal filters may be used to remove bacteria, odor and restore water clarity. | https://en.wikipedia.org/wiki/Iron-oxidizing_bacteria |
Iron fertilization is the intentional introduction of iron -containing compounds (like iron sulfate ) to iron-poor areas of the ocean surface to stimulate phytoplankton production. This is intended to enhance biological productivity and/or accelerate carbon dioxide (CO 2 ) sequestration from the atmosphere. Iron is a trace element necessary for photosynthesis in plants. It is highly insoluble in sea water and in a variety of locations is the limiting nutrient for phytoplankton growth. Large algal blooms can be created by supplying iron to iron-deficient ocean waters. These blooms can nourish other organisms.
Ocean iron fertilization is an example of a geoengineering technique. [ 1 ] Iron fertilization [ 2 ] attempts to encourage phytoplankton growth , which removes carbon from the atmosphere for at least a period of time. [ 3 ] [ 4 ] This technique is controversial because there is limited understanding of its complete effects on the marine ecosystem , [ 5 ] including side effects and possibly large deviations from expected behavior. Such effects potentially include release of nitrogen oxides , [ 6 ] and disruption of the ocean's nutrient balance. [ 1 ] Controversy remains over the effectiveness of atmospheric CO 2 sequestration and ecological effects. [ 7 ] Since 1990, 13 major large scale experiments have been carried out to evaluate efficiency and possible consequences of iron fertilization in ocean waters. A study in 2017 considered that the method is unproven; the sequestering efficiency was low and sometimes no effect was seen and the amount of iron deposits needed to make a small cut in the carbon emissions would be in the million tons per year. [ 8 ] However since 2021, interest is renewed in the potential of iron fertilization, among other from a white paper study of NOAA, the US National Oceanographic and Atmospheric Administration, which rated iron fertilization as having "moderate potential for cost, scalability and how long carbon might be stored compared to other marine sequestration ideas" [ 9 ]
Approximately 25 per cent of the ocean surface has ample macronutrients, with little plant biomass (as defined by chlorophyll). The production in these high-nutrient low-chlorophyll (HNLC) waters is primarily limited by micronutrients , especially iron. [ 10 ] The cost of distributing iron over large ocean areas is large compared with the expected value of carbon credits . [ 11 ] Research in the early 2020s suggested that it could only permanently sequester a small amount of carbon. [ 12 ]
Ocean iron fertilization is an example of a geoengineering technique that involves intentional introduction of iron-rich deposits into oceans, and is aimed to enhance biological productivity of organisms in ocean waters in order to increase carbon dioxide ( CO 2 ) uptake from the atmosphere, possibly resulting in mitigating its global warming effects . [ 13 ] [ 14 ] [ 15 ] [ 16 ] [ 17 ] Iron is a trace element in the ocean and its presence is vital for photosynthesis in plants, and in particular phytoplanktons, as it has been shown that iron deficiency can limit ocean productivity and phytoplankton growth. [ 18 ] For this reason, the "iron hypothesis" was put forward by Martin in late 1980s where he suggested that changes in iron supply in iron-deficient seawater can bloom plankton growth and have a significant effect on the concentration of atmospheric carbon dioxide by altering rates of carbon sequestration. [ 19 ] [ 20 ] In fact, fertilization is an important process that occurs naturally in the ocean waters. For instance, upwellings of ocean currents can bring nutrient-rich sediments to the surface. [ 21 ] Another example is through transfer of iron-rich minerals, dust, and volcanic ash over long distances by rivers, glaciers, or wind. [ 22 ] [ 23 ] Moreover, it has been suggested that whales can transfer iron-rich ocean dust to the surface, where planktons can take it up to grow. It has been shown that reduction in the number of sperm whales in the Southern Ocean has resulted in a 200,000 tonnes/yr decrease in the atmospheric carbon uptake, possibly due to limited phytoplankton growth. [ 24 ]
Phytoplankton is photosynthetic : it needs sunlight and nutrients to grow, and takes up carbon dioxide in the process. Plankton can take up and sequester atmospheric carbon through generating calcium or silicon-carbonate skeletons. When these organisms die they sink to the ocean floor where their carbonate skeletons can form a major component of the carbon-rich deep sea precipitation, thousands of meters below plankton blooms, known as marine snow . [ 25 ] [ 26 ] [ 27 ] Nonetheless, based on the definition, carbon is only considered "sequestered" when it is deposited in the ocean floor where it can be retained for millions of years. However, most of the carbon-rich biomass generated from plankton is generally consumed by other organisms (small fish, zooplankton , etc.) [ 28 ] [ 29 ] and substantial part of rest of the deposits that sink beneath plankton blooms may be re-dissolved in the water and gets transferred to the surface where it eventually returns to the atmosphere, thus, nullifying any possible intended effects regarding carbon sequestration. [ 30 ] [ 31 ] [ 32 ] [ 33 ] [ 34 ] Nevertheless, supporters of the idea of iron fertilization believe that carbon sequestration should be re-defined over much shorter time frames and claim that since the carbon is suspended in the deep ocean it is effectively isolated from the atmosphere for hundreds of years, and thus, carbon can be effectively sequestered. [ 35 ]
Assuming the ideal conditions, the upper estimates for possible effects of iron fertilisation in slowing down global warming is about 0.3W/m 2 of averaged negative forcing which can offset roughly 15–20% of the current anthropogenic CO 2 emissions. [ 36 ] [ 37 ] [ 38 ] This approach, which stimulates phytoplankton growth by introducing iron into nutrient-poor regions of the ocean, could be seen as a potentially easy and scalable method to reduce atmospheric CO 2 levels. However, while it offers a theoretical means of mitigating climate change, ocean iron fertilisation remains highly controversial and debated due to its potential negative impacts on marine ecosystems . [ 31 ] [ 39 ] [ 40 ] [ 41 ]
Research in this field suggests that introducing large amounts of iron-rich dust into the ocean can significantly disturb the ocean's nutrient balance. These disruptions can create serious issues within the food chain , threatening the survival of marine organisms that rely on stable nutrient cycles. [ 42 ] [ 43 ] [ 44 ] [ 45 ] [ 46 ] [ 47 ] [ 48 ] Excessive iron may also alter the structure of plankton communities, potentially favouring certain species over others, thereby reducing the diversity vital for a healthy marine ecosystem. [ 49 ] Moreover, iron fertilisation can trigger expansive phytoplankton blooms, which, as they decompose, could create hypoxic or anoxic zones in the ocean, posing severe risks to marine life and biodiversity. [ 50 ] In some cases, iron fertilisation has been linked to harmful algal blooms, which can produce toxins detrimental to marine organisms and humans. [ 50 ] [ 51 ] For example, trials in the Southern Ocean, including the SOFeX experiments, demonstrated that iron fertilisation can lead to the rapid growth of harmful algae, with potential consequences for local ecosystems and food chains. [ 52 ] [ 53 ]
In addition to ecological concerns, there are challenges related to the effectiveness and long-term stability of carbon sequestration through iron fertilisation. While phytoplankton can capture CO 2 and sink to the ocean floor, a significant portion of this carbon may eventually be released back into the atmosphere due to various oceanic processes, diminishing the technique's long-term effectiveness. [ 54 ] Recent research indicates that the success of carbon sequestration is highly variable, influenced by factors such as ocean currents and temperature. [ 55 ] Furthermore, feedback mechanisms, such as alterations in the ocean's biogeochemical cycles or changes in marine species populations, may weaken the overall effectiveness of iron fertilisation as a climate change mitigation strategy. [ 52 ]
There are two ways of performing artificial iron fertilization: ship based direct into the ocean and atmospheric deployment. [ 56 ]
Trials of ocean fertilization using iron sulphate added directly to the surface water from ships are described in detail in the experiment section below.
Iron-rich dust rising into the atmosphere is a primary source of ocean iron fertilization. [ 57 ] For example, wind blown dust from the Sahara desert fertilizes the Atlantic Ocean [ 58 ] and the Amazon rainforest . [ 59 ] The naturally occurring iron oxide in atmospheric dust reacts with hydrogen chloride from sea spray to produce iron chloride, which degrades methane and other greenhouse gases, brightens clouds and eventually falls with the rain in low concentration across a wide area of the globe. [ 56 ] Unlike ship based deployment, no trials have been performed of increasing the natural level of atmospheric iron. Expanding this atmospheric source of iron could complement ship-based deployment.
One proposal is to boost the atmospheric iron level with iron salt aerosol . [ 56 ] Iron(III) chloride added to the troposphere could increase natural cooling effects including methane removal , cloud brightening and ocean fertilization, helping to prevent or reverse global warming. [ 56 ]
Martin hypothesized that increasing phytoplankton photosynthesis could slow or even reverse global warming by sequestering CO 2 in the sea. He died shortly thereafter during preparations for Ironex I, [ 60 ] a proof of concept research voyage, which was successfully carried out near the Galapagos Islands in 1993 by his colleagues at Moss Landing Marine Laboratories . [ 61 ] Thereafter 12 international ocean studies examined the phenomenon:
John Martin , director of the Moss Landing Marine Laboratories , hypothesized that the low levels of phytoplankton in these regions are due to a lack of iron. In 1989 he tested this hypothesis (known as the Iron Hypothesis ) by an experiment using samples of clean water from Antarctica . [ 85 ] Iron was added to some of these samples. After several days the phytoplankton in the samples with iron fertilization grew much more than in the untreated samples. This led Martin to speculate that increased iron concentrations in the oceans could partly explain past ice ages. [ 86 ]
This experiment was followed by a larger field experiment (IRONEX I) where 445 kg of iron was added to a patch of ocean near the Galápagos Islands . The levels of phytoplankton increased three times in the experimental area. [ 87 ] The success of this experiment and others led to proposals to use this technique to remove carbon dioxide from the atmosphere. [ 88 ]
In 2000 and 2004, iron sulfate was discharged from the EisenEx. 10 to 20 percent of the resulting algal bloom died and sank to the sea floor. [ 89 ]
Planktos was a US company that abandoned its plans to conduct 6 iron fertilization cruises from 2007 to 2009, each of which would have dissolved up to 100 tons of iron over a 10,000 km 2 area of ocean. Their ship Weatherbird II was refused entry to the port of Las Palmas in the Canary Islands where it was to take on provisions and scientific equipment. [ 90 ]
In 2007 commercial companies such as Climos and GreenSea Ventures and the Australian-based Ocean Nourishment Corporation, planned to engage in fertilization projects. These companies invited green co-sponsors to finance their activities in return for provision of carbon credits to offset investors' CO 2 emissions. [ 91 ]
LOHAFEX was an experiment initiated by the German Federal Ministry of Research and carried out by the German Alfred Wegener Institute (AWI) in 2009 to study fertilization in the South Atlantic . India was also involved. [ 92 ]
As part of the experiment, the German research vessel Polarstern deposited 6 tons of ferrous sulfate in an area of 300 square kilometers. It was expected that the material would distribute through the upper 15 metres (49 ft) of water and trigger an algal bloom. A significant part of the carbon dioxide dissolved in sea water would then be bound by the emerging bloom and sink to the ocean floor.
The Federal Environment Ministry called for the experiment to halt, partly because environmentalists predicted damage to marine plants. Others predicted long-term effects that would not be detectable during short-term observation [ 93 ] [ unreliable source? ] or that this would encourage large-scale ecosystem manipulation. [ 94 ] [ unreliable source? ] [ 95 ]
A 2012 study deposited iron fertilizer in an eddy near Antarctica. The resulting algal bloom sent a significant amount of carbon into the deep ocean, where it was expected to remain for centuries to millennia. The eddy was chosen because it offered a largely self-contained test system. [ 96 ]
As of day 24, nutrients, including nitrogen, phosphorus and silicic acid that diatoms use to construct their shells, declined. Dissolved inorganic carbon concentrations were reduced below equilibrium with atmospheric CO 2 . In surface water, particulate organic matter (algal remains) including silica and chlorophyll increased. [ 96 ]
After day 24, however, the particulate matter fell to between 100 metres (330 ft) to the ocean floor. Each iron atom converted at least 13,000 carbon atoms into algae. At least half of the organic matter sank below, 1,000 metres (3,300 ft). [ 96 ]
In July 2012, the Haida Salmon Restoration Corporation dispersed 100 short tons (91 t) of iron sulphate dust into the Pacific Ocean several hundred miles west of the islands of Haida Gwaii . The Old Massett Village Council financed the action as a salmon enhancement project with $2.5 million in village funds. [ 97 ] The concept was that the formerly iron -deficient waters would produce more phytoplankton that would in turn serve as a "pasture" to feed salmon . Then-CEO Russ George hoped to sell carbon offsets to recover the costs. The project was accompanied by charges of unscientific procedures and recklessness. George contended that 100 tons was negligible compared to what naturally enters the ocean. [ 98 ]
Some environmentalists called the dumping a "blatant violation" of two international moratoria. [ 97 ] [ 99 ] George said that the Old Massett Village Council and its lawyers approved the effort and at least seven Canadian agencies were aware of it. [ 98 ]
According to George, the 2013 salmon runs increased from 50 million to 226 million fish. [ 100 ] However, many experts contend that changes in fishery stocks since 2012 cannot necessarily be attributed to the 2012 iron fertilization; many factors contribute to predictive models, and most data from the experiment are considered to be of questionable scientific value. [ 101 ]
On 15 July 2014, the data gathered during the project were made publicly available under the ODbL license. [ 102 ]
In 2022, a UK/India research team plans to place iron-coated rice husks in the Arabian Sea , to test whether increasing time at the surface can stimulate a bloom using less iron. The iron will be confined within a plastic bag reaching from the surface several kilometers down to the sea bottom. [ 103 ] [ 104 ] The Centre for Climate Repair at the University of Cambridge, along with India's Institute of Maritime Studies assessed the impact of iron seeding in another experiment. They spread iron-coated rice husks across an area of the Arabian Sea. Iron is a limiting nutrient in many ocean waters. They hoped that the iron would fertilize algae, which would bolster the bottom of the marine food chain and sequester carbon as uneaten algae died. The experiment was demolished by a storm, leaving inconclusive results. [ 105 ]
The maximum possible result from iron fertilization, assuming the most favourable conditions and disregarding practical considerations, is 0.29 W/m 2 of globally averaged negative forcing, [ 106 ] offsetting 1/6 of current levels of anthropogenic CO 2 emissions. These benefits have been called into question by research suggesting that fertilization with iron may deplete other essential nutrients in the seawater causing reduced phytoplankton growth elsewhere — in other words, that iron concentrations limit growth more locally than they do on a global scale. [ 107 ] [ 108 ]
Ocean fertilization occurs naturally when upwellings bring nutrient-rich water to the surface, as occurs when ocean currents meet an ocean bank or a sea mount . This form of fertilization produces the world's largest marine habitats . Fertilization can also occur when weather carries wind blown dust long distances over the ocean, or iron-rich minerals are carried into the ocean by glaciers , [ 109 ] rivers and icebergs. [ 110 ]
About 70% of the world's surface is covered in oceans. The part of these where light can penetrate is inhabited by algae (and other marine life). In some oceans, algae growth and reproduction is limited by the amount of iron. Iron is a vital micronutrient for phytoplankton growth and photosynthesis that has historically been delivered to the pelagic sea by dust storms from arid lands. This Aeolian dust contains 3–5% iron and its deposition has fallen nearly 25% in recent decades. [ 111 ]
The Redfield ratio describes the relative atomic concentrations of critical nutrients in plankton biomass and is conventionally written "106 C: 16 N: 1 P." This expresses the fact that one atom of phosphorus and 16 of nitrogen are required to " fix " 106 carbon atoms (or 106 molecules of CO 2 ). Research expanded this constant to "106 C: 16 N: 1 P: .001 Fe" signifying that in iron deficient conditions each atom of iron can fix 106,000 atoms of carbon, [ 112 ] or on a mass basis, each kilogram of iron can fix 83,000 kg of carbon dioxide. The 2004 EIFEX experiment reported a carbon dioxide to iron export ratio of nearly 3000 to 1. The atomic ratio would be approximately: "3000 C: 58,000 N: 3,600 P: 1 Fe". [ 113 ]
Therefore, small amounts of iron (measured by mass parts per trillion) in HNLC zones can trigger large phytoplankton blooms on the order of 100,000 kilograms of plankton per kilogram of iron. The size of the iron particles is critical. Particles of 0.5–1 micrometer or less seem to be ideal both in terms of sink rate and bioavailability. Particles this small are easier for cyanobacteria and other phytoplankton to incorporate and the churning of surface waters keeps them in the euphotic or sunlit biologically active depths without sinking for long periods. One way to add small amounts of iron to HNLC zones would be Atmospheric Methane Removal .
Atmospheric deposition is an important iron source. Satellite images and data (such as PODLER, MODIS, MSIR) [ 114 ] [ 115 ] [ 116 ] combined with back-trajectory analyses identified natural sources of iron–containing dust. Iron-bearing dusts erode from soil and are transported by wind. Although most dust sources are situated in the Northern Hemisphere, the largest dust sources are located in northern and southern Africa, North America, central Asia and Australia. [ 117 ]
Heterogeneous chemical reactions in the atmosphere modify the speciation of iron in dust and may affect the bioavailability of deposited iron. The soluble form of iron is much higher in aerosols than in soil (~0.5%). [ 117 ] [ 118 ] [ 119 ] Several photo-chemical interactions with dissolved organic acids increase iron solubility in aerosols. [ 120 ] [ 121 ] Among these, photochemical reduction of oxalate -bound Fe(III) from iron-containing minerals is important. The organic ligand forms a surface complex with the Fe (III) metal center of an iron-containing mineral (such as hematite or goethite ). On exposure to solar radiation the complex is converted to an excited energy state in which the ligand, acting as bridge and an electron donor , supplies an electron to Fe(III) producing soluble Fe(II). [ 122 ] [ 123 ] [ 124 ] Consistent with this, studies documented a distinct diel variation in the concentrations of Fe (II) and Fe(III) in which daytime Fe(II) concentrations exceed those of Fe(III). [ 125 ] [ 126 ] [ 127 ] [ 128 ]
Volcanic ash has a significant role in supplying the world's oceans with iron. [ 129 ] Volcanic ash is composed of glass shards, pyrogenic minerals, lithic particles and other forms of ash that release nutrients at different rates depending on structure and the type of reaction caused by contact with water. [ 130 ]
Increases of biogenic opal in the sediment record are associated with increased iron accumulation over the last million years. [ 131 ] In August 2008, an eruption in the Aleutian Islands deposited ash in the nutrient-limited Northeast Pacific. This ash and iron deposition resulted in one of the largest phytoplankton blooms observed in the subarctic. [ 132 ]
Previous instances of biological carbon sequestration triggered major climatic changes, lowering the temperature of the planet, such as the Azolla event . Plankton that generate calcium or silicon carbonate skeletons, such as diatoms , coccolithophores and foraminifera , account for most direct sequestration. [ citation needed ] When these organisms die their carbonate skeletons sink relatively quickly and form a major component of the carbon-rich deep sea precipitation known as marine snow . Marine snow also includes fish fecal pellets and other organic detritus, and steadily falls thousands of meters below active plankton blooms. [ 133 ]
Of the carbon-rich biomass generated by plankton blooms, half (or more) is generally consumed by grazing organisms ( zooplankton , krill , small fish, etc.) but 20 to 30% sinks below 200 meters (660 ft) into the colder water strata below the thermocline . [ 134 ] Much of this fixed carbon continues into the abyss, but a substantial percentage is redissolved and remineralized. At this depth, however, this carbon is now suspended in deep currents and effectively isolated from the atmosphere for centuries.
Evaluation of the biological effects and verification of the amount of carbon actually sequestered by any particular bloom involves a variety of measurements, combining ship-borne and remote sampling, submarine filtration traps, tracking buoy spectroscopy and satellite telemetry . Unpredictable ocean currents can remove experimental iron patches from the pelagic zone, invalidating the experiment.
The potential of fertilization to tackle global warming is illustrated by the following figures. If phytoplankton converted all the nitrate and phosphate present in the surface mixed layer across the entire Antarctic circumpolar current into organic carbon , the resulting carbon dioxide deficit could be compensated by uptake from the atmosphere amounting to about 0.8 to 1.4 gigatonnes of carbon per year. [ 135 ] This quantity is comparable in magnitude to annual anthropogenic fossil fuels combustion of approximately 6 gigatonnes. The Antarctic circumpolar current region is one of several in which iron fertilization could be conducted—the Galapagos islands area another potentially suitable location.
Some species of plankton produce dimethyl sulfide (DMS), a portion of which enters the atmosphere where it is oxidized by hydroxyl radicals (OH), atomic chlorine (Cl) and bromine monoxide (BrO) to form sulfate particles, and potentially increase cloud cover. This may increase the albedo of the planet and so cause cooling—this proposed mechanism is central to the CLAW hypothesis . [ 136 ] This is one of the examples used by James Lovelock to illustrate his Gaia hypothesis . [ 137 ]
During SOFeX, DMS concentrations increased by a factor of four inside the fertilized patch. Widescale iron fertilization of the Southern Ocean could lead to significant sulfur-triggered cooling in addition to that due to the CO 2 uptake and that due to the ocean's albedo increase, however the amount of cooling by this particular effect is very uncertain. [ 138 ]
Beginning with the Kyoto Protocol , several countries and the European Union established carbon offset markets which trade certified emission reduction credits (CERs) and other types of carbon credit instruments. In 2007 CERs sold for approximately €15–20/ton CO e 2 . [ 139 ] Iron fertilization is relatively inexpensive compared to scrubbing , direct injection and other industrial approaches, and can theoretically sequester for less than €5/ton CO 2 , creating a substantial return. [ 140 ] In August, 2010, Russia established a minimum price of €10/ton for offsets to reduce uncertainty for offset providers. [ 141 ] Scientists have reported a 6–12% decline in global plankton production since 1980. [ 111 ] [ 142 ] A full-scale plankton restoration program could regenerate approximately 3–5 billion tons of sequestration capacity worth €50-100 billion in carbon offset value. However, a 2013 study indicates the cost versus benefits of iron fertilization puts it behind carbon capture and storage and carbon taxes. [ 143 ]
While ocean iron fertilization could represent a potent means to slow global warming, there is a current debate surrounding the efficacy of this strategy and the potential adverse effects of this.
The precautionary principle is a proposed guideline regarding environmental conservation. According to an article published in 2021, the precautionary principle (PP) is a concept that states, "The PP means that when it is scientifically plausible that human activities may lead to morally unacceptable harm, actions shall be taken to avoid or diminish that harm: uncertainty should not be an excuse to delay action." [ 144 ] Based on this principle, and because there is little data quantifying the effects of iron fertilization, it is the responsibility of leaders in this field to avoid the harmful effects of this procedure. This school of thought is one argument against using iron fertilization on a wide scale, at least until more data is available to analyze the repercussions of this.
Critics are concerned that fertilization will create harmful algal blooms (HAB) as many toxic algae are often favored when iron is deposited into the marine ecosystem. A 2010 study of iron fertilization in an oceanic high-nitrate, low-chlorophyll environment, however, found that fertilized Pseudo-nitzschia diatom spp., which are generally nontoxic in the open ocean, began producing toxic levels of domoic acid . Even short-lived blooms containing such toxins could have detrimental effects on marine food webs. [ 145 ] Most species of phytoplankton are harmless or beneficial, given that they constitute the base of the marine food chain. Fertilization increases phytoplankton only in the open oceans (far from shore) where iron deficiency is substantial. Most coastal waters are replete with iron and adding more has no useful effect. [ 146 ] Further, it has been shown that there are often higher mineralization rates with iron fertilization, leading to a turn over in the plankton masses that are produced. This results in no beneficial effects and actually causes an increase in CO 2 . [ 147 ]
Finally, a 2010 study showed that iron enrichment stimulates toxic diatom production in high-nitrate, low-chlorophyll areas [ 148 ] which, the authors argue, raises "serious concerns over the net benefit and sustainability of large-scale iron fertilizations". Nitrogen released by cetaceans and iron chelate are a significant benefit to the marine food chain in addition to sequestering carbon for long periods of time. [ 149 ]
A 2009 study tested the potential of iron fertilization to reduce both atmospheric CO 2 and ocean acidity using a global ocean carbon model. The study found that, "Our simulations show that ocean iron fertilization, even in the extreme scenario by depleting global surface macronutrient concentration to zero at all time, has a minor effect on mitigating CO2-induced acidification at the surface ocean." [ 150 ] Unfortunately, the impact on ocean acidification would likely not change due to the low effects that iron fertilization has on CO 2 levels. [ 147 ]
Consideration of iron's importance to phytoplankton growth and photosynthesis dates to the 1930s when Dr Thomas John Hart , a British marine biologist based on the RRS Discovery II in the Southern Ocean speculated - in "On the phytoplankton of the South-West Atlantic and Bellingshausen Sea, 1929-31" - that great "desolate zones" (areas apparently rich in nutrients, but lacking in phytoplankton activity or other sea life) might be iron-deficient. [ 61 ] Hart returned to this issue in a 1942 paper entitled "Phytoplankton periodicity in Antarctic surface waters", but little other scientific discussion was recorded until the 1980s, when oceanographer John Martin of the Moss Landing Marine Laboratories renewed controversy on the topic with his marine water nutrient analyses. His studies supported Hart's hypothesis. These "desolate" regions came to be called " high-nutrient, low-chlorophyll regions " (HNLC). [ 61 ]
John Gribbin was the first scientist to publicly suggest that climate change could be reduced by adding large amounts of soluble iron to the oceans. [ 151 ] Martin's 1988 quip four months later at Woods Hole Oceanographic Institution , "Give me a half a tanker of iron and I will give you an ice age ," [ 61 ] [ 152 ] [ 153 ] drove a decade of research.
The findings suggested that iron deficiency was limiting ocean productivity and offered an approach to mitigating climate change as well. Perhaps the most dramatic support for Martin's hypothesis came with the 1991 eruption of Mount Pinatubo in the Philippines . Environmental scientist Andrew Watson analyzed global data from that eruption and calculated that it deposited approximately 40,000 tons of iron dust into oceans worldwide. This single fertilization event preceded an easily observed global decline in atmospheric CO 2 and a parallel pulsed increase in oxygen levels. [ 154 ]
The parties to the London Dumping Convention adopted a non-binding resolution in 2008 on fertilization (labeled LC-LP.1(2008)). The resolution states that ocean fertilization activities, other than legitimate scientific research, "should be considered as contrary to the aims of the Convention and Protocol and do not currently qualify for any exemption from the definition of dumping". [ 155 ] An Assessment Framework for Scientific Research Involving Ocean Fertilization, regulating the dumping of wastes at sea (labeled LC-LP.2(2010)) was adopted by the Contracting Parties to the Convention in October 2010 (LC 32/LP 5). [ 156 ]
Multiple ocean labs, scientists and businesses have explored fertilization. Beginning in 1993, thirteen research teams completed ocean trials demonstrating that phytoplankton blooms can be stimulated by iron augmentation. [ 147 ] Controversy remains over the effectiveness of atmospheric CO 2 sequestration and ecological effects. [ 7 ] Ocean trials of ocean iron fertilization took place in 2009 in the South Atlantic by project LOHAFEX , and in July 2012 in the North Pacific off the coast of British Columbia , Canada, by the Haida Salmon Restoration Corporation ( HSRC ). [ 157 ] | https://en.wikipedia.org/wiki/Iron_fertilization |
An iron founder (also iron-founder or ironfounder ) in its more general sense is a worker in molten ferrous metal, generally working within an iron foundry . [ 1 ] However, the term 'iron founder' is usually reserved for the owner or manager of an iron foundry, a person also known in Victorian England as a 'master'. Workers in a foundry are generically described as 'foundrymen'; however, the various craftsmen working in foundries, such as moulders and pattern makers, are often referred to by their specific trades. [ 2 ] [ 3 ]
Historically the appellation "founder" was given to the supervisor of a blast furnace , and persons who made castings in iron or other heavy metal. [ 4 ] The term is also often applied to the company or works in which an iron foundry operates.
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The term iron frame describes the structural use of either cast iron or wrought iron in the columns and beams of a building. While popular in the 19th century, the iron frame was displaced by the steel frame in the early 20th century. [ 1 ]
Columns made of cast iron were introduced in the 1770s, the first building with multiple storeys using cast iron for both columns and beams is the Ditherington Flax Mill in Shrewsbury (1797). [ 2 ] Columns were joined usually at the floor level and sometimes bolted together, [ 3 ] the longer beams were made of sections that were also kept together by bolts. [ 4 ] At first, the stiffness of the frame was achieved through the use of masonry that filled the openings in the frame, but since 1844, a rigid frame was used that was stable by itself (former fire station at the Portsmouth Dockyard ). [ 5 ]
With its high compression strength, the cast iron is well-suited for columns. At first, the cruciform profile was used, later displaced by the hollow round shape and H-beams . [ 3 ] Relative tensile weakness made the cast iron not the best choice for the beams and girders , this was compensated by making the bottom flange of an I-beam (the one experiencing the tension) much wider than the top, compressed, one and varying the beam profile to be wider at the middle, where the stress was higher. Cast iron was rapidly replaced in the beams by the wrought iron in the mid-19th century, the process had accelerated after the Dee Bridge disaster of 1847. [ 4 ]
Use of wrought iron in construction has a long history ( cramps made from wrought iron were used in classical antiquity ). [ 6 ] The first all-wrought iron roof was apparently installed in 1837 at the Euston railway station in London . [ 7 ]
Beams and girders were made of wrought iron with I-beam cross-section. The material was rarely used for the columns, as the cast was both stronger under compression and cheaper, so a typical iron frame building in the second half of the 19th century had cast iron columns and wrought iron beams. Columns at the Crystal Palace (1851), as well as short trusses, were made from the cast iron, while longer beams used wrought iron. A less-known precursor to the modern steel frame construction, the four-storey Boat Store ("Shed 78", 1858–1860), has its rigid frame constructed also from cast iron columns and wrought iron girders. With no internal walls and external walls made from sheet metal , the stability of this structure is provided exclusively through the rigid column-beam joints. [ 8 ]
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Iron is an important biological element. [ 1 ] [ 2 ] [ 3 ] It is used in both the ubiquitous iron-sulfur proteins [ 1 ] and in vertebrates it is used in hemoglobin which is essential for blood and oxygen transport. [ 4 ]
Iron is required for life. [ 1 ] [ 2 ] [ 3 ] The iron–sulfur clusters are pervasive and include nitrogenase , the enzymes responsible for biological nitrogen fixation . Iron-containing proteins participate in transport, storage and use of oxygen. [ 1 ] Iron proteins are involved in electron transfer . [ 5 ] The ubiquity of Iron in life has led to the Iron–sulfur world hypothesis that iron was a central component of the environment of early life. [ 6 ] [ 7 ] [ 8 ] [ 9 ] [ 10 ]
Examples of iron-containing proteins in higher organisms include hemoglobin, cytochrome (see high-valent iron ), and catalase . [ 1 ] [ 11 ] The average adult human contains about 0.005% body weight of iron, or about four grams, of which three quarters is in hemoglobin – a level that remains constant despite only about one milligram of iron being absorbed each day, [ 5 ] because the human body recycles its hemoglobin for the iron content. [ 12 ]
Microbial growth may be assisted by oxidation of iron(II) or by reduction of iron (III). [ 13 ]
Iron acquisition poses a problem for aerobic organisms because ferric iron is poorly soluble near neutral pH. Thus, these organisms have developed means to absorb iron as complexes, sometimes taking up ferrous iron before oxidising it back to ferric iron. [ 1 ] In particular, bacteria have evolved very high-affinity sequestering agents called siderophores . [ 14 ] [ 15 ] [ 16 ]
After uptake in human cells , iron storage is precisely regulated. [ 1 ] [ 17 ] A major component of this regulation is the protein transferrin , which binds iron ions absorbed from the duodenum and carries it in the blood to cells. [ 1 ] [ 18 ] Transferrin contains Fe 3+ in the middle of a distorted octahedron , bonded to one nitrogen, three oxygens and a chelating carbonate anion that traps the Fe 3+ ion: it has such a high stability constant that it is very effective at taking up Fe 3+ ions even from the most stable complexes. At the bone marrow, transferrin is reduced from Fe 3+ and Fe 2+ and stored as ferritin to be incorporated into hemoglobin. [ 5 ]
The most commonly known and studied bioinorganic iron compounds (biological iron molecules) are the heme proteins : examples are hemoglobin , myoglobin , and cytochrome P450 . [ 1 ] These compounds participate in transporting gases, building enzymes , and transferring electrons . [ 5 ] Metalloproteins are a group of proteins with metal ion cofactors . Some examples of iron metalloproteins are ferritin and rubredoxin . [ 5 ] Many enzymes vital to life contain iron, such as catalase , [ 19 ] lipoxygenases , [ 20 ] and IRE-BP . [ 21 ]
Hemoglobin is an oxygen carrier that occurs in red blood cells and contributes their color, transporting oxygen in the arteries from the lungs to the muscles where it is transferred to myoglobin , which stores it until it is needed for the metabolic oxidation of glucose , generating energy. [ 1 ] Here the hemoglobin binds to carbon dioxide , produced when glucose is oxidized, which is transported through the veins by hemoglobin (predominantly as bicarbonate anions) back to the lungs where it is exhaled. [ 5 ] In hemoglobin, the iron is in one of four heme groups and has six possible coordination sites; four are occupied by nitrogen atoms in a porphyrin ring, the fifth by an imidazole nitrogen in a histidine residue of one of the protein chains attached to the heme group, and the sixth is reserved for the oxygen molecule it can reversibly bind to. [ 5 ] When hemoglobin is not attached to oxygen (and is then called deoxyhemoglobin), the Fe 2+ ion at the center of the heme group (in the hydrophobic protein interior) is in a high-spin configuration . It is thus too large to fit inside the porphyrin ring, which bends instead into a dome with the Fe 2+ ion about 55 picometers above it. In this configuration, the sixth coordination site reserved for the oxygen is blocked by another histidine residue. [ 5 ]
When deoxyhemoglobin picks up an oxygen molecule, this histidine residue moves away and returns once the oxygen is securely attached to form a hydrogen bond with it. This results in the Fe 2+ ion switching to a low-spin configuration, resulting in a 20% decrease in ionic radius so that now it can fit into the porphyrin ring, which becomes planar. [ 5 ] (Additionally, this hydrogen bonding results in the tilting of the oxygen molecule, resulting in a Fe–O–O bond angle of around 120° that avoids the formation of Fe–O–Fe or Fe–O 2 –Fe bridges that would lead to electron transfer, the oxidation of Fe 2+ to Fe 3+ , and the destruction of hemoglobin.) This results in a movement of all the protein chains that leads to the other subunits of hemoglobin changing shape to a form with larger oxygen affinity. Thus, when deoxyhemoglobin takes up oxygen, its affinity for more oxygen increases, and vice versa. [ 5 ] Myoglobin, on the other hand, contains only one heme group and hence this cooperative effect cannot occur. Thus, while hemoglobin is almost saturated with oxygen in the high partial pressures of oxygen found in the lungs, its affinity for oxygen is much lower than that of myoglobin, which oxygenates even at low partial pressures of oxygen found in muscle tissue. [ 5 ] As described by the Bohr effect (named after Christian Bohr , the father of Niels Bohr ), the oxygen affinity of hemoglobin diminishes in the presence of carbon dioxide. [ 5 ]
Carbon monoxide and [[phosphorus trifluoride¿†¿ ⟨⟩ ]] are poisonous to humans because they bind to hemoglobin similarly to oxygen, but with much more strength, so that oxygen can no longer be transported throughout the body. Hemoglobin bound to carbon monoxide is known as carboxyhemoglobin . This effect also plays a minor role in the toxicity of cyanide , but there the major effect is by far its interference with the proper functioning of the electron transport protein cytochrome a. [ 5 ] The cytochrome proteins also involve heme groups and are involved in the metabolic oxidation of glucose by oxygen. The sixth coordination site is then occupied by either another imidazole nitrogen or a methionine sulfur, so that these proteins are largely inert to oxygen – with the exception of cytochrome a, which bonds directly to oxygen and thus is very easily poisoned by cyanide. [ 5 ] Here, the electron transfer takes place as the iron remains in low spin but changes between the +2 and +3 oxidation states. Since the reduction potential of each step is slightly greater than the previous one, the energy is released step-by-step and can thus be stored in adenosine triphosphate . Cytochrome a is slightly distinct, as it occurs at the mitochondrial membrane, binds directly to oxygen, and transports protons as well as electrons, as follows: [ 5 ]
Although the heme proteins are the most important class of iron-containing proteins, the iron–sulfur proteins are also very important, being involved in electron transfer, which is possible since iron can exist stably in either the +2 or +3 oxidation states. These have one, two, four, or eight iron atoms that are each approximately tetrahedrally coordinated to four sulfur atoms; because of this tetrahedral coordination, ths in the surrounding peptide chains. Another important class of iron–sulfur proteins is the ferredoxins , which have multiple iron atoms. Transferrin does not belong to either of these classes. [ 5 ]
The ability of sea mussels to maintain their grip on rocks in the ocean is facilitated by their use of organometallic iron-based bonds in their protein-rich cuticles . Based on synthetic replicas, the presence of iron in these structures increased elastic modulus 770 times, tensile strength 58 times, and toughness 92 times. The amount of stress required to permanently damage them increased 76 times. [ 23 ]
In vertebrates, iron is an essential component of hemoglobin , the oxygen transport protein. [ 4 ]
Most well-nourished people in industrialized countries have 4 to 5 grams of iron in their bodies (~38 mg iron/kg body weight for women and ~50 mg iron/kg body for men). [ 24 ] Of this, about 2.5 g is contained in the hemoglobin needed to carry oxygen through the blood (around 0.5 mg of iron per mL of blood), [ 25 ] and most of the rest (approximately 2 grams in adult men, and somewhat less in women of childbearing age) is contained in ferritin complexes that are present in all cells, but most common in bone marrow, liver , and spleen . The liver stores of ferritin are the primary physiologic source of reserve iron in the body. The reserves of iron in industrialized countries tend to be lower in children and women of child-bearing age than in men and in the elderly. Women who must use their stores to compensate for iron lost through menstruation , pregnancy or lactation have lower non-hemoglobin body stores, which may consist of 500 mg , or even less.
Of the body's total iron content, about 400 mg is devoted to cellular proteins that use iron for important cellular processes like storing oxygen (myoglobin) or performing energy-producing redox reactions ( cytochromes ). A relatively small amount (3–4 mg) circulates through the plasma , bound to transferrin. [ 26 ] Because of its toxicity, free soluble iron is kept in low concentration in the body.
Iron deficiency first affects the storage of iron in the body, and depletion of these stores is thought to be relatively asymptomatic, although some vague and non-specific symptoms have been associated with it. Since iron is primarily required for hemoglobin, iron deficiency anemia is the primary clinical manifestation of iron deficiency. Iron-deficient people will suffer or die from organ damage well before their cells run out of the iron needed for intracellular processes like electron transport.
Macrophages of the reticuloendothelial system store iron as part of the process of breaking down and processing hemoglobin from engulfed red blood cells. Iron is also stored as a pigment called hemosiderin , which is an ill-defined deposit of protein and iron, created by macrophages where excess iron is present, either locally or systemically, e.g., among people with iron overload due to frequent blood cell destruction and the necessary transfusions their condition calls for. If systemic iron overload is corrected, over time the hemosiderin is slowly resorbed by the macrophages.
Human iron homeostasis is regulated at two different levels. Systemic iron levels are balanced by the controlled absorption of dietary iron by enterocytes , the cells that line the interior of the intestines , and the uncontrolled loss of iron from epithelial sloughing, sweat, injuries and blood loss. In addition, systemic iron is continuously recycled. Cellular iron levels are controlled differently by different cell types due to the expression of particular iron regulatory and transport proteins.
The absorption of dietary iron is a variable and dynamic process. The amount of iron absorbed compared to the amount ingested is typically low, but may range from 5% to as much as 35% depending on circumstances and type of iron. The efficiency with which iron is absorbed varies depending on the source. Generally, the best-absorbed forms of iron come from animal products. Absorption of dietary iron in iron salt form (as in most supplements) varies somewhat according to the body's need for iron, and is usually between 10% and 20% of iron intake. Absorption of iron from animal products, and some plant products, is in the form of heme iron, and is more efficient, allowing absorption of from 15% to 35% of intake. Heme iron in animals is from blood and heme-containing proteins in meat and mitochondria, whereas in plants, heme iron is present in mitochondria in all cells that use oxygen for respiration.
Like most mineral nutrients, the majority of the iron absorbed from digested food or supplements is absorbed in the duodenum by enterocytes of the duodenal lining. These cells have special molecules that allow them to move iron into the body. To be absorbed, dietary iron can be absorbed as part of a protein such as heme protein or iron must be in its ferrous Fe 2+ form. A ferric reductase enzyme on the enterocytes' brush border , duodenal cytochrome B ( Dcytb ), reduces ferric Fe 3+ to Fe 2+ . [ 27 ] A protein called divalent metal transporter 1 ( DMT1 ), which can transport several divalent metals across the plasma membrane, then transports iron across the enterocyte's cell membrane into the cell. If the iron is bound to heme it is instead transported across the apical membrane by heme carrier protein 1 (HCP1). [ 28 ]
These intestinal lining cells can then either store the iron as ferritin , which is accomplished by Fe 2+ binding to apoferritin (in which case the iron will leave the body when the cell dies and is sloughed off into feces ), or the cell can release it into the body via the only known iron exporter in mammals, ferroportin . Hephaestin , a ferroxidase that can oxidize Fe 2+ to Fe 3+ and is found mainly in the small intestine, helps ferroportin transfer iron across the basolateral end of the intestine cells. In contrast, ferroportin is post-translationally repressed by hepcidin , a 25-amino acid peptide hormone. The body regulates iron levels by regulating each of these steps. For instance, enterocytes synthesize more Dcytb, DMT1 and ferroportin in response to iron deficiency anemia. [ 29 ] Iron absorption from diet is enhanced in the presence of vitamin C and diminished by excess calcium, zinc, or manganese. [ 30 ]
The human body's rate of iron absorption appears to respond to a variety of interdependent factors, including total iron stores, the extent to which the bone marrow is producing new red blood cells, the concentration of hemoglobin in the blood, and the oxygen content of the blood. The body also absorbs less iron during times of inflammation , in order to deprive bacteria of iron. Recent discoveries demonstrate that hepcidin regulation of ferroportin is responsible for the syndrome of anemia of chronic disease.
Most of the iron in the body is hoarded and recycled by the reticuloendothelial system, which breaks down aged red blood cells. In contrast to iron uptake and recycling, there is no physiologic regulatory mechanism for excreting iron. People lose a small but steady amount by gastrointestinal blood loss, sweating and by shedding cells of the skin and the mucosal lining of the gastrointestinal tract . The total amount of loss for healthy people in the developed world amounts to an estimated average of 1 mg a day for men, and 1.5–2 mg a day for women with regular menstrual periods. [ 31 ] People with gastrointestinal parasitic infections, more commonly found in developing countries, often lose more. [ 32 ] Those who cannot regulate absorption well enough get disorders of iron overload. In these diseases, the toxicity of iron starts overwhelming the body's ability to bind and store it. [ 33 ]
Most cell types take up iron primarily through receptor-mediated endocytosis via transferrin receptor 1 (TFR1), transferrin receptor 2 (TFR2) and GAPDH . TFR1 has a 30-fold higher affinity for transferrin-bound iron than TFR2 and thus is the main player in this process. [ 34 ] [ 35 ] The higher order multifunctional glycolytic enzyme glyceraldehyde-3-phosphate dehydrogenase (GAPDH) also acts as a transferrin receptor. [ 36 ] [ 37 ] Transferrin-bound ferric iron is recognized by these transferrin receptors, triggering a conformational change that causes endocytosis. Iron then enters the cytoplasm from the endosome via importer DMT1 after being reduced to its ferrous state by a STEAP family reductase. [ 38 ]
Alternatively, iron can enter the cell directly via plasma membrane divalent cation importers such as DMT1 and ZIP14 (Zrt-Irt-like protein 14). [ 39 ] Again, iron enters the cytoplasm in the ferrous state after being reduced in the extracellular space by a reductase such as STEAP2, STEAP3 (in red blood cells), Dcytb (in enterocytes) and SDR2. [ 38 ]
In the cytoplasm, ferrous iron is found in a soluble, chelatable state which constitutes the labile iron pool (~0.001 mM). [ 40 ] In this pool, iron is thought to be bound to low-mass compounds such as peptides, carboxylates and phosphates, although some might be in a free, hydrated form ( aqua ions ). [ 40 ] Alternatively, iron ions might be bound to specialized proteins known as metallochaperones . [ 41 ] Specifically, poly-r(C)-binding proteins PCBP1 and PCBP2 appear to mediate transfer of free iron to ferritin (for storage) and non-heme iron enzymes (for use in catalysis). [ 39 ] [ 42 ] The labile iron pool is potentially toxic due to iron's ability to generate reactive oxygen species. Iron from this pool can be taken up by mitochondria via mitoferrin to synthesize Fe-S clusters and heme groups. [ 38 ]
Iron can be stored in ferritin as ferric iron due to the ferroxidase activity of the ferritin heavy chain. [ 43 ] Dysfunctional ferritin may accumulate as hemosiderin , which can be problematic in cases of iron overload. [ 44 ] The ferritin storage iron pool is much larger than the labile iron pool, ranging in concentration from 0.7 mM to 3.6 mM. [ 40 ]
Iron export occurs in a variety of cell types, including neurons , red blood cells, macrophages and enterocytes. The latter two are especially important since systemic iron levels depend upon them. There is only one known iron exporter, ferroportin . [ 45 ] It transports ferrous iron out of the cell, generally aided by ceruloplasmin and/or hephaestin (mostly in enterocytes), which oxidize iron to its ferric state so it can bind ferritin in the extracellular medium. [ 38 ] Hepcidin causes the internalization of ferroportin, decreasing iron export. Besides, hepcidin seems to downregulate both TFR1 and DMT1 through an unknown mechanism. [ 46 ] Another player assisting ferroportin in effecting cellular iron export is GAPDH. [ 47 ] A specific post translationally modified isoform of GAPDH is recruited to the surface of iron loaded cells where it recruits apo-transferrin in close proximity to ferroportin so as to rapidly chelate the iron extruded. [ 48 ]
The expression of hepcidin, which only occurs in certain cell types such as hepatocytes , is tightly controlled at the transcriptional level and it represents the link between cellular and systemic iron homeostasis due to hepcidin's role as "gatekeeper" of iron release from enterocytes into the rest of the body. [ 38 ] Erythroblasts produce erythroferrone , a hormone which inhibits hepcidin and so increases the availability of iron needed for hemoglobin synthesis. [ 49 ]
Although some control exists at the transcriptional level, the regulation of cellular iron levels is ultimately controlled at the translational level by iron-responsive element-binding proteins IRP1 and especially IRP2. [ 50 ] When iron levels are low, these proteins are able to bind to iron-responsive elements (IREs). IREs are stem loop structures in the untranslated regions (UTRs) of mRNA. [ 38 ]
Both ferritin and ferroportin contain an IRE in their 5' UTRs, so that under iron deficiency their translation is repressed by IRP2, preventing the unnecessary synthesis of storage protein and the detrimental export of iron. In contrast, TFR1 and some DMT1 variants contain 3' UTR IREs, which bind IRP2 under iron deficiency, stabilizing the mRNA, which guarantees the synthesis of iron importers. [ 38 ]
Iron plays an essential role in marine systems and can act as a limiting nutrient for planktonic activity. [ 51 ] Because of this, too much of a decrease in iron may lead to a decrease in growth rates in phytoplanktonic organisms such as diatoms. [ 52 ] Iron can also be oxidized by marine microbes under conditions that are high in iron and low in oxygen. [ 53 ]
Iron can enter marine systems through adjoining rivers and directly from the atmosphere. Once iron enters the ocean, it can be distributed throughout the water column through ocean mixing and through recycling on the cellular level. [ 54 ] In the arctic, sea ice plays a major role in the store and distribution of iron in the ocean, depleting oceanic iron as it freezes in the winter and releasing it back into the water when thawing occurs in the summer. [ 55 ] The iron cycle can fluctuate the forms of iron from aqueous to particle forms altering the availability of iron to primary producers. [ 56 ] Increased light and warmth increases the amount of iron that is in forms that are usable by primary producers. [ 57 ] | https://en.wikipedia.org/wiki/Iron_in_biology |
In computer architecture , the iron law of processor performance (or simply iron law of performance) describes the performance trade-off between complexity and the number of primitive instructions that processors use to perform calculations. [ 1 ] This formulation of the trade-off spurred the development [ citation needed ] of Reduced Instruction Set Computers (RISC) whose instruction set architectures (ISAs) leverage a smaller set of core instructions to improve performance. The term was coined by Douglas Clark [ 2 ] based on research performed by Clark and Joel Emer in the 1980s. [ 3 ]
The performance of a processor is the time it takes to execute a program: T i m e P r o g r a m {\displaystyle \mathrm {\tfrac {Time}{Program}} } . This can be further broken down into three factors: [ 4 ]
I n s t r u c t i o n s P r o g r a m × C l o c k C y c l e s I n s t r u c t i o n × T i m e C l o c k C y c l e s {\displaystyle \mathrm {{\frac {Instructions}{Program}}\times {\frac {ClockCycles}{Instruction}}\times {\frac {Time}{ClockCycles}}} } Selection of an instruction set architecture affects I n s t r u c t i o n s P r o g r a m × C l o c k C y c l e s I n s t r u c t i o n {\displaystyle \mathrm {{\tfrac {Instructions}{Program}}\times {\tfrac {ClockCycles}{Instruction}}} } , whereas T i m e C l o c k C y c l e s {\displaystyle \mathrm {\tfrac {Time}{ClockCycles}} } is largely determined by the manufacturing technology. Classic Complex Instruction Set Computer (CISC) ISAs optimized I n s t r u c t i o n s P r o g r a m {\displaystyle \mathrm {\tfrac {Instructions}{Program}} } by providing a larger set of more complex CPU instructions . Generally speaking, however, complex instructions inflate the number of clock cycles per instruction C l o c k C y c l e s I n s t r u c t i o n {\displaystyle \mathrm {\tfrac {ClockCycles}{Instruction}} } because they must be decoded into simpler micro-operations actually performed by the hardware. After converting X86 binary to the micro-operations used internally, the total number of operations is close to what is produced for a comparable RISC ISA. [ 5 ] The iron law of processor performance makes this trade-off explicit and pushes for optimization of T i m e P r o g r a m {\displaystyle \mathrm {\tfrac {Time}{Program}} } as a whole, not just a single component.
While the iron law is credited for sparking the development of RISC architectures, [ citation needed ] it does not imply that a simpler ISA is always faster. If that were the case, the fastest ISA would consist of simple binary logic. A single CISC instruction can be faster than the equivalent set of RISC instructions when it enables multiple micro-operations to be performed in a single clock cycle. In practice, however, the regularity of RISC instructions allowed a pipelined implementation where the total execution time of an instruction was (typically) ~5 clock cycles, but each instruction followed the previous instruction ~1 clock cycle later. [ citation needed ] CISC processors can also achieve higher performance using techniques such as modular extensions, predictive logic, compressed instructions , and macro-operation fusion. [ 6 ] [ 5 ] [ 7 ]
This computer-engineering -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Iron_law_of_processor_performance |
Iron metallurgy in Africa concerns the origin and development of ferrous metallurgy on the African continent . Whereas the development of iron metallurgy in North Africa and the Horn closely mirrors that of the Ancient Near East and Mediterranean region , the three-age system is ill-suited to Sub-Saharan Africa , where copper metallurgy generally does not precede iron working. [ 1 ] Whether iron metallurgy in Sub-Saharan Africa originated as an independent innovation or a product of technological diffusion remains a point of contention between scholars. [ 1 ] [ 2 ] [ 3 ] Following the beginning of iron metallurgy in Western and Central Africa by 800 BC - 400 BC , and possibly earlier, [ 4 ] [ 3 ] [ 5 ] agriculturalists of the Chifumbaze Complex would ultimately introduce the technology to Eastern and Southern Africa by the end of the first millennium AD . [ 6 ]
In the first decades of the twenty-first century, radiocarbon and thermoluminescence dating of artifacts associated with iron metallurgy in Nigeria and the Central African Republic have yielded dates as early as the third millennium BC . [ 1 ] [ 7 ] [ 8 ] Although a number of scholars have scrutinized these dates on methodological and theoretical grounds, [ 5 ] [ 9 ] [ 10 ] others contend that they undermine the diffusionist model for the origins of iron metallurgy in Sub-Saharan Africa. [ 1 ] [ 8 ] [ 11 ] [ 12 ] [ 13 ]
Iron metallurgy may have been independently developed in the Nok culture between the 9th century BCE and 550 BCE. [ 14 ] [ 15 ] The nearby Djenné-Djenno culture of the Niger Valley in Mali shows evidence of iron production from c. 250 BCE. The Bantu expansion spread the technology to Eastern and Southern Africa between 500 BCE and 400 CE, as shown in the Urewe culture. [ 16 ]
Although the origins of iron working in Africa have been the subject of scholarly interest since the 1860s, it is still not known whether this technology diffused into sub-Saharan Africa from the Mediterranean region, or whether it was invented there independently of iron working elsewhere. [ 2 ] Although some nineteenth-century European scholars favored an indigenous invention of iron working in sub-Saharan Africa, archaeologists writing between 1945 and 1965 mostly favored diffusion of iron smelting technology from Carthage across the Sahara to West Africa and/or from Meroe on the upper Nile to central Africa. [ 17 ] This in turn has been questioned by more recent research which argues for an independent invention. [ 18 ] [ 8 ]
The invention of radiocarbon dating in the late 1950s enabled dating of metallurgical sites by the charcoal fuel used for smelting and forging. By the late 1960s some surprisingly early radiocarbon dates had been obtained for iron smelting sites in both Niger and central Africa (Rwanda, Burundi), reviving the view that iron-making was independently invented by Africans in sub-Saharan Africa [ 19 ] [ 20 ] as far back as 3600 BCE. [ 21 ] These dates preceded the known antiquity of ironworking in Carthage or Meroe, weakening the diffusion hypothesis. In the 1990s, evidence was found of Phoenician iron smelting in the western Mediterranean (900–800 BCE), [ 22 ] though specifically in North Africa it seems to date only to the 5th to 4th centuries BCE, or the 7th century BCE at the earliest, contemporary to or later than the oldest known iron metallurgy dates from sub-Saharan Africa. [ 8 ] According to archaeometallurgist Manfred Eggert, "Carthage cannot be reliably considered the point of origin for sub-Saharan iron ore reduction." [ 23 ] It is still not known when iron working was first practiced in Kush and Meroe in modern Sudan, but the earliest known iron metallurgy dates from Meroe and Egypt do not predate those from sub-Saharan Africa, and thus the Nile Valley is also considered unlikely to be the source of sub-Saharan iron metallurgy. [ 24 ]
From the mid-1970s there were new claims for independent invention of iron smelting in central Niger [ 25 ] [ 26 ] [ 27 ] and from 1994 to 1999 UNESCO funded an initiative "Les Routes du Fer en Afrique/The Iron Routes in Africa" to investigate the origins and spread of iron metallurgy in Africa. This funded both the conference on early iron in Africa and the Mediterranean [ 22 ] and a volume, published by UNESCO, that generated some controversy because it included only authors sympathetic to the independent-invention view. [ 28 ]
Two reviews of the evidence from the mid-2000s found technical flaws in the studies claiming independent invention, raising three major issues. [ 3 ] [ 2 ] The first was whether the material dated by radiocarbon was in secure archaeological association with iron-working residues. Many of the dates from Niger, for example, were on organic matter in potsherds that were lying on the ground surface together with iron objects. The second issue was the possible effect of "old carbon": wood or charcoal much older than the time at which iron was smelted. This is a particular problem in Niger, where the charred stumps of ancient trees are a potential source of charcoal, and have sometimes been misidentified as smelting furnaces. A third issue is the weaker precision of the radiocarbon method for dates between 800 and 400 BCE, attributable to irregular production of radiocarbon in the upper atmosphere. Unfortunately most radiocarbon dates for the initial spread of iron metallurgy in sub-Saharan Africa fall within this range.
Controversy flared again in 2007 with the publication of excavations by Étienne Zangato and colleagues in the Central African Republic. [ 29 ] [ 30 ] At Oboui they excavated an undated iron forge yielding eight consistent radiocarbon dates of 2000 BCE. This would make Oboui the oldest iron-working site in the world, and more than a thousand years older than any other dated evidence of iron in Central Africa. Opinion among African archaeologists is sharply divided. Some specialists accept this interpretation, but archaeologist Bernard Clist has argued that Oboui is a highly disturbed site, with older charcoal having been brought up to the level of the forge by the digging of pits into older levels. [ 31 ] Clist also raised questions about the unusually good state of preservation of metallic iron from the site. [ 21 ] However, archaeologists such as Craddock, Eggert, and Holl have argued that such disturbance or disruption is highly unlikely given the nature of the site. Additionally, Holl, regarding the state of preservation, argues that this observation was based on published illustrations representing a small unrepresentative number of atypically well-preserved objects selected for publication. [ 32 ] At Gbabiri, also in the Central African Republic, Eggert has found evidence of an iron reduction furnace and blacksmith workshop with earliest dates of 896–773 BCE and 907–796 BCE respectively. [ 33 ] In north-central Burkina Faso, remains of an iron smelting furnace near Douroula was also dated to the 8th century BCE, leading to the creation of the Ancient Ferrous Metallurgy Sites of Burkina Faso World Heritage Site. [ 34 ] In the Nsukka region of southeast Nigeria (now Igboland ), archaeological sites containing iron smelting furnaces and slag have been excavated dating to 750 BCE in Opi (Augustin Holl 2009) and 2,000 BCE in Lejja (Pamela Eze-Uzomaka 2009). [ 35 ] [ 36 ] [ 37 ] According to Augustin Holl (2018), there is evidence of ironworking dated to 2,153–2,044 BCE and 2,368–2,200 BCE from the site of Gbatoro, Cameroon. [ 8 ]
Archaeometallurgical scientific knowledge and technological development originated in numerous centers of Africa; the centers of origin were located in West Africa , Central Africa , and East Africa ; consequently, as these origin centers are located within inner Africa, these archaeometallurgical developments are thus native African technologies. [ 11 ] Iron metallurgical development occurred 2631 BCE – 2458 BCE at Lejja, in Nigeria, 2136 BCE – 1921 BCE at Obui, in Central Africa Republic, 1895 BCE – 1370 BCE at Tchire Ouma 147, in Niger, and 1297 BCE – 1051 BCE at Dekpassanware, in Togo. [ 11 ]
In 2014, archaeo-metallurgist Manfred Eggert argued that, though still inconclusive, the evidence overall suggests an independent invention of iron metallurgy in sub-Saharan Africa. [ 38 ] In a 2018 study, archaeologist Augustin Holl also argues that an independent invention is most likely. [ 8 ]
While the origins of iron smelting are difficult to date by radiocarbon, there are fewer problems with using it to track the spread of ironworking after 400 BCE. In the 1960s it was suggested that iron working was spread by speakers of Bantu languages , whose original homeland has been located by linguists in the Benue River valley of eastern Nigeria and Western Cameroon. Although some assert that no words for iron or ironworking can be traced to reconstructed proto-Bantu , [ 39 ] place-names in West Africa suggest otherwise, for example (Okuta) Ilorin, literally "site of iron-work". The linguist Christopher Ehret argues that the first words for iron-working in Bantu languages were borrowed from Central Sudanic languages in the vicinity of modern Uganda and Kenya, [ 40 ] while Jan Vansina [ 41 ] argues instead that they originated in non-Bantu languages in Nigeria, and that iron metallurgy spread southwards and eastwards to Bantu speakers, who had already dispersed into the Congo rainforest and the Great Lakes region. Archaeological evidence clearly indicates that starting in the first century BCE, iron and cereal agriculture (millet and sorghum) spread together southward from southern Tanzania and northern Zambia, all the way to the eastern Cape region of present South Africa by the third or fourth century CE. [ 42 ] It seems highly probable that this occurred through migrations of Bantu-speaking peoples. [ citation needed ]
All indigenous African iron smelting processes are variants of the bloomery process. A much wider range of bloomery smelting processes has been recorded on the African continent than elsewhere in the Old World, probably because bloomeries remained in use into the 20th century in many parts of sub-Saharan Africa, whereas in Europe and most parts of Asia they were replaced by the blast furnace before most varieties of bloomeries could be recorded. W.W. Cline's compilation of eye-witness records of bloomery iron smelting over the past 250 years in Africa [ 43 ] is invaluable, and has been supplemented by more recent ethnoarchaeological and archaeological studies. Furnaces used in the 19th and 20th centuries ranges from small bowl furnaces, dug down from the ground surface and powered by bellows , through bellows-powered shaft furnaces up to 1.5 m tall, to 6.5m natural-draft furnaces (i.e. furnaces designed to operate without bellows at all).
Over much of tropical Africa the ore used was laterite , which is widely available on the old continental cratons in West, Central and Southern Africa. Magnetite sand, concentrated in streams by flowing water, was often used in more mountainous areas, after beneficiation to raise the concentration of iron. Precolonial iron workers in present South Africa even smelted iron-titanium ores that modern blast furnaces are not designed to use. [ 44 ] Bloomery furnaces were less productive than blast furnaces, but were far more versatile.
The fuel used was invariably charcoal, and the products were the bloom (a solid mass of iron) and slag (a liquid waste product). African ironworkers regularly produced inhomogeneous steel blooms, especially in the large natural-draft furnaces. The blooms invariably contained some entrapped slag, and after removal from the furnace had to be reheated and hammered to expel as much of the slag as possible. Semi-finished bars of iron or steel were widely traded in some parts of West Africa, as for example at Sukur on the Nigeria-Cameroon border, which in the nineteenth century exported thousands of bars per year north to the Lake Chad Basin. [ 45 ] Although many African ironworkers produced steel blooms, there is little evidence in sub-Saharan as yet for hardening of steel by quenching and tempering or for the manufacture of composite tools combining a hard steel cutting edge with a soft but tough iron body. Relatively little metallography of ancient African iron tools has yet been done, so this conclusion may perhaps be modified by future work.
Unlike bloomery iron-workers in Europe, India or China, African metalworkers did not make use of water power to blow bellows in furnaces too large to be blown by hand-powered bellows. This is partly because sub-Saharan Africa has much less potential for water power than these other regions, [ citation needed ] but also because there were no engineering techniques developed for converting rotary motion to linear motion. African ironworkers did however invent a way to increase the size of their furnaces, and thus the amount of metal produced per charge, without using bellows. This was the natural-draft furnace, which is designed to reach the temperatures necessary to form and drain slag by using a chimney effect – hot air leaving the topic of the furnace draws in more air through openings at the base. (Natural-draft furnaces should not be confused with wind-powered furnaces, which were invariably small). The natural-draft furnace was the one African innovation in ferrous metallurgy that spread widely. [ 46 ] Natural draft furnaces were particularly characteristic of African savanna woodlands, and were used in two belts – across the Sahelian woodlands from Senegal in the west to Sudan in the east, and in the Brachystegia-Julbenardia (miombo) woodlands from southern Tanzania south to northern Zimbabwe. The oldest natural-draft furnaces yet found are in Burkina Faso and date to the seventh/eight centuries [ 47 ] The large masses of slag (10,000 to 60,000 tons) noted in some locations in Togo, Burkina Faso and Mali reflect the great expansion of iron production in West Africa after 1000 CE that is associated with the spread of natural-draft furnace technology. [ 48 ] [ 49 ] But not all large scale iron production in Africa was associated with natural draft furnaces – those of Meroe (Sudan, first to fifth centuries CE) were produced by slag-tapping bellows-driven furnaces, [ 50 ] and the large 18th-19th century iron industry of the Cameroon grasslands by non-tapping bellows-driven furnaces. [ 51 ] All of the large-scale iron smelting recorded so far are in the Sahelian and Sudanic zones that stretch from Senegal in the west to Sudan in the east; there were no iron-smelting concentrations like these in central or southern Africa.
There is also evidence that carbon steel was made in Western Tanzania by the ancestors of the Haya people as early as 2,300-2,000 years ago by a complex process of "pre-heating" allowing temperatures inside a furnace to reach up to 1800°C. [ 52 ] [ 53 ] [ 54 ] [ 55 ] [ 56 ] [ 57 ]
These techniques are now extinct in all regions of sub-Saharan Africa, except, in the case of some of techniques, for some very remote regions of Ethiopia. In most regions of Africa they fell out of use before 1950. The main reason for this was the increasing availability of iron imported from Europe. Blacksmiths still work in rural areas of Africa to make and repair agricultural tools, but the iron that they use is imported, or recycled from old motor vehicles.
Iron was not the only metal to be used in Africa; copper and brass were widely utilised too. However the steady spread of iron meant it must have had more favourable properties for many different uses. Its durability over copper meant that it was used to make many tools from farming pieces to weaponry. Iron was used for personal adornment in jewelry , impressive pieces of artwork and even instruments. It was used for coins and currencies of varying forms. For example, kisi pennies; a traditional form of iron currency used for trading in West Africa. They are twisted iron rods ranging from <30 cm to >2m in length. Suggestions for their uses vary from marital transactions, or simply that they were a convenient shape for transportation, melting down and reshaping into a desired object. There are many different forms of iron currency , often regionally differing in shape and value. Iron did not replace other materials, such as stone and wooden tools, but the quantity of production and variety of uses met were significantly high by comparison.
It is important to recognize that while iron production had great influence over Africa both culturally in trade and expansion (Martinelli, 1993, 1996, 2004), as well as socially in beliefs and rituals, there is great regional variation. Much of the evidence for cultural significance comes from the practises still carried out today by different African cultures. Ethnographical information has been very useful in reconstructing the events surrounding iron production in the past, however the reconstructions could have become distorted through time and influence by anthropologist's studies.
The control of iron production was often by ironworkers themselves, or a "central power" in larger societies such as kingdoms or states (Barros 2000, p. 154). [ 58 ] The demand for trade is believed to have resulted in some societies working only as smelters or smiths, specialising in just one of the many skills necessary to the production process. It is possible that this also led to tradesmen specialising in transporting and trading iron (Barros 2000, pg152). However, not every region benefited from industrialising iron production, others created environmental problems that arose due to the massive deforestation required to provide the charcoal for fuelling furnaces (for example the ecological crisis of the Mema Region (Holl 2000, pg48)).
Iron smelters and smiths received different social status depending on their culture. Some were lower in society due to the aspect of manual labour and associations with witchcraft, for example in the Maasai and Tuareg (Childs et al. 2005 pg 288). In other cultures the skills are often passed down through family and would receive great social status (sometimes even considered as witchdoctors) within their community. Their powerful knowledge allowed them to produce materials on which the whole community relied. In some communities they were believed to have such strong supernatural powers that they were regarded as highly as the king or chief. For example, an excavation at the royal tomb of King Rugira (Great Lakes, Eastern Africa) found two iron anvils placed at his head (Childs et al. 2005, p. 288 in Herbert 1993:ch.6). In some cultures mythical stories have been built around the premise of the iron smelter emphasising their godlike significance.
The smelting process was often carried out away from the rest of the community. Ironworkers engaged in rituals designed to encourage good production and to ward off bad spirits, including song and prayers, plus the giving of medicines and sacrifices. The latter were usually put in the furnace itself or buried under the base of the furnace. Examples of these date back as far as the early Iron Age in Tanzania and Rwanda (Schmidt 1997 in Childs et al., 2005 p. 293). [ 59 ] Men who possessed the knowledge and skills to work with iron, held a high social status and were often revered for their expertise. The ideology behind this was that, these 'Blacksmiths' possessed some spiritual and super human abilities which enabled them to extract the bloom from iron ore, eventually earning them a higher place of social status.
Some cultures associated sexual symbolism with iron production. Smelting was integrated with the fertility of their society, The production of the bloom was compared to human conception and birth. There were sexual taboos surrounding the process. The smelting process was carried out entirely by men and often away from the village. For women to touch any of the materials or be present could jeopardise the success of the production. The furnaces were also often adorned to resemble a woman, the mother of the bloom. [ 60 ] | https://en.wikipedia.org/wiki/Iron_metallurgy_in_Africa |
Nanoscale iron particles are sub-micrometer particles of iron metal. [ 1 ] Due to their high catalytic activity , permanent magnetic properties, low toxicity, and strong adsorption capacity, iron-based nanoparticles are widely utilized in drug delivery , production of magnetic tapes (e.g., camcorders and backup tapes of computers [ 2 ] ), gene therapy , and environmental remediation . [ 3 ]
Iron nanoparticles can be synthesized using two primary approaches: top-down and bottom-up methods. [ 4 ]
Top-down approaches create nanoparticles by breaking down larger bulk materials into smaller particles, including laser ablation and mechanical grinding. [ 3 ]
Bottom-up approaches involve the chemical and biological synthesis of iron nanoparticles from metal precursors (e.g., Fe(II) and Fe(III)). [ 3 ] This method is widely regarded as the most effective and commonly used strategy for nanoparticle preparation. [ 4 ] For example, iron nanoparticles can be chemically prepared by reducing Fe(II) or Fe(III) salts with sodium borohydride in an aqueous medium. This process can be described by the following equations: [ 5 ] [ 6 ]
Iron nanoparticles are prone to oxidation when exposed to air and water. [ 3 ] This redox process can occur under both acidic and neutral/basic conditions: [ 7 ]
Research has shown that nanoscale iron particles can be effectively used to treat several forms of ground contamination , including grounds contaminated by polychlorinated biphenyls (PCBs), chlorinated organic solvents, and organochlorine pesticides. Nanoscale iron particles are easily transportable through ground water, allowing for in situ treatment. Additionally, the nanoparticle-water slurry can be injected into the contaminated area and stay there for long periods of time. [ 8 ] These factors combine to make this method cheaper than the most currently used alternative.
Researchers have found that although metallic iron nanoparticles remediate contaminants well, they tend to agglomerate on the soil surfaces. In response, carbon nanoparticles and water-soluble polyelectrolytes have been used as supports for the metallic iron nanoparticles. The hydrophobic contaminants adsorb to these supports, improving permeability in sand and soil. [ 8 ]
In field tests have generally confirmed lab findings. However, research is still ongoing and nanoscale iron particles are not yet commonly used for treating ground contamination.
Iron oxide nanoparticles (IONPs) have widespread applications in biomedicine, including their use in magnetic resonance imaging and cancer therapy via magnetic hyperthermia [ 9 ] [ 10 ]
In addition to these applications, IONPs exhibit strong antibacterial activity and have been explored for drug and viral vector delivery to target cells. [ 11 ] Known microorganisms susceptible to the toxic effects of IONPs include Gram-negative bacteria (e.g., Escherichia coli and Klebsiella sp.) and Gram-positive bacteria (e.g., Bacillus sp. and Corynebacterium sp.) [ 11 ] .
The antibacterial activity of IONPs is primarily attributed to the generation of reactive oxygen species (ROS), a mechanism similar to the Fenton reaction. [ 11 ] Specifically, Fe 2+ ions react with hydrogen peroxide (H 2 O 2 ), producing Fe 3+ ions and hydroxyl radicals . [ 12 ] These highly reactive species induce oxidative damage to bacterial DNA , ultimately leading to cell death. | https://en.wikipedia.org/wiki/Iron_nanoparticle |
Iron oxide adsorption is a water treatment process that is used to remove arsenic from drinking water . Arsenic is a common natural contaminant of well water and is highly carcinogenic . Iron oxide adsorption treatment for arsenic in groundwater is a commonly practiced removal process which involves the chemical treatment of arsenic species such that they adsorb onto iron oxides and create larger particles that may be filtered out of the water stream.
The addition of ferric chloride , FeCl 3 , to well water immediately after the well at the influent to the treatment plant creates ferric hydroxide, Fe(OH) 3 , and hydrochloric acid , HCl.
Fe(OH) 3 in water is a strong adsorbent of arsenate, As(V), provided that the pH is low. HCl lowers pH, assuring arsenic adsorption, and the disassociated chlorine oxidizes iron in solution from Fe +2 to Fe +3 , which then may bond with hydroxide ions, OH − , thus creating more adsorbent.
This adjustment also lowers the pH of the well water, decreasing alkalinity and allowing more cationic species such Fe(+) or As(+) as to exist freely within the flow. Low pH also decreases the solubility of some iron and arsenic species as well as increasing the adsorptive reactivity of arsenate, As(V).
Additional oxidation of Fe +2 to Fe +3 , also referred to as iron(II) and iron(III), is induced by the addition of sodium hypochlorite , NaOCl, at the well head. NaOCl is usually added for disinfection although it may be used in this case towards the objectives of a distribution system free chlorine residual of 1 mg/L and the oxidation of aqueous As(III) to As(V), and aqueous iron Fe +2 to Fe +3 , which will bond with hydroxide for further adsorption.
The filter media usually consists of anthracite , iron-manganese oxidizing sand, and garnet sand over support gravel . [ 1 ] | https://en.wikipedia.org/wiki/Iron_oxide_adsorption |
For chemical reactions , the iron oxide cycle (Fe 3 O 4 /FeO) is the original two-step thermochemical cycle proposed for use for hydrogen production . [ 1 ] It is based on the reduction and subsequent oxidation of iron ions, particularly the reduction and oxidation between Fe 3+ and Fe 2+ . The ferrites , or iron oxide, begins in the form of a spinel and depending on the reaction conditions, dopant metals and support material forms either Wüstites or different spinels.
The thermochemical two-step water splitting process uses two redox steps. The steps of solar hydrogen production by iron based two-step cycle are:
Where M can by any number of metals, often Fe itself, Co , Ni , Mn , Zn or mixtures thereof.
The endothermic reduction step (1) is carried out at high temperatures greater than 1400 °C , though the " Hercynite cycle" is capable of temperatures as low as 1200 °C . The oxidative water splitting step (2) occurs at a lower ~ 1000 °C temperature which produces the original ferrite material in addition to hydrogen gas. The temperature level is realized by using geothermal heat from magma [ 2 ] or a solar power tower and a set of heliostats to collect the solar thermal energy .
Like the traditional iron oxide cycle, the hercynite is based on the oxidation and reduction of iron atoms. However unlike the traditional cycle, the ferrite material reacts with a second metal oxide, aluminum oxide , rather than simply decomposing. The reactions take place via the following two reactions:
The reduction step of the hercynite reaction takes place at temperature ~ 200 °C lower than the traditional water splitting cycle ( 1200 °C ). [ 3 ] This leads to lower radiation losses, which scale as temperature to the fourth power.
The advantages of the ferrite cycles are: they have lower reduction temperatures than other 2-step systems, no metallic gasses are produced, high specific H 2 production capacity, non-toxicity of the elements used and abundance of the constituent elements.
The disadvantages of the ferrite cycles are: similar reduction and melting temperature of the spinels (except for the hercynite cycle as aluminates have very high melting temperatures), and slow rates of the oxidation, or water splitting , reaction. | https://en.wikipedia.org/wiki/Iron_oxide_cycle |
Iron oxide nanoparticles are iron oxide particles with diameters between about 1 and 100 nanometers . The two main forms are composed of magnetite ( Fe 3 O 4 ) and its oxidized form maghemite (γ- Fe 2 O 3 ). They have attracted extensive interest due to their superparamagnetic properties and their potential applications in many fields (although cobalt and nickel are also highly magnetic materials, they are toxic and easily oxidized) including molecular imaging . [ 1 ]
Applications of iron oxide nanoparticles include terabit magnetic storage devices, catalysis , sensors , superparamagnetic relaxometry , high-sensitivity biomolecular magnetic resonance imaging , magnetic particle imaging , magnetic fluid hyperthermia , separation of biomolecules, and targeted drug and gene delivery for medical diagnosis and therapeutics. These applications require coating of the nanoparticles by agents such as long-chain fatty acids , alkyl-substituted amines , and diols . [ citation needed ] They have been used in formulations for supplementation. [ 2 ]
Magnetite has an inverse spinel structure with oxygen forming a face-centered cubic crystal system . In magnetite, all tetrahedral sites are occupied by Fe 3+ and octahedral sites are occupied by both Fe 3+ and Fe 2+ . Maghemite differs from magnetite in that all or most of the iron is in the trivalent state ( Fe 3+ ) and by the presence of cation vacancies in the octahedral sites. Maghemite has a cubic unit cell in which each cell contains 32 oxygen ions, 21 1 ⁄ 3 Fe 3+ ions and 2 2 ⁄ 3 vacancies. The cations are distributed randomly over the 8 tetrahedral and 16 octahedral sites. [ 3 ] [ 4 ]
Due to its 4 unpaired electrons in 3d shell , an iron atom has a strong magnetic moment . Ions Fe 2+ have also 4 unpaired electrons in 3d shell and Fe 3+ have 5 unpaired electrons in 3d shell. Therefore, when crystals are formed from iron atoms or ions Fe 2+ and Fe 3+ they can be in ferromagnetic , antiferromagnetic , or ferrimagnetic states.
In the paramagnetic state, the individual atomic magnetic moments are randomly oriented, and the substance has a zero net magnetic moment if there is no magnetic field . These materials have a relative magnetic permeability greater than one and are attracted to magnetic fields. The magnetic moment drops to zero when the applied field is removed. But in a ferromagnetic material, all the atomic moments are aligned even without an external field. A ferrimagnetic material is similar to a ferromagnet but has two different types of atoms with opposing magnetic moments. The material has a magnetic moment because the opposing moments have different strengths. If they have the same magnitude, the crystal is antiferromagnetic and possesses no net magnetic moment. [ 5 ]
When an external magnetic field is applied to a ferromagnetic material, the magnetization ( M ) increases with the strength of the magnetic field ( H ) until it approaches saturation . Over some range of fields the magnetization has hysteresis because there is more than one stable magnetic state for each field. Therefore, a remanent magnetization will be present even after removing the external magnetic field. [ 5 ]
A single domain magnetic material (e. g. magnetic nanoparticles) that has no hysteresis loop is said to be superparamagnetic . The ordering of magnetic moments in ferromagnetic, antiferromagnetic, and ferrimagnetic materials decreases with increasing temperature. Ferromagnetic and ferrimagnetic materials become disordered and lose their magnetization beyond the Curie temperature T C {\displaystyle T_{C}} and antiferromagnetic materials lose their magnetization beyond the Néel temperature T N {\displaystyle T_{N}} . Magnetite is ferrimagnetic at room temperature and has a Curie temperature of 850 K . Maghemite is ferrimagnetic at room temperature, unstable at high temperatures, and loses its susceptibility with time. (Its Curie temperature is hard to determine). Both magnetite and maghemite nanoparticles are superparamagnetic at room temperature. [ 5 ] This superparamagnetic behavior of iron oxide nanoparticles can be attributed to their size. When the size gets small enough (<10 nm), thermal fluctuations can change the direction of magnetization of the entire crystal. A material with many such crystals behaves like a paramagnet , except that the moments of entire crystals are fluctuating instead of individual atoms. [ 5 ]
Furthermore, the unique superparamagnetic behavior of iron oxide nanoparticles allows them to be manipulated magnetically from a distance. In the latter sections, external manipulation will be discussed in regards to biomedical applications of iron oxide nanoparticles. Forces are required to manipulate the path of iron oxide particles. A spatially uniform magnetic field can result in a torque on the magnetic particle, but cannot cause particle translation; therefore, the magnetic field must be a gradient to cause translational motion. The force on a point-like magnetic dipole moment m due to a magnetic field B is given by the equation:
In biological applications, iron oxide nanoparticles will be translate through some kind of fluid, possibly bodily fluid, [ 6 ] in which case the aforementioned equation can be modified to: [ 7 ]
Based on these equations, there will be the greatest force in the direction of the largest positive slope of the energy density scalar field.
Another important consideration is the force acting against the magnetic force. As iron oxide nanoparticles translate toward the magnetic field source, they experience Stokes' drag force in the opposite direction. The drag force is expressed below.
In this equation, η is the fluid viscosity, R is the hydrodynamic radius of the particle, and 𝑣 is the velocity of the particle. [ 8 ]
The preparation method has a large effect on shape, size distribution, and surface chemistry of the particles. It also determines to a great extent the distribution and type of structural defects or impurities in the particles. All these factors affect magnetic behavior. Recently, many attempts have been made to develop processes and techniques that would yield " monodisperse colloids " consisting of nanoparticles uniform in size and shape.
By far the most employed method is coprecipitation . This method can be further divided into two types.
In the first, ferrous hydroxide suspensions are partially oxidized with different oxidizing agents. For example, spherical magnetite particles of narrow size distribution with mean diameters between 30 and 100 nm can be obtained from a Fe(II) salt, a base and a mild oxidant ( nitrate ions). [ 9 ] The other method consists in ageing stoichiometric mixtures of ferrous and ferric hydroxides in aqueous media, yielding spherical magnetite particles homogeneous in size. [ 10 ] In the second type, the following chemical reaction occurs:
Optimum conditions for this reaction are pH between 8 and 14, Fe 3+ / Fe 2+ ratio of 2:1 and a non-oxidizing environment. Being highly susceptibile to oxidation, magnetite ( Fe 3 O 4 ) is transformed to maghemite (γ Fe 2 O 3 ) in the presence of oxygen: [ 3 ]
The size and shape of the nanoparticles can be controlled by adjusting pH, ionic strength , temperature, nature of the salts ( perchlorates , chlorides , sulfates , and nitrates), or the Fe(II) / Fe(III) concentration ratio. [ 3 ]
A microemulsion is a stable isotropic dispersion of 2 immiscible liquids consisting of nanosized domains of one or both liquids in the other stabilized by an interfacial film of surface-active molecules. Microemulsions may be categorized further as oil-in-water (o/w) or water-in-oil (w/o), depending on the dispersed and continuous phases. [ 4 ] Water-in-oil is more popular for synthesizing many kinds of nanoparticles. The water and oil are mixed with an amphiphillic surfactant . The surfactant lowers the surface tension between water and oil, making the solution transparent. The water nanodroplets act as nanoreactors for synthesizing nanoparticles. The shape of the water pool is spherical. The size of the nanoparticles will depend on size of the water pool to a great extent. Thus, the size of the spherical nanoparticles can be tailored and tuned by changing the size of the water pool. [ 11 ]
The decomposition of iron precursors in the presence of hot organic surfactants results in samples with good size control, narrow size distribution (5-12 nm) and good crystallinity ; and the nanoparticles are easily dispersed. For biomedical applications like magnetic resonance imaging, magnetic cell separation or magnetorelaxometry, where particle size plays a crucial role, magnetic nanoparticles produced by this method are very useful. Viable iron precursors include Fe( Cup ) 3 , Fe(CO) 5 , or Fe( acac ) 3 in organic solvents with surfactant molecules. A combination of Xylenes and Sodium Dodecylbenezensulfonate as a surfactant are used to create nanoreactors for which well dispersed iron(II) and iron (III) salts can react. [ 3 ]
Magnetite and maghemite are preferred in biomedicine because they are biocompatible and potentially non-toxic to humans [ citation needed ] . Iron oxide is easily degradable and therefore useful for in vivo applications [ citation needed ] . Results from exposure of a human mesothelium cell line and a murine fibroblast cell line to seven industrially important nanoparticles showed a nanoparticle specific cytotoxic mechanism for uncoated iron oxide. [ 12 ] Solubility was found to strongly influence the cytotoxic response.
Labelling cells (e.g. stem cells , dendritic cells ) with iron oxide nanoparticles is an interesting new tool to monitor such labelled cells in real time by magnetic resonance tomography . [ 13 ] [ 14 ] Some forms of Iron oxide nanoparticle have been found to be toxic and cause transcriptional reprogramming. [ 15 ] [ 16 ]
Iron oxide nanoparticles are used in cancer magnetic nanotherapy that is based on the magneto-spin effects in free-radical reactions and semiconductor material ability to generate oxygen radicals , furthermore, control oxidative stress in biological media under inhomogeneous electromagnetic radiation . The magnetic nanotherapy is remotely controlled by external electromagnetic field reactive oxygen species (ROS) and reactive nitrogen species (RNS) -mediated local toxicity in the tumor during chemotherapy with antitumor magnetic complex and lesser side effects in normal tissues. Magnetic complexes with magnetic memory that consist of iron oxide nanoparticles loaded with antitumor drug have additional advantages over conventional antitumor drugs due to their ability to be remotely controlled while targeting with a constant magnetic field and further strengthening of their antitumor activity by moderate inductive hyperthermia (below 40 °C). The combined influence of inhomogeneous constant magnetic and electromagnetic fields during nanotherapy has initiated splitting of electron energy levels in magnetic complex and unpaired electron transfer from iron oxide nanoparticles to anticancer drug and tumor cells . In particular, anthracycline antitumor antibiotic doxorubicin, the native state of which is diamagnetic , acquires the magnetic properties of paramagnetic substances. Electromagnetic radiation at the hyperfine splitting frequency can increase the time that radical pairs are in the triplet state and hence the probability of dissociation and so the concentration of free radicals . Free radicals in cancer cells induce changes in mechanochemical tumor heterogeneity by modifying bonds which influence the spatial arrangement of molecules in cell structures. The translation of the magnetic force exerted on the tumor and its microenvironment by magnetic nanoparticles into biochemical signaling pathways is known as the magneto-mechanochemical effect. This leads to the formation of regions with different biomechanical and biochemical properties within the tumor. The reactivity of magnetic particles depends on their spin state . The experimental data was received about correlation between the frequency of electromagnetic field radiation with magnetic properties and quantity paramagnetic centres of complex. It is possible to control the kinetics of malignant tumor. Cancer cells are then particularly vulnerable to an oxidative assault and induction of high levels of oxidative stress locally in tumor tissue, that has the potential to destroy or arrest the growth of cancer cells and can be thought as therapeutic strategy against cancer. Multifunctional magnetic complexes with magnetic memory can combine cancer magnetic nanotherapy, tumor targeting and medical imaging functionalities in theranostics approach for personalized cancer medicine. [ 17 ] [ 18 ] [ 19 ] [ 20 ] [ 21 ]
Yet, the use of inhomogeneous stationary magnetic fields to target iron oxide magnetic nanoparticles can result in enhanced tumor growth. Magnetic force transmission through magnetic nanoparticles to the tumor due to the action of the inhomogeneous stationary magnetic field reflects mechanical stimuli converting iron-induced reactive oxygen species generation to the modulation of biochemical signals. [ 22 ]
Iron oxide nanoparticles may also be used in magnetic hyperthermia as a cancer treatment method. In this method, the ferrofluid which contains iron oxide is injected to the tumor and then heated up by an alternating high frequency magnetic field. The temperature distribution produced by this heat generation may help to destroy cancerous cells inside the tumor. [ 23 ] [ 24 ] [ 25 ]
The use of superparamagnetic iron oxide (SPIO) can also be used as a tracer in sentinel node biopsy instead of radioisotope. [ 26 ]
Media related to Magnetite nanoparticles at Wikimedia Commons | https://en.wikipedia.org/wiki/Iron_oxide_nanoparticle |
The iron peak is a local maximum in the vicinity of Fe ( Cr , Mn , Fe, Co and Ni ) on the graph of the abundances of the chemical elements .
For elements lighter than iron on the periodic table , nuclear fusion releases energy . For iron, and for all of the heavier elements, nuclear fusion consumes energy . Chemical elements up to the iron peak are produced in ordinary stellar nucleosynthesis , with the alpha elements being particularly abundant. Some heavier elements are produced by less efficient processes such as the r-process and s-process . Elements with atomic numbers close to iron are produced in large quantities in supernovae due to explosive oxygen and silicon fusion , followed by radioactive decay of nuclei such as Nickel-56 . On average, heavier elements are less abundant in the universe, but some of those near iron are comparatively more abundant than would be expected from this trend. [ 1 ]
A graph of the nuclear binding energy per nucleon for all the elements shows a sharp increase to a peak near nickel and then a slow decrease to heavier elements. Increasing values of binding energy represent energy released when a collection of nuclei is rearranged into another collection for which the sum of nuclear binding energies is higher. Light elements such as hydrogen release large amounts of energy (a big increase in binding energy) when combined to form heavier nuclei. Conversely, heavy elements such as uranium release energy when converted to lighter nuclei through alpha decay and nuclear fission . 56 28 Ni is the most thermodynamically favorable in the cores of high-mass stars . Although iron-58 and nickel-62 have even higher (per nucleon) binding energy, their synthesis cannot be achieved in large quantities, because the required number of neutrons is typically not available in the stellar nuclear material, and they cannot be produced in the alpha process (their mass numbers are not multiples of 4). | https://en.wikipedia.org/wiki/Iron_peak |
Iron phosphide is a chemical compound of iron and phosphorus , with a formula of FeP.< [ 1 ] Its physical appearance is grey needles.
Manufacturing of iron phosphide takes place at elevated temperatures, where the elements combine directly. [ 1 ] Iron phosphide reacts with moisture and acids producing phosphine (PH 3 ), a toxic and pyrophoric gas.
Iron phosphide is a good electric and heat conductor. [ 2 ]
Below a Néel temperature of about 119 K, FeP takes on an helimagnetic structure. [ 3 ] | https://en.wikipedia.org/wiki/Iron_phosphide |
Iron Pipe Size (IPS or I.P.S.) pipe sizing system based on the inside diameter (ID) of pipe. It was widely used from the early 19th century to the mid 20th century and is still in use by some industries, including major PVC pipe manufacturers, as well as for some legacy drawings and equipment.
The iron pipe size standard came into being early in the 19th century and remained in effect until after World War II. The IPS system was primarily used in the United States and the United Kingdom. In the 1920s, the Copper Tube Size (CTS) standard was combined with the IPS standard.
During the IPS period, pipes were cast in halves and welded together, and pipe sizes referred to the inside diameters. [ 1 ] The inside diameters under IPS were roughly the same as the more modern Ductile Iron Pipe Standard (DIPS) and Nominal Pipe Size (NPS) Standards, and some of the wall thicknesses were also retained with a different designator. In 1948, the DIPS came into effect, when greater control of a pipe's wall thickness was possible.
CTS diameter always specifies the outside diameter (OD) of a tube, where pipe diameter specifications only approximate the pipe inside diameter (ID) for sizes of 12 inch or less, and STD wall thickness.
The IPS number (reference to an OD) is the same as the NPS number, but the schedules were limited to Standard Wall (STD), Extra Strong, (XS) and Double Extra Strong (XXS). STD is identical to Schedule 40 for NPS 1/8 to NPS 10, inclusive, and indicates .375" wall thickness for NPS 12 and larger. XS is identical to SCH 80 for NPS 1/8 to NPS 8, inclusive, and indicates .500" wall thickness for NPS 8 and larger. Different definitions exist for XXS, but it is generally thicker than schedule 160. [ 2 ] | https://en.wikipedia.org/wiki/Iron_pipe_size |
Iron plantations were rural localities emergent in the late-18th century and predominant in the early-19th century that specialized in the production of pig iron and bar iron from crude iron ore . [ 1 ]
Such plantations derive their name from two sources. First, because they were nearly self-sufficient communities despite an almost singular focus on the production of iron to be sold on the market, and second, because of the large swaths of forest and land necessary to provide charcoal fuel and ore for their operations.
The first plantations stretched across the Northeast , Midwest , and Southern United States , "the chief charcoal iron producing states [being] Pennsylvania, Ohio, New York, Virginia, Connecticut, Maryland, Missouri, Tennessee, and Kentucky." [ 2 ] Many produced raw materials used in the American Revolution or to be exported to England. [ 3 ]
For the rest of the 19th century, however, only locations that adopted new technologies first introduced by competing coal- and coke-powered smelters in the rapidly industrializing field persisted.
Plantations typically consisted of a nearly self-sufficient community, including the head iron master, workers and their families, and other shopkeepers, blacksmiths, and agricultural workers needed to sustain mining and smelting operations as well as life on the plantation. [ 1 ] Plantations were foremost land-intensive operations, commonly comprising thousands of acres. The grounds were typically defined by a conspicuous mansion, belonging to the iron master, which looked out on the charcoal furnace or iron forge from atop a geographically higher location. [ 1 ]
The iron master was also in charge of hiring skilled labor and investing capital in construction and maintenance of charcoal furnaces and forges for the refining and working of iron. Workers on the plantation were often not paid directly in wages. Rather, the master tallied an employee’s earnings on a balance sheet, which he then offset with purchases of merchandise from the community’s stores. [ 1 ] While an iron master lived a rather luxurious life with the opportunity to afford travel, tutors for his children, and expensive home furnishings, workers had few material possessions of their own. Workers were not well traveled outside of the plantations, and little news outside of the confines of the plantation concerned their daily lives. Notably, however, poverty was not well known on the plantations, even in times of economic depression, and workers’ wages in the United States greatly surpassed comparable wages in the European iron industry.
Work forces on iron plantations consisted of a wide array of labor and included indentured servants, slaves, and free laborers. Indentured servants composed the largest group. [ 3 ] Indentured servants and slaves typically performed the least skilled tasks on plantations, serving as woodcutters to supply the charcoal furnaces or as miners to dig iron ore. [ 3 ] Few opportunities were afforded to laborers for upwards mobility on plantations.
More efficient fossil fuels eventually substituted for wood-based charcoal, and “the semi-feudal iron plantation was replaced by the urban establishment and the company town” typically possessing a coke furnace. [ 4 ]
The lack of nearby ore deposits additionally limited many plantations from being able to economically transport large quantities of ore over long distances to be smelted on the plantations themselves. [ 2 ] Wagon transport of bar and pig iron to cities further added to costs and could run as high as forty percent of the market price per ton of pig iron in 1728, according to John Potts, a member of an iron plantation in Pennsylvania .
Iron plantations in Alabama, Tennessee, Georgia, Michigan, Wisconsin, and Missouri in particular better survived the evolving technological landscape by adopting practices that increased charcoal energy efficiency, that is, the amount of charcoal consumed per ton of iron smelted. One such technique was to raise the heights of furnaces to create a longer and more uniform reaction chamber to produce more homogeneous pig iron. Whereas antebellum furnaces were built with brick and mortar and reached only 30-35 feet in height, new furnaces remodeled in the 1840s reached as high as 65 feet. [ 2 ] Continued demand for pig iron to be transported westward provided an additional competitive advantage to plantations in these states.
The iron industry shifted to one largely determined by the production of steel during the British Industrial Revolution and in the later half of the 19th and early 20th centuries. [ 5 ] As such, blast furnaces, steam and electric power, and coke fuel replaced the largely land- and labor-intensive practices of iron making on plantations dependent on large tracts of land to produce charcoal and additional labor to sustain both the iron making operations and the community at large. Though iron produced on plantations remained practically useful for Westward Expansion, the eastern United States and Europe increasingly demanded more pliable and resistant steel for use in buildings, ships, engines, and railroads. [ 5 ] Though demand still remained for pig iron as an ingredient in steel production, most iron plantations were no longer economically competitive with coke-powered smelters which located themselves increasingly closer to the major cities requiring their products. | https://en.wikipedia.org/wiki/Iron_plantation |
Iron stress repressed RNA (IsrR) is a cis-encoded antisense RNA which regulates the expression of the photosynthetic protein isiA. IsiA expression is activated by the Ferric uptake regulator protein (Fur) under iron stress conditions. IsiA enhances photosynthesis by forming a ring around photosystem I which acts as an additional antenna complex. [ 1 ]
IsrR is abundant when there is a sufficient iron concentration. IsrR is encoded for within the opposite stand of isiA gene and contains a conserved stem loop secondary structure. Under sufficient iron conditions IsrR binds to its complementary region which corresponds to the central third of the isiA mRNA . The resulting duplex RNA is then targeted for degradation. This allows the antisense RNA to act as a reversible switch that responds to changes in environmental conditions to modulate the expression of the isiA protein.
IsrR was originally identified within cyanobacteria but may be conserved throughout a number of photosynthetic species from multiple kingdoms. At present, IsrR is the only non coding RNA identified that has a regulatory role on photosynthetic proteins.
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Iron_stress_repressed_RNA |
Iron sulfide or Iron sulphide can refer to range of chemical compounds composed of iron and sulfur .
By increasing order of stability: | https://en.wikipedia.org/wiki/Iron_sulfide |
Iron tetraboride (FeB 4 ) is a superhard superconductor ( T c < 3 K ) consisting of iron and boron . Iron tetraboride does not occur in nature and can be created synthetically. [ 1 ] [ 2 ] Its molecular structure was predicted using computer models. [ 3 ]
This article about materials science is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Iron_tetraboride |
An ironmaster is the manager, and usually owner, of a forge or blast furnace for the processing of iron. It is a term mainly associated with the period of the Industrial Revolution , especially in Great Britain.
The ironmaster was usually a large-scale entrepreneur and thus an important member of a community. He would have a large country house or mansion as his residence. The organization of operations surrounding the smelting , refining , and casting of iron was labour-intensive, and so there would be numerous workers reliant on the furnace works.
There were ironmasters (possibly not called such) from the 17th century onward, but they became more prominent with the great expansion in the British iron industry during the Industrial Revolution.
An early ironmaster was John Winter (about 1600–1676) who owned substantial holdings in the Forest of Dean . During the English Civil War he cast cannons for Charles I . [ 1 ] Following the Restoration , Winter developed his interest in the iron industry, and experimented with a new type of coking oven . This was a precursor to the later work of Abraham Darby I who successfully used coke to smelt iron. [ 2 ]
Three successive generations of the same family all bearing the name Abraham Darby are renowned for their contributions to the development of the English iron industry. Their works at Coalbrookdale in Shropshire nurtured the start of improvements in metallurgy that allowed large-scale production of the iron that made the development of steam engines and railways possible, although their most notable innovation was The Iron Bridge . [ 3 ]
One of the best-known ironmasters of the early part of the industrial revolution was John Wilkinson (1728–1808), who was considered to have "iron madness", extending even to making cast iron coffins. [ 4 ] Wilkinson's patented method for boring iron cylinders was first used to create cannons, but later provided the precision needed to create James Watt 's first steam engines. [ 5 ]
Samuel Van Leer was a well-known ironmaster and a United States Army officer during the American Revolutionary War . He started a military career with enthusiasm with his neighbor General Anthony Wayne in 1775. [ 6 ] His furnace, Reading Furnace in Pennsylvania, supplied cannon and cannonballs for the Continental Army . [ 7 ] Van Leer's furnace was a center of colonial ironmaking and is associated with the introduction of the Franklin Stove , and the retreat of George Washington 's army following its defeat at the Battle of Brandywine , where they came for musket repairs. [ 8 ] The location is listed as a temporary George Washington Headquarter .
W [ 9 ] Van Leer's children all joined the iron business as well. [ 10 ]
Lowthian Bell (1816–1904) was, like Abraham Darby, the forceful patriarch of an ironmaking dynasty. Both his son Hugh Bell and his grandson Maurice Bell were directors of the Bell iron and steel company. His father, Thomas Bell, was a founder of Losh, Wilson and Bell , an iron and alkali company. The firm had works at Walker, near Newcastle upon Tyne , and at Port Clarence , Middlesbrough , contributing largely to the growth of those towns and of the economy of the northeast of England. Bell accumulated a large fortune, with mansions including Washington New Hall , Rounton Grange near Northallerton , and the mediaeval Mount Grace Priory near Osmotherley . [ 11 ] [ 12 ] [ 13 ]
Henry Bolckow (1806–1878) and John Vaughan (1799–1868) were lifelong business partners, friends, and brothers-in-law. They established what became the largest of all Victorian era iron and steel companies, Bolckow Vaughan , in Middlesbrough. Bolckow brought financial acumen, and Vaughan brought ironmaking and engineering expertise. The two men trusted each other implicitly and "never interfered in the slightest degree with each other's work. Mr. Bolckow had the entire management of the financial department, while Mr. Vaughan as worthily controlled the practical work of the establishment." At its peak the firm was the largest steel producer in Britain, possibly in the world. [ 14 ] [ 15 ]
Andrew Handyside (1805–1887) was born in Edinburgh and set up works in Derby where he made ornamental items, bridges and pillar boxes, many of which survive today.
Samuel Richards (1769–1842) was born in Philadelphia to William Richards, the manager of the Batsto Iron Works beginning in 1784. Samuel Richards was heavily involved with the early 19th century iron industry in southern New Jersey . His most notable enterprise was the management of the iron works at Atsion, New Jersey from 1824 until his death in 1842. He was also involved with Martha Furnace , and Weymouth Furnace. | https://en.wikipedia.org/wiki/Ironmaster |
Iron–nickel (Fe–Ni) clusters are metal clusters consisting of iron and nickel , i.e. Fe–Ni structures displaying polyhedral frameworks held together by two or more metal–metal bonds per metal atom, where the metal atoms are located at the vertices of closed, triangulated polyhedra. [ 1 ]
Individually, iron (Fe) and nickel (Ni) generally form metal clusters with π-acceptor ligands. Π acceptor ligands are ligands that remove some of the electron density from the metal. [ 2 ]
Figure 1 contains pictures of representative cluster shapes. Clusters take the form of closed, triangulated polyhedral . [ 1 ]
Corresponding bulk systems of Fe and Ni atoms show a variety of composition-dependent abnormalities and unusual effects. Fe–Ni composites are studied in hopes to understand and utilize these unusual and new properties.
Fe–Ni clusters are used for several main purposes. Fe–Ni clusters ranging from single to hundreds of atoms are used in catalysis , depending on the reaction mechanism. Additionally, Fe–Ni clusters, usually of one or two metal atoms, are used in biological systems. These applications are discussed below.
Several general trends are recognized in determining the structure of Fe–Ni clusters. Larger clusters, containing both iron and nickel, are most stable with Fe atoms located in the inner parts of the cluster and Ni metals on outside. In other terms, when iron and nickel form body-centered cubic structures the preferred position of Ni atoms is at the surface, instead of at the center of the cluster, as it is energetically unfavorable for two nickel atoms to occupy nearest-neighbor positions. [ 3 ]
Metal–metal bonds, being d-orbital interactions, happen at larger distances. More stable metal–metal bonds are expected to be longer than unstable bonds. This is shown by the fact that the Fe–Ni bond length is in between Ni–Ni and Fe–Fe bond lengths. [ 4 ] For example, in Fe–Ni four-atom clusters (FeNi) 2 which are most stable in a tetrahedral structure, the bond length of metal–metal Fe–Ni bond is 2.65Å and Fe–Fe bond is 2.85 Å. [ 4 ] When bonding in these structures is examined, it follows that lowest energy cluster structures of iron and nickel are given by geometries with a maximum number of Fe–Fe bonds, and a small number of Ni–Ni bonds. [ 3 ]
The simplest Fe–Ni clusters are of one iron atom and one nickel atom bonded together. More complex clusters can be added through the addition of another atom. Some pictures of sample geometries are shown in Fig. 2.
All Fe–Ni clusters exhibit some degree of distortion from usual geometry. This distortion generally becomes more pronounced as the number of Fe atoms increases. [ 3 ]
Notice how in the above cluster diagrams, as calculated by Rollmann and colleagues, the symmetry of the cluster changes from a pure octahedron (D 3h ) to a square pyramid (C 4v ) as more iron atoms are added. [ 3 ]
As mentioned previously, the relative bonding between Ni atoms in (FeNi) n clusters is weak and the stability of these clusters could be enhanced by increasing the number of Fe–Fe and Fe–Ni bonds. [ 5 ] One measure of stability in Fe–Ni clusters is the binding energy , or how much energy is required to break the bonds between two atoms. The larger the binding energy, the stronger the bond. Binding energies of Fe n-x Ni x clusters are found to generally decrease by successive substitutions of Ni atoms for Fe atoms. [ 6 ]
The average magnetic moment (μ av ) increases in a Fe–Ni cluster through the replacement of more and more Fe atoms. [ 4 ] This is due to fact that magnetic moments of Fe atom/ Fe bulk are more than that of Ni atom/ Ni bulk values. The local magnetic moment of Ni (μ atom,local ) decreases by a proportional increase of Fe atoms. [ 4 ] This is due to charge transfer from nickel's 4s orbital and iron atoms to nickel's 3d orbitals.
Below is a table of the bond length (R e , in Å), binding energy (E b , in eV), and magnetic moment (M, in μ a ) of the small clusters Fe 2 , Ni 2 , and FeNi from two authors. Notice how both authors show that Fe 2 has the smallest bond length, the lowest binding energy, and the largest magnetic moment of the cluster combinations.
Below is another table of bond length (R e ), binding energy (E b ), and magnetic moment (M) of Fe–Ni clusters containing five atoms.
The magnetic properties of metal clusters are strongly influenced by their size and surface ligands . In general, the magnetic moments in small metal clusters are larger than in the case of a macroscopic bulk metal structure. [ 7 ] For example, the average magnetic moment per atom in Ni clusters was found to be 0.7-0.8 μB, as compared with 0.6 μB for bulk Ni. [ 8 ] This is explained by longer metal–metal bonds in cluster structures than in bulk structures, a consequence of a larger s character of metal–metal bonds in clusters. Magnetic moments approach bulk values as cluster size increases, though this is often difficult to predict computationally.
Magnetic quenching is an important phenomenon that is well documented for Ni clusters, and represents a significant effect of ligands on metal cluster magnetism . It has been shown that CO ligands cause the magnetic moments of surface Ni atoms to go to zero and the magnetic moment of inner Ni atoms to decrease to 0.5 μB. [ 7 ] In this case, the 4s-derived Ni–Ni bonding molecular orbitals experience repulsion with the Ni-CO σ orbital, which causes its energy level to increase so that 3d-derived molecular orbitals are filled instead. Furthermore, Ni-CO π backbonding leaves Ni slightly positive, causing more transfer of electrons to 3d-derived orbitals, which are less disperse than those of 4s. Together, these effects result in a 3d 10 , diamagnetic character of the ligated Ni atoms, and their magnetic moment decreases to zero. [ 7 ] [ 9 ]
Density functional theory (DFT) calculations have shown that these ligand-induced electronic effects are limited to only surface Ni atoms, and inner cluster atoms are virtually unperturbed. Experimental findings have described two electronically distinct cluster atoms, inner atoms and surface atoms. [ 9 ] These results indicate the significant effect that a cluster's size has on its properties, magnetic and other.
Fe–Ni metal clusters are crucial for energy production in many bacteria . A primary source of energy in bacteria is the oxidation and reduction of H 2 which is performed by hydrogenase enzymes.
These enzymes are able to create a charge gradient across the cell membrane which serves as an energy store. In aerobic environments, the oxidation and reduction of oxygen is the primary energy source. However, many bacteria are capable of living in environments where O 2 supply is limited and use H 2 as their primary energy source . The hydrogense enzymes which provide energy to the bacteria are centered around either a Fe–Fe or Fe–Ni active site . H 2 metabolism is not used by humans or other complex life forms, but proteins in the mitochondria of mammalian life appear to have evolved from hydrogenase enzymes, indicating that hydrogenase is a crucial step in the evolutionary development of metabolism. [ 10 ]
The active site of Fe–Ni containing hydrogenase enzymes often is composed of one or more bridging sulfur ligands, carbonyl , cyanide and terminal sulfur ligands . The non-bridging sulfur ligands are often cystine amino acid residues that attach the active site to the protein backbone. Metal–metal bonds between the Fe and Ni have not been observed. Several oxidation states of the Fe–Ni core have been observed in a variety of enzymes, though not all appear to be catalytically relevant. [ 12 ]
The extreme oxygen and carbon monoxide sensitivity of these enzymes presents a challenge when studying the enzymes, but many crystallographic studies have been performed. Crystal structures for enzymes isolated from D. gigas , Desulfovibrio vulgaris , Desulfovibrio fructosovorans , Desulfovibrio desulfuricans , and Desulfomicrobium baculatum have been obtained, among others. A few bacteria, such as R. eutropha , have adapted to survive under ambient oxygen levels. [ 13 ]
These enzymes have inspired study of structural and functional model complexes in hopes of making synthetic catalysis for hydrogen production (see Fe–Ni and hydrogen production, below, for more detail).
In the search for a clean, renewable energy source to replace fossil fuels , hydrogen has gained much attention as a possible fuel for the future. One of the challenges that must be overcome if this is to become a reality is an efficient way to produce and consume hydrogen. Currently, we have the technology to generate hydrogen from coal , natural gas , biomass and water. [ 12 ] The majority of hydrogen currently produced comes from natural gas reformation, and hence does not help remove fossil fuel as an energy source. A variety of sustainable methods for hydrogen production are currently being researched, including solar, geothermal and catalytic hydrogen production .
Platinum is currently used to catalyze hydrogen production, but as Pt is expensive, found in limited supply, and easily poisoned by carbon monoxide during H 2 production, it is not a practical for large-scale use. [ 11 ] Catalysts inspired by the Fe–Ni active site of many hydrogen producing enzymes are particularly desirable due to the readily available and inexpensive metals.
The synthesis of Fe–Ni biomimetic catalytic complexes has proved difficult, primarily due to the extreme oxygen-sensitivity of such complexes. To date, only one example of a Fe–Ni model complex that is stable enough to withstand the range of electronic potential required for catalysis has been published. [ 14 ]
When designing model complexes, it is crucial to preserve the key features of the active site of the Fe–Ni hydrogenases: the iron organometallic moiety with CO or CN − ligands, nickel coordinated to terminal sulfur ligands, and the thiolate bridge between the metals. [ 11 ] By preserving these traits of the enzyme active site, it is hoped that the synthetic complexes will operate at the electrochemical potential necessary for catalysis, have a high turnover frequency and be robust. | https://en.wikipedia.org/wiki/Iron–nickel_clusters |
Iron–sulfur clusters are molecular ensembles of iron and sulfide . They are most often discussed in the context of the biological role for iron–sulfur proteins , which are pervasive. [ 2 ] Many Fe–S clusters are known in the area of organometallic chemistry and as precursors to synthetic analogues of the biological clusters. It is supposed that the last universal common ancestor had many iron-sulfur clusters. [ 3 ]
Organometallic Fe–S clusters include the sulfido carbonyls with the formula Fe 2 S 2 (CO) 6 , H 2 Fe 3 S(CO) 9 , and Fe 3 S 2 (CO) 9 . Compounds are also known that incorporate cyclopentadienyl ligands , such as (C 5 H 5 ) 4 Fe 4 S 4 . [ 4 ]
Iron–sulfur clusters occur in many biological systems, often as components of electron transfer proteins. The ferredoxin proteins are the most common Fe–S clusters in nature. They feature either 2Fe–2S or 4Fe–4S centers. They occur in all branches of life. [ 5 ]
Fe–S clusters can be classified according to their Fe:S stoichiometry [2Fe–2S], [4Fe–3S], [3Fe–4S], and [4Fe–4S]. [ 6 ] The [4Fe–4S] clusters occur in two forms: normal ferredoxins and high potential iron proteins (HiPIP). Both adopt cuboidal structures, but they utilize different oxidation states . They are found in all forms of life. [ 7 ]
The relevant redox couple in all Fe–S proteins is Fe(II)/Fe(III). [ 7 ]
Many clusters have been synthesized in the laboratory with the formula [Fe 4 S 4 (SR) 4 ] 2− , which are known for many R substituents, and with many cations. Variations have been prepared including the incomplete cubanes [Fe 3 S 4 (SR) 3 ] 3− . [ 8 ] | https://en.wikipedia.org/wiki/Iron–sulfur_cluster |
Iron–sulfur proteins are proteins characterized by the presence of iron–sulfur clusters containing sulfide -linked di-, tri-, and tetrairon centers in variable oxidation states . Iron–sulfur clusters are found in a variety of metalloproteins , such as the ferredoxins , as well as NADH dehydrogenase , hydrogenases , coenzyme Q – cytochrome c reductase , succinate – coenzyme Q reductase and nitrogenase . [ 1 ] Iron–sulfur clusters are best known for their role in the oxidation-reduction reactions of electron transport in mitochondria and chloroplasts . Both Complex I and Complex II of oxidative phosphorylation have multiple Fe–S clusters. They have many other functions including catalysis as illustrated by aconitase , generation of radicals as illustrated by SAM -dependent enzymes, and as sulfur donors in the biosynthesis of lipoic acid and biotin . Additionally, some Fe–S proteins regulate gene expression. Fe–S proteins are vulnerable to attack by biogenic nitric oxide , forming dinitrosyl iron complexes . In most Fe–S proteins, the terminal ligands on Fe are thiolate , but exceptions exist. [ 2 ]
The prevalence of these proteins on the metabolic pathways of most organisms leads to theories that iron–sulfur compounds had a significant role in the origin of life in the iron–sulfur world theory .
In some instances Fe–S clusters are redox-inactive, but are proposed to have structural roles. Examples include endonuclease III and MutY. [ 3 ] [ 4 ]
In almost all Fe–S proteins, the Fe centers are tetrahedral and the terminal ligands are thiolato sulfur centers from cysteinyl residues. The sulfide groups are either two- or three-coordinated. Three distinct kinds of Fe–S clusters with these features are most common.
Iron–sulfur proteins are involved in various biological electron transport processes, such as photosynthesis and cellular respiration, which require rapid electron transfer to sustain the energy or biochemical needs of the organism. To serve their various biological roles, iron-sulfur proteins effect rapid electron transfers and span the whole range of physiological redox potentials from -600 mV to +460 mV.
Fe 3+ -SR bonds have unusually high covalency which is expected. [ according to whom? ] When comparing the covalency of Fe 3+ with the covalency of Fe 2+ , Fe 3+ has almost double the covalency of Fe 2+ (20% to 38.4%). [ 5 ] Fe 3+ is also much more stabilized than Fe 2+ . Hard ions like Fe 3+ normally have low covalency because of the energy mismatch of the metal lowest unoccupied molecular orbital with the ligand highest occupied molecular orbital .
External water molecules positioned close to the iron-sulfur active site reduces covalency; this can be shown by lyophilization experiments where water is removed from the protein. This reduction is because external water hydrogen bonds with cysteine S, decreasing the latter's lone pair electron donation to the Fe 3+/2+ by pulling away S electrons. [ 5 ] Since covalency stabilizes Fe 3+ more than Fe 2+ , Fe 3+ is more destabilized by the HOH-S hydrogen-bonding.
The Fe 3+ 3d orbital energies follow the "inverted" bonding scheme which fortuitously has the Fe 3+ d-orbitals closely matched in energy with the sulfur 3p orbitals, giving high covalency in the resulting bonding molecular orbital. [ 3 ] This high covalency lowers the inner sphere reorganization energy [ 3 ] and ultimately contributes to a rapid electron transfer.
The simplest polymetallic system, the [Fe 2 S 2 ] cluster, is constituted by two iron ions bridged by two sulfide ions and coordinated by four cysteinyl ligands (in Fe 2 S 2 ferredoxins ) or by two cysteines and two histidines (in Rieske proteins ). The oxidized proteins contain two Fe 3+ ions, whereas the reduced proteins contain one Fe 3+ and one Fe 2+ ion. These species exist in two oxidation states, (Fe III ) 2 and Fe III Fe II . CDGSH iron sulfur domain is also associated with 2Fe-2S clusters.
The Rieske proteins contain Fe–S clusters that coordinate as a 2Fe–2S structure and can be found in the membrane bound cytochrome bc1 complex III in the mitochondria of eukaryotes and bacteria. They are also a part of the proteins of the chloroplast such as the cytochrome b 6 f complex in photosynthetic organisms. These photosynthetic organisms include plants, green algae, and cyanobacteria , the bacterial precursor to chloroplasts. Both are part of the electron transport chain of their respective organisms which is a crucial step in the energy harvesting for many organisms. [ 6 ]
A common motif features a four iron ions and four sulfide ions placed at the vertices of a cubane-type cluster . The Fe centers are typically further coordinated by cysteinyl ligands. The [Fe 4 S 4 ] electron-transfer proteins ([Fe 4 S 4 ] ferredoxins ) may be further subdivided into low-potential (bacterial-type) and high-potential (HiPIP) ferredoxins . Low- and high-potential ferredoxins are related by the following redox scheme:
In HiPIP, the cluster shuttles between [2Fe 3+ , 2Fe 2+ ] (Fe 4 S 4 2+ ) and [3Fe 3+ , Fe 2+ ] (Fe 4 S 4 3+ ). The potentials for this redox couple range from 0.4 to 0.1 V. In the bacterial ferredoxins, the pair of oxidation states are [Fe 3+ , 3Fe 2+ ] (Fe 4 S 4 + ) and [2Fe 3+ , 2Fe 2+ ] (Fe 4 S 4 2+ ). The potentials for this redox couple range from −0.3 to −0.7 V. The two families of 4Fe–4S clusters share the Fe 4 S 4 2+ oxidation state. The difference in the redox couples is attributed to the degree of hydrogen bonding, which strongly modifies the basicity of the cysteinyl thiolate ligands. [ citation needed ] A further redox couple, which is still more reducing than the bacterial ferredoxins is implicated in the nitrogenase .
Some 4Fe–4S clusters bind substrates and are thus classified as enzyme cofactors. In aconitase , the Fe–S cluster binds aconitate at the one Fe centre that lacks a thiolate ligand. The cluster does not undergo redox, but serves as a Lewis acid catalyst to convert citrate to isocitrate . In radical SAM enzymes, the cluster binds and reduces S-adenosylmethionine to generate a radical, which is involved in many biosyntheses. [ 7 ]
The second cubane shown here with mixed valence pairs (2 Fe3+ and 2 Fe2+), has a greater stability from covalent communication and strong covalent delocalization of the “extra” electron from the reduced Fe2+ that results in full ferromagnetic coupling.
Proteins are also known to contain [Fe 3 S 4 ] centres, which feature one iron less than the more common [Fe 4 S 4 ] cores. Three sulfide ions bridge two iron ions each, while the fourth sulfide bridges three iron ions. Their formal oxidation states may vary from [Fe 3 S 4 ] + (all-Fe 3+ form) to [Fe 3 S 4 ] 2− (all-Fe 2+ form). In a number of iron–sulfur proteins, the [Fe 4 S 4 ] cluster can be reversibly converted by oxidation and loss of one iron ion to a [Fe 3 S 4 ] cluster. E.g., the inactive form of aconitase possesses an [Fe 3 S 4 ] and is activated by addition of Fe 2+ and reductant.
Examples include the active sites of a number of enzymes:
The biosynthesis of the Fe–S clusters has been well studied. [ 15 ] [ 16 ] [ 17 ] The biogenesis of iron sulfur clusters has been studied most extensively in the bacteria E. coli and A. vinelandii and yeast S. cerevisiae . At least three different biosynthetic systems have been identified so far, namely nif, suf, and isc systems, which were first identified in bacteria. The nif system is responsible for the clusters in the enzyme nitrogenase. The suf and isc systems are more general.
The yeast isc system is the best described. Several proteins constitute the biosynthetic machinery via the isc pathway. The process occurs in two major steps:
(1) the Fe/S cluster is assembled on a scaffold protein followed by (2) transfer of the preformed cluster to the recipient proteins.
The first step of this process occurs in the cytoplasm of prokaryotic organisms or in the mitochondria of eukaryotic organisms. In the higher organisms the clusters are therefore transported out of the mitochondrion to be incorporated into the extramitochondrial enzymes. These organisms also possess a set of proteins involved in the Fe/S clusters transport and incorporation processes that are not homologous to proteins found in prokaryotic systems.
Synthetic analogues of the naturally occurring Fe–S clusters were first reported by Holm and coworkers. [ 18 ] Treatment of iron salts with a mixture of thiolates and sulfide affords derivatives such as ( Et 4 N ) 2 Fe 4 S 4 (SCH 2 Ph) 4 ]. [ 19 ] [ 20 ] | https://en.wikipedia.org/wiki/Iron–sulfur_protein |
The iron–sulfur world hypothesis is a set of proposals for the origin of life and the early evolution of life advanced in a series of articles between 1988 and 1992 by Günter Wächtershäuser , a Munich patent lawyer with a degree in chemistry, who had been encouraged and supported by philosopher Karl R. Popper to publish his ideas. The hypothesis proposes that early life may have formed on the surface of iron sulfide minerals, hence the name. [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ excessive citations ] It was developed by retrodiction (making a " prediction " about the past) from extant biochemistry (non-extinct, surviving biochemistry) in conjunction with chemical experiments.
Wächtershäuser proposes that the earliest form of life, termed the "pioneer organism", originated in a volcanic hydrothermal flow at high pressure and high (100 °C) temperature. It had a composite structure of a mineral base with catalytic transition metal centers (predominantly iron and nickel , but also perhaps cobalt , manganese , tungsten and zinc ). The catalytic centers catalyzed autotrophic carbon fixation pathways generating small molecule (non-polymer) organic compounds from inorganic gases (e.g. carbon monoxide , carbon dioxide , hydrogen cyanide and hydrogen sulfide ). These organic compounds were retained on or in the mineral base as organic ligands of the transition metal centers with a flow retention time in correspondence with their mineral bonding strength thereby defining an autocatalytic "surface metabolism". The catalytic transition metal centers became autocatalytic by being accelerated by their organic products turned ligands. The carbon fixation metabolism became autocatalytic by forming a metabolic cycle in the form of a primitive sulfur-dependent version of the reductive citric acid cycle . Accelerated catalysts expanded the metabolism and new metabolic products further accelerated the catalysts. The idea is that once such a primitive autocatalytic metabolism was established, its intrinsically synthetic chemistry began to produce ever more complex organic compounds, ever more complex pathways and ever more complex catalytic centers.
The water–gas shift reaction (CO + H 2 O → CO 2 + H 2 ) occurs in volcanic fluids with diverse catalysts or without catalysts. [ 6 ] The combination of ferrous sulfide (FeS, troilite ) and hydrogen sulfide ( H 2 S ) as reducing agents (both reagents are simultaneously oxidized in the reaction here under creating the disulfide bond, S–S) in conjunction with pyrite ( FeS 2 ) formation:
has been demonstrated under mild volcanic conditions. [ 7 ] [ 8 ] This key result has been disputed. [ 9 ] Nitrogen fixation has been demonstrated for the isotope 15 N 2 in conjunction with pyrite formation. [ 10 ] Ammonia forms from nitrate with FeS/H 2 S as reductant . [ 11 ] Methylmercaptan [CH 3 -SH] and carbon oxysulfide [COS] form from CO 2 and FeS/H 2 S, [ 12 ] or from CO and H 2 in the presence of NiS . [ 13 ]
Reaction of carbon monoxide (CO), hydrogen sulfide (H 2 S) and methanethiol CH 3 SH in the presence of nickel sulfide and iron sulfide generates the methyl thioester of acetic acid [CH 3 -CO-SCH 3 ] and presumably thioacetic acid (CH 3 -CO-SH) as the simplest activated acetic acid analogues of acetyl-CoA . These activated acetic acid derivatives serve as starting materials for subsequent exergonic synthetic steps. [ 13 ] They also serve for energy coupling with endergonic reactions , notably the formation of (phospho)anhydride compounds. [ 14 ] However, Huber and Wächtershäuser reported low 0.5% acetate yields based on the input of CH 3 SH ( methanethiol ) (8 mM) in the presence of 350 mM CO. This is about 500 times and 3700 times [ 15 ] the highest CH 3 SH and CO concentrations respectively measured to date in a natural hydrothermal vent fluid. [ 16 ]
Reaction of nickel hydroxide with hydrogen cyanide (HCN) (in the presence or absence of ferrous hydroxide , hydrogen sulfide or methyl mercaptan ) generates nickel cyanide , which reacts with carbon monoxide (CO) to generate pairs of α-hydroxy and α-amino acids : e.g. glycolate / glycine , lactate / alanine , glycerate / serine ; as well as pyruvic acid in significant quantities. [ 17 ] Pyruvic acid is also formed at high pressure and high temperature from CO, H 2 O, FeS in the presence of nonyl mercaptan. [ 18 ] Reaction of pyruvic acid or other α-keto acids with ammonia in the presence of ferrous hydroxide or in the presence of ferrous sulfide and hydrogen sulfide generates alanine or other α-amino acids . [ 19 ] Reaction of α-amino acids in aqueous solution with COS or with CO and H 2 S generates a peptide cycle wherein dipeptides , tripeptides etc. are formed and subsequently degraded via N-terminal hydantoin moieties and N-terminal urea moieties and subsequent cleavage of the N-terminal amino acid unit. [ 20 ] [ 21 ] [ 22 ]
Proposed reaction mechanism for reduction of CO 2 on FeS: Ying et al. (2007) [ citation needed ] have shown that direct transformation of mackinawite (FeS) to pyrite (FeS 2 ) on reaction with H 2 S till 300 °C is not possible without the presence of critical amount of oxidant. In the absence of any oxidant, FeS reacts with H 2 S up to 300 °C to give pyrrhotite. Farid et al. [ citation needed ] have experimentally shown that mackinawite (FeS) has ability to reduce CO 2 to CO at temperature higher than 300 °C. They reported that the surface of FeS is oxidized, which on reaction with H 2 S gives pyrite (FeS 2 ). It is expected that CO reacts with H 2 O in the Drobner experiment to give H 2 .
Early evolution is defined as beginning with the origin of life and ending with the last universal common ancestor (LUCA). According to the iron–sulfur world theory it covers a coevolution of cellular organization ( cellularization ), the genetic machinery and enzymatization of the metabolism .
Cellularization occurs in several stages. It may have begun with the formation of primitive lipids (e.g. fatty acids or isoprenoids ) in the surface metabolism . These lipids accumulate on or in the mineral base. This lipophilizes the outer or inner surfaces of the mineral base, which promotes condensation reactions over hydrolytic reactions by lowering the activity of water and protons.
In the next stage lipid membranes are formed. While still anchored to the mineral base they form a semi-cell bounded partly by the mineral base and partly by the membrane. Further lipid evolution leads to self-supporting lipid membranes and closed cells. The earliest closed cells are pre-cells ( sensu Kandler ) because they allow frequent exchange of genetic material (e.g. by fusions). According to Woese , this frequent exchange of genetic material is the cause for the existence of the common stem in the tree of life and for a very rapid early evolution. [ 23 ] Nick Lane and coauthors state that "Non-enzymatic equivalents of glycolysis, the pentose phosphate pathway and gluconeogenesis have been identified as well. Multiple syntheses of amino acids from α-keto acids by direct reductive amination and by transamination reactions can also take place. Long-chain fatty acids can be formed by hydrothermal Fischer-Tropsch-type synthesis which chemically resembles the process of fatty acid elongation. Recent work suggests that nucleobases might also be formed following the universally conserved biosynthetic pathways, using metal ions as catalysts". [ 24 ]
Metabolic intermediates in glycolysis and the pentose phosphate pathway such as glucose, pyruvate, ribose 5-phosphate , and erythrose-4-phosphate are spontaneously generated in the presence of Fe(II). [ 25 ] Fructose 1,6-biphosphate , a metabolic intermediate in gluconeogenesis , was shown to have been continuously accumulated but only in a frozen solution. The formation of fructose 1,6-biphosphate was accelerated by lysine and glycine which implies the earliest anabolic enzymes were amino acids. [ 26 ] It had been reported that 4Fe-4S, 2Fe-2S, and mononuclear iron clusters are spontaneously formed in low concentrations of cysteine and alkaline pH. [ 27 ] Methyl thioacetate, a precursor to acetyl-CoA can be synthesized in conditions relevant to hydrothermal vents. Phosphorylation of methyl thioacetate leads to the synthesis of thioacetate, a simpler precursor to acetyl-CoA. Thioacetate in more cooler and neutral conditions promotes synthesis of acetyl phosphate which is a precursor to adenosine triphosphate and is capable of phosphorylating ribose and nucleosides . This suggests that acetyl phosphate was likely synthesized in thermophoresis and mixing between the acidic seawater and alkaline hydrothermal fluid in interconnected micropores. It is possible that it could promote nucleotide polymerization at mineral surfaces or at low water activity. [ 28 ] Thermophoresis at hydrothermal vent pores can concentrate polyribonucleotides, [ 29 ] but it remains unknown as to how it could promote coding and metabolic reactions. [ 30 ]
In mathematical simulations, autocatalytic nucleotide synthesis is proposed to promote protocell growth as nucleotides also catalyze CO 2 fixation. Strong nucleotide catalysis of fatty acids and amino acids slow down protocell growth and if competition between catalytic function were to occur, this would disrupt the protocell. Weak or moderate nucleotide catalysis of amino acids via CO 2 fixation would favor protocell division and growth. [ 31 ] In 2017, a computational simulation of a protocell at an alkaline hydrothermal vent environment showed that "Some hydrophobic amino acids chelate FeS nanocrystals, producing three positive feedbacks: (i) an increase in catalytic surface area; (ii) partitioning of FeS nanocrystals to the membrane; and (iii) a proton-motive active site for carbon fixing that mimics the enzyme Ech". [ 32 ] Maximal ATP synthesis would have occurred at high water activity in freshwater and high concentrations of Mg 2+ and Ca 2+ prevented synthesis of ATP, however the concentrations of divalent cations in Hadean oceans were much lower than in modern oceans and alkaline hydrothermal vent concentrations of Mg 2+ and Ca 2+ are typically lower than in the ocean. Such environments would have generated Fe 3+ which would have promoted ADP phosphorylation. The mixture of seawater and alkaline hydrothermal vent fluid can promote cycling between Fe 3+ and Fe 2+ . [ 33 ] Experimental research of biomimetic prebiotic reactions such as the reduction of NAD + [ 34 ] and phosphoryl transfer [ 35 ] also support an origin of life occurring at an alkaline hydrothermal vent .
William Martin and Michael Russell suggest that the first cellular life forms may have evolved inside alkaline hydrothermal vents at seafloor spreading zones in the deep sea . [ 36 ] [ 37 ] These structures consist of microscale caverns that are coated by thin membraneous metal sulfide walls. Therefore, these structures would resolve several critical points germane to Wächtershäuser's suggestions at once:
This model locates the "last universal common ancestor" ( LUCA ) within the inorganically formed physical confines of an alkaline hydrothermal vent, rather than assuming the existence of a free-living form of LUCA. The last evolutionary step en route to bona fide free-living cells would be the synthesis of a lipid membrane that finally allows the organisms to leave the microcavern system of the vent. This postulated late acquisition of the biosynthesis of lipids as directed by genetically encoded peptides is consistent with the presence of completely different types of membrane lipids in archaea and bacteria (plus eukaryotes ). The kind of vent at the foreground of their suggestion is chemically more similar to the warm (ca. 100 °C) off ridge vents such as Lost City than to the more familiar black smoker type vents (ca. 350 °C).
In an abiotic world, a thermocline of temperatures and a chemocline in concentration is associated with the pre-biotic synthesis of organic molecules, hotter in proximity to the chemically rich vent, cooler but also less chemically rich at greater distances. The migration of synthesized compounds from areas of high concentration to areas of low concentration gives a directionality that provides both source and sink in a self-organizing fashion, enabling a proto-metabolic process by which acetic acid production and its eventual oxidization can be spatially organized.
In this way many of the individual reactions that are today found in central metabolism could initially have occurred independent of any developing cell membrane . Each vent microcompartment is functionally equivalent to a single cell. Chemical communities having greater structural integrity and resilience to wildly fluctuating conditions are then selected for; their success would lead to local zones of depletion for important precursor chemicals. Progressive incorporation of these precursor components within a cell membrane would gradually increase metabolic complexity within the cell membrane, whilst leading to greater environmental simplicity in the external environment. In principle, this could lead to the development of complex catalytic sets capable of self-maintenance .
Russell adds a significant factor to these ideas, by pointing out that semi-permeable mackinawite (an iron sulfide mineral) and silicate membranes could naturally develop under these conditions and electrochemically link reactions separated in space, if not in time [ clarification needed ] . [ 38 ] [ 39 ]
The 6 of the 11 metabolic intermediates in reverse Krebs cycle promoted by Fe, Zn 2+ , and Cr 3+ in acidic conditions imply that protocells possibly emerged in locally metal-rich and acidic terrestrial hydrothermal fields. The acidic conditions are seemingly consistent with the stabilization of RNA. [ 40 ] These hydrothermal fields would have exhibited cycling of freezing and thawing and a variety of temperature gradients that would promote nonenzymatic reactions of gluconeogenesis, nucleobase synthesis, nonenzymatic polymerization, and RNA replication. [ 26 ] ATP synthesis and oxidation of ferrous iron via photochemical reactions or oxidants such as nitric oxide derived from lightning strikes, meteorite impacts, or volcanic emissions could have also occurred at hydrothermal fields. [ 41 ]
Wet-dry cycling of hydrothermal fields would polymerize RNA and peptides, protocell aggregation in a moist gel phase during wet-dry cycling would allow diffusion of metabolic products across neighboring protocells. Protocell aggregation could be described as a primitive version of horizontal gene transfer. Fatty acid vesicles would be stabilized by polymers in the presence of Mg 2+ required for ribozyme activity. [ 42 ] These prebiotic processes might have occurred in shaded areas that protect the emergence of early cellular life under ultraviolet irradiation. [ 43 ] Long chain alcohols and monocarboxylic acids would have also been synthesized via Fischer–Tropsch synthesis . [ 44 ] Hydrothermal fields would also have precipitates of transition metals [ 4 ] and concentrated many elements including CHNOPS . [ 45 ] Geothermal convection could also be a source of energy for the emergence of the proton motive force, phosphoryl group transfer, coupling between oxidation-reduction, and active transport. [ 4 ] It's noted by David Deamer and Bruce Damer that these environments seemingly resemble Charles Darwin 's idea of a "warm little pond". [ 42 ]
The problems with the hypothesis of a subaerial hydrothermal field of abiogenesis is that the proposed chemistry doesn't resemble known biochemical reactions. [ 46 ] The abundance of subaerial hydrothermal fields would have been rare and offered no protection from either meteorites or ultraviolet irradiation. Clay minerals at subaerial hydrothermal fields would absorb organic reactants. Pyrophosphate has low solubility in water and can't be phosphorylated without a phosphorylating agent. [ 44 ] It doesn't offer explanations for the origin of chemiosmosis and differences between Archaea and Bacteria. [ 47 ] | https://en.wikipedia.org/wiki/Iron–sulfur_world_hypothesis |
In radiometry , irradiance is the radiant flux received by a surface per unit area. The SI unit of irradiance is the watt per square metre (symbol W⋅m −2 or W/m 2 ). The CGS unit erg per square centimetre per second (erg⋅cm −2 ⋅s −1 ) is often used in astronomy . Irradiance is often called intensity , but this term is avoided in radiometry where such usage leads to confusion with radiant intensity . In astrophysics, irradiance is called radiant flux . [ 1 ]
Spectral irradiance is the irradiance of a surface per unit frequency or wavelength , depending on whether the spectrum is taken as a function of frequency or of wavelength. The two forms have different dimensions and units: spectral irradiance of a frequency spectrum is measured in watts per square metre per hertz (W⋅m −2 ⋅Hz −1 ), while spectral irradiance of a wavelength spectrum is measured in watts per square metre per metre (W⋅m −3 ), or more commonly watts per square metre per nanometre (W⋅m −2 ⋅nm −1 ).
Irradiance of a surface, denoted E e ("e" for "energetic", to avoid confusion with photometric quantities), is defined as [ 2 ]
where
The radiant flux emitted by a surface is called radiant exitance .
Spectral irradiance in frequency of a surface, denoted E e,ν , is defined as [ 2 ]
where ν is the frequency.
Spectral irradiance in wavelength of a surface, denoted E e,λ , is defined as [ 2 ]
where λ is the wavelength.
Irradiance of a surface is also, according to the definition of radiant flux , equal to the time-average of the component of the Poynting vector perpendicular to the surface:
where
For a propagating sinusoidal linearly polarized electromagnetic plane wave , the Poynting vector always points to the direction of propagation while oscillating in magnitude. The irradiance of a surface is then given by [ 3 ]
where
This formula assumes that the magnetic susceptibility is negligible; i.e. that μ r ≈ 1 ( μ ≈ μ 0 ) where μ r is the relative magnetic permeability of the propagation medium. This assumption is typically valid in transparent media in the optical frequency range .
A point source of light produces spherical wavefronts. The irradiance in this case varies inversely with the square of the distance from the source.
where
For quick approximations, this equation indicates that doubling the distance reduces irradiation to one quarter; or similarly, to double irradiation, reduce the distance to 71%.
In astronomy, stars are routinely treated as point sources even though they are much larger than the Earth. This is a good approximation because the distance from even a nearby star to the Earth is much larger than the star's diameter. For instance, the irradiance of Alpha Centauri A (radiant flux: 1.5 L ☉ , distance: 4.34 ly ) is about 2.7 × 10 −8 W/m 2 on Earth.
The global irradiance on a horizontal surface on Earth consists of the direct irradiance E e,dir and diffuse irradiance E e,diff . On a tilted plane, there is another irradiance component, E e,refl , which is the component that is reflected from the ground. The average ground reflection is about 20% of the global irradiance. Hence, the irradiance E e on a tilted plane consists of three components: [ 4 ]
The integral of solar irradiance over a time period is called " solar exposure " or " insolation ". [ 4 ] [ 5 ]
Average solar irradiance at the top of the Earth's atmosphere is roughly 1361 W/m 2 , but at surface irradiance is approximately 1000 W/m 2 on a clear day. | https://en.wikipedia.org/wiki/Irradiance |
Irradiation is the process by which an object is exposed to radiation . An irradiator is a device used to expose an object to radiation, [ 1 ] most often gamma radiation , [ 2 ] for a variety of purposes. Irradiators may be used for sterilizing medical and pharmaceutical supplies, preserving foodstuffs, alteration of gemstone colors, studying radiation effects, eradicating insects through sterile male release programs, or calibrating thermoluminescent dosimeters (TLDs). [ 3 ]
The exposure can originate from various sources, including natural sources. Most frequently the term refers to ionizing radiation , and to a level of radiation that will serve a specific purpose, rather than radiation exposure to normal levels of background radiation . The term irradiation usually excludes the exposure to non-ionizing radiation, such as infrared , visible light , microwaves from cellular phones or electromagnetic waves emitted by radio and television receivers and power supplies.
If administered at appropriate levels, all forms of ionizing radiation can sterilize objects, including medical instruments, disposables such as syringes , and food. Ionizing radiation ( electron beams , X-rays and gamma rays ) [ 4 ] may be used to kill bacteria in food or other organic material, including blood. [ citation needed ] Food irradiation , while effective, is seldom used due to lack of public acceptance. [ 5 ]
Irradiation is used in diagnostic imaging , cancer therapy and blood transfusion . [ 6 ]
In 2011 researchers found that irradiation was successful in the novel theranostic technique involving co-treatment with heptamethine dyes to elucidate tumor cells and attenuate their growth with minimal side effects. [ 7 ] [ 8 ]
Ion irradiation is routinely used to implant impurities atoms into materials, especially semiconductors , to modify their properties. This process, usually known
as ion implantation , is an important step in the manufacture of silicon integrated circuits . [ 9 ]
Ion irradiation means in general using particle accelerators to shoot energetic ions on a material. Ion implantation is a variety of ion irradiation, as is swift heavy ions irradiation from particle accelerators induces ion tracks that can be used for nanotechnology . [ 10 ] [ 11 ]
The irradiation process is widely practiced in jewelry industry [ 12 ] and enabled the creation of gemstone colors that do not exist or are extremely rare in nature. [ 13 ] However, particularly when done in a nuclear reactor , the processes can make gemstones radioactive. Health risks related to the residual radioactivity of the treated gemstones have led to government regulations in many countries. [ 13 ] [ 14 ]
Irradiation is used to cross-link plastics . Due to its efficiency, electron beam processing is often used in the irradiation treatment of polymer-based products to improve their mechanical, thermal, and chemical properties, and often to add unique properties. Cross-linked polyethylene pipe (PEX), high-temperature products such as tubing and gaskets, wire and cable jacket curing, curing of composite materials, and crosslinking of tires are a few examples.
After its discovery by Lewis Stadler at the University of Missouri , irradiation of seed and plant germplasm has resulted in creating many widely-grown cultivars of food crops worldwide. [ 15 ] The process, which consists of striking plant seeds or germplasm with radiation in the form of X-rays , UV waves , heavy-ion beams , or gamma rays , essentially induce lesions of the DNA , leading to mutations in the genome . The UN has been an active participant through the International Atomic Energy Agency . Irradiation is also employed to prevent the sprouting of certain cereals , onions , potatoes and garlic . [ 16 ] Appropriate irradiation doses are also used to produce insects for use in the sterile insect technique of pest control. [ 17 ]
The U.S. Department of Agriculture 's (USDA) Food Safety and Inspection Service (FSIS) recognizes irradiation as an important technology to protect consumers . Fresh meat and poultry including whole or cut up birds, skinless poultry, pork chops , roasts , stew meat , liver, hamburgers , ground meat , and ground poultry are approved for irradiation. [ 18 ]
Gheorghe Gheorghiu-Dej , who died of lung cancer in Bucharest on March 19, 1965, may have been intentionally irradiated during a visit to Moscow, due to his political stance. [ 19 ]
In 1999, an article in Der Spiegel alleged that the East German MfS intentionally irradiated political prisoners with high-dose radiation, possibly to provoke cancer. [ 20 ] [ 21 ]
Alexander Litvinenko , a secret serviceman who was tackling organized crime in Russia, was intentionally poisoned with polonium-210 ; the very large internal doses of radiation he received caused his death.
In the nuclear industry , irradiation may refer to the phenomenon of exposure of the structure of a nuclear reactor to neutron flux, making the material radioactive and causing irradiation embrittlement , [ 22 ] [ 23 ] or irradiation of the nuclear fuel .
During the 2001 anthrax attacks , the US Postal Service irradiated mail to protect members of the US government and other possible targets. This was of some concern to people who send digital media through the mail, including artists. According to the ART in Embassies program, "incoming mail is irradiated, and the process destroys slides, transparencies and disks." [ citation needed ] | https://en.wikipedia.org/wiki/Irradiation |
In mathematics , the irrational numbers are all the real numbers that are not rational numbers . That is, irrational numbers cannot be expressed as the ratio of two integers . When the ratio of lengths of two line segments is an irrational number, the line segments are also described as being incommensurable , meaning that they share no "measure" in common, that is, there is no length ("the measure"), no matter how short, that could be used to express the lengths of both of the two given segments as integer multiples of itself.
Among irrational numbers are the ratio π of a circle's circumference to its diameter, Euler's number e , the golden ratio φ , and the square root of two . [ 1 ] In fact, all square roots of natural numbers , other than of perfect squares , are irrational. [ 2 ]
Like all real numbers, irrational numbers can be expressed in positional notation , notably as a decimal number. In the case of irrational numbers, the decimal expansion does not terminate, nor end with a repeating sequence . For example, the decimal representation of π starts with 3.14159, but no finite number of digits can represent π exactly, nor does it repeat. Conversely, a decimal expansion that terminates or repeats must be a rational number. These are provable properties of rational numbers and positional number systems and are not used as definitions in mathematics.
Irrational numbers can also be expressed as non-terminating continued fractions (which in some cases are periodic ), and in many other ways.
As a consequence of Cantor's proof that the real numbers are uncountable and the rationals countable, it follows that almost all real numbers are irrational. [ 3 ]
The first proof of the existence of irrational numbers is usually attributed to a Pythagorean (possibly Hippasus of Metapontum ), [ 4 ] who probably discovered them while identifying sides of the pentagram . [ 5 ] The Pythagorean method would have claimed that there must be some sufficiently small, indivisible unit that could fit evenly into one of these lengths as well as the other. Hippasus in the 5th century BC, however, was able to deduce that there was no common unit of measure, and that the assertion of such an existence was a contradiction. He did this by demonstrating that if the hypotenuse of an isosceles right triangle was indeed commensurable with a leg, then one of those lengths measured in that unit of measure must be both odd and even, which is impossible. His reasoning is as follows:
Greek mathematicians termed this ratio of incommensurable magnitudes alogos , or inexpressible. Hippasus, however, was not lauded for his efforts: according to one legend, he made his discovery while out at sea, and was subsequently thrown overboard by his fellow Pythagoreans 'for having produced an element in the universe which denied the... doctrine that all phenomena in the universe can be reduced to whole numbers and their ratios.' [ 7 ] Another legend states that Hippasus was merely exiled for this revelation. Whatever the consequence to Hippasus himself, his discovery posed a very serious problem to Pythagorean mathematics, since it shattered the assumption that numbers and geometry were inseparable; a foundation of their theory.
The discovery of incommensurable ratios was indicative of another problem facing the Greeks: the relation of the discrete to the continuous. This was brought to light by Zeno of Elea , who questioned the conception that quantities are discrete and composed of a finite number of units of a given size. Past Greek conceptions dictated that they necessarily must be, for "whole numbers represent discrete objects, and a commensurable ratio represents a relation between two collections of discrete objects", [ 8 ] but Zeno found that in fact "[quantities] in general are not discrete collections of units; this is why ratios of incommensurable [quantities] appear... .[Q]uantities are, in other words, continuous". [ 8 ] What this means is that contrary to the popular conception of the time, there cannot be an indivisible, smallest unit of measure for any quantity. In fact, these divisions of quantity must necessarily be infinite . For example, consider a line segment: this segment can be split in half, that half split in half, the half of the half in half, and so on. This process can continue infinitely, for there is always another half to be split. The more times the segment is halved, the closer the unit of measure comes to zero, but it never reaches exactly zero. This is just what Zeno sought to prove. He sought to prove this by formulating four paradoxes , which demonstrated the contradictions inherent in the mathematical thought of the time. While Zeno's paradoxes accurately demonstrated the deficiencies of contemporary mathematical conceptions, they were not regarded as proof of the alternative. In the minds of the Greeks, disproving the validity of one view did not necessarily prove the validity of another, and therefore, further investigation had to occur.
The next step was taken by Eudoxus of Cnidus , who formalized a new theory of proportion that took into account commensurable as well as incommensurable quantities. Central to his idea was the distinction between magnitude and number. A magnitude "...was not a number but stood for entities such as line segments, angles, areas, volumes, and time which could vary, as we would say, continuously. Magnitudes were opposed to numbers, which jumped from one value to another, as from 4 to 5". [ 9 ] Numbers are composed of some smallest, indivisible unit, whereas magnitudes are infinitely reducible. Because no quantitative values were assigned to magnitudes, Eudoxus was then able to account for both commensurable and incommensurable ratios by defining a ratio in terms of its magnitude, and proportion as an equality between two ratios. By taking quantitative values (numbers) out of the equation, he avoided the trap of having to express an irrational number as a number. "Eudoxus' theory enabled the Greek mathematicians to make tremendous progress in geometry by supplying the necessary logical foundation for incommensurable ratios". [ 10 ] This incommensurability is dealt with in Euclid's Elements, Book X, Proposition 9. It was not until Eudoxus developed a theory of proportion that took into account irrational as well as rational ratios that a strong mathematical foundation of irrational numbers was created. [ 11 ]
As a result of the distinction between number and magnitude, geometry became the only method that could take into account incommensurable ratios. Because previous numerical foundations were still incompatible with the concept of incommensurability, Greek focus shifted away from numerical conceptions such as algebra and focused almost exclusively on geometry. In fact, in many cases, algebraic conceptions were reformulated into geometric terms. This may account for why we still conceive of x 2 and x 3 as x squared and x cubed instead of x to the second power and x to the third power. Also crucial to Zeno's work with incommensurable magnitudes was the fundamental focus on deductive reasoning that resulted from the foundational shattering of earlier Greek mathematics. The realization that some basic conception within the existing theory was at odds with reality necessitated a complete and thorough investigation of the axioms and assumptions that underlie that theory. Out of this necessity, Eudoxus developed his method of exhaustion , a kind of reductio ad absurdum that "...established the deductive organization on the basis of explicit axioms..." as well as "...reinforced the earlier decision to rely on deductive reasoning for proof". [ 12 ] This method of exhaustion is the first step in the creation of calculus.
Theodorus of Cyrene proved the irrationality of the surds of whole numbers up to 17, but stopped there probably because the algebra he used could not be applied to the square root of 17. [ 13 ]
Geometrical and mathematical problems involving irrational numbers such as square roots were addressed very early during the Vedic period in India. There are references to such calculations in the Samhitas , Brahmanas , and the Shulba Sutras (800 BC or earlier). [ 14 ]
It is suggested that the concept of irrationality was implicitly accepted by Indian mathematicians since the 7th century BC, when Manava (c. 750 – 690 BC) believed that the square roots of numbers such as 2 and 61 could not be exactly determined. [ 15 ] Historian Carl Benjamin Boyer , however, writes that "such claims are not well substantiated and unlikely to be true". [ 16 ]
Later, in their treatises, Indian mathematicians wrote on the arithmetic of surds including addition, subtraction, multiplication, rationalization, as well as separation and extraction of square roots. [ 17 ]
Mathematicians like Brahmagupta (in 628 AD) and Bhāskara I (in 629 AD) made contributions in this area as did other mathematicians who followed. In the 12th century Bhāskara II evaluated some of these formulas and critiqued them, identifying their limitations.
During the 14th to 16th centuries, Madhava of Sangamagrama and the Kerala school of astronomy and mathematics discovered the infinite series for several irrational numbers such as π and certain irrational values of trigonometric functions . Jyeṣṭhadeva provided proofs for these infinite series in the Yuktibhāṣā . [ 18 ]
In the Middle Ages , the development of algebra by Muslim mathematicians allowed irrational numbers to be treated as algebraic objects . [ 19 ] Middle Eastern mathematicians also merged the concepts of " number " and " magnitude " into a more general idea of real numbers , criticized Euclid's idea of ratios , developed the theory of composite ratios, and extended the concept of number to ratios of continuous magnitude. [ 20 ] In his commentary on Book 10 of the Elements , the Persian mathematician Al-Mahani (d. 874/884) examined and classified quadratic irrationals and cubic irrationals. He provided definitions for rational and irrational magnitudes, which he treated as irrational numbers. He dealt with them freely but explains them in geometric terms as follows: [ 20 ]
"It will be a rational (magnitude) when we, for instance, say 10, 12, 3%, 6%, etc., because its value is pronounced and expressed quantitatively. What is not rational is irrational and it is impossible to pronounce and represent its value quantitatively. For example: the roots of numbers such as 10, 15, 20 which are not squares, the sides of numbers which are not cubes etc. "
In contrast to Euclid's concept of magnitudes as lines, Al-Mahani considered integers and fractions as rational magnitudes, and square roots and cube roots as irrational magnitudes. He also introduced an arithmetical approach to the concept of irrationality, as he attributes the following to irrational magnitudes: [ 20 ]
"their sums or differences, or results of their addition to a rational magnitude, or results of subtracting a magnitude of this kind from an irrational one, or of a rational magnitude from it."
The Egyptian mathematician Abū Kāmil Shujā ibn Aslam (c. 850 – 930) was the first to accept irrational numbers as solutions to quadratic equations or as coefficients in an equation in the form of square roots and fourth roots . [ 21 ] In the 10th century, the Iraqi mathematician Al-Hashimi provided general proofs (rather than geometric demonstrations) for irrational numbers, as he considered multiplication, division, and other arithmetical functions. [ 20 ]
Many of these concepts were eventually accepted by European mathematicians sometime after the Latin translations of the 12th century . Al-Hassār , a Moroccan mathematician from Fez specializing in Islamic inheritance jurisprudence during the 12th century, first mentions the use of a fractional bar, where numerators and denominators are separated by a horizontal bar. In his discussion he writes, "..., for example, if you are told to write three-fifths and a third of a fifth, write thus, 3 1 5 3 {\displaystyle {\frac {3\quad 1}{5\quad 3}}} ." [ 22 ] This same fractional notation appears soon after in the work of Leonardo Fibonacci in the 13th century. [ 23 ]
The 17th century saw imaginary numbers become a powerful tool in the hands of Abraham de Moivre , and especially of Leonhard Euler . The completion of the theory of complex numbers in the 19th century entailed the differentiation of irrationals into algebraic and transcendental numbers , the proof of the existence of transcendental numbers, and the resurgence of the scientific study of the theory of irrationals, largely ignored since Euclid . The year 1872 saw the publication of the theories of Karl Weierstrass (by his pupil Ernst Kossak), Eduard Heine ( Crelle's Journal , 74), Georg Cantor (Annalen, 5), and Richard Dedekind . Méray had taken in 1869 the same point of departure as Heine, but the theory is generally referred to the year 1872. Weierstrass's method has been completely set forth by Salvatore Pincherle in 1880, [ 24 ] and Dedekind's has received additional prominence through the author's later work (1888) and the endorsement by Paul Tannery (1894). Weierstrass, Cantor, and Heine base their theories on infinite series, while Dedekind founds his on the idea of a cut (Schnitt) in the system of all rational numbers , separating them into two groups having certain characteristic properties. The subject has received later contributions at the hands of Weierstrass, Leopold Kronecker (Crelle, 101), and Charles Méray .
Continued fractions , closely related to irrational numbers (and due to Cataldi, 1613), received attention at the hands of Euler, and at the opening of the 19th century were brought into prominence through the writings of Joseph-Louis Lagrange . Dirichlet also added to the general theory, as have numerous contributors to the applications of the subject.
Johann Heinrich Lambert proved (1761) that π cannot be rational, and that e n is irrational if n is rational (unless n = 0). [ 25 ] While Lambert's proof is often called incomplete, modern assessments support it as satisfactory, and in fact for its time it is unusually rigorous. Adrien-Marie Legendre (1794), after introducing the Bessel–Clifford function , provided a proof to show that π 2 is irrational, whence it follows immediately that π is irrational also. The existence of transcendental numbers was first established by Liouville (1844, 1851). Later, Georg Cantor (1873) proved their existence by a different method , which showed that every interval in the reals contains transcendental numbers. Charles Hermite (1873) first proved e transcendental, and Ferdinand von Lindemann (1882), starting from Hermite's conclusions, showed the same for π. Lindemann's proof was much simplified by Weierstrass (1885), still further by David Hilbert (1893), and was finally made elementary by Adolf Hurwitz [ citation needed ] and Paul Gordan . [ 26 ]
The square root of 2 was likely the first number proved irrational. [ 27 ] The golden ratio is another famous quadratic irrational number. The square roots of all natural numbers that are not perfect squares are irrational and a proof may be found in quadratic irrationals .
The proof for the irrationality of the square root of two can be generalized using the fundamental theorem of arithmetic . This asserts that every integer has a unique factorization into primes. Using it we can show that if a rational number is not an integer then no integral power of it can be an integer, as in lowest terms there must be a prime in the denominator that does not divide into the numerator whatever power each is raised to. Therefore, if an integer is not an exact k th power of another integer, then that first integer's k th root is irrational.
Perhaps the numbers most easy to prove irrational are certain logarithms . Here is a proof by contradiction that log 2 3 is irrational (log 2 3 ≈ 1.58 > 0).
Assume log 2 3 is rational. For some positive integers m and n , we have
It follows that
The number 2 raised to any positive integer power must be even (because it is divisible by 2) and the number 3 raised to any positive integer power must be odd (since none of its prime factors will be 2). Clearly, an integer cannot be both odd and even at the same time: we have a contradiction. The only assumption we made was that log 2 3 is rational (and so expressible as a quotient of integers m / n with n ≠ 0). The contradiction means that this assumption must be false, i.e. log 2 3 is irrational, and can never be expressed as a quotient of integers m / n with n ≠ 0.
Cases such as log 10 2 can be treated similarly.
An irrational number may be algebraic , that is a real root of a polynomial with integer coefficients. Those that are not algebraic are transcendental .
The real algebraic numbers are the real solutions of polynomial equations
where the coefficients a i {\displaystyle a_{i}} are integers and a n ≠ 0 {\displaystyle a_{n}\neq 0} . An example of an irrational algebraic number is x 0 = (2 1/2 + 1) 1/3 . It is clearly algebraic since it is the root of an integer polynomial, ( x 3 − 1 ) 2 = 2 {\displaystyle (x^{3}-1)^{2}=2} , which is equivalent to ( x 6 − 2 x 3 − 1 ) = 0 {\displaystyle (x^{6}-2x^{3}-1)=0} . This polynomial has no rational roots, since the rational root theorem shows that the only possibilities are ±1, but x 0 is greater than 1. So x 0 is an irrational algebraic number. There are countably many algebraic numbers, since there are countably many integer polynomials.
Almost all irrational numbers are transcendental . Examples are e r and π r , which are transcendental for all nonzero rational r.
Because the algebraic numbers form a subfield of the real numbers, many irrational real numbers can be constructed by combining transcendental and algebraic numbers. For example, 3 π + 2, π + √ 2 and e √ 3 are irrational (and even transcendental).
The decimal expansion of an irrational number never repeats (meaning the decimal expansion does not repeat the same number or sequence of numbers) or terminates (this means there is not a finite number of nonzero digits), unlike any rational number. The same is true for binary , octal or hexadecimal expansions, and in general for expansions in every positional notation with natural bases.
To show this, suppose we divide integers n by m (where m is nonzero). When long division is applied to the division of n by m , there can never be a remainder greater than or equal to m . If 0 appears as a remainder, the decimal expansion terminates. If 0 never occurs, then the algorithm can run at most m − 1 steps without using any remainder more than once. After that, a remainder must recur, and then the decimal expansion repeats.
Conversely, suppose we are faced with a repeating decimal , we can prove that it is a fraction of two integers. For example, consider:
Here the repetend is 162 and the length of the repetend is 3. First, we multiply by an appropriate power of 10 to move the decimal point to the right so that it is just in front of a repetend. In this example we would multiply by 10 to obtain:
Now we multiply this equation by 10 r where r is the length of the repetend. This has the effect of moving the decimal point to be in front of the "next" repetend. In our example, multiply by 10 3 :
The result of the two multiplications gives two different expressions with exactly the same "decimal portion", that is, the tail end of 10,000 A matches the tail end of 10 A exactly. Here, both 10,000 A and 10 A have .162 162 162 ... after the decimal point.
Therefore, when we subtract the 10 A equation from the 10,000 A equation, the tail end of 10 A cancels out the tail end of 10,000 A leaving us with:
Then
is a ratio of integers and therefore a rational number.
Dov Jarden gave a simple non- constructive proof that there exist two irrational numbers a and b , such that a b is rational: [ 28 ] [ 29 ]
Although the above argument does not decide between the two cases, the Gelfond–Schneider theorem shows that 2 {\displaystyle {\sqrt {2}}} 2 {\displaystyle {\sqrt {2}}} is transcendental , hence irrational. This theorem states that if a and b are both algebraic numbers , and a is not equal to 0 or 1, and b is not a rational number, then any value of a b is a transcendental number (there can be more than one value if complex number exponentiation is used).
An example that provides a simple constructive proof is [ 30 ]
The base of the left side is irrational and the right side is rational, so one must prove that the exponent on the left side, log 2 3 {\displaystyle \log _{\sqrt {2}}3} , is irrational. This is so because, by the formula relating logarithms with different bases,
which we can assume, for the sake of establishing a contradiction , equals a ratio m/n of positive integers. Then log 2 3 = m / 2 n {\displaystyle \log _{2}3=m/2n} hence 2 log 2 3 = 2 m / 2 n {\displaystyle 2^{\log _{2}3}=2^{m/2n}} hence 3 = 2 m / 2 n {\displaystyle 3=2^{m/2n}} hence 3 2 n = 2 m {\displaystyle 3^{2n}=2^{m}} , which is a contradictory pair of prime factorizations and hence violates the fundamental theorem of arithmetic (unique prime factorization).
A stronger result is the following: [ 31 ] Every rational number in the interval ( ( 1 / e ) 1 / e , ∞ ) {\displaystyle ((1/e)^{1/e},\infty )} can be written either as a a for some irrational number a or as n n for some natural number n . Similarly, [ 31 ] every positive rational number can be written either as a a a {\displaystyle a^{a^{a}}} for some irrational number a or as n n n {\displaystyle n^{n^{n}}} for some natural number n .
In constructive mathematics , excluded middle is not valid, so it is not true that every real number is rational or irrational. Thus, the notion of an irrational number bifurcates into multiple distinct notions. One could take the traditional definition of an irrational number as a real number that is not rational. [ 35 ] However, there is a second definition of an irrational number used in constructive mathematics, that a real number r {\displaystyle r} is an irrational number if it is apart from every rational number, or equivalently, if the distance | r − q | {\displaystyle \vert r-q\vert } between r {\displaystyle r} and every rational number q {\displaystyle q} is positive. This definition is stronger than the traditional definition of an irrational number. This second definition is used in Errett Bishop 's proof that the square root of 2 is irrational . [ 36 ]
Since the reals form an uncountable set, of which the rationals are a countable subset, the complementary set of
irrationals is uncountable.
Under the usual ( Euclidean ) distance function d ( x , y ) = | x − y | {\displaystyle d(x,y)=\vert x-y\vert } , the real numbers are a metric space and hence also a topological space . Restricting the Euclidean distance function gives the irrationals the structure of a metric space. Since the subspace of irrationals is not closed,
the induced metric is not complete . Being a G-delta set —i.e., a countable intersection of open subsets—in a complete metric space, the space of irrationals is completely metrizable : that is, there is a metric on the irrationals inducing the same topology as the restriction of the Euclidean metric, but with respect to which the irrationals are complete. One can see this without knowing the aforementioned fact about G-delta sets: the continued fraction expansion of an irrational number defines a homeomorphism from the space of irrationals to the space of all sequences of positive integers, which is easily seen to be completely metrizable.
Furthermore, the set of all irrationals is a disconnected metrizable space. In fact, the irrationals equipped with the subspace topology have a basis of clopen groups so the space is zero-dimensional . | https://en.wikipedia.org/wiki/Irrational_number |
Irrationality is cognition , thinking, talking, or acting without rationality .
Irrationality often has a negative connotation, as thinking and actions that are less useful or more illogical than other more rational alternatives. [ 1 ] [ 2 ] The concept of irrationality is especially important in Albert Ellis 's rational emotive behavior therapy , where it is characterized specifically as the tendency and leaning that humans have to act, emote and think in ways that are inflexible, unrealistic, absolutist and most importantly self-defeating and socially defeating and destructive. [ 3 ]
However, irrationality is not always viewed as a negative. Much subject matter in literature can be seen as an expression of human longing for the irrational. The Romantics valued irrationality over what they perceived as the sterile, calculating and emotionless philosophy which they thought to have been brought about by the Age of Enlightenment and the Industrial Revolution . [ 4 ] Dada Surrealist art movements embraced irrationality as a means to "reject reason and logic". André Breton , for example, argued for a rejection of pure logic and reason which are seen as responsible for many contemporary social problems. [ 5 ] | https://en.wikipedia.org/wiki/Irrationality |
In mathematics , an irrationality measure of a real number x {\displaystyle x} is a measure of how "closely" it can be approximated by rationals .
If a function f ( t , λ ) {\displaystyle f(t,\lambda )} , defined for t , λ > 0 {\displaystyle t,\lambda >0} , takes positive real values and is strictly decreasing in both variables, consider the following inequality :
for a given real number x ∈ R {\displaystyle x\in \mathbb {R} } and rational numbers p q {\displaystyle {\frac {p}{q}}} with p ∈ Z , q ∈ Z + {\displaystyle p\in \mathbb {Z} ,q\in \mathbb {Z} ^{+}} . Define R {\displaystyle R} as the set of all λ ∈ R + {\displaystyle \lambda \in \mathbb {R} ^{+}} for which only finitely many p q {\displaystyle {\frac {p}{q}}} exist, such that the inequality is satisfied. Then λ ( x ) = inf R {\displaystyle \lambda (x)=\inf R} is called an irrationality measure of x {\displaystyle x} with regard to f . {\displaystyle f.} If there is no such λ {\displaystyle \lambda } and the set R {\displaystyle R} is empty , x {\displaystyle x} is said to have infinite irrationality measure λ ( x ) = ∞ {\displaystyle \lambda (x)=\infty } .
Consequently, the inequality
has at most only finitely many solutions p q {\displaystyle {\frac {p}{q}}} for all ε > 0 {\displaystyle \varepsilon >0} . [ 1 ]
The irrationality exponent or Liouville–Roth irrationality measure is given by setting f ( q , μ ) = q − μ {\displaystyle f(q,\mu )=q^{-\mu }} , [ 1 ] a definition adapting the one of Liouville numbers — the irrationality exponent μ ( x ) {\displaystyle \mu (x)} is defined for real numbers x {\displaystyle x} to be the supremum of the set of μ {\displaystyle \mu } such that 0 < | x − p q | < 1 q μ {\displaystyle 0<\left|x-{\frac {p}{q}}\right|<{\frac {1}{q^{\mu }}}} is satisfied by an infinite number of coprime integer pairs ( p , q ) {\displaystyle (p,q)} with q > 0 {\displaystyle q>0} . [ 2 ] [ 3 ] : 246
For any value n < μ ( x ) {\displaystyle n<\mu (x)} , the infinite set of all rationals p / q {\displaystyle p/q} satisfying the above inequality yields good approximations of x {\displaystyle x} . Conversely, if n > μ ( x ) {\displaystyle n>\mu (x)} , then there are at most finitely many coprime ( p , q ) {\displaystyle (p,q)} with q > 0 {\displaystyle q>0} that satisfy the inequality.
For example, whenever a rational approximation p q ≈ x {\displaystyle {\frac {p}{q}}\approx x} with p , q ∈ N {\displaystyle p,q\in \mathbb {N} } yields n + 1 {\displaystyle n+1} exact decimal digits, then
for any ε > 0 {\displaystyle \varepsilon >0} , except for at most a finite number of "lucky" pairs ( p , q ) {\displaystyle (p,q)} .
A number x ∈ R {\displaystyle x\in \mathbb {R} } with irrationality exponent μ ( x ) ≤ 2 {\displaystyle \mu (x)\leq 2} is called a diophantine number , [ 4 ] while numbers with μ ( x ) = ∞ {\displaystyle \mu (x)=\infty } are called Liouville numbers .
Rational numbers have irrationality exponent 1, while (as a consequence of Dirichlet's approximation theorem ) every irrational number has irrationality exponent at least 2.
On the other hand, an application of Borel-Cantelli lemma shows that almost all numbers, including all algebraic irrational numbers , have an irrationality exponent exactly equal to 2. [ 3 ] : 246
It is μ ( x ) = μ ( r x + s ) {\displaystyle \mu (x)=\mu (rx+s)} for real numbers x {\displaystyle x} and rational numbers r ≠ 0 {\displaystyle r\neq 0} and s {\displaystyle s} . If for some x {\displaystyle x} we have μ ( x ) ≤ μ {\displaystyle \mu (x)\leq \mu } , then it follows μ ( x 1 / 2 ) ≤ 2 μ {\displaystyle \mu (x^{1/2})\leq 2\mu } . [ 5 ] : 368
For a real number x {\displaystyle x} given by its simple continued fraction expansion x = [ a 0 ; a 1 , a 2 , . . . ] {\displaystyle x=[a_{0};a_{1},a_{2},...]} with convergents p i / q i {\displaystyle p_{i}/q_{i}} it holds: [ 1 ]
If we have lim sup n → ∞ 1 n ln | q n | ≤ σ {\displaystyle \limsup _{n\to \infty }{\tfrac {1}{n}}{\ln |q_{n}|}\leq \sigma } and lim n → ∞ 1 n ln | q n x − p n | = − τ {\displaystyle \lim _{n\to \infty }{\tfrac {1}{n}}{\ln |q_{n}x-p_{n}|}=-\tau } for some positive real numbers σ , τ {\displaystyle \sigma ,\tau } , then we can establish an upper bound for the irrationality exponent of x {\displaystyle x} by: [ 6 ] [ 7 ]
For most transcendental numbers , the exact value of their irrationality exponent is not known. [ 5 ] Below is a table of known upper and lower bounds.
Examples include numbers which continued fractions behave predictably such as
e = [ 2 ; 1 , 2 , 1 , 1 , 4 , 1 , 1 , 6 , 1 , . . . ] {\displaystyle e=[2;1,2,1,1,4,1,1,6,1,...]} and I 0 ( 2 ) / I 1 ( 2 ) = [ 1 ; 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , . . . ] {\displaystyle I_{0}(2)/I_{1}(2)=[1;2,3,4,5,6,7,8,9,10,...]} .
The irrationality base or Sondow irrationality measure is obtained by setting f ( q , β ) = β − q {\displaystyle f(q,\beta )=\beta ^{-q}} . [ 1 ] [ 6 ] It is a weaker irrationality measure, being able to distinguish how well different Liouville numbers can be approximated, but yielding β ( x ) = 1 {\displaystyle \beta (x)=1} for all other real numbers:
Let x {\displaystyle x} be an irrational number. If there exist real numbers β ≥ 1 {\displaystyle \beta \geq 1} with the property that for any ε > 0 {\displaystyle \varepsilon >0} , there is a positive integer q ( ε ) {\displaystyle q(\varepsilon )} such that
for all integers p , q {\displaystyle p,q} with q ≥ q ( ε ) {\displaystyle q\geq q(\varepsilon )} then the least such β {\displaystyle \beta } is called the irrationality base of x {\displaystyle x} and is represented as β ( x ) {\displaystyle \beta (x)} .
If no such β {\displaystyle \beta } exists, then β ( x ) = ∞ {\displaystyle \beta (x)=\infty } and x {\displaystyle x} is called a super Liouville number .
If a real number x {\displaystyle x} is given by its simple continued fraction expansion x = [ a 0 ; a 1 , a 2 , . . . ] {\displaystyle x=[a_{0};a_{1},a_{2},...]} with convergents p i / q i {\displaystyle p_{i}/q_{i}} then it holds:
Any real number x {\displaystyle x} with finite irrationality exponent μ ( x ) < ∞ {\displaystyle \mu (x)<\infty } has irrationality base β ( x ) = 1 {\displaystyle \beta (x)=1} , while any number with irrationality base β ( x ) > 1 {\displaystyle \beta (x)>1} has irrationality exponent μ ( x ) = ∞ {\displaystyle \mu (x)=\infty } and is a Liouville number.
The number L = [ 1 ; 2 , 2 2 , 2 2 2 , . . . ] {\displaystyle L=[1;2,2^{2},2^{2^{2}},...]} has irrationality exponent μ ( L ) = ∞ {\displaystyle \mu (L)=\infty } and irrationality base β ( L ) = 1 {\displaystyle \beta (L)=1} .
The numbers τ a = ∑ n = 0 ∞ 1 n a = 1 + 1 a + 1 a a + 1 a a a + 1 a a a a + . . . {\displaystyle \tau _{a}=\sum _{n=0}^{\infty }{\frac {1}{^{n}a}}=1+{\frac {1}{a}}+{\frac {1}{a^{a}}}+{\frac {1}{a^{a^{a}}}}+{\frac {1}{a^{a^{a^{a}}}}}+...} ( n a {\displaystyle {^{n}a}} represents tetration , a = 2 , 3 , 4... {\displaystyle a=2,3,4...} ) have irrationality base β ( τ a ) = a {\displaystyle \beta (\tau _{a})=a} .
The number S = 1 + 1 2 1 + 1 4 2 1 + 1 8 4 2 1 + 1 16 8 4 2 1 + 1 32 16 8 4 2 1 + … {\displaystyle S=1+{\frac {1}{2^{1}}}+{\frac {1}{4^{2^{1}}}}+{\frac {1}{8^{4^{2^{1}}}}}+{\frac {1}{16^{8^{4^{2^{1}}}}}}+{\frac {1}{32^{16^{8^{4^{2^{1}}}}}}}+\ldots } has irrationality base β ( S ) = ∞ {\displaystyle \beta (S)=\infty } , hence it is a super Liouville number.
Although it is not known whether or not e π {\displaystyle e^{\pi }} is a Liouville number, [ 32 ] : 20 it is known that β ( e π ) = 1 {\displaystyle \beta (e^{\pi })=1} . [ 5 ] : 371
Setting f ( q , M ) = ( M q 2 ) − 1 {\displaystyle f(q,M)=(Mq^{2})^{-1}} gives a stronger irrationality measure: the Markov constant M ( x ) {\displaystyle M(x)} . For an irrational number x ∈ R ∖ Q {\displaystyle x\in \mathbb {R} \setminus \mathbb {Q} } it is the factor by which Dirichlet's approximation theorem can be improved for x {\displaystyle x} . Namely if c < M ( x ) {\displaystyle c<M(x)} is a positive real number, then the inequality
has infinitely many solutions p q ∈ Q {\displaystyle {\frac {p}{q}}\in \mathbb {Q} } . If c > M ( x ) {\displaystyle c>M(x)} there are at most finitely many solutions.
Dirichlet's approximation theorem implies M ( x ) ≥ 1 {\displaystyle M(x)\geq 1} and Hurwitz's theorem gives M ( x ) ≥ 5 {\displaystyle M(x)\geq {\sqrt {5}}} both for irrational x {\displaystyle x} . [ 33 ]
This is in fact the best general lower bound since the golden ratio gives M ( φ ) = 5 {\displaystyle M(\varphi )={\sqrt {5}}} . It is also M ( 2 ) = 2 2 {\displaystyle M({\sqrt {2}})=2{\sqrt {2}}} .
Given x = [ a 0 ; a 1 , a 2 , . . . ] {\displaystyle x=[a_{0};a_{1},a_{2},...]} by its simple continued fraction expansion, one may obtain: [ 34 ]
Bounds for the Markov constant of x = [ a 0 ; a 1 , a 2 , . . . ] {\displaystyle x=[a_{0};a_{1},a_{2},...]} can also be given by p 2 + 4 ≤ M ( x ) < p + 2 {\displaystyle {\sqrt {p^{2}+4}}\leq M(x)<p+2} with p = lim sup n → ∞ a n {\displaystyle p=\limsup _{n\to \infty }a_{n}} . [ 35 ] This implies that M ( x ) = ∞ {\displaystyle M(x)=\infty } if and only if ( a k ) {\displaystyle (a_{k})} is not bounded and in particular M ( x ) < ∞ {\displaystyle M(x)<\infty } if x {\displaystyle x} is a quadratic irrational number . A further consequence is M ( e ) = ∞ {\displaystyle M(e)=\infty } .
Any number with μ ( x ) > 2 {\displaystyle \mu (x)>2} or β ( x ) > 1 {\displaystyle \beta (x)>1} has an unbounded simple continued fraction and hence M ( x ) = ∞ {\displaystyle M(x)=\infty } .
For rational numbers r {\displaystyle r} it may be defined M ( r ) = 0 {\displaystyle M(r)=0} .
The values M ( e ) = ∞ {\displaystyle M(e)=\infty } and μ ( e ) = 2 {\displaystyle \mu (e)=2} imply that the inequality 0 < | e − p q | < 1 c q 2 {\displaystyle 0<\left|e-{\frac {p}{q}}\right|<{\frac {1}{cq^{2}}}} has for all c ∈ R + {\displaystyle c\in \mathbb {R} ^{+}} infinitely many solutions p q ∈ Q {\displaystyle {\frac {p}{q}}\in \mathbb {Q} } while the inequality 0 < | e − p q | < 1 q 2 + ε {\displaystyle 0<\left|e-{\frac {p}{q}}\right|<{\frac {1}{q^{2+\varepsilon }}}} has for all ε ∈ R + {\displaystyle \varepsilon \in \mathbb {R} ^{+}} only at most finitely many solutions p q ∈ Q {\displaystyle {\frac {p}{q}}\in \mathbb {Q} } . This gives rise to the question what the best upper bound is. The answer is given by: [ 36 ]
which is satisfied by infinitely many p q ∈ Q {\displaystyle {\frac {p}{q}}\in \mathbb {Q} } for c > 1 2 {\displaystyle c>{\tfrac {1}{2}}} but not for c < 1 2 {\displaystyle c<{\tfrac {1}{2}}} .
This makes the number e {\displaystyle e} alongside the rationals and quadratic irrationals an exception to the fact that for almost all real numbers x ∈ R {\displaystyle x\in \mathbb {R} } the inequality below has infinitely many solutions p q ∈ Q {\displaystyle {\frac {p}{q}}\in \mathbb {Q} } : [ 5 ] (see Khinchin's theorem )
Kurt Mahler extended the concept of an irrationality measure and defined a so-called transcendence measure , drawing on the idea of a Liouville number and partitioning the transcendental numbers into three distinct classes. [ 3 ]
Instead of taking for a given real number x {\displaystyle x} the difference | x − p / q | {\displaystyle |x-p/q|} with p / q ∈ Q {\displaystyle p/q\in \mathbb {Q} } , one may instead focus on term | q x − p | = | L ( x ) | {\displaystyle |qx-p|=|L(x)|} with p , q ∈ Z {\displaystyle p,q\in \mathbb {Z} } and L ∈ Z [ x ] {\displaystyle L\in \mathbb {Z} [x]} with deg L = 1 {\displaystyle \deg L=1} . Consider the following inequality:
0 < | q x − p | ≤ max ( | p | , | q | ) − ω {\displaystyle 0<|qx-p|\leq \max(|p|,|q|)^{-\omega }} with p , q ∈ Z {\displaystyle p,q\in \mathbb {Z} } and ω ∈ R 0 + {\displaystyle \omega \in \mathbb {R} _{0}^{+}} .
Define R {\displaystyle R} as the set of all ω ∈ R 0 + {\displaystyle \omega \in \mathbb {R} _{0}^{+}} for which infinitely many solutions p , q ∈ Z {\displaystyle p,q\in \mathbb {Z} } exist, such that the inequality is satisfied. Then ω 1 ( x ) = sup M {\displaystyle \omega _{1}(x)=\sup M} is Mahler's irrationality measure. It gives ω 1 ( p / q ) = 0 {\displaystyle \omega _{1}(p/q)=0} for rational numbers, ω 1 ( α ) = 1 {\displaystyle \omega _{1}(\alpha )=1} for algebraic irrational numbers and in general ω 1 ( x ) = μ ( x ) − 1 {\displaystyle \omega _{1}(x)=\mu (x)-1} , where μ ( x ) {\displaystyle \mu (x)} denotes the irrationality exponent.
Mahler's irrationality measure can be generalized as follows: [ 2 ] [ 3 ] Take P {\displaystyle P} to be a polynomial with deg P ≤ n ∈ Z + {\displaystyle \deg P\leq n\in \mathbb {Z} ^{+}} and integer coefficients a i ∈ Z {\displaystyle a_{i}\in \mathbb {Z} } . Then define a height function H ( P ) = max ( | a 0 | , | a 1 | , . . . , | a n | ) {\displaystyle H(P)=\max(|a_{0}|,|a_{1}|,...,|a_{n}|)} and consider for complex numbers z {\displaystyle z} the inequality:
0 < | P ( z ) | ≤ H ( P ) − ω {\displaystyle 0<|P(z)|\leq H(P)^{-\omega }} with ω ∈ R 0 + {\displaystyle \omega \in \mathbb {R} _{0}^{+}} .
Set R {\displaystyle R} to be the set of all ω ∈ R 0 + {\displaystyle \omega \in \mathbb {R} _{0}^{+}} for which infinitely many such polynomials exist, that keep the inequality satisfied. Further define ω n ( z ) = sup R {\displaystyle \omega _{n}(z)=\sup R} for all n ∈ Z + {\displaystyle n\in \mathbb {Z} ^{+}} with ω 1 ( z ) {\displaystyle \omega _{1}(z)} being the above irrationality measure, ω 2 ( z ) {\displaystyle \omega _{2}(z)} being a non-quadraticity measure , etc.
Then Mahler's transcendence measure is given by:
The transcendental numbers can now be divided into the following three classes:
If for all n ∈ Z + {\displaystyle n\in \mathbb {Z} ^{+}} the value of ω n ( z ) {\displaystyle \omega _{n}(z)} is finite and ω ( z ) {\displaystyle \omega (z)} is finite as well, z {\displaystyle z} is called an S-number (of type ω ( z ) {\displaystyle \omega (z)} ).
If for all n ∈ Z + {\displaystyle n\in \mathbb {Z} ^{+}} the value of ω n ( z ) {\displaystyle \omega _{n}(z)} is finite but ω ( z ) {\displaystyle \omega (z)} is infinite, z {\displaystyle z} is called an T-number .
If there exists a smallest positive integer N {\displaystyle N} such that for all n ≥ N {\displaystyle n\geq N} the ω n ( z ) {\displaystyle \omega _{n}(z)} are infinite, z {\displaystyle z} is called an U-number (of degree N {\displaystyle N} ).
The number z {\displaystyle z} is algebraic (and called an A-number ) if and only if ω ( z ) = 0 {\displaystyle \omega (z)=0} .
Almost all numbers are S-numbers. In fact, almost all real numbers give ω ( x ) = 1 {\displaystyle \omega (x)=1} while almost all complex numbers give ω ( z ) = 1 2 {\displaystyle \omega (z)={\tfrac {1}{2}}} . [ 37 ] : 86 The number e is an S-number with ω ( e ) = 1 {\displaystyle \omega (e)=1} . The number π is either an S- or T-number. [ 37 ] : 86 The U-numbers are a set of measure 0 but still uncountable. [ 38 ] They contain the Liouville numbers which are exactly the U-numbers of degree one.
Another generalization of Mahler's irrationality measure gives a linear independence measure. [ 2 ] [ 13 ] For real numbers x 1 , . . . , x n ∈ R {\displaystyle x_{1},...,x_{n}\in \mathbb {R} } consider the inequality
0 < | c 1 x 1 + . . . + c n x n | ≤ max ( | c 1 | , . . . , | c n | ) − ν {\displaystyle 0<|c_{1}x_{1}+...+c_{n}x_{n}|\leq \max(|c_{1}|,...,|c_{n}|)^{-\nu }} with c 1 , . . . , c n ∈ Z {\displaystyle c_{1},...,c_{n}\in \mathbb {Z} } and ν ∈ R 0 + {\displaystyle \nu \in \mathbb {R} _{0}^{+}} .
Define R {\displaystyle R} as the set of all ν ∈ R 0 + {\displaystyle \nu \in \mathbb {R} _{0}^{+}} for which infinitely many solutions c 1 , . . . c n ∈ Z {\displaystyle c_{1},...c_{n}\in \mathbb {Z} } exist, such that the inequality is satisfied. Then ν ( x 1 , . . . , x n ) = sup R {\displaystyle \nu (x_{1},...,x_{n})=\sup R} is the linear independence measure.
If the x 1 , . . . , x n {\displaystyle x_{1},...,x_{n}} are linearly dependent over Q {\displaystyle \mathbb {\mathbb {Q} } } then ν ( x 1 , . . . , x n ) = 0 {\displaystyle \nu (x_{1},...,x_{n})=0} .
If 1 , x 1 , . . . , x n {\displaystyle 1,x_{1},...,x_{n}} are linearly independent algebraic numbers over Q {\displaystyle \mathbb {\mathbb {Q} } } then ν ( 1 , x 1 , . . . , x n ) ≤ n {\displaystyle \nu (1,x_{1},...,x_{n})\leq n} . [ 32 ]
It is further ν ( 1 , x ) = ω 1 ( x ) = μ ( x ) − 1 {\displaystyle \nu (1,x)=\omega _{1}(x)=\mu (x)-1} .
Jurjen Koksma in 1939 proposed another generalization, similar to that of Mahler, based on approximations of complex numbers by algebraic numbers. [ 3 ] [ 37 ]
For a given complex number z {\displaystyle z} consider algebraic numbers α {\displaystyle \alpha } of degree at most n {\displaystyle n} . Define a height function H ( α ) = H ( P ) {\displaystyle H(\alpha )=H(P)} , where P {\displaystyle P} is the characteristic polynomial of α {\displaystyle \alpha } and consider the inequality:
0 < | z − α | ≤ H ( α ) − ω ∗ − 1 {\displaystyle 0<|z-\alpha |\leq H(\alpha )^{-\omega ^{*}-1}} with ω ∗ ∈ R 0 + {\displaystyle \omega ^{*}\in \mathbb {R} _{0}^{+}} .
Set R {\displaystyle R} to be the set of all ω ∗ ∈ R 0 + {\displaystyle \omega ^{*}\in \mathbb {R} _{0}^{+}} for which infinitely many such algebraic numbers α {\displaystyle \alpha } exist, that keep the inequality satisfied. Further define ω n ∗ ( z ) = sup R {\displaystyle \omega _{n}^{*}(z)=\sup R} for all n ∈ Z + {\displaystyle n\in \mathbb {Z} ^{+}} with ω 1 ∗ ( z ) {\displaystyle \omega _{1}^{*}(z)} being an irrationality measure, ω 2 ∗ ( z ) {\displaystyle \omega _{2}^{*}(z)} being a non-quadraticity measure , [ 17 ] etc.
Then Koksma's transcendence measure is given by:
The complex numbers can now once again be partitioned into four classes A*, S*, T* and U*. However it turns out that these classes are equivalent to the ones given by Mahler in the sense that they produce exactly the same partition. [ 37 ] : 87
Given a real number x ∈ R {\displaystyle x\in \mathbb {R} } , an irrationality measure of x {\displaystyle x} quantifies how well it can be approximated by rational numbers p q {\displaystyle {\frac {p}{q}}} with denominator q ∈ Z + {\displaystyle q\in \mathbb {Z} ^{+}} . If x = α {\displaystyle x=\alpha } is taken to be an algebraic number that is also irrational one may obtain that the inequality
has only at most finitely many solutions p q ∈ Q {\displaystyle {\frac {p}{q}}\in \mathbb {Q} } for μ > 2 {\displaystyle \mu >2} . This is known as Roth's theorem .
This can be generalized: Given a set of real numbers x 1 , . . . , x n ∈ R {\displaystyle x_{1},...,x_{n}\in \mathbb {R} } one can quantify how well they can be approximated simultaneously by rational numbers p 1 q , . . . , p n q {\displaystyle {\frac {p_{1}}{q}},...,{\frac {p_{n}}{q}}} with the same denominator q ∈ Z + {\displaystyle q\in \mathbb {Z} ^{+}} . If the x i = α i {\displaystyle x_{i}=\alpha _{i}} are taken to be algebraic numbers, such that 1 , α 1 , . . . , α n {\displaystyle 1,\alpha _{1},...,\alpha _{n}} are linearly independent over the rational numbers Q {\displaystyle \mathbb {Q} } it follows that the inequalities
have only at most finitely many solutions ( p 1 q , . . . , p n q ) ∈ Q n {\displaystyle \left({\frac {p_{1}}{q}},...,{\frac {p_{n}}{q}}\right)\in \mathbb {Q} ^{n}} for μ > 1 + 1 n {\displaystyle \mu >1+{\frac {1}{n}}} . This result is due to Wolfgang M. Schmidt . [ 39 ] [ 40 ] | https://en.wikipedia.org/wiki/Irrationality_measure |
In mathematics, a sequence of positive integers a n is called an irrationality sequence if it has the property that for every sequence x n of positive integers, the sum of the series
exists (that is, it converges ) and is an irrational number . [ 1 ] [ 2 ] The problem of characterizing irrationality sequences was posed by Paul Erdős and Ernst G. Straus , who originally called the property of being an irrationality sequence "Property P". [ 3 ]
The powers of two whose exponents are powers of two , 2 2 n {\displaystyle 2^{2^{n}}} , form an irrationality sequence. However, although Sylvester's sequence
(in which each term is one more than the product of all previous terms) also grows doubly exponentially , it does not form an irrationality sequence. For, letting x n = 1 {\displaystyle x_{n}=1} for all n {\displaystyle n} gives
a series converging to a rational number . Likewise, the factorials , n ! {\displaystyle n!} , do not form an irrationality sequence because the sequence given by x n = n + 2 {\displaystyle x_{n}=n+2} for all n {\displaystyle n} leads to a series with a rational sum,
For any sequence a n to be an irrationality sequence, it must grow at a rate such that
This includes sequences that grow at a more than doubly exponential rate as well as some doubly exponential sequences that grow more quickly than the powers of powers of two. [ 1 ]
Every irrationality sequence must grow quickly enough that
However, it is not known whether there exists such a sequence in which the greatest common divisor of each pair of terms is 1 (unlike the powers of powers of two) and for which
Analogously to irrationality sequences, Hančl (1996) has defined a transcendental sequence to be an integer sequence a n such that, for every sequence x n of positive integers, the sum of the series
exists and is a transcendental number . [ 6 ] | https://en.wikipedia.org/wiki/Irrationality_sequence |
In mathematics , the concept of irreducibility is used in several ways. | https://en.wikipedia.org/wiki/Irreducibility_(mathematics) |
An irreducible fraction (or fraction in lowest terms , simplest form or reduced fraction ) is a fraction in which the numerator and denominator are integers that have no other common divisors than 1 (and −1, when negative numbers are considered). [ 1 ] In other words, a fraction a / b is irreducible if and only if a and b are coprime , that is, if a and b have a greatest common divisor of 1. In higher mathematics , " irreducible fraction " may also refer to rational fractions such that the numerator and the denominator are coprime polynomials . [ 2 ] Every rational number can be represented as an irreducible fraction with positive denominator in exactly one way. [ 3 ]
An equivalent definition is sometimes useful: if a and b are integers, then the fraction a / b is irreducible if and only if there is no other equal fraction c / d such that | c | < | a | or | d | < | b | , where | a | means the absolute value of a . [ 4 ] (Two fractions a / b and c / d are equal or equivalent if and only if ad = bc .)
For example, 1 / 4 , 5 / 6 , and −101 / 100 are all irreducible fractions. On the other hand, 2 / 4 is reducible since it is equal in value to 1 / 2 , and the numerator of 1 / 2 is less than the numerator of 2 / 4 .
A fraction that is reducible can be reduced by dividing both the numerator and denominator by a common factor. It can be fully reduced to lowest terms if both are divided by their greatest common divisor . [ 5 ] In order to find the greatest common divisor, the Euclidean algorithm or prime factorization can be used. The Euclidean algorithm is commonly preferred because it allows one to reduce fractions with numerators and denominators too large to be easily factored. [ 6 ]
In the first step both numbers were divided by 10, which is a factor common to both 120 and 90. In the second step, they were divided by 3. The final result, 4 / 3 , is an irreducible fraction because 4 and 3 have no common factors other than 1.
The original fraction could have also been reduced in a single step by using the greatest common divisor of 90 and 120, which is 30. As 120 ÷ 30 = 4 , and 90 ÷ 30 = 3 , one gets
Which method is faster "by hand" depends on the fraction and the ease with which common factors are spotted. In case a denominator and numerator remain that are too large to ensure they are coprime by inspection, a greatest common divisor computation is needed anyway to ensure the fraction is actually irreducible.
Every rational number has a unique representation as an irreducible fraction with a positive denominator [ 3 ] (however 2 / 3 = −2 / −3 although both are irreducible). Uniqueness is a consequence of the unique prime factorization of integers, since a / b = c / d implies ad = bc , and so both sides of the latter must share the same prime factorization, yet a and b share no prime factors so the set of prime factors of a (with multiplicity) is a subset of those of c and vice versa, meaning a = c and by the same argument b = d .
The fact that any rational number has a unique representation as an irreducible fraction is utilized in various proofs of the irrationality of the square root of 2 and of other irrational numbers. For example, one proof notes that if 2 {\displaystyle {\sqrt {2}}} could be represented as a ratio of integers, then it would have in particular the fully reduced representation a / b where a and b are the smallest possible; but given that a / b equals 2 {\displaystyle {\sqrt {2}}} so does 2 b − a / a − b (since cross-multiplying this with a / b shows that they are equal). Since a > b (because 2 {\displaystyle {\sqrt {2}}} is greater than 1), the latter is a ratio of two smaller integers. This is a contradiction , so the premise that the square root of two has a representation as the ratio of two integers is false.
The notion of irreducible fraction generalizes to the field of fractions of any unique factorization domain : any element of such a field can be written as a fraction in which denominator and numerator are coprime, by dividing both by their greatest common divisor. [ 7 ] This applies notably to rational expressions over a field. The irreducible fraction for a given element is unique up to multiplication of denominator and numerator by the same invertible element. In the case of the rational numbers this means that any number has two irreducible fractions, related by a change of sign of both numerator and denominator; this ambiguity can be removed by requiring the denominator to be positive. In the case of rational functions the denominator could similarly be required to be a monic polynomial . [ 8 ] | https://en.wikipedia.org/wiki/Irreducible_fraction |
In mathematics , an irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the product of two non-constant polynomials . The property of irreducibility depends on the nature of the coefficients that are accepted for the possible factors, that is, the ring to which the coefficients of the polynomial and its possible factors are supposed to belong. For example, the polynomial x 2 − 2 is a polynomial with integer coefficients, but, as every integer is also a real number , it is also a polynomial with real coefficients. It is irreducible if it is considered as a polynomial with integer coefficients, but it factors as ( x − 2 ) ( x + 2 ) {\displaystyle \left(x-{\sqrt {2}}\right)\left(x+{\sqrt {2}}\right)} if it is considered as a polynomial with real coefficients. One says that the polynomial x 2 − 2 is irreducible over the integers but not over the reals.
Polynomial irreducibility can be considered for polynomials with coefficients in an integral domain , and there are two common definitions. Most often, a polynomial over an integral domain R is said to be irreducible if it is not the product of two polynomials that have their coefficients in R , and that are not unit in R . Equivalently, for this definition, an irreducible polynomial is an irreducible element in a ring of polynomials over R . If R is a field, the two definitions of irreducibility are equivalent. For the second definition, a polynomial is irreducible if it cannot be factored into polynomials with coefficients in the same domain that both have a positive degree. Equivalently, a polynomial is irreducible if it is irreducible over the field of fractions of the integral domain. For example, the polynomial 2 ( x 2 − 2 ) ∈ Z [ x ] {\displaystyle 2(x^{2}-2)\in \mathbb {Z} [x]} is irreducible for the second definition, and not for the first one. On the other hand, x 2 − 2 {\displaystyle x^{2}-2} is irreducible in Z [ x ] {\displaystyle \mathbb {Z} [x]} for the two definitions, while it is reducible in R [ x ] . {\displaystyle \mathbb {R} [x].}
A polynomial that is irreducible over any field containing the coefficients is absolutely irreducible . By the fundamental theorem of algebra , a univariate polynomial is absolutely irreducible if and only if its degree is one. On the other hand, with several indeterminates , there are absolutely irreducible polynomials of any degree, such as x 2 + y n − 1 , {\displaystyle x^{2}+y^{n}-1,} for any positive integer n .
A polynomial that is not irreducible is sometimes said to be a reducible polynomial . [ 1 ] [ 2 ]
Irreducible polynomials appear naturally in the study of polynomial factorization and algebraic field extensions .
It is helpful to compare irreducible polynomials to prime numbers : prime numbers (together with the corresponding negative numbers of equal magnitude) are the irreducible integers . They exhibit many of the general properties of the concept of "irreducibility" that equally apply to irreducible polynomials, such as the essentially unique factorization into prime or irreducible factors. When the coefficient ring is a field or other unique factorization domain , an irreducible polynomial is also called a prime polynomial , because it generates a prime ideal .
If F is a field, a non-constant polynomial is irreducible over F if its coefficients belong to F and it cannot be factored into the product of two non-constant polynomials with coefficients in F .
A polynomial with integer coefficients, or, more generally, with coefficients in a unique factorization domain R , is sometimes said to be irreducible (or irreducible over R ) if it is an irreducible element of the polynomial ring , that is, it is not invertible , not zero, and cannot be factored into the product of two non-invertible polynomials with coefficients in R . This definition generalizes the definition given for the case of coefficients in a field, because, over a field, the non-constant polynomials are exactly the polynomials that are non-invertible and non-zero.
Another definition is frequently used, saying that a polynomial is irreducible over R if it is irreducible over the field of fractions of R (the field of rational numbers , if R is the integers). This second definition is not used in this article. The equivalence of the two definitions depends on R .
The following six polynomials demonstrate some elementary properties of reducible and irreducible polynomials:
Over the integers , the first three polynomials are reducible (the third one is reducible because the factor 3 is not invertible in the integers); the last two are irreducible. (The fourth, of course, is not a polynomial over the integers.)
Over the rational numbers , the first two and the fourth polynomials are reducible, but the other three polynomials are irreducible (as a polynomial over the rationals, 3 is a unit , and, therefore, does not count as a factor).
Over the real numbers , the first five polynomials are reducible, but p 6 ( x ) {\displaystyle p_{6}(x)} is irreducible.
Over the complex numbers , all six polynomials are reducible.
Over the complex field , and, more generally, over an algebraically closed field , a univariate polynomial is irreducible if and only if its degree is one. This fact is known as the fundamental theorem of algebra in the case of the complex numbers and, in general, as the condition of being algebraically closed.
It follows that every nonconstant univariate polynomial can be factored as
where n {\displaystyle n} is the degree, a {\displaystyle a} is the leading coefficient and z 1 , … , z n {\displaystyle z_{1},\dots ,z_{n}} are the zeros of the polynomial (not necessarily distinct, and not necessarily having explicit algebraic expressions ).
There are irreducible multivariate polynomials of every degree over the complex numbers. For example, the polynomial
which defines a Fermat curve , is irreducible for every positive n .
Over the field of reals , the degree of an irreducible univariate polynomial is either one or two. More precisely, the irreducible polynomials are the polynomials of degree one and the quadratic polynomials a x 2 + b x + c {\displaystyle ax^{2}+bx+c} that have a negative discriminant b 2 − 4 a c . {\displaystyle b^{2}-4ac.} It follows that every non-constant univariate polynomial can be factored as a product of polynomials of degree at most two. For example, x 4 + 1 {\displaystyle x^{4}+1} factors over the real numbers as ( x 2 + 2 x + 1 ) ( x 2 − 2 x + 1 ) , {\displaystyle \left(x^{2}+{\sqrt {2}}x+1\right)\left(x^{2}-{\sqrt {2}}x+1\right),} and it cannot be factored further, as both factors have a negative discriminant: ( ± 2 ) 2 − 4 = − 2 < 0. {\displaystyle \left(\pm {\sqrt {2}}\right)^{2}-4=-2<0.}
Every polynomial over a field F may be factored into a product of a non-zero constant and a finite number of irreducible (over F ) polynomials. This decomposition is unique up to the order of the factors and the multiplication of the factors by non-zero constants whose product is 1.
Over a unique factorization domain the same theorem is true, but is more accurately formulated by using the notion of primitive polynomial. A primitive polynomial is a polynomial over a unique factorization domain, such that 1 is a greatest common divisor of its coefficients.
Let F be a unique factorization domain. A non-constant irreducible polynomial over F is primitive. A primitive polynomial over F is irreducible over F if and only if it is irreducible over the field of fractions of F . Every polynomial over F may be decomposed into the product of a non-zero constant and a finite number of non-constant irreducible primitive polynomials. The non-zero constant may itself be decomposed into the product of a unit of F and a finite number of irreducible elements of F . Both factorizations are unique up to the order of the factors and the multiplication of the factors by a unit of F .
This is this theorem which motivates that the definition of irreducible polynomial over a unique factorization domain often supposes that the polynomial is non-constant.
All algorithms which are presently implemented for factoring polynomials over the integers and over the rational numbers use this result (see Factorization of polynomials ).
The irreducibility of a polynomial over the integers Z {\displaystyle \mathbb {Z} } is related to that over the field F p {\displaystyle \mathbb {F} _{p}} of p {\displaystyle p} elements (for a prime p {\displaystyle p} ). In particular, if a univariate polynomial f over Z {\displaystyle \mathbb {Z} } is irreducible over F p {\displaystyle \mathbb {F} _{p}} for some prime p {\displaystyle p} that does not divide the leading coefficient of f (the coefficient of the highest power of the variable), then f is irreducible over Z {\displaystyle \mathbb {Z} } (that is, it is not the product of two non-constant polynomials with integer coefficients). Eisenstein's criterion is a variant of this property where irreducibility over p 2 {\displaystyle p^{2}} is also involved.
The converse, however, is not true: there are polynomials of arbitrarily large degree that are irreducible over the integers and reducible over every finite field. [ 3 ] A simple example of such a polynomial is x 4 + 1. {\displaystyle x^{4}+1.}
The relationship between irreducibility over the integers and irreducibility modulo p is deeper than the previous result: to date, all implemented algorithms for factorization and irreducibility over the integers and over the rational numbers use the factorization over finite fields as a subroutine .
The number of degree n irreducible monic polynomials over a field F q {\displaystyle \mathbb {F} _{q}} for q a prime power is given by Moreau's necklace-counting function : [ 4 ] [ 5 ]
where μ is the Möbius function . For q = 2 , such polynomials are commonly used to generate pseudorandom binary sequences .
In some sense, almost all polynomials with coefficients zero or one are irreducible over the integers. More precisely, if a version of the Riemann hypothesis for Dedekind zeta functions is assumed, the probability of being irreducible over the integers for a polynomial with random coefficients in {0, 1} tends to one when the degree increases. [ 6 ] [ 7 ]
The unique factorization property of polynomials does not mean that the factorization of a given polynomial may always be computed. Even the irreducibility of a polynomial may not always be proved by a computation: there are fields over which no algorithm can exist for deciding the irreducibility of arbitrary polynomials. [ 8 ]
Algorithms for factoring polynomials and deciding irreducibility are known and implemented in computer algebra systems for polynomials over the integers, the rational numbers, finite fields and finitely generated field extension of these fields. All these algorithms use the algorithms for factorization of polynomials over finite fields .
The notions of irreducible polynomial and of algebraic field extension are strongly related, in the following way.
Let x be an element of an extension L of a field K . This element is said to be algebraic if it is a root of a nonzero polynomial with coefficients in K . Among the polynomials of which x is a root, there is exactly one which is monic and of minimal degree, called the minimal polynomial of x . The minimal polynomial of an algebraic element x of L is irreducible, and is the unique monic irreducible polynomial of which x is a root. The minimal polynomial of x divides every polynomial which has x as a root (this is Abel's irreducibility theorem ).
Conversely, if P ( X ) ∈ K [ X ] {\displaystyle P(X)\in K[X]} is a univariate polynomial over a field K , let L = K [ X ] / P ( X ) {\displaystyle L=K[X]/P(X)} be the quotient ring of the polynomial ring K [ X ] {\displaystyle K[X]} by the ideal generated by P . Then L is a field if and only if P is irreducible over K . In this case, if x is the image of X in L , the minimal polynomial of x is the quotient of P by its leading coefficient .
An example of the above is the standard definition of the complex numbers as C = R [ X ] / ( X 2 + 1 ) . {\displaystyle \mathbb {C} =\mathbb {R} [X]\;/\left(X^{2}+1\right).}
If a polynomial P has an irreducible factor Q over K , which has a degree greater than one, one may apply to Q the preceding construction of an algebraic extension, to get an extension in which P has at least one more root than in K . Iterating this construction, one gets eventually a field over which P factors into linear factors. This field, unique up to a field isomorphism , is called the splitting field of P .
If R is an integral domain , an element f of R that is neither zero nor a unit is called irreducible if there are no non-units g and h with f = gh . One can show that every prime element is irreducible; [ 9 ] the converse is not true in general but holds in unique factorization domains . The polynomial ring F [ x ] over a field F (or any unique-factorization domain) is again a unique factorization domain. Inductively, this means that the polynomial ring in n indeterminates (over a ring R ) is a unique factorization domain if the same is true for R . | https://en.wikipedia.org/wiki/Irreducible_polynomial |
In mathematics , specifically in the representation theory of groups and algebras , an irreducible representation ( ρ , V ) {\displaystyle (\rho ,V)} or irrep of an algebraic structure A {\displaystyle A} is a nonzero representation that has no proper nontrivial subrepresentation ( ρ | W , W ) {\displaystyle (\rho |_{W},W)} , with W ⊂ V {\displaystyle W\subset V} closed under the action of { ρ ( a ) : a ∈ A } {\displaystyle \{\rho (a):a\in A\}} .
Every finite-dimensional unitary representation on a Hilbert space V {\displaystyle V} is the direct sum of irreducible representations. Irreducible representations are always indecomposable (i.e. cannot be decomposed further into a direct sum of representations), but the converse may not hold, e.g. the two-dimensional representation of the real numbers acting by upper triangular unipotent matrices is indecomposable but reducible.
Group representation theory was generalized by Richard Brauer from the 1940s to give modular representation theory , in which the matrix operators act on a vector space over a field K {\displaystyle K} of arbitrary characteristic , rather than a vector space over the field of real numbers or over the field of complex numbers . The structure analogous to an irreducible representation in the resulting theory is a simple module . [ citation needed ]
Let ρ {\displaystyle \rho } be a representation i.e. a homomorphism ρ : G → G L ( V ) {\displaystyle \rho :G\to GL(V)} of a group G {\displaystyle G} where V {\displaystyle V} is a vector space over a field F {\displaystyle F} . If we pick a basis B {\displaystyle B} for V {\displaystyle V} , ρ {\displaystyle \rho } can be thought of as a function (a homomorphism) from a group into a set of invertible matrices and in this context is called a matrix representation . However, it simplifies things greatly if we think of the space V {\displaystyle V} without a basis. ρ {\displaystyle \rho } is d-dimensional if the vector space V {\displaystyle V} it acts over has dimension d {\displaystyle d} .
A linear subspace W ⊂ V {\displaystyle W\subset V} is called G {\displaystyle G} -invariant if ρ ( g ) w ∈ W {\displaystyle \rho (g)w\in W} for all g ∈ G {\displaystyle g\in G} and all w ∈ W {\displaystyle w\in W} . The co-restriction of ρ {\displaystyle \rho } to the general linear group of a G {\displaystyle G} -invariant subspace W ⊂ V {\displaystyle W\subset V} is known as a subrepresentation . A representation ρ : G → G L ( V ) {\displaystyle \rho :G\to GL(V)} is said to be irreducible if it has only trivial subrepresentations (all representations can form a subrepresentation with the trivial G {\displaystyle G} -invariant subspaces, e.g. the whole vector space V {\displaystyle V} , and {0} ). If there is a proper nontrivial invariant subspace, ρ {\displaystyle \rho } is said to be reducible .
Group elements can be represented by matrices , although the term "represented" has a specific and precise meaning in this context. A representation of a group is a mapping from the group elements to the general linear group of matrices. As notation, let a , b , c , ... denote elements of a group G with group product signified without any symbol, so ab is the group product of a and b and is also an element of G , and let representations be indicated by D . The representation of a is written as
By definition of group representations, the representation of a group product is translated into matrix multiplication of the representations:
If e is the identity element of the group (so that ae = ea = a , etc.), then D ( e ) is an identity matrix , or identically a block matrix of identity matrices, since we must have
and similarly for all other group elements. The last two statements correspond to the requirement that D is a group homomorphism .
A representation is reducible if it contains a nontrivial G-invariant subspace, that is to say, all the matrices D ( a ) {\displaystyle D(a)} can be put in upper triangular block form by the same invertible matrix P {\displaystyle P} . In other words, if there is a similarity transformation:
which maps every matrix in the representation into the same pattern upper triangular blocks. Every ordered sequence minor block is a group subrepresentation. That is to say, if the representation is, for example, of dimension 2, then we have: D ′ ( a ) = P − 1 D ( a ) P = ( D ( 11 ) ( a ) D ( 12 ) ( a ) 0 D ( 22 ) ( a ) ) , {\displaystyle D'(a)=P^{-1}D(a)P={\begin{pmatrix}D^{(11)}(a)&D^{(12)}(a)\\0&D^{(22)}(a)\end{pmatrix}},}
where D ( 11 ) ( a ) {\displaystyle D^{(11)}(a)} is a nontrivial subrepresentation. If we are able to find a matrix P {\displaystyle P} that makes D ( 12 ) ( a ) = 0 {\displaystyle D^{(12)}(a)=0} as well, then D ( a ) {\displaystyle D(a)} is not only reducible but also decomposable.
Notice: Even if a representation is reducible, its matrix representation may still not be the upper triangular block form. It will only have this form if we choose a suitable basis, which can be obtained by applying the matrix P − 1 {\displaystyle P^{-1}} above to the standard basis.
A representation is decomposable if all the matrices D ( a ) {\displaystyle D(a)} can be put in block-diagonal form by the same invertible matrix P {\displaystyle P} . In other words, if there is a similarity transformation : [ 1 ]
which diagonalizes every matrix in the representation into the same pattern of diagonal blocks . Each such block is then a group subrepresentation independent from the others. The representations D ( a ) and D′ ( a ) are said to be equivalent representations . [ 2 ] The ( k -dimensional, say) representation can be decomposed into a direct sum of k > 1 matrices :
so D ( a ) is decomposable , and it is customary to label the decomposed matrices by a superscript in brackets, as in D ( n ) ( a ) for n = 1, 2, ..., k , although some authors just write the numerical label without parentheses.
The dimension of D ( a ) is the sum of the dimensions of the blocks:
If this is not possible, i.e. k = 1 , then the representation is indecomposable. [ 1 ] [ 3 ]
Notice : Even if a representation is decomposable, its matrix representation may not be the diagonal block form. It will only have this form if we choose a suitable basis, which can be obtained by applying the matrix P − 1 {\displaystyle P^{-1}} above to the standard basis.
An irreducible representation is by nature an indecomposable one. However, the converse may fail.
But under some conditions, we do have an indecomposable representation being an irreducible representation.
All groups G {\displaystyle G} have a zero-dimensional, irreducible trivial representation by mapping all group elements to the identity transformation.
Any one-dimensional representation is irreducible since it has no proper nontrivial invariant subspaces.
The irreducible complex representations of a finite group G can be characterized using results from character theory . In particular, all complex representations decompose as a direct sum of irreps, and the number of irreps of G {\displaystyle G} is equal to the number of conjugacy classes of G {\displaystyle G} . [ 5 ]
In quantum physics and quantum chemistry , each set of degenerate eigenstates of the Hamiltonian operator comprises a vector space V for a representation of the symmetry group of the Hamiltonian, a "multiplet", best studied through reduction to its irreducible parts. Identifying the irreducible representations therefore allows one to label the states, predict how they will split under perturbations; or transition to other states in V . Thus, in quantum mechanics, irreducible representations of the symmetry group of the system partially or completely label the energy levels of the system, allowing the selection rules to be determined. [ 6 ]
The irreps of D ( K ) and D ( J ) , where J is the generator of rotations and K the generator of boosts, can be used to build to spin representations of the Lorentz group, because they are related to the spin matrices of quantum mechanics. This allows them to derive relativistic wave equations . [ 7 ] | https://en.wikipedia.org/wiki/Irreducible_representation |
The irregularity of distributions problem, stated first by Hugo Steinhaus , is a numerical problem with a surprising result. The problem is to find N numbers, x 1 , … , x N {\displaystyle x_{1},\ldots ,x_{N}} , all between 0 and 1, for which the following conditions hold:
Mathematically, we are looking for a sequence of real numbers
such that for every n ∈ {1, ..., N } and every k ∈ {1, ..., n } there is some i ∈ {1, ..., k } such that
The surprising result is that there is a solution up to N = 17, but starting at N = 18 and above it is impossible. A possible solution for N ≤ 17 is shown diagrammatically on the right; numerically it is as follows:
In this example, considering for instance the first 5 numbers, we have
Mieczysław Warmus concluded that 768 (1536, counting symmetric solutions separately) distinct sets of intervals satisfy the conditions for N = 17. | https://en.wikipedia.org/wiki/Irregularity_of_distributions |
The irresistible force paradox (also unstoppable force paradox or shield and spear paradox ), is a classic paradox formulated as "What happens when an unstoppable force meets an immovable object?" The immovable object and the unstoppable force are both implicitly assumed to be indestructible, or else the question would have a trivial resolution. Furthermore, it is assumed that they are two entities.
The paradox arises because it rests on two incompatible premises—that there can exist simultaneously such things as unstoppable forces and immovable objects . [ 1 ]
An example of this paradox in eastern thought can be found in the origin of the Chinese word for contradiction ( Chinese : 矛盾 ; pinyin : máodùn ; lit. 'spear-shield'). This term originates from a story (see Kanbun § Example ) in the 3rd century BC philosophical book Han Feizi . [ 2 ] In the story, a man trying to sell a spear and a shield claimed that his spear could pierce any shield, and then claimed that his shield was unpierceable. Then, asked about what would happen if he were to take his spear to strike his shield, the seller could not answer. This led to the idiom of " zìxīang máodùn " (自相矛盾, "from each-other spear shield"), or "self-contradictory".
Another ancient and mythological example illustrating this theme can be found in the story of the Teumessian fox , which can never be caught, and the hound Laelaps , which never misses what it hunts. Realizing the paradox , Zeus , Lord of the Sky, turns both creatures into static constellations. [ 3 ]
The problems associated with this paradox can be applied to any other conflict between two abstractly defined extremes that are opposite.
One of the answers generated by seeming paradoxes like these is that there is no contradiction – that there is not a false dilemma . Christopher Kaczor suggested that the need to change indicates a lack of power rather than the possession thereof, and as such a person who was omniscient would never need to change their mind – not changing the future would be consistent with omniscience rather than contradicting it. [ 4 ] | https://en.wikipedia.org/wiki/Irresistible_force_paradox |
Irreversible electroporation or IRE is a soft tissue ablation technique using short but strong electrical fields to create permanent and hence lethal nanopores in the cell membrane , to disrupt cellular homeostasis . The resulting cell death results from induced apoptosis or necrosis induced by either membrane disruption or secondary breakdown of the membrane due to transmembrane transfer of electrolytes and adenosine triphosphate . [ 1 ] [ 2 ] [ 3 ] [ 4 ] The main use of IRE lies in tumor ablation in regions where precision and conservation of the extracellular matrix , blood flow and nerves are of importance. The first generation of IRE for clinical use, in the form of the NanoKnife System, became commercially available for research purposes in 2009, solely for the surgical ablation of soft tissue tumors. [ 5 ] Cancerous tissue ablation via IRE appears to show significant cancer specific immunological responses which are currently being evaluated alone and in combination with cancer immunotherapy . [ 6 ] [ 7 ] [ 8 ] [ 9 ]
First observations of IRE effects go back to 1754. Nollet reported the first systematic observations of the appearance of red spots on animal and human skin that was exposed to electric sparks. [ 10 ] However, its use for modern medicine began in 1982 with the seminal work of Neumann and colleagues. [ 11 ] Pulsed electric fields were used to temporarily permeabilize cell membranes to deliver foreign DNA into cells. In the following decade, the combination of high-voltage pulsed electric fields with the chemotherapeutic drug bleomycin and with DNA yielded novel clinical applications: electrochemotherapy and gene electrotransfer , respectively. [ 12 ] [ 13 ] [ 14 ] [ 15 ] [ 16 ] The use of irreversible electroporation for therapeutic applications was first suggested by Davalos, Mir, and Rubinsky. [ 17 ]
Utilizing ultra short pulsed but very strong electrical fields, micropores and nanopores are induced in the phospholipid bilayers which form the outer cell membranes. [ citation needed ] Two kinds of damage can occur:
It should be stated that even though the ablation method is generally accepted to be apoptosis, some findings seem to contradict a pure apoptotic cell death, making the exact process by which IRE causes cell death unclear. [ 18 ] [ 4 ] In any case, all studies agree that the cell death is an induced one with the cells dying over a varying time period of hours to days and does not rely on local extreme heating and melting of tissue via high energy deposition like most ablation technologies (see radiofrequency ablation , microwave ablation , High-intensity focused ultrasound ). [ citation needed ]
When an electrical field of more than 0.5 V/nm [ 19 ] is applied to the resting trans-membrane potential, it is proposed that water enters the cell during this dielectric breakdown. Hydrophilic pores are formed. [ 20 ] [ 21 ] A molecular dynamics simulation by Tarek [ 22 ] illustrates this proposed pore formation in two steps: [ 23 ]
It is proposed that as the applied electrical field increases, the greater is the perturbation of the phospholipid head groups, which in turn increases the number of water filled pores. [ 24 ] This entire process can occur within a few nanoseconds. [ 22 ] Average sizes of nanopores are likely cell-type specific. In swine livers, they average around 340-360 nm, as found using SEM . [ 23 ]
A secondary described mode of cell death was described to be from a breakdown of the membrane due to transmembrane transfer of electrolytes and adenosine triphosphate. [ 3 ] Other effects like heat [ 25 ] or electrolysis [ 26 ] [ 27 ] were also shown to play a role in the currently clinically applied IRE pulse protocols.
A number of electrodes, in the form of long needles, are placed around the target volume. The point of penetration for the electrodes is chosen according to anatomical conditions. Imaging is essential to the placement and can be achieved by ultrasound, magnetic resonance imaging or tomography. The needles are then connected to the IRE-generator, which then proceeds to sequentially build up a potential difference between two electrodes. The geometry of the IRE-treatment field is calculated in real time and can be influenced by the user. Depending on the treatment-field and number of electrodes used, the ablation takes between 1 and 10 minutes. In general muscle relaxants are administered, since even under general anesthetics, strong muscle contractions are induced by excitation of the motor end-plate. [ citation needed ]
Typical parameters (1st generation IRE system): [ citation needed ]
The shortly pulsed, strong electrical fields are induced through thin, sterile, disposable electrodes. The potential differences are calculated and applied by a computer system between these electrodes in accordance to a previously planned treatment field. [ 39 ]
One specific device for the IRE procedure is the NanoKnife system manufactured by AngioDynamics, which received FDA 510k clearance on October 24, 2011. [ 40 ] The NanoKnife system has also received an Investigational Device Exemption (IDE) from the FDA that allows AngioDynamics to conduct clinical trials using this device. [ 40 ] The Nanoknife system transmits a low-energy direct current from a generator to electrode probes placed in the target tissues for the surgical ablation of soft tissue. In 2011, AngioDynamics received an FDA warning letter for promoting the device for indications for which it had not received approval. [ 41 ]
In 2013, the UK National Institute for Health and Clinical Excellence issued a guidance that the safety and efficacy of the use of irreversible electroporation of the treatment of various types of cancer has not yet been established. [ 42 ]
Newer generations of Electroporation-based ablation systems are being developed specifically to address the shortcomings of the first generation of IRE but, as of June 2020, none of the technologies are available as a medical device. [ 27 ] [ 43 ] [ 44 ]
Potential organ systems, where IRE might have a significant impact due to its properties include the pancreas, liver, prostate and the kidneys, which were the main focus of the studies listed in Table 1-3 (state: June 2020).
None of the potential organ systems, which may be treated for various conditions and tumors, are covered by randomized multicenter trials or long-term follow-ups (state. June 2020).
2016 [ 47 ]
3.0 cm
laparoscopic
(n = 20)
2013 [ 48 ]
CRLM (n = 20),
Other (n = 10);
2.5 cm
(n = 28), open
(n = 14), laparoscopic
(n = 2)
2017 [ 49 ]
CRLM (n = 23),
other (n = 7); 2.4 cm
(n = 30)
(at 6 months)
2014 [ 50 ]
2.7 cm
(n = 28)
2012 [ 51 ]
CRLM (n = 21),
other (n = 5);
1.0 cm
(n = 6), open
(n = 22)
2014 [ 52 ]
CRLM (n = 20),
CCC (n = 5);
2.7 cm
(n = 67)
2015 [ 53 ]
CRLM (n = 16),
CCC (n = 6),
other (n = 4); 1.7 cm
(n = 25)
2016 [ 54 ]
CRLM (n = 22),
CCC (n = 5),
other (n = 5); 2.4 cm
(n = 34)
2017 [ 55 ]
CRLM (n = 16),
CCC (n = 6), other
(n = 4); 2.3 cm
(n = 71)
2013 [ 56 ]
CRLM (n = 23),
CCC (n = 2),
other (n = 22);
3.8 cm
(NS) open
(NS)
2014 [ 57 ]
2.4 cm
2011 [ 58 ]
CRLM (n = 15), other
(n = 31); 2.5 cm
(n = 25)
Hepatic IRE appears to be safe, even when performed near vessels and bile ducts [ 59 ] [ 60 ] with an overall complication rate of 16%, with most complications being needle related (pneumothorax and hemorrhage).The COLDFIRE-2 trial with 50 patients showed 76% local tumor progression-free survival after 1 year. [ 61 ] Whilst there are no studies comparing IRE to other ablative therapies yet, thermal ablations have shown a higher efficacy in that matter with around 96% progression free survival. Therefor Bart et al. [ 36 ] concluded that IRE should currently only be performed for only truly unresectable and non-ablatable tumors.
Patients
and Median
Largest Tumor Diameter
Follow-up
(mo)
Overall
Survival (mo)
Recurrence
(%)
Downstaging
Caused by IRE
2017 [ 62 ]
2019 [ 63 ]
(88% after chemotherapy or radiation
therapy)
(n = 32), open (n = 1)
10.7 (IRE)
2016 [ 64 ]
2016 [ 65 ]
percutaneous (n = 2)
2018 [ 66 ]
chemotherapy)
2016 [ 67 ]
chemotherapy)
7.0 (IRE)
2019 [ 68 ]
chemotherapy)
2015 [ 69 ]
chemo- or radiation
therapy)
18 (IRE)
et al., 2016 [ 70 ]
(after chemo- or radiation therapy)
14.2 (IRE)
2015 [ 71 ]
6.4 (IRE)
2019 [ 72 ]
and local recurrence (n = 10), 4.0 cm (68% after chemotherapy)
9.6 (IRE)
2017 [ 73 ]
(52% after chemotherapy)
11.0 (IRE)
2018 [ 74 ]
percutaneous, NS
2017 [ 75 ]
2016 [ 76 ]
2017 [ 77 ]
Animal studies have shown the safety and efficacy of IRE on pancreatic tissue. [ 78 ] The overall survival rates in studies on the use of IRE for pancreatic cancer provide an encouraging nonvariable endpoint and show an additive beneficial effect of IRE compared with standard-of care chemotherapeutic treatment with FOLFIRINOX (a combination of 5-fluorouracil, leucovorin, irinotecan, and oxaliplatin) (median OS, 12–14months). [ 79 ] [ 80 ] However, IRE appears to be more effective in conjunction with systemic therapy and is not suggested as first-line treatment. [ 68 ] Despite that IRE makes adjuvant tumor mass reduction therapy for LAPC possible, IRE remains, in its current state, a high risk procedure requiring additional safety data before it can be used widely. [ 81 ]
Patients
Concurrent Treatment
(% of patients)
(no. of patients)
(2010) [ 82 ]
3+4: n = 6
4+4: n = 3
urinary incontinence 0% erectile dysfunction 0%
out-of-field occurrence, n = 1
(2016) [ 83 ]
4+3: n = 3
4+4: n = 2
4 weeks after IRE
complete fibrosis or necrosis of ablation zone
(2018) [ 84 ]
3+4: n = 38
4+3: n = 16
Grade 2: 11%
Grade 3–5: 0%
urinary incontinence 0%;
erectile dysfunction 23%
out-of-field recurrence, n = 4
(2019) [ 85 ]
3+4/4+3:
n = 225
4+4: n = 68
5+3/3+5: n = 3
>4+4 = 42
prostatectomy (n = 21),
radiation therapy (n = 28),
TURP (n = 17),
HIFU (n = 8)
ADT (n = 29)
urinary incontinence 0%;
erectile dysfunction 3%
local recurrence, n = 20;
out-of-field recurrence, n = 27
(2014) [ 86 ]
3+4: n = 19
4+3: n = 5
4+4: n = 1
incontinence 0%;
erectile dysfunction 5%
only one histologic verification. Out-of-field
recurrence, NS
(2016) [ 87 ]
3+4: n = 15
4+3: n = 8
4+4: n = 0
Grade 2: 29%
Grade 3–5: 0%
incontinence 0%;
erectile dysfunction, unknown
out-of-fieldrecurrence, n = 5 (with histologic verification)
3+4: n = 37
4+3: n = 6
4+4: n = 2
Grade 2: 9
Grade 3–5: 0%
erectile dysfunction 6%
out-of-field recurrence, NS
Focal ablation using IRE for PCa in the distal apex appears safe and feasible.
The concept of treating prostate cancer with IRE was first proposed by Gary Onik and Boris Rubinsky in 2007. [ 89 ] Prostate carcinomas are frequently located near sensitive structures which might be permanently damaged by thermal treatments or radiation therapy. The applicability of surgical methods is often limited by accessibility and precision. Surgery is also associated with a long healing time and high rate of side effects. [ 90 ] Using IRE, the urethra, bladder, rectum and neurovascular bundle and lower urinary sphincter can potentially be included in the treatment field without creating (permanent) damage. [ citation needed ]
IRE has been in use against prostate cancer since 2011, partly in form of clinical trials, compassionate care or individualized treatment approach. As for all other ablation technologies and also most conventional methods, no studies employed a randomized multi-center approach or targeted cancer-specific mortality as endpoint. Cancer-specific mortality or overall survival are notoriously hard to assess for prostate cancer, as the trials require more than a decade and usually several treatment types are performed during the years making treatment-specific survival advantages difficult to quantify. Therefore, the results of ablation-based treatments and focal treatments in general usually use local recurrences and functional outcome (quality of life) as endpoint. In that regard, the clinical results collected so far and listed in Table 3 shown encouraging results and uniformly state IRE as a safe and effective treatment (at least for focal ablation) but all warrant further studies. The largest cohort presented by Guenther et al. [ 85 ] with up to 6-year follow-up is limited as a heterogeneous retrospective analysis and no prospective clinical trial. Therefore, despite that several hospitals in Europe have been employing the method for many years with one private clinic even listing more than one thousand treatments as of June 2020, [ 91 ] IRE for prostate cancer is currently not recommended in treatment guidelines.
While nephron-sparing surgery is the gold standard treatment for small, malignant renal masses, ablative therapies are considered a viable option in patients who are poor surgical candidates. Radiofrequency ablation (RFA) and cryoablation have been used since the 1990s; however, in lesions larger than 3 cm, their efficacy is limited. The newer ablation modalities, such as IRE, microwave ablation (MWA), and high-intensity focused ultrasound, may help overcome the challenges in tumor size. [ 92 ]
The first human studies have proven the safety of IRE for the ablation of renal masses; however, the effectiveness of IRE through histopathological examination of an ablated renal tumor in humans is yet to be known. Wagstaff et al. have set out to investigate the safety and effectiveness of IRE ablation of renal masses and to evaluate the efficacy of ablation using MRI and contrast-enhanced ultrasound imaging. In accordance with the prospective protocol designed by the authors, the treated patients will subsequently undergo radical nephrectomy to assess IRE ablation success. [ 93 ]
Later phase 2 prospective trials showed good results in terms of safety and feasibility [ 94 ] [ 95 ] for small renal masses but the cohort was limited in numbers (7 and 10 patients respectively), hence efficacy is not yet sufficiently determined. IRE appears safe for small renal masses up to 4 cm. However, the consensus is that current evidence is still inadequate in quality and quantity. [ 36 ]
In a prospective, single-arm, multi-center, phase II clinical trial, the safety and efficacy of IRE on lung cancers were evaluated. The trial included patients with primary and secondary lung malignancies and preserved lung function. The expected effectiveness was not met at interim analysis and the trial was stopped prematurely. Complications included pneumothoraces (11 of 23 patients), alveolar hemorrhage not resulting in significant hemoptysis, and needle tract seeding was found in 3 cases (13%). Disease progression was seen in 14 of 23 patients (61%). Stable disease was found in 1 (4%), partial remission in 1 (4%) and complete remission in 7 (30%) patients. The authors concluded that IRE is not effective for the treatment of lung malignancies. [ 96 ] Similarly poor treatment outcomes have been observed in other studies. [ 97 ] [ 98 ]
A major obstacle of IRE in the lung is the difficulty in positioning the electrodes; placing the probes in parallel alignment is made challenging by the interposition of ribs. Additionally, the planned and actual ablation zones in the lung are dramatically different due to the differences in conductivity between tumor, lung parenchyma, and air. [ 99 ]
Maor et el have demonstrated the safety and efficiency of IRE as an ablation modality for smooth muscle cells in the walls of large vessels in rat model. [ 100 ] Therefore, IRE has been suggested as preventive treatment for coronary artery re-stenosis after percutaneous coronary intervention . [ citation needed ]
Numerous studies in animals have demonstrated the safety and efficiency of IRE as a non-thermal ablation modality for pulmonary veins in the context of atrial fibrillation treatment. [ 101 ] In 2023, irreversible electroporation is being widely used and evaluated in humans, as cardiac ablation therapy to kill very small areas of heart muscle. This is done to treat irregularities of heart rhythm . A cardiac catheter delivers trains of high-voltage ultra-rapid electrical pulses that form irreversible pores in cell membranes, resulting in cell death. It is thought to allow better selectivity than the previous techniques, which used heat or cold to kill larger volumes of muscle. [ 102 ]
IRE has also been investigated in ex-vivo human eye models for treatment of uveal melanoma [ 103 ] and in thyroid cancer. [ 104 ]
Successful ablations in animal tumor models have been conducted for lung, [ 105 ] [ 106 ] brain, [ 107 ] [ 108 ] heart, [ 109 ] skin, [ 110 ] [ 111 ] bone, [ 112 ] [ 113 ] head and neck cancer, [ 114 ] and blood vessels. [ 115 ] | https://en.wikipedia.org/wiki/Irreversible_electroporation |
In thermodynamics , an irreversible process is a process that cannot be undone. All complex natural processes are irreversible, [ 1 ] [ 2 ] [ 3 ] [ 4 ] although a phase transition at the coexistence temperature (e.g. melting of ice cubes in water) is well approximated as reversible.
A change in the thermodynamic state of a system and all of its surroundings cannot be precisely restored to its initial state by infinitesimal changes in some property of the system without expenditure of energy . A system that undergoes an irreversible process may still be capable of returning to its initial state. Because entropy is a state function , the change in entropy of the system is the same whether the process is reversible or irreversible. However, the impossibility occurs in restoring the environment to its own initial conditions. An irreversible process increases the total entropy of the system and its surroundings. The second law of thermodynamics can be used to determine whether a hypothetical process is reversible or not.
Intuitively, a process is reversible if there is no dissipation . For example, Joule expansion is irreversible because initially the system is not uniform. Initially, there is part of the system with gas in it, and part of the system with no gas. For dissipation to occur, there needs to be such a non uniformity. This is just the same as if in a system one section of the gas was hot, and the other cold. Then dissipation would occur; the temperature distribution would become uniform with no work being done, and this would be irreversible because you couldn't add or remove heat or change the volume to return the system to its initial state. Thus, if the system is always uniform, then the process is reversible, meaning that you can return the system to its original state by either adding or removing heat, doing work on the system, or letting the system do work. As another example, to approximate the expansion in an internal combustion engine as reversible, we would be assuming that the temperature and pressure uniformly change throughout the volume after the spark. Obviously, this is not true and there is a flame front and sometimes even engine knocking . One of the reasons that Diesel engines are able to attain higher efficiency is that the combustion is much more uniform, so less energy is lost to dissipation and the process is closer to reversible. [ citation needed ]
The phenomenon of irreversibility results from the fact that if a thermodynamic system , which is any system of sufficient complexity, of interacting molecules is brought from one thermodynamic state to another, the configuration or arrangement of the atoms and molecules in the system will change in a way that is not easily predictable. [ 5 ] [ 6 ] Some "transformation energy" will be used as the molecules of the "working body" do work on each other when they change from one state to another. During this transformation, there will be some heat energy loss or dissipation due to intermolecular friction and collisions. This energy will not be recoverable if the process is reversed.
Many biological processes that were once thought to be reversible have been found to actually be a pairing of two irreversible processes. Whereas a single enzyme was once believed to catalyze both the forward and reverse chemical changes, research has found that two separate enzymes of similar structure are typically needed to perform what results in a pair of thermodynamically irreversible processes. [ 7 ]
Thermodynamics defines the statistical behaviour of large numbers of entities, whose exact behavior is given by more specific laws. While the fundamental theoretical laws of physics are all time-reversible, [ 8 ] experimentally the probability of real reversibility is low and the former state of system and surroundings is recovered only to certain extent (see: uncertainty principle ). The reversibility of thermodynamics must be statistical in nature; that is, it must be merely highly unlikely, but not impossible, that a system will lower in entropy. In other words, time reversibility is fulfilled if the process happens the same way if time were to flow in reverse or the order of states in the process is reversed (the last state becomes the first and vice versa).
The German physicist Rudolf Clausius , in the 1850s, was the first to mathematically quantify the discovery of irreversibility in nature through his introduction of the concept of entropy . In his 1854 memoir "On a Modified Form of the Second Fundamental Theorem in the Mechanical Theory of Heat," Clausius states:
It may, moreover, happen that instead of a descending transmission of heat accompanying, in the one and the same process, the ascending transmission, another permanent change may occur which has the peculiarity of not being reversible without either becoming replaced by a new permanent change of a similar kind, or producing a descending transmission of heat.
Simply, Clausius states that it is impossible for a system to transfer heat from a cooler body to a hotter body. For example, a cup of hot coffee placed in an area of room temperature (~72 °F) will transfer heat to its surroundings and thereby cool down with the temperature of the room slightly increasing (to ~72.3 °F ). However, that same initial cup of coffee will never absorb heat from its surroundings, causing it to grow even hotter, with the temperature of the room decreasing (to ~71.7 °F ). Therefore, the process of the coffee cooling down is irreversible unless extra energy is added to the system.
However, a paradox arose when attempting to reconcile microanalysis of a system with observations of its macrostate. Many processes are mathematically reversible in their microstate when analyzed using classical Newtonian mechanics. This paradox clearly taints microscopic explanations of macroscopic tendency towards equilibrium, such as James Clerk Maxwell 's 1860 argument that molecular collisions entail an equalization of temperatures of mixed gases. [ 9 ] From 1872 to 1875, Ludwig Boltzmann reinforced the statistical explanation of this paradox in the form of Boltzmann's entropy formula , stating that an increase of the number of possible microstates a system might be in, will increase the entropy of the system, making it less likely that the system will return to an earlier state. His formulas quantified the analysis done by William Thomson, 1st Baron Kelvin , who had argued that: [ 10 ] [ 11 ]
The equations of motion in abstract dynamics are perfectly reversible; any solution of these equations remains valid when the time variable t is replaced by –t. On the other hand, physical processes are irreversible: for example, the friction of solids, conduction of heat, and diffusion. Nevertheless, the principle of dissipation of energy is compatible with a molecular theory in which each particle is subject to the laws of abstract dynamics.
Another explanation of irreversible systems was presented by French mathematician Henri Poincaré . In 1890, he published his first explanation of nonlinear dynamics, also called chaos theory . Applying chaos theory to the second law of thermodynamics , the paradox of irreversibility can be explained in the errors associated with scaling from microstates to macrostates and the degrees of freedom used when making experimental observations. Sensitivity to initial conditions relating to the system and its environment at the microstate compounds into an exhibition of irreversible characteristics within the observable, physical realm. [ 12 ]
In the physical realm, many irreversible processes are present to which the inability to achieve 100% efficiency in energy transfer can be attributed. The following is a list of spontaneous events which contribute to the irreversibility of processes. [ 13 ]
A Joule expansion is an example of classical thermodynamics, as it is easy to work out the resulting increase in entropy. It occurs where a volume of gas is kept in one side of a thermally isolated container (via a small partition), with the other side of the container being evacuated; the partition between the two parts of the container is then opened, and the gas fills the whole container. The internal energy of the gas remains the same, while the volume increases. The original state cannot be recovered by simply compressing the gas to its original volume, since the internal energy will be increased by this compression. The original state can only be recovered by then cooling the re-compressed system, and thereby irreversibly heating the environment. The diagram to the right applies only if the first expansion is "free" (Joule expansion), i.e. there can be no atmospheric pressure outside the cylinder and no weight lifted.
The difference between reversible and irreversible events has particular explanatory value in complex systems (such as living organisms, or ecosystems ). According to the biologists Humberto Maturana and Francisco Varela , living organisms are characterized by autopoiesis , which enables their continued existence. More primitive forms of self-organizing systems have been described by the physicist and chemist Ilya Prigogine . In the context of complex systems, events which lead to the end of certain self-organising processes, like death , extinction of a species or the collapse of a meteorological system can be considered as irreversible. Even if a clone with the same organizational principle (e.g. identical DNA-structure) could be developed, this would not mean that the former distinct system comes back into being. Events to which the self-organizing capacities of organisms, species or other complex systems can adapt, like minor injuries or changes in the physical environment are reversible. However, adaptation depends on import of negentropy into the organism, thereby increasing irreversible processes in its environment. [ 17 ] Ecological principles, like those of sustainability and the precautionary principle can be defined with reference to the concept of reversibility. [ 18 ] [ 19 ] [ 20 ] [ 21 ] [ 22 ] [ 23 ] [ 5 ] [ 24 ] [ 25 ] | https://en.wikipedia.org/wiki/Irreversible_process |
Irritation , in biology and physiology , is a state of inflammation or painful reaction to allergy or cell-lining damage. A stimulus or agent which induces the state of irritation is an irritant . Irritants are typically thought of as chemical agents (for example phenol and capsaicin ) but mechanical, thermal (heat), and radiative stimuli (for example ultraviolet light or ionising radiations ) can also be irritants. Irritation also has non-clinical usages referring to bothersome physical or psychological pain or discomfort.
Irritation can also be induced by some allergic response due to exposure of some allergens for example contact dermatitis, irritation of mucosal membranes and pruritus. Mucosal membrane is the most common site of irritation because it contains secretory glands that release mucus which attracts the allergens due to its sticky nature.
Chronic irritation is a medical term signifying that afflictive health conditions have been present for a while. There are many disorders that can cause chronic irritation, the majority involve the skin, vagina, eyes and lungs.
In higher organisms, an allergic response may be the cause of irritation. An allergen is defined distinctly from an irritant, however, as allergy requires a specific interaction with the immune system and is thus dependent on the (possibly unique) sensitivity of the organism involved while an irritant, classically, acts in a non-specific manner.
It is a form of stress , but conversely, if one is stressed by unrelated matters, mild imperfections can cause more irritation than usual: one is irritable ; see also sensitivity (human) .
In more basic organisms, the status of pain is the perception of the being stimulated, which is not observable although it may be shared (see Gate control theory ).
It is not proven that oysters can feel pain, but it is known that they react to irritants. When an irritating object becomes trapped within an oyster's shell, it deposits layers of calcium carbonate (CaCO 3 ), slowly increasing in size and producing a pearl . This is purely a defense mechanism, to trap a potentially threatening irritant such as a parasite inside its shell, or an attack from outside, injuring the mantle tissue. The oyster creates a pearl sac to seal off the irritation.
It has also been observed that an amoeba avoids being prodded with a pin, but there is not enough evidence to suggest how much it feels this. Irritation is apparently the only universal sense shared by even single-celled creatures.
It is postulated that most such beings also feel pain, but this is a projection – empathy . Some philosophers, notably René Descartes , denied it entirely, even for such higher mammals as dogs or primates like monkeys ; Descartes considered intelligence a pre-requisite for the feeling of pain. [ citation needed ]
Modern office work with use of office equipment has raised concerns about possible adverse health effects. [ 1 ] Since the 1970s, reports have linked mucosal, skin, and general symptoms to work with self-copying paper. Emission of various particulate and volatile substances has been suggested as specific causes. These symptoms have been related to Sick Building Syndrome , which involves symptoms such as irritation to the eyes, skin, and upper airways, headache and fatigue. [ 2 ]
The eye is also a source of chronic irritation. Disorders like Sjögren's syndrome , where one does not make tears, can cause a dry eye sensation which feels very unpleasant. The condition is difficult to treat and is lifelong. Besides artificial tears, there is a drug called Restasis which may help. [ 3 ]
Blepharitis is dryness and itching on the upper eyelids. This condition is often seen in young people and can lead to reddish dry eye and scaly eyebrows. To relieve the itching sensation, one may need to apply warm compresses and use topical corticosteroid creams.
Eczema is another cause of chronic irritation and affects millions of individuals. Eczema simply means a dry skin which is itchy. The condition usually starts at an early age and continues throughout life. The major complaint of people with eczema is an itchy dry skin. Sometimes, the itching will be associated with a skin rash . The affected areas are always dry, scaly, reddish and may ooze sometimes. Eczema cannot be cured, but its symptoms can be controlled. One should use moisturizers, use cold compresses and avoid frequent hot showers. There are over the counter corticosteroids creams which can be applied. Sometimes, an anti histamine has to be used to prevent the chronic itching sensations. There are also many individuals who have allergies to a whole host of substances like nuts, hair, dander , plants and fabrics. For these individuals, even the minimal exposure can lead to a full blown skin rash, itching, wheezing and coughing. Unfortunately, other than avoidance, there is no other cure. There are allergy shots which can help desensitize against an allergen but often the results are poor and the treatments are expensive. Most of these individuals with chronic irritation from allergens usually need to take anti histamines or use a bronchodilator to relieve symptoms. [ 4 ]
Another common irritation disorder in females is intertrigo . This disorder is associated with chronic irritation under folds of skin. This is typically seen under large breasts, groins and folds of the abdomen in obese individuals. Candida quickly grows in warm moist areas of these folds and presents as a chronic itch. Over time, the skin becomes red and often oozes. Perspiration is also a chronic type of irritation which can be very annoying. Besides being socially unacceptable, sweat stain the clothes and can present with a foul odor. In some individuals, the warm moist areas often become easily infected. The best way to treat excess sweating is good hygiene, frequent change of clothes and use of deodorants/antiperspirants.
One of the most common areas of the body associated with irritation is the vagina . Many women complain of an itch, dryness, or discharge in the perineum at some point in their lives. There are several causes of vaginal irritation including fungal vaginitis (like candida) or trichomoniasis . Often, herpes simplex infection of the mouth or genitalia can be recurrent and prove to be extremely irritating.
Sometimes, the irritation can be of the chronic type and it can be so intense that it also causes painful intercourse. Aside from infections, chronic irritation of the vagina may be related to the use of contraceptives and condoms made from latex. The majority of contraceptives are made of synthetic chemicals which can induce allergies, rash and itching. Sometimes the lubricant used for intercourse may cause irritation.
Another cause of irritation in women is post menopausal vaginitis. The decline in the female sex hormones leads to development of dryness and itching in the vagina. This is often accompanied by painful sexual intercourse . Cracks and tears often develop on outer aspects of the labia which becomes red from chronic scratching. Post menopausal vaginitis can be treated with short term use of vaginal estrogen pessary and use of a moisturizer .
Individuals who smoke or are exposed to smog or other airborne pollutants can develop a condition known as COPD . In this disorder, there is constant irritation of the breathing tubes (trachea) and the small airways. The constant irritation results in excess production of mucus which makes breathing difficult. Frequently, these individuals wake up in the morning with copious amounts of foul smelling mucus and a cough which lasts all day. Wheeze and heavy phlegm are common findings. COPD is a lifelong disorder and there is no cure. Eventually most people develop recurrent pneumonia , lack any type of endurance, and are unable to work productively. One of the ways to avoid chronic bronchitis is to stop or not smoke. [ 5 ]
Gastritis or stomach upset is a common irritating disorder affecting millions of people. Gastritis is basically inflammation of the stomach wall lining and has many causes. Smoking, excess alcohol consumption and the use of non-steroidal anti-inflammatory drugs (NSAIDs), such as ibuprofen , account for the majority of causes of gastritis. In some cases, gastritis may develop after surgery, a major burn, infection or emotional stress. The most common symptoms of gastritis include sharp abdominal pain which may radiate to the back. This may be associated with nausea , vomiting , abdominal bloating and a lack of appetite. When the condition is severe it may even result in loss of blood on the stools. The condition often comes and goes for years because most people continue to drink alcohol or use NSAIDs . Treatment includes the use of antacids or acid neutralizing drugs, antibiotics, and avoiding spicy food and alcohol. [ 6 ] | https://en.wikipedia.org/wiki/Irritation |
Irssi ( Finnish pronunciation: [ˈirsːi] ( listen ) ) is an Internet Relay Chat (IRC) client program for Linux , FreeBSD , macOS and Microsoft Windows . It was originally written by Timo Sirainen , and released under the terms of the GNU GPL-2.0-or-later in January 1999. [ 1 ]
The program has a text-based user interface was written from scratch using C . It may be customized by editing its config files or by installing plugins and Perl scripts . Though initially developed for Unix-like operating systems , it has been successfully ported to both Windows and macOS .
Irssi is written in the C programming language and in normal operation uses a text-mode user interface. [ 5 ]
According to the developers, Irssi was written from scratch, not based on ircII (like BitchX and epic). [ 6 ] This freed the developers from having to deal with the constraints of an existing codebase, allowing them to maintain tighter control over issues such as security and customization. [ 6 ] Numerous Perl scripts have been made available for Irssi to customise how it looks and operates. [ 7 ] Plugins are available which add encryption [ 8 ] [ 9 ] and protocols such as ICQ and XMPP . [ 10 ] [ 11 ]
Irssi may be configured by using its user interface or by manually editing its configuration files , which use a syntax resembling Perl data structures. [ 5 ]
Irssi was written primarily to run on Unix-like operating systems, and binaries and packages are available for Gentoo Linux , Debian , Slackware , SUSE ( openSUSE ), Frugalware , Fedora , FreeBSD , OpenBSD , [ 12 ] NetBSD , DragonFly BSD , Solaris , [ 13 ] Arch Linux , [ 14 ] Ubuntu , [ 13 ] NixOS , [ 15 ] and others.
Irssi builds and runs on Microsoft Windows under Cygwin , and in 2006, an official Windows standalone build was released. [ 16 ]
For the Unix-based macOS , text mode ports are available from the Homebrew , MacPorts , and Fink package managers, and two graphical clients have been written based on Irssi, IrssiX, and MacIrssi. [ 13 ] The Cocoa client Colloquy was previously based on Irssi, [ 17 ] but it now uses its own IRC core implementation. [ 18 ] | https://en.wikipedia.org/wiki/Irssi |
IruSoft ( Arabic : آيروسوفت) is an insurance regulatory platform designated for licensing, supervision and inspection of the insurance sector within a country. The platform introduced unique supervision-technology (suptech) , insurance-technology (insurtech) and regulatory-technology (regtech) automated modules by which a regulator requires less resources to ensure fairness, transparency and competition and to prevent conflicts of interest in the sector. IruSoft was founded by Abdullah Al-Salloum and owned by the Insurance Regulatory Unit in Kuwait. [ 1 ] [ 2 ] [ 3 ] [ 4 ]
The Insurance Regulatory Unit optimized processing insurance-sector 's customer complaints by issuing Resolution No. (1) of 2022 that introduced IruSoft's complaints public module; an automated resolution center, by which the process of receiving submitted complaints, passing them on to the platforms of licensed insurance companies, tracking matter-related discussions and updates and getting them escalated if unresolved to be discussed by a committee assigned by the unit is integrally automated and analyzed for better key performance indicators . [ 5 ] [ 6 ] [ 7 ] [ 8 ]
This software article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/IruSoft |
Irving Kaplansky (March 22, 1917 – June 25, 2006) was a mathematician , college professor , author , and amateur musician . [ 2 ]
Kaplansky or "Kap" as his friends and colleagues called him was born in Toronto , Ontario , Canada, to Polish-Jewish immigrants. [ 3 ] [ 4 ] His father worked as a tailor, and his mother ran a grocery and, eventually, a chain of bakeries. [ 5 ] [ 6 ] [ 7 ] He went to Harbord Collegiate Institute receiving the Prince of Wales Scholarship as a teenager. He attended the University of Toronto as an undergraduate and finished first in his class for three consecutive years. [ 8 ] In his senior year, he competed in the first William Lowell Putnam Mathematical Competition , becoming one of the first five recipients of the Putnam Fellowship, which paid for graduate studies at Harvard University . [ 5 ] Administered by the Mathematical Association of America , the competition is widely considered to be the most difficult mathematics examination in the world and "its difficulty is such that the median score is often zero or one (out of 120) despite being attempted by students specializing in mathematics." [ 9 ]
After receiving his Ph.D. from Harvard in 1941 [ 1 ] as Saunders Mac Lane 's first student, he remained at Harvard as a Benjamin Peirce Instructor, and in 1944 moved with Mac Lane to Columbia University for one year to collaborate on work surrounding World War II [ 10 ] working on "miscellaneous studies in mathematics applied to warfare analysis with emphasis upon aerial gunnery, studies of fire control equipment, and rocketry and toss bombing" [ 11 ] with the Applied Mathematics Panel . [ 12 ] [ 13 ] He was a member of the Institute for Advanced Study and attended the 1946 Princeton University Bicentennial. [ 14 ]
He was professor of mathematics at the University of Chicago from 1945 to 1984, and Chair of the department from 1962 to 1967. In 1968, Kaplansky was presented an honorary doctoral degree from Queen's University with the university noting "we honour as a Canadian whose clarity of lectures, elegance of writing, and profundity of research have won him widespread acclaim as the greatest mathematician this country has so far produced." [ 15 ] From 1967 to 1969, Kaplansky wrote the mathematics section of Encyclopædia Britannica . [ 16 ] [ 17 ] [ 18 ] Kaplansky was the Director of the Mathematical Sciences Research Institute from 1984 to 1992, and the President of the American Mathematical Society from 1985 to 1986. [ 19 ]
Kaplansky was also an accomplished amateur musician. He had perfect pitch , studied piano until the age of 15, earned money in high school as a dance band musician, taught Tom Lehrer , [ 20 ] and played in Harvard's jazz band in graduate school. He also had a regular program on Harvard's student radio station. After moving to the University of Chicago , he stopped playing for two decades, but then returned to music as an accompanist for student-run Gilbert and Sullivan productions and as a calliope player in football game parades. [ 5 ] He often composed music based on mathematical themes. One of those compositions, A Song About Pi , is a melody based on assigning notes to the first 14 decimal places of pi , and has occasionally been performed by his daughter, singer-songwriter Lucy Kaplansky . [ 21 ]
Kaplansky made major contributions to group theory , ring theory , the theory of operator algebras and field theory and created the Kaplansky density theorem , Kaplansky's game and Kaplansky conjecture . He published more than 150 articles and 11 mathematical books. [ 2 ]
Kaplansky was the doctoral supervisor of 55 students including notable mathematicians Hyman Bass , Susanna S. Epp , Günter Lumer , Eben Matlis , Donald Ornstein , Ed Posner , Alex F. T. W. Rosenberg , Judith D. Sally , and Harold Widom . He has over 950 academic descendants , including many through his academic grandchildren David J. Foulis (who studied with Kaplansky at the University of Chicago before completing his doctorate under the supervision of Kaplansky's student Fred Wright, Jr.) and Carl Pearcy (the student of H. Arlen Brown, who had been jointly supervised by Kaplansky and Paul Halmos ). [ 1 ]
Kaplansky was a member of the National Academy of Sciences and the American Academy of Arts and Sciences , Director of the Mathematical Sciences Research Institute , and President of the American Mathematical Society . He was the plenary speaker at the British Mathematical Colloquium in 1966. Won the William Lowell Putnam Mathematical Competition , the Guggenheim Fellowship , the Jeffery–Williams Prize , and the Leroy P. Steele Prize . [ 13 ] [ 15 ] | https://en.wikipedia.org/wiki/Irving_Kaplansky |
The Irving Langmuir Prize in Chemical Physics is awarded annually, in even years by the American Chemical Society and in odd years by the American Physical Society . The award is meant to recognize and encourage outstanding interdisciplinary research in chemistry and physics , in the spirit of Irving Langmuir . A nominee must have made an outstanding contribution to chemical physics or physical chemistry within the 10 years preceding the year in which the award is made. The award will be granted without restriction, except that the recipient must be a resident of the United States .
The award was established in 1931 by Dr. A.C. Langmuir, brother of Nobel Prize -winning chemist Irving Langmuir , to recognize the best young chemist in the United States. A $10,000 prize was to be awarded annually by the American Chemical Society. The first recipient was Linus Pauling . [ 1 ] In 1964, the General Electric Foundation took over the financial backing of the prize, which was renamed the Irving Langmuir Award and the modern selection process was created. In 2006 the GE Global Research took over sponsorship of the award, and since 2009 the award has been co-sponsored between GE Global Research and the ACS Division of Physical Chemistry. [ 2 ]
Source: American Physical Society and American Chemical Society | https://en.wikipedia.org/wiki/Irving_Langmuir_Award |
The Irving–Williams series refers to the relative stabilities of complexes formed by transition metals . In 1953 Harry Irving and Robert Williams observed that the stability of complexes formed by divalent first-row transition metal ions generally increase across the period to a maximum stability at copper: Mn(II) < Fe(II) < Co(II) < Ni(II) < Cu(II) > Zn(II). [ 1 ]
Specifically, the Irving–Williams series refers to the exchange of aqua (H 2 O) ligands for any other ligand (L) within a metal complex. In other words, the Irving–Williams series is almost exclusively independent of the nature of the incoming ligand, L.
The main application of the series is to empirically suggest an order of stability within first row transition metal complexes (where the transition metal is in oxidation state II).
Another application of the Irving–Williams series is to use it as a correlation "ruler" in comparing the first stability constant for replacement of water in the aqueous ion by a ligand. [ 2 ]
Three explanations are frequently used to explain the series:
However, none of the above explanations can satisfactorily explain the success of the Irving–Williams series in predicting the relative stabilities of transition metal complexes. A recent study of metal-thiolate complexes indicates that an interplay between covalent and electrostatic contributions in metal–ligand binding energies might result in the Irving–Williams series. [ 3 ]
Some actual CFSE values for octahedral complexes of first-row transition metals (∆ oct ) are 0.4Δ (4 Dq) for iron, 0.8Δ (8 Dq) for cobalt and 1.2Δ (12 Dq) for nickel. When the stability constants are quantitatively adjusted for these values they follow the trend that is predicted, in the absence of crystal field effects, between manganese and zinc. [ clarification needed ] This was an important factor contributing to the acceptance of crystal field theory, the first theory to successfully account for the thermodynamic, spectroscopic and magnetic properties of complexes of the transition metal ions and precursor to ligand field theory . [ 4 ]
Natural proteins' affinities for metal binding also follow the Irving–Williams series. However, in a recent study published in the journal Nature , researchers have reported a protein-design approach to overcome the Irving-Williams series restriction, allowing proteins to bind other metals over copper ions vice versa to Irving–Williams series. [ 5 ] [ 6 ] | https://en.wikipedia.org/wiki/Irving–Williams_series |
Irwin Douglas "Tack" Kuntz is an important figure in the field of computer-aided drug design and molecular modeling . He is a pioneer in the development and conception of the area of study known as molecular docking . One of the first docking programs DOCK was developed in his group in 1982. [ 3 ] [ 4 ]
Tack received his Bachelor of Arts degree in physical chemistry from Princeton University in 1961 [ citation needed ] and his PhD from the University of California, Berkeley in 1965 for spectroscopic studies of photosynthesis . [ 5 ]
He moved to the Department of Pharmaceutical Chemistry the University of California, San Francisco in the early 1970s. [ 6 ] He founded the Molecular Design Institute at UCSF in 1993. [ 7 ] He was awarded the UCSF medal in 2018. [ 8 ] | https://en.wikipedia.org/wiki/Irwin_"Tack"_Kuntz |
In the fields of toxicology and pathology , the Irwin screen is utilised to determine whether the subject(s) show adverse effects from a course of pharmaceutical treatment or environmental pollution . It is an observational methodology . [ 1 ]
Mice were first used systematically to determine a drug 's central nervous system side effects by S. Irwin in 1962 and then again in 1968. [ 1 ] Its use in the pharmaceutical industry has become ingrained since then, as below.
The National Academy of Sciences issued in 1975 a position paper on the "Principles for Evaluating Chemicals in the Environment." This paper influenced government and academic circles, and was adopted by e.g. Brimblecombe for his study of atmospheric arsenic levels. [ 2 ] The critical review in 1982 by Mitchell and Tilson, [ 3 ] caused the US EPA to develop guidelines for several behavioural tests including a test series based on the Irwin Screen, named the Functional Observational Battery (FOB) by Sette in 1989. [ 4 ] In 1998, the FOB was published in the late 1990s as EPA Human Health 870 Series Test Guidelines, [ 1 ] [ 5 ] [ 6 ] and in praxis the Irwin screen and the FOB "overlap and to some extent are interchangeable." [ 1 ]
The American batteries were harmonised with the OECD 's from the same era. [ 7 ] [ 8 ] [ 9 ] [ 10 ] Similar tests on food chemicals were recommended by the FDA in their Red Book . [ 11 ] Behavioural test batteries are now required for new drugs by the S7A group of the International Council for Harmonisation of Technical Requirements for Pharmaceuticals for Human Use (ICH). [ citation needed ]
The Irwin screen was as of 2010 in the pharmaceutical industry almost exclusively used with lab mice , whereas the FOB, or some modification thereof, was used with lab rats and other nonrodent species, such as rabbits , dogs , guinea pigs and nonhuman primates . [ 1 ]
A sample Irwin screen [ 12 ] includes overt behavior observations and autonomic observations:
Overt Behavior
Autonomic Observations | https://en.wikipedia.org/wiki/Irwin_screen |
Irène Joliot-Curie ( French: [iʁɛn ʒɔljo kyʁi] ⓘ ; née Curie ; 12 September 1897 – 17 March 1956) was a French chemist and physicist who received the 1935 Nobel Prize in Chemistry with her husband, Frédéric Joliot-Curie , for their discovery of induced radioactivity . They were the second married couple , after her parents, to win the Nobel Prize, adding to the Curie family legacy of five Nobel Prizes. This made the Curies the family with the most Nobel laureates to date. [ 1 ]
Her mother Marie Skłodowska-Curie and herself also form the only mother–daughter pair to have won Nobel Prizes [ 2 ] whilst Pierre and Irène Curie form the only father-daughter pair to have won Nobel Prizes by the same occasion, whilst there are six father-son pairs who have won Nobel Prizes by comparison. [ 3 ]
She was also one of the first three women to be a member of a French government, becoming undersecretary for Scientific Research under the Popular Front in 1936. [ 4 ] Both children of the Joliot-Curies, Hélène and Pierre , are also scientists. [ 5 ]
In 1945, she was one of the six commissioners of the new French Alternative Energies and Atomic Energy Commission (CEA) created by de Gaulle and the Provisional Government of the French Republic . She died in Paris on 17 March 1956 from an acute leukemia linked to her exposure to polonium and X-rays .
Irène was born in Paris, France, on 12 September 1897 and was the first of Marie and Pierre 's two daughters. Her sister was Ève , born in 1904. [ 6 ] They lost their father early on in 1906 due to a horse-drawn wagon incident and Marie was left to raise them. [ 6 ] Education was important to Marie and Irène's education began at a school near the Paris Observatory. [ 7 ] This school was chosen because it had a more challenging curriculum than the school nearby the Curie's home. [ 7 ] In 1906, it was obvious Irène was talented in mathematics and her mother chose to focus on that instead of public school. [ 7 ] Marie joined forces with a number of eminent French scholars, including the prominent French physicist Paul Langevin , to form " The Cooperative ", which included a private gathering of nine students that were children of the most distinguished academics in France. Each contributed to educating these children in their respective homes. [ 7 ] The curriculum of The Cooperative was varied and included not only the principles of science and scientific research but such diverse subjects as Chinese and sculpture and with great emphasis placed on self-expression and play. [ 8 ] Irène studied in this environment for about two years. [ 9 ]
Irène and her sister Ève were sent to Poland to spend the summer with their Aunt Bronia (Marie's sister) when Irène was thirteen. [ 6 ] Irène's education was so rigorous that she still had a German and trigonometry lesson every day of that break. [ 6 ] Irène re-entered a more orthodox learning environment by going back to high school at the Collège Sévigné in central Paris until 1914. She then went onto the Faculty of Science at the Sorbonne to complete her baccalaureate , until 1916 when her studies were interrupted by World War I . [ 9 ]
Irène took a nursing course during college to assist her mother, Marie Curie, in the field as her assistant. [ 10 ] She began her work as a nurse radiographer on the battlefield alongside her mother, but after a few months she was left to work alone at a radiological facility in Belgium. [ 6 ] She taught doctors how to locate shrapnel in bodies using radiology and taught herself how to repair the equipment. [ 6 ] She moved throughout facilities and battlegrounds including two bombsites, Furnes and Ypres , and Amiens . [ 6 ] She received a military medal for her assistance in X-ray facilities in France and Belgium. [ 7 ]
After the war, Irène returned to the Sorbonne in Paris to complete her second baccalaureate degree in mathematics and physics in 1918. [ 10 ] Irène then went on to work as her mother's assistant, teaching radiology at the Radium Institute , which had been built by her parents. [ 7 ] [ 11 ] Her doctoral thesis was concerned with the alpha decay of polonium , the element discovered by her parents (along with radium) and named after Marie's country of birth, Poland. Irène became a Doctor of Science in 1925. [ 7 ]
As she neared the end of her doctorate in 1924, Irène Curie was asked to teach the precision laboratory techniques required for radiochemical research to the young chemical engineer Frédéric Joliot , whom she would later wed. From 1928 Joliot-Curie and her husband Frédéric combined their research efforts on the study of atomic nuclei. [ 11 ] In 1932, Joliot-Curie and her husband Frédéric had full access to Marie's polonium. Experiments were done using gamma rays to identify the positron . [ 9 ] Though their experiments identified both the positron and the neutron , they failed to interpret the significance of the results and the discoveries were later claimed by Carl David Anderson and James Chadwick respectively. [ 11 ] These discoveries would have secured greatness indeed, as together with J. J. Thomson 's discovery of the electron in 1897, they finally replaced John Dalton 's model of atoms as solid spherical particles. [ citation needed ]
However, in 1933, Joliot-Curie and her husband were the first to calculate the accurate mass of the neutron. [ 11 ] The Joliot-Curies continued trying to get their name into the scientific community; in doing so they developed a new theory from an interesting experiment they conducted. During an experiment bombarding aluminium with alpha rays, they discovered that only protons were detected. Based on the undetectable electron and positron pair, they proposed that the protons changed into neutrons and positrons. [ 11 ] Later in October 1933, this new theory was presented to the Seventh Solvay Conference . The Solvay Conferences consisted of prominent scientists in the physics and chemistry community. [ 11 ] Irene and her husband presented their theory and results to their fellow scientists, but they received criticism of their finding from most of the 46 scientists attending. [ 11 ] However they were able to build on the controversial theory later on. [ citation needed ]
In 1934, the Joliot-Curies finally made the discovery that sealed their place in scientific history. Building on the work of Marie and Pierre Curie, who had isolated naturally occurring radioactive elements, the Joliot-Curies realised the alchemist's dream of turning one element into another: creating radioactive nitrogen from boron , radioactive isotopes of phosphorus from aluminium, and silicon from magnesium . Irradiating the natural stable isotope of aluminium with alpha particles (i.e. helium nuclei) resulted in an unstable isotope of phosphorus : 27 Al + 4 He → 30 P + 1 n. [ 12 ] [ 13 ] [ 14 ] This phosporus isotope is not found in nature and decays emitting a positron. This discovery is formally known as positron emission or beta decay , where a proton in the radioactive nucleus changes to a neutron and releases a positron and an electron neutrino. By then, the application of radioactive materials for use in medicine was growing and this discovery allowed radioactive materials to be created quickly, cheaply, and plentifully. The Nobel Prize for chemistry in 1935 brought with it fame and recognition from the scientific community and Joliot-Curie was awarded a professorship at the Faculty of Science.
The work that Irène's laboratory pioneered, research into radium nuclei, would also help another group of physicists within Germany. Otto Hahn and Fritz Strassman on 19 December 1938 bombarded uranium with neutrons, but misinterpreted their findings. Lise Meitner and Otto Frisch would theoretically correct Hahn and Strassmann's findings, and after replicating their experiment based on Hungarian physicist Leo Szilard's theory that he had confided to Meitner back in 1933, confirmed on 13 January 1939 that Hahn and Strassmann had indeed observed nuclear fission : the splitting of the nucleus itself, emitting vast amounts of energy. Lise Meitner's now-famous calculations actually disproved Irène's results and proved that nuclear fission was possible and replicable. [ 15 ]
In 1948, using work on nuclear fission, the Joliot-Curies along with other scientists created the first French nuclear reactor. [ 11 ] [ 9 ] The Joliot-Curies were a part of the organization in charge of the project, the Atomic Energy Commission, Commissariat à l'énergie atomique (CEA). Irène was the commissioner of the CEA and Irène's husband, Frédéric, was the director of the CEA. [ 11 ] The reactor, Zoé (Zéro énergie Oxyde et Eau lourde) used nuclear fission to generate five kilowatts of power. [ 11 ] [ 9 ] This was the beginning of nuclear energy as a source of power for France.
Years of working so closely with radioactive materials finally caught up with Joliot-Curie and she was diagnosed with leukemia . [ 16 ] [ 11 ] She had been accidentally exposed to polonium when a sealed capsule of the element exploded on her laboratory bench in 1946. [ 17 ] Treatment with antibiotics and a series of operations relieved her suffering temporarily but her condition continued to deteriorate. Despite this, Joliot-Curie continued to work and in 1955 drew up plans for new physics laboratories at the Orsay Faculty of Sciences , which is now a part of the Paris-Saclay University , south of Paris. [ citation needed ]
The Joliot-Curies had become increasingly aware of the growth of the fascist movement. [ 16 ] [ 11 ] They opposed its ideals and joined the Socialist Party in 1934, the Comité de vigilance des intellectuels antifascistes a year later, and in 1936 they actively supported the Republican faction in the Spanish Civil War . [ 16 ] In the same year, Joliot-Curie was appointed Undersecretary of State for Scientific Research by the French government, in which capacity she helped in founding the Centre National de la Recherche Scientifique . [ 16 ]
Frédéric and Irène visited Moscow for the two hundred and twentieth anniversary of the Russian Academy of Science and returned sympathizing with Russian colleagues. Frédéric's close connection with the Communist Party caused Irène to later be detained on Ellis Island during her third trip to the US, coming to speak in support of Spanish refugees, at the Joint Antifascist Refugee Committee 's invitation. [ 18 ]
The Joliot-Curies had continued Pierre and Marie's policy of publishing all of their work for the benefit of the global scientific community, but afraid of the danger that might result should it be developed for military use, they stopped: on 30 October 1939, they placed all of their documentation on nuclear fission in the vaults of the French Academy of Sciences, where it remained until 1949. [ 16 ]
Joliot-Curie's political career continued after the war and she became a commissioner in the Commissariat à l'énergie atomique . [ 16 ] However, she still found time for scientific work and in 1946 became director of her mother's Institut Curie . [ 16 ] [ 11 ]
Joliot-Curie became actively involved in promoting women's education, serving on the National Committee of the Union of French Women ( Comité National de l'Union des Femmes Françaises ) and the World Peace Council . The Joliot-Curies were given memberships to the French Légion d'honneur ; Irène as an officer and Frédéric as a commander, recognising his earlier work for the resistance. [ 16 ] [ 11 ]
Irène and Frédéric hyphenated their surnames to Joliot-Curie after they married in 1926. The Joliot-Curies had two children, Hélène , born eleven months after they were married, and Pierre , born in 1932. [ 16 ]
Between 1941 and 1943 during World War II , Joliot-Curie contracted tuberculosis and was forced to spend time convalescing in Switzerland. [ 16 ] Concern for her own health together with the anguish of her husband's being in the resistance against the German troops and her children in occupied France was hard to bear. [ 16 ] She did make several dangerous visits back to France, enduring detention by German troops at the Swiss border on more than one occasion. Finally, in 1944, Joliot-Curie judged it too dangerous for her family to remain in France and she took her children back to Switzerland. [ 16 ] Later in September 1944, after not hearing from Frédéric for months, Irene and her children were finally able to rejoin him. [ 16 ]
Irène fought through these struggles to advocate for her own personal views. [ 11 ] She was a passionate member of the feminist movement, especially regarding the sciences, and also advocated for peace. She continually applied to the French Academy of Sciences , an elite scientific organization, knowing that she would be denied. She did so to draw attention to the fact they did not accept women in the organization. [ 11 ] Irène was also involved in many speaking functions such as the International Women's Day conference. [ 11 ] She also played a big role for the French contingent at the World Congress of Intellectuals for Peace , which promoted the World Peace movement. [ 11 ] In 1948, during a strike involving coal miners, Joliot-Curie reached out to Paris Newsletters to convince families to temporarily adopt the children of the coal miners during the strike. The Joliot-Curies adopted two girls during that time. [ 11 ]
In 1956, after a final convalescent period in the French Alps, Joliot-Curie was admitted to the Curie Hospital in Paris, where she died on 17 March at the age of 58 from leukemia, possibly due to radiation from polonium-210 . [ 19 ] [ 20 ] Frédéric's health was also declining, and he died in 1958 from liver disease, which too was said to be the result of overexposure to radiation. [ 21 ]
Joliot-Curie was an atheist and anti-war. [ 16 ] [ 22 ] [ 23 ] When the French government held a national funeral in her honor, Irène's family asked to have the religious and military portions of the funeral omitted. [ 16 ] Frédéric was also given a national funeral by the French government. [ 16 ]
Joliot-Curie's daughter, Hélène Langevin-Joliot , went on to become a nuclear physicist and professor at the University of Paris . Joliot-Curie's son, Pierre Joliot , went on to become a biochemist at the Centre National de la Recherche Scientifique . [ 16 ]
Her name was added to the Monument to the X-ray and Radium Martyrs of All Nations erected in Hamburg , Germany. | https://en.wikipedia.org/wiki/Irène_Joliot-Curie |
The Irène Joliot-Curie Prize is a French prize for women in science and technology, founded in 2001. It is awarded by the Ministry of Higher Education, Research and Innovation , the Airbus Group corporate foundation, the French Academy of Sciences and the Academy of Technologies, it aims at rewarding women for their work in the fields of science and technology". [ 1 ]
The prize is named after French scientist Irène Joliot-Curie , [ 2 ] [ 3 ] a French chemist, physicist and politician who won the Nobel Prize in Chemistry in 1935 for the discovery of artificial radioactivity. [ 4 ] (This prize should be distinguished from a different prize with the same name, offered since 1956 by the Société Française de Physique . which rewards work in the field of physics each year. [ 5 ] )
Each year three awards are given: one for the female scientist of the year, a second to a young female scientist, and a third to a woman in business and technology. In addition, until 2009, of the award a fourth category of awards was given, to an individual or group in recognition of their mentorship of women in science. [ 6 ] In 2023, a new category was recognized in a special prize for engagement. [ 7 ]
Since 2011, the award winners have been chosen by the French Academy of Sciences and the French Academy of Technologies . [ 8 ] [ 9 ]
The winners have included: | https://en.wikipedia.org/wiki/Irène_Joliot-Curie_Prize |
The IsaKidd Technology is a copper electrorefining and electrowinning technology that was developed independently by Copper Refineries Proprietary Limited (“CRL”), a Townsville , Queensland , subsidiary of MIM Holdings Limited (which is now part of the Glencore group of companies), and at the Falconbridge Limited (“Falconbridge”) now-dismantled Kidd Creek refinery that was at Timmins , Ontario . It is based around the use of reusable cathode starter sheets for copper electrorefining and the automated stripping of the deposited “cathode copper” from them. [ 1 ]
The usual process of electrorefining copper consists of placing a copper anode (about 99.5–99.7% pure copper [ 2 ] [ 3 ] ) in sulfuric acid (H 2 SO 4 ) bath of copper electrolyte, together with a cathode, and passing a current between the anode and cathode through an external circuit. [ 3 ] At the applied electropotential , copper and less noble elements dissolve in the electrolyte , while elements more noble than copper, such as gold (Au) and silver (Ag), do not. [ 3 ] Under the influence of the applied electrical potential , copper ions migrate from the anode and deposit on the cathode, forming cathode copper. [ 3 ]
The current IsaKidd technology represents the merger of the copper refining technologies developed by the two different organisations. The initial Isa Process development in the late 1970s, with its reusable stainless-steel cathode starter sheets, represented an advance on the previous technology of single-use starter sheets of pure copper, [ 1 ] the production of which was a labour-intensive process.
The production of the single-use starter sheets involved laying down a sheet of copper by electrolysis on each side of a “mother plate”. [ 1 ] Generating the sheet took a day, and thousands of sheets could be needed every day. [ 1 ] Originally, the copper starter sheets were separated from the mother plate manually, but over time the process was automated. [ 1 ] [ 4 ] In addition, limitations associated with the use of copper starter sheets meant that it was difficult to meet the purity specifications of some new copper applications that were, in the 1970s and 1980s, demanding higher quality copper.
The development of the Isa Process tank house technology at CRL eliminated the whole process and cost of producing the starter sheets by using stainless-steel permanent cathodes. [ 1 ] It also included substantial automation of the process of inserting the permanent cathodes into the electrolytic cells and their subsequent removal and stripping of the sheets of deposited cathode copper. [ 1 ] The labour force required to operate a refinery using the IsaKidd technology has been estimated at 60–70% less of that required for refineries using starter sheets. [ 2 ] [ 5 ]
MIM Holdings began marketing the Isa Process technology in 1980, as a result of demand from other refinery operators.
Falconbridge subsequently independently developed a similar process to improve operations at its Kidd Creek copper refinery, near Timmins , Ontario . [ 6 ] The initial development of permanent cathodes was for internal use, but marketing of the Kidd Process was initiated in 1992 after requests from other refinery operators. [ 7 ]
The two technologies were brought together as the IsaKidd Technology in 2006, when Xstrata bought Falconbridge. [ 6 ]
The IsaKidd Technology now dominates global copper refining. It has been licensed to 102 users and Xstrata Technology, which markets the technology, reports on its website a total installed capacity of some 12 million tonnes per year (“t/y”) of copper production, as of October 2011. [ 8 ] This is about 60% of the estimated 2011 global refined copper production of 19.7 million tonnes. [ 9 ]
The development of the IsaKidd technology allowed increased productivity, reduced operating costs and the production of consistent, high-quality cathode copper. [ 2 ]
Electrolytic refining of copper was first patented in England by James Elkington in 1865 and the first electrolytic copper refinery was built by Elkington in Burry Port, South Wales in 1869.
There were teething problems with the new technology. For example, the early refineries had trouble producing firm deposits on the cathodes. [ 2 ] As a result, there was much secrecy between refinery operators as each strove to maintain a competitive edge. [ 2 ]
The nature of the cathode used to collect the copper is a critical part of the technology. The properties of copper are highly susceptible to impurities. For example, an arsenic content of 0.1% can reduce the conductivity of copper by 23% and a bismuth content of just 0.001% makes copper brittle. [ 10 ] The material used in the cathode must not contaminate the copper being deposited, or it will not meet the required specifications.
The current efficiency of the refining process depends, in part, on how close the anodes and cathodes can be placed in the electrolytic cell. This, in turn, depends on the straightness of both the anode and the cathode. Bumps and bends in either can lead to short-circuiting or otherwise affect the current distribution and also the quality of the cathode copper. [ 3 ]
Prior to the development of the Isa Process technology, the standard approach was to use a starter sheet of high-purity copper as the initial cathode. [ 1 ] These starter sheets are produced in special electrolytic cells by electrodeposition of copper for 24 hours [ 2 ] onto a plate made of copper coated with oil [ 1 ] (or treated with other similar face-separation materials) or of titanium . [ 2 ] Thousands of sheets could be needed every day, [ 4 ] and the original method of separating the starter sheet from the “mother plate” (referred to as “stripping”) was entirely manual. [ 1 ]
Starter sheets are usually quite light. For example, the starter sheets used in the CRL refinery weighed 10 pounds (4.53 kilograms). [ 11 ] Thus, they are thin and need to be handled carefully to avoid bending.
Over time, the formation of starter sheets was improved by mechanisation, but there was still a high labour input. [ 1 ]
Once the starter sheets were formed, they had to be flattened, to reduce the likelihood of short circuits, and then cut, formed and punched to make loops from which the starter sheets are hung from conductive copper hanger bars in the electrolytic cells (see Figure 1). [ 2 ]
The starter sheets are inserted in the refining cells and dissolved copper electrodeposits on them to produce the cathode copper product (see Figure 2). Because of the manufacturing cost of the starter sheets, refineries using them tend to keep them in the cells as long as possible, usually 12–14 days. [ 2 ] On the other hand, the anodes normally reside in the cells for 24–28 days, meaning that there are two cathodes produced from each anode. [ 2 ]
The starter sheets have a tendency to warp, due to the mechanical stresses they encounter and often need to be removed from the refining cells after about two days to be straightened in presses before being returned to the cells. [ 12 ] The tendency to warp leads to frequent short-circuiting. [ 12 ]
Due to their limitations, it is difficult for copper produced on starter sheets to meet modern specifications for the highest-purity copper. [ 13 ]
The development of the Isa Process tank house technology had its beginning in the zinc industry. [ 2 ] During the mid-1970s, MIM Holdings Limited (“MIM”) was considering building a zinc refinery in Townsville to treat the zinc concentrate produced by its Mount Isa operations. [ 2 ] As a result, MIM staff visited the zinc smelters using the best-practice technology and found that modern electrolytic zinc smelters had adopted permanent cathode plate and mechanised stripping technology. [ 2 ]
MIM recognised that the performance of traditional copper refineries was constrained by the poor cathode geometry inherent in using copper starter sheets. [ 14 ]
MIM then developed a research program aimed at developing similar permanent cathode technology for copper refining. [ 2 ] CRL had been operating in Townsville since 1959, [ 11 ] using conventional starter-sheet technology [ 1 ] and treating blister copper produced in the Mount Isa Mines Limited copper smelter at Mount Isa in Queensland. [ 11 ] CRL incorporated the permanent cathode technology in its 1978 refinery modernisation project. [ 1 ] [ 2 ] The material initially selected was 316L stainless steel, [ 15 ] stitch-welded to a 304L stainless-steel hanger bar. [ 16 ] The hanger-bar assembly was then electroplated with copper to a thickness of 1.3 millimeters (“mm”) (later increased to 2.5 mm and then 3.0 mm to improve the corrosion resistance of the hanger bar) to approximately 15 mm down onto the blade, which provided sufficient electrical conductivity and gave the assembly some corrosion resistance. [ 16 ]
Electrodeposited copper adheres quite firmly to the stainless steel so that it does not detach during refining. [ 12 ] The vertical edges of the stainless steel plates are covered with tight-fitting polymer edge strips to prevent copper depositing around the edge of the cathode plate and so make it easier to strip the cathode copper from them. [ 12 ] The bottom of the cathode plates were masked with a thin film of wax, again to prevent the copper depositing around the bottom edge. [ 2 ] Wax was used rather than an edge strip to avoid having a ledge that would collect falling anode slimes and contaminate the cathode copper. [ 2 ]
Wax was also used on the vertical edges to prolong the life of the vertical edge strip. [ 2 ]
The original cathode stripping machine was based on that used at the Hikoshima plant of the Mitsui Mining and Smelting Company of Japan . [ 2 ] However, considerable development work was necessary to modify the design to handle the copper cathodes, which were heavier than those at Hikoshima, and to process the cathode plates without damaging them. [ 2 ] The machines also had to be redesigned to allow for waxing the sides and bottoms of the cathode plates to allow the next copper cathode sheets to be removed easily. [ 2 ]
The stripping machines included receiving and discharge conveyors, washing, separation, cathode stacking and discharging, cathode plate separation for refurbishing, and the wax applications for the sides and bottoms of the cathode plates. [ 5 ]
The original CRL stripping machine had the capability of stripping 250 cathode plates per hour. [ 2 ]
The lower cost of the cathode plates compared to starter sheets means that shorter cathode cycle times are possible. [ 2 ] The cycle time can range from 5 to 14 days, but a seven-day cathode cycle is common. [ 2 ] This shorter cycle time improves current efficiency as less short circuits occur and there is less nodulation of the cathode surface. [ 2 ]
Initially, other refinery operators regarded the developments at CRL with scepticism. [ 1 ] Stainless steel had been tried unsuccessfully as mother-plate material for copper starter sheets. [ 1 ] They suffered from rapid deterioration of their strippability, resulting in “an almost daily increase in difficulty of stripping”. [ 1 ] However, following the success of early installations in Townsville, Timmins, and many other places, the permanent stainless steel cathode technology has had widespread introduction. [ 12 ]
The Isa Process was originally developed for the CRL copper electrorefinery in Townsville. It was subsequently licensed to the Copper Range Company for its White Pine copper refinery. [ 8 ]
The next licence issued was for an electrowinning application at the Broken Hill Associated Smelters (“BHAS”) lead smelter at Port Pirie , in South Australia . BHAS commissioned in 1985 a solvent extraction and electrowinning (“SX–EW”) to recover copper from copper–lead matte produced as a by-product of the lead smelting operations. [ 17 ] The process used involves leaching the copper from the material using an acidic chloride–sulfate solution, followed by solvent extraction to concentrate the leached copper and electrowinning. [ 18 ]
Electrowinning copper differs from electrorefining in that electrorefining uses a copper anode that is dissolved and redeposited on the cathode, while in electrowinning the copper is already in solution and is extracted from the solution by passing a current through the solution using an inert lead-alloy anode, and a cathode. [ 19 ]
The chloride in the leach solution at Port Pirie proved to be a problem for the stainless steel cathodes of the Isa Process. [ 17 ] A small amount of the chloride ions in the leach solution passed through the solvent into the electrolyte, leading to a reported chloride concentration of 80 milligrams per liter (“mg/L”) in the electrolyte. [ 17 ] The presence of the chloride in the electrolyte caused pitting corrosion of the stainless steel cathode plates. [ 17 ] After trying other types of stainless steel, [ 17 ] BHAS switched to using titanium cathode plates. [ 18 ]
Other electrowinning operations followed, including Gibraltar Mines ’ McLeese Lake operation and Magma Copper’s San Manuel copper mine in 1986, the Mexicana de Cananea operation in Mexico in 1989, and the Gunpowder Copper Limited operation at Gunpowder in north-west Queensland 1990. [ 8 ] These operations did not suffer the chloride corrosion problems experienced by BHAS.
Falconbridge Limited in mid-1981 commissioned a copper smelter and refinery near Timmins, Ontario, to treat concentrate from its Kidd Mine . [ 20 ] However, at the outset, the quality of the cathode copper produced in the Kidd refinery suffered from the presence of higher than usual concentrations of lead and selenium in the copper smelter’s anodes. [ 7 ] Kidd cathode copper was not able to meet its customers’ specifications and obtaining product certification for the London Metal Exchange (“LME”) became a key focus. [ 7 ]
After several process improvements were instigated, it was ultimately realised that the use of copper starter sheets was preventing the Kidd refinery meeting its cathode quality targets. [ 7 ] Test work then began on the use of permanent stainless-steel cathodes. [ 7 ] Preliminary tests using full-scale titanium blanks showed a reduction in the lead content of the cathode copper of a factor of four and a six-fold reduction in the selenium content, compared with the use of copper starter sheets. [ 7 ]
The focus then shifted to developing a stripping machine, to develop stainless steel cathodes incorporating the existing header bars and evaluating edge-strip technology. [ 7 ] The company’s board of directors gave approval for the conversion of the refinery to the Kidd technology in April 1985. [ 7 ] The conversion was completed in 1986 [ 7 ] and the Kidd refinery became the third [ 8 ] to install permanent cathode and automated stripping technology.
Falconbridge began marketing the technology in 1992, after many requests from other refinery operators. [ 6 ] Thus, the Kidd Process created competition between two suppliers of permanent cathode technology. The main differences between them were the cathode header bar, edge stripping and the stripping machine technology. [ 21 ]
In contrast to the stainless steel header bar then used in the Isa Process cathode, the Kidd Process cathode used a solid copper header bar, which was welded onto the stainless steel sheet. [ 13 ] This gave a lower voltage drop (by 8–10 millivolts) than the Isa Process cathode. [ 13 ]
The Isa Process technology used the waxed edge at the bottom of the cathode plate to stop the copper depositing around the plate’s bottom to form a single mass of copper running from the top of one side of the cathode plate around the bottom to the top of the other side. [ 15 ] The copper was stripped from the cathode plates as two separate sheets. [ 15 ] The Kidd Process technology did not use wax, as it was thought that it could exacerbate the impurity problems with which the plant had been struggling. At Kidd, the stripping approach was to remove the copper from the cathode plate as a single V-shaped cathode product, akin to a taco shell. [ 15 ]
The Kidd Process initially used a “carousel” stripping machine, but a linear installation was subsequently developed to provide machines with lower to medium stripping capacities for electrowinning plants and smaller refineries. [ 13 ] The linear stripping machines, first installed in 1996, were more compact, less complex and had lower installation costs than the carousel machines. [ 13 ]
As outlined above, the Kidd Process did not use wax on its permanent cathodes. [ 2 ] This highlighted disadvantages associated with the use of wax by the Isa Process. [ 2 ] Cathode copper consumers applied pressure to producers to remove residual wax from the cathode copper, and the use of wax also created “housekeeping” problems for Isa Process operators. [ 2 ]
Consequently, MIM commenced a development program in 1997 aimed at eliminating the use of wax. [ 2 ] This resulted in a new process called the Isa 2000 technology, which was able to produce single-sheet cathode (as opposed to the Kidd taco shell cathode) without using wax. [ 2 ]
This was achieved by machining a 90° “V”-groove into the bottom edge of the cathode. [ 22 ] The groove weakens the structure of the copper growing at the bottom edge of the cathode plate because the copper crystals grow perpendicular to the cathode plate from opposite sides of the groove, causing them to intersect at right angles to each other. [ 22 ] A discontinuity in the structure is formed at the intersection that results in a weak zone, along which the copper splits during stripping. [ 22 ]
Figure 4 is a microscope view of the cross-section a copper cathode growing at the tip of a cathode plate. The yellow lines show the orientation and direction of crystal growth. [ 22 ]
The standard Isa Process cathodes have slightly higher electrical resistance than solid-copper hanger bar systems used by the Kidd Process, meaning that there is a higher power cost. [ 22 ] However, this cost is offset by greater reliability and predictability in the increase in resistance over time, allowing for maintenance planning. [ 16 ]
The solid-copper hanger bars, on the other hand, lose electrical performance over a shorter period of time due to corrosive attack on the joint and sudden failure is possible. [ 16 ] The maintenance costs of such systems are greater and less predictable. [ 16 ] A trial of approximately 3000 solid-copper hanger bars, found over time a lower current efficiency in the solid-copper hanger bars of about 2.4%. [ 16 ]
The MIM development team looked for other ways to reduce the resistance of the cathode plates and developed a new low-resistance cathode, which it called ISA Cathode BR. [ 16 ] This new design extended the copper plating from 15–17 mm down the blade to approximately 55 mm, and it increased the thickness of the copper to 3.0 mm from the 2.5 mm used on the standard cathode. [ 16 ]
The new cathode plate design was tested in the CRL refinery in Townsville and at Compania Minera Zaldivar in Chile. [ 16 ] The Chilean results indicated the new cathode design had the potential to reduce power costs by approximately US$100,000 in 2003 for the plant, compared to using conventional Isa Process cathode designs. [ 16 ]
From 2001 to 2007, nickel prices rose from an average of US$5945 [ 23 ] to US$37,216. [ 24 ] Nickel is a key constituent of 316L stainless steel. [ 22 ] This, combined with increases in some of the other constituents of the 316L alloy, prompted Xstrata Technology (by then the marketing organisation for the Isa Process technology) to seek an alternative material for the cathode plates. [ 22 ]
Xstrata Technology personnel investigated the use of a new low-alloyed duplex stainless steel , LDX 2101 and 304L stainless steel . [ 22 ] The LDX 2101 contains 1.5% nickel compared to 10–14% in 316L stainless steel.
LDX 2101 has superior mechanical strength to the 316L stainless steel, allowing thinner sheets to be used for the cathode plates. [ 22 ] However, the flatness tolerance of commercially available LDX 2101 steel did not meet the required specifications. [ 22 ] Xstrata Technology worked with a manufacturer to produce sheets that did meet the required flatness tolerance. [ 22 ]
Xstrata Technology also had to develop a finish that allowed the surface to function in the same way as 316L. [ 22 ]
Cathode plates using LDX 2010 have equivalent corrosion resistance to 316L plates. [ 25 ]
The LDX 2101 alloy provides an alternative to the 316L stainless steel, [ 22 ] with the selection depending on relatively prices of the various steels.
The Kidd Process development team modified its cathode plates to cope with high-corrosion environments, such as the liberator cells used to remove contaminants in refineries and some high-corrosion environments in electrowinning plants. [ 13 ]
The design of the plate features a stainless-steel jacket that surrounds a solid-copper hanger bar, protecting it from corrosion. [ 13 ] A corrosion-resistant resin inside the stainless steel jacket protects the conductive interior weld between the header bar and the plate. [ 13 ] The hanger bar is then finished with high-quality sealing to prevent ingress of electrolytes into the conductive interior weld. [ 13 ]
This corrosion resistance electrode is marketed as the HP cathode plate. [ 25 ]
After the initial carousel stripping machine development and the later development of the linear stripping machine, Falconbridge personnel developed the Kidd Process High Capacity Linear Machine (“HCLM”). [ 13 ] This machine included a loading and unloading system that was based on robotics. [ 13 ]
The new design improved, among other things, the discharge area of the stripper. This had been a problem area for the carousel stripping machines, in which copper released from the cathode plate fell into an envelope and was then transferred to a material handling device. [ 13 ] Copper that misbehaved and failed to transfer often required manual intervention. [ 13 ] The new robot discharge system eliminated the free falling of the copper and physically transferred the released copper to the discharge location. [ 13 ]
After Falconbridge’s 1992 decision to market the Kidd technology, the Falconbridge and the then MIM Process Technologies groups competed for the tank house technology market. Between 1992 and 2006, 25 Kidd technology licences were sold, [ 8 ] while there were 52 Isa process licences sold in the same period. [ 8 ]
Xstrata plc (now Glencore) took over MIM Holdings in 2003. [ 26 ] The Isa Process technology continued to be developed and marketed by Xstrata Technology. Xstrata subsequently took over Falconbridge in 2006. [ 27 ] The Kidd Process technology consequently became part of the Xstrata Technology tank house package and together they began to be marketed as IsaKidd, [ 6 ] a name that represents the dual heritage of the technology.
The result has been a technology package that combined what were mutually regarded as the best of both versions. [ 15 ] This combination led to the development of new stripping systems and new cathode designs are in development. [ 15 ]
The variation in copper deposits on the cathode plates was one of the difficulties encountered with the earlier stripping machines. [ 15 ] Areas of thin copper on the cathode plates, which are caused by short circuits, are difficult to separate from the stainless steel plate due to their lack of rigidity. Plates bearing such areas generally had to be rejected from the stripping machine and stripped manually. [ 15 ] Similarly, sticky copper deposits (generally related to poor surface condition on the cathode plate, such as corroded surfaces or improper mechanical treatment), heavily nodulated cathode and laminated copper caused problems for stripping. [ 15 ]
Stripping machine development focussed on developing a device that could be seen as a more accommodating and universal stripping machine that could handle cathode plates with problem copper deposits without rejecting them or slowing the stripping rate. [ 15 ]
The result of this work was a new robotic cathode stripping machine. [ 15 ] It incorporated the following features:
The stripping wedges are mounted on two robotic arms, one for each side of the cathode plate. [ 15 ] These arms strip the copper from the plate and lay the sheets of cathode copper onto conveyors for them to be taken away for bundling. [ 15 ]
Advantages cited for the IsaKidd technology include:
Staff of the Cyprus Miami copper refinery wrote after their installation of the Isa Process technology that: “It is now well proven that tankhouses applying stainless steel cathode technology can consistently produce high quality cathodes while operating at higher cathode current density and at a lower cathode spacing than those used in conventional tankhouses.” [ 31 ] | https://en.wikipedia.org/wiki/IsaKidd_refining_technology |
IsaPlanner [ 1 ] is a proof planner for the interactive proof assistant , Isabelle . Originally developed by Lucas Dixon [ 2 ] as part of his PhD thesis at the University of Edinburgh , it is now maintained by members of the Mathematical Reasoning Group, in the School of Informatics at Edinburgh.
IsaPlanner is the latest of a series of proof planners written at Edinburgh. Earlier planners include Clam and LambdaClam.
IsaPlanner allows the user to encode reasoning techniques, using a combinator language, for conjecturing and proving theorems . IsaPlanner works by manipulating reasoning states, records of open goals, the current proof plan and other important information, and combinators are functions mapping reasoning states to lazy lists of successor reasoning states.
IsaPlanner's library supplies combinators for branching and iteration , amongst other tasks, and powerful reasoning techniques can be created by combining simpler reasoning techniques with these combinators.
Several reasoning techniques come ready implemented within IsaPlanner, notably, IsaPlanner features an implementation of dynamic rippling , a rippling heuristic capable of working in higher order settings, a best-first rippling heuristic and a reasoning technique for proofs by induction .
Additional features include an interactive tracing tool, for manually stepping through proof attempts and a module for viewing and manipulating hierarchical proofs.
Features currently [ when? ] being implemented, or planned for the future, are an expanded set of proof critics , suitable for use in higher order domains, dynamic relational rippling, a rippling heuristic suitable for rippling over relational expressions as opposed to functional expressions, again suitable for use in higher order domains, and integration of IsaPlanner with Proof General . [ citation needed ] | https://en.wikipedia.org/wiki/IsaPlanner |
Isaac B. Bersuker (Russian: Исаáк Бóрухович (Бори́сович) Берсýкер; born February 12, 1928) is a Romanian-born Soviet - Moldоvan -American theoretical physicist and quantum chemist whose principal research is in chemical physics , solid-state physics , and theoretical chemistry . Known for his "life-long years of experience in theoretical chemistry" [ 1 ] working on the electronic structure and properties of coordination compounds , Isaac B. Bersuker is “one of the most widely recognized authorities” [ 2 ] in the theory of the Jahn–Teller effect (JTE) and the pseudo-Jahn–Teller effect (PJTE). His accomplishments include explaining the polarization of the atomic core in Rydberg atoms , the effect of tunneling splitting in molecules and solids with a strong JTE, and the discovery of the PJTE origin of ferroelectricity in cubic perovskites . Known as the leading expert in JTE and PJTE, Bersuker is the permanent chairman of the international steering committee of the Jahn–Teller symposia. [ 3 ] His present affiliation is with the Oden Institute for Computational Engineering and Science of the Department of Chemistry of the University of Texas at Austin .
Isaac (Izya) Bersuker was born on February 12, 1928, in Chișinău , then part of Greater Romania , to a low-income family of Bessarabian Jewish descent. His father Boruch Bersuker was a carpenter, and his mother Bella Bersuker (Russian: Бéлла Хáймовна Берсýкер, 1896–1981) was a housewife with five kids. As a boy in a family of a modest background, Isaac got his elementary school education in Talmud Torah and ORT . He was 13 years old when the tragic events of World War II forced his Jewish family to run from the Nazis to an Azerbaijan village. [ 4 ] Deprived of the traditional middle and high-school education, he spent four years farming in Azerbaijan kolkhoz . [ 5 ] However, he never gave up his dream of getting a higher education and becoming an intellectual. After the war, native Romanian, he barely spoke Russian. Yet, in a self-education way, in а two-year term, he managed to complete a four-year high-school program in a Russian school and enrolled at Chișinău State University . [ 5 ] In the best meaning of this expression, Isaac is a self-made man. [ 4 ] A fascinating autobiographical section in [ 5 ] describes "his scientific ascent, starting from a Jewish childhood in Bessarabia and frequently hampered by antisemitic state directives under the Stalin regime." [ 6 ] Dedicated to the study of theoretical physics , in 1952, just six years after being an illiterate boy shepherding sheep, Bersuker graduated from this university with a master's degree in physics. He began his scientific research in atomic spectroscopy as a post-graduate student at Leningrad State University , working under Mikhail G. Veselov [ 7 ] at the Division of Quantum Mechanics [ 8 ] led by its Chair Vladimir A. Fock . Here, in 1957, Bersuker received his doctorate ( Candidate of Sciences , Russian: Кандидáт наýк) and in 1964 his habilitation degree ( Doctor of Sciences , Russian: Дóктор наýк). From 1964 to 1993, back in Chișinău, Bersuker continued his scientific research at the Institute of Chemistry [ 9 ] of the Moldavian branch of the USSR Academy of Sciences . Organizationally, Bersuker's success was the creation in 1964, and the leadership of the Laboratory of Quantum Chemistry [ 10 ] also dubbed ‘‘the Chișinău school of the Jahn–Teller effect.’’ [ 6 ] Elected as a Corresponding Member of this academy in 1972 and a full Member [ 11 ] in 1989, Isaac B. Bersuker moved to the United States In 1993. He became a senior research scientist and professor of the department of chemistry [ 12 ] at the University of Texas at Austin . Isaac B. Bersuker served as a doctoral and habilitation supervisor for 31 post-graduate students and post-docs. According to K. Alex Müller , Bersuker was and still is "in full swing at the university, writing books, discussing with great wit, and quick to understand ‒ as I had known him for well over thirty years." [ 13 ] In the late 1980s, owing to Bersuker's high motivating role, leadership, and creative ingenuity, Bersuker's school was called "the capital of the Jahn–Teller effect" by some. [ 4 ] Bersuker's academic publications have a high impact on the scientific community. According to Google Scholar, [ 14 ] since 1993 when he moved to the United States, Bersuker's papers were cited 10428 times, his h-index is 41, and his i10-index is 141.
In his Ph.D. thesis, Bersuker developed the theory of core polarization and its effect on optical transitions in Rydberg atoms . [ 15 ] At the time, this was a puzzling problem in absorption spectroscopy . The absorption of light by alkali atoms appeared to violate the electric dipole sum rule . According to Bersuker, the solution to the problem is in the instantaneous polarization of the atomic core by the incident electromagnetic wave creating an additional perturbation to the excitation of the valence electron . Related to this problem, he worked out the adiabatic separation of motion of the valence and the atomic core electrons in electronic structure calculations of atoms. [ 16 ] [ 17 ] First introduced in 1957, still, decades later, Bersuker's ideas of electron polarization by the incident electromagnetic wave and of the atomic core polarization by the valence electron is used and further explored in atomic spectroscopy. [ 18 ]
Bersuker's contributions to the JTE and PJTE theory with applications to physical and chemical phenomena are reflected in his several monographs (some of them written and published with the assistance and involvement of other authors) and major reviews on this subject (see the latest in [ 19 ] [ 20 ] [ 21 ] [ 22 ] [ 23 ] [ 24 ] [ 25 ] ). First published in 1961–1962, his contributions to the theory of the JTE predicted the tunneling splitting of the vibronic energy levels of the systems with the JTE, [ 26 ] [ 27 ] later confirmed experimentally. The splitting is due to the tunneling transitions between the equivalent wells on the multiminimum adiabatic potential energy surface produced by this effect. In 1976, "The phenomenon of tunneling splitting of energy levels of polyatomic systems in the state of electronic degeneracy" was qualified as a scientific discovery and registered in the State Register of the USSR (Diploma No. 202). [ 28 ] In addition, Bersuker is known for revealing the significance of the PJTE and showing that it may take place at any energy gaps between entangled electronic states. Most important, he proved that the JTE and PJTE are the only sources of structural instability and spontaneous symmetry breaking (SSB) in polyatomic systems. [ 19 ] [ 20 ] [ 29 ] Thus, according to Bersuker, if a polyatomic system has broken symmetry properties, undoubtedly, they are of JTE or PJTE origin. This conclusion elevates the two effects from their assumed earlier rare particular features to general tools for exploring molecular and solid-state properties. [ 19 ] [ 20 ] [ 21 ] [ 22 ] [ 30 ] [ 23 ] [ 25 ]
The generality of this result was challenged by the existence of some molecular systems with SSB. For example, in the ozone O 3 molecule, neither the JTE nor the PJTE is seen explicitly in the high-symmetry configuration. Bersuker eliminated this controversy by revealing the hidden JTE and PJTE. [ 31 ] They take place in the excited states of the system but, being strong enough, penetrate the ground state of the high-symmetry configuration and form an additional, coexisting equilibrium state with lower symmetry. The latter may also have a different spin state leading to an interesting phenomenon of spin-crossover and magnetic-dielectric bistability. [ 32 ] Involving excited states, Bersuker also showed that the PJTE is instrumental in explaining the origin of chemical activation and sudden polarization in photochemical reactions. [ 33 ] [ 34 ] Revealed by Bersuker, other applications of the JTE and PJTE are briefly mentioned below.
Another fundamental contribution of Isaac B. Bersuker to the early developments of this field was applying the PJTE to explain the origin of ferroelectricity in perovskite -type crystals. [ 35 ] This first application of the PJTE to solve an important solid-state problem led to developing a whole trend in the studies of local and cooperative properties in crystals. The origin of crystals' temperature-controlled spontaneous dielectric polarization was the subject of discussion for many decades involving high-rank physicists at the time. However, with the development of the experimental technics, the "displacive theories" encountered increasing controversies that had no explanation.
Using perovskite crystals as an example, Bersuker showed (first in 1964, published in 1966 [ 35 ] ) that the PJTE produces a spontaneous symmetry breaking resulting under certain conditions in local dipolar instability. It exists in all the crystal phases, and the spontaneous polarization results from the order-disorder interaction between these PJTE-induced local dipolar distortions. Performed in the local octahedral TiO 6 center in the BaTiO 3 crystal (taken as an example), where vibronic coupling mixes ground 1 A 1g and close in energy exited 1 T 1u states of opposite parity (but same multiplicity), detailed analysis with calculations proved the PJTE to produce the dipolar distortion. Thus, it shows that Bersuker's PJTE theory of ferroelectricity agrees with the available empirical data and predicts new properties, [ 25 ] [ 36 ] confirmed experimentally.
From the fact that PJTE does not entangle states with different spin multiplicity , Bersuker deduced conditions and predicted possible multiferroics in some cubic perovskites. [ 37 ] According to Bersuker, only the d n cations with the close-energy ground and excited states of opposite parity, but with the same multiplicity, may meet the necessary conditions of ferroelectricity in the presence of unpaired spins. [ 37 ]
Under external unipolar perturbations, polar gases and liquids manifest two kinds of polarization , displacive and orientational. The latter is by orders of magnitude larger than the former. So far, solids were known to undergo only displacive polarization. Bersuker showed that in ABO 3 type perovskites, dipolar distortions are due to the PJTE. [ 38 ] [ 36 ] [ 39 ] [ 40 ] Similar to the other cases of the JTE and PJTE, [ 35 ] the adiabatic potential energy surface of the metallic B center has eight equivalent wells positioned along the eight diagonals of the cube, meaning eight symmetry-equivalent positions of the PJTE-induced dipole moment with small barriers between them. As a result, these dipoles can rotate under external perturbations realizing orientational polarization. [ 39 ] [ 40 ] Predicted more than a century ago by P. Debye , solids with intrinsic dipoles behave like polar liquids with orientational polarization. However, enhanced polarizability of such solids was not well understood until Bersuker's works [ 35 ] [ 38 ] [ 39 ] [ 40 ] (see also in [ 25 ] [ 36 ] ). As shown by Bersuker, experimentally observed giant flexoelectricity, permittivity, and electrostriction result from PJTE-induced orientational polarization. [ 25 ] [ 36 ] [ 39 ] [ 40 ]
Given that the PJTE is the unique source of structural instability, Bersuker applied this idea to planar configurations of some molecules in nondegenerate states. Bersuker was the first to demonstrate that the puckering (or buckling) of planar two-dimensional systems is of PJTE origin. [ 19 ] [ 20 ] [ 21 ] Hence, following Bersuker, their planarity can be driven by external influence targeting the PJTE parameters. [ 41 ] As the starting example, he suggested hemoglobin oxygenation. The out-of-plane displacement of the iron atom was shown to be due to the PJTE. At the same time, the coordination of the oxygen atom violates the condition of the PJTE instability, thus restoring the planar configuration. [ 42 ] In a more general setup, such manipulations became more critical recently because of the applications of two-dimensional molecular systems in electronics. According to Bersuker, planarity can be operated by targeted redox perturbations, coordination with other atomic groups, and chemical substitutions. [ 41 ] A similar modification of a crystal lattice by redox influencing its local JTE centers was also realized. [ 43 ]
There is quite a list of other theoretical chemistry , chemical physics , and quantum chemistry fields with a remarkable Bersuker's contribution. In a number of his seminal papers, Bersuker introduced and developed theoretical models of vibronic mechanisms in redox properties, electron-conformational effects, [ 44 ] chemical reactivity , and catalysis . [ 45 ] [ 46 ] He is known for revealing the role of JTE and PJTE in the properties of mixed-valence compounds . [ 47 ] In addition, he discovered the effect of coordination covalent bonding and the JTE in the "plasticity effect". [ 48 ] Also, Bersuker worked out a quantum mechanics/molecular mechanics method of electronic structure calculations of large organometallic systems when there is charge transfer between the QM and MM parts. [ 49 ] The name of Bersuker is associated with the semiempirical approach to relativistic electronic structure calculations [ 50 ] [ 51 ] and a method of estimating molecular-orbital parameters from Mossbauer spectra . [ 52 ] [ 53 ] In another series of publications, he created and applied the electron-conformational method to computer-aided drug design and toxicology . [ 54 ] [ 55 ] [ 56 ] Within this methodology, the chemical origin of odorant activity was also revealed, including the source of musk odor . [ 57 ]
Isaac B. Bersuker wrote 15 books, first in 1962, and more than 400 academic papers. [ 14 ] [ 58 ] [ 59 ] [ 60 ] [ 61 ] His books on the JTE and PJTE, published in 1984, [ 62 ] 1989, [ 20 ] and 2006, [ 19 ] were most influential. [ 63 ] [ 64 ] [ 6 ] [ 65 ] [ 66 ] According to Google Scholar, [ 14 ] cumulatively, these three monographs were cited more than 3000 times.
Isaac B. Bersuker was married in 1951 to Liliya Bersuker (Russian: Ли́лия Бори́совна Берсýкер, 1930–2003), a chemist. He has one son, Gennadi I. Bersuker [ 67 ] (born 1953), a theoretical physicist, and two grandsons, Eugene G. Bersuker (born 1979) and Kirill G. Bersuker [ 68 ] (born 1985), a molecular biologist. | https://en.wikipedia.org/wiki/Isaac_B._Bersuker |
Isaak Moiseevich Yaglom [ 1 ] ( Russian : Исаа́к Моисе́евич Ягло́м ; 6 March 1921 – 17 April 1988) [ 2 ] [ 3 ] was a Soviet mathematician and author of popular mathematics books, some with his twin Akiva Yaglom .
Yaglom received a Ph.D. from Moscow State University in 1945 as student of Veniamin Kagan . [ 4 ] As the author of several books, translated into English, that have become academic standards of reference, he has an international stature. His attention to the necessities of learning ( pedagogy ) make his books pleasing experiences for students. The seven authors of his Russian obituary recount "…the breadth of his interests was truly extraordinary: he was seriously interested in history and philosophy, passionately loved and had a good knowledge of literature and art, often came forward with reports and lectures on the most diverse topics (for example, on Alexander Blok , Anna Akhmatova , and the Dutch painter M. C. Escher ), actively took part in the work of the cinema club in Yaroslavl and the music club at the House of Composers in Moscow , and was a continual participant of conferences on mathematical linguistics and on semiotics ." [ 5 ]
Yaglom started his higher education at Moscow State University in 1938. During World War II he volunteered, but due to myopia he was deferred from military service. In the evacuation of Moscow he went with his family to Sverdlovsk in the Ural Mountains . He studied at Sverdlovsk State University , graduated in 1942, and when the usual Moscow faculty assembled in Sverdlovsk during the war, he took up graduate study. Under the geometer Veniamin Kagan he developed his Ph.D. thesis which he defended in Moscow in 1945. It is reported that this thesis "was devoted to projective metrics on a plane and their connections with different types of complex numbers a + j b {\displaystyle a+jb} (where j j = − 1 {\displaystyle jj=-1} , or j j = + 1 {\displaystyle jj=+1} , or else j j = 0 {\displaystyle jj=0} )." [ 5 ]
During his career, Yaglom was affiliated with these institutions: [ 5 ]
In 1962 Yaglom and Vladimir G. Ashkinuse published Ideas and Methods of Affine and Projective Geometry , in Russian. The text is limited to affine geometry since projective geometry was put off to a second volume that did not appear. The concept of hyperbolic angle is developed through area of hyperbolic sectors . A treatment of Routh's theorem is given at page 193. This textbook, published by the Ministry of Education , includes 234 exercises with hints and solutions in an appendix.
Isaac Yaglom wrote over 40 books and many articles. Several were translated, and appeared in the year given:
Translated by Eric J. F. Primrose, published by Academic Press (N.Y.). The trinity of complex number planes is laid out and exploited. Topics include line coordinates in the Euclidean and Lobachevski planes, and inversive geometry .
The first three books were originally published in English by Random House as part of the series New Mathematical Library (Volumes 8, 21, and 24). They were keenly appreciated by proponents of the New Math in the U.S.A., but represented only a part of Yaglom's two-volume original published in Russian in 1955 and 56. More recently the final portion of Yaglom's work was translated into English and published by the Mathematical Association of America . All four volumes are now available from the MAA in the series Anneli Lax New Mathematical Library (Volumes 8, 21, 24, and 44).
Subtitle: An elementary account of Galilean geometry and the Galilean principle of relativity . Translated by Abe Shenitzer, published by Springer-Verlag . In his prefix, the translator says the book is "a fascinating story which flows from one geometry to another, from geometry to algebra, and from geometry to kinematics , and in so doing crosses artificial boundaries separating one area of mathematics from another and mathematics from physics." The author's own prefix speaks of "the important connection between Klein's Erlanger Program and the principles of relativity."
The approach taken is elementary; simple manipulations by shear mapping lead on page 68 to the conclusion that "the difference between the Galilean geometry of points and the Galilean geometry of lines is just a matter of terminology".
The concepts of the dual number and its "imaginary" ε, ε 2 = 0, do not appear in the development of Galilean geometry. However, Yaglom shows that the common slope concept in analytic geometry corresponds to the Galilean angle . Yaglom extensively develops his non-Euclidean geometry including the theory of cycles (pp. 77–79), duality , and the circumcycle and incycle of a triangle (p. 104).
Yaglom continues with his Galilean study to the inversive Galilean plane by including a special line at infinity and showing the topology with a stereographic projection. The Conclusion of the book delves into the Minkowskian geometry of hyperbolas in the plane, including the nine-point hyperbola . Yaglom also covers the inversive Minkowski plane .
Co-author: A. M. Yaglom . Russian editions in 1956, 59 and 72. Translated by V. K. Jain, published by D. Reidel and the Hindustan Publishing Corporation, India.
The channel capacity work of Claude Shannon is developed from first principles in four chapters: probability, entropy and information, information calculation to solve logical problems, and applications to information transmission. The final chapter is well-developed including code efficiency, Huffman codes , natural language and biological information channels, influence of noise, and error detection and correction.
Co-author: A. M. Yaglom . Two volumes. Russian edition in 1954. First English edition 1964–1967
Subtitle: The evolution of the idea of symmetry in the 19th century.
In his chapter on "Felix Klein and his Erlangen Program", Yaglom says that "finding a general description of all geometric systems [was] considered by mathematicians the central question of the day." [ 6 ] The subtitle more accurately describes the book than the main title, since a great number of mathematicians are credited in this account of the modern tools and methods of symmetry.
In 2009 the book was republished by Ishi Press as Geometry, Groups and Algebra in the Nineteenth Century . The new edition, designed by Sam Sloan , has a foreword by Richard Bozulich . | https://en.wikipedia.org/wiki/Isaak_Yaglom |
Isabella M. Gioia is an Italian astrophysicist. She is currently a Research Associate at INAF in Bologna, Italy .
While a visiting astronomer at the University of Hawaii Institute for Astronomy, she was a member of the Chandra Science Center. [ 1 ] As of 2012, she had been a member of the American Astronomical Society for 25 years. [ 2 ] She was included in the 1996-1997 edition of Who's Who in Science and Engineering . [ 3 ] She was listed in ISI's 1120 World's Most Cited Physicists (1981–1997) with 65 articles, 2397 citations, and an average of 36.88 citations per article as of the time of publication. [ 4 ] | https://en.wikipedia.org/wiki/Isabella_M._Gioia |
Isadore Perlman (April 12, 1915 – August 3, 1991) was an American nuclear chemist noted for his research of Alpha particle decay . [ 1 ] [ 2 ] [ 3 ] [ 4 ] The National Academy of Sciences called Perlman "a world leader on the systematics of alpha decay". [ 2 ] He was also recognized for his research of nuclear structure of the heavy elements. [ 2 ] He was also noted for his isolation of Curium , [ 5 ] [ 6 ] as well as for fission of tantalum , bismuth , lead , thallium and platinum . [ 7 ] Perlman discovered uses of radioactive iodine and phosphorus for medical purposes. [ 2 ] He played a key role in Manhattan Project 's plutonium production. [ 2 ]
He was also a top expert in the field of archaeometry . He pioneered high-precision methods of neutron activation analysis at the Lawrence Berkeley Laboratory in the US. Neutron activation analysis helps to determine the origin of ancient pottery and other artifacts through the analysis of the clay from which they were made. He was helped in the project by another noted scientist Frank Asaro . Second millennium BC pottery known as Cypriot Bichrome ware was one of the first archaeological projects that Perlman and Asaro undertook.
Perlman was a member of the National Academy of Sciences , [ 2 ] [ 8 ] a member of the American Academy of Arts and Sciences , [ 2 ] a member of the Danish Royal Academy, [ 2 ] chairman of the Department of Chemistry of the University of California, Berkeley , [ 2 ] head of the Nuclear Chemistry Division and an associate director of the Lawrence Radiation Laboratory . [ 2 ]
In 2006, Perlman's former student and collaborator Frank Asaro transferred archives of their work at Lawrence Berkeley National Laboratory to the University of Missouri Research Reactor Center with the request that they transcribe these data and share them with the scientific community. After more than a decade, a (nearly) comprehensive archive of the work of Asaro, Perlman, and Michel on the geochemistry of archaeological and geological samples was produced by Matthew T. Boulanger. [ 9 ] This archive was provided to the scientific community via the Digital Archaeological Record (tDAR) . The knowledge and experiences gained through working with these records has been used to recommend best practices to modern laboratories producing similar data to ensure that they remain useful into the future. [ 9 ] [ 10 ] | https://en.wikipedia.org/wiki/Isadore_Perlman |
Isaiah Shavitt ( Hebrew : ישעיהו שביט ) was a Polish-born Israeli and American theoretical chemist .
He was born Isaiah Kruk [ 1 ] on July 29, 1925, in Kutno , Poland but his family moved to what would become Israel in 1929. After undergraduate degrees in chemistry (1950) and chemical engineering (1951) from the Technion in Haifa , he started a Ph.D. in experimental physical chemistry, but shortly after traveled to Cambridge University on a British Council Scholarship and completed his Ph.D. (1957) under the aegis of pioneering computational chemist S. Francis Boys . [ 2 ]
Following postdoctoral work with Joseph O. Hirschfelder , a stint as a temporary assistant professor at Brandeis University , and further postdoctoral research with Martin Karplus , he became a professor at his alma mater in 1962. In 1967 he moved to a senior research position at Battelle Memorial Institute in Columbus , Ohio , United States . In 1968 he also became a part-time faculty member at the department of chemistry at Ohio State University and moved there full-time in 1981. In 1994 he retired from this position and continued part-time as an emeritus professor. Until his death he was also an adjunct professor in the department of chemistry at the University of Illinois at Urbana-Champaign , US. [ 2 ]
Shavitt's landmark achievements include being responsible for two of the first applications of the then newly available computer to chemistry; developing the Gaussian transform method [ 3 ] for calculating multicenter integrals of Slater-type orbitals ; coining the concept of contracted Gaussian-type orbitals ; the GUGA (Graphical Unitary Group Approach) to fast configuration interaction calculations; and major contributions to coupled cluster theory.
He is one of the founding authors of the COLUMBUS suite of ab initio computational chemistry programs.
An International Conference, entitled Molecular Quantum Mechanics: Methods and Applications" was held in memory of S. Francis Boys and in honor of Isaiah Shavitt in September, 1995 at St Catharine's College, Cambridge , and the proceedings published as a special issue [ 4 ] of the Journal of Physical Chemistry .
He was a member of the International Academy of Quantum Molecular Science .
Shavitt died at the age of 87 on Dec. 8, 2012 at Carle Foundation Hospital , Urbana. [ 1 ]
See also Zimmerman, S. C.; Pitzer, R. M. (2014). "Isaiah Shavitt: Computational chemistry pioneer". Theoretical Chemistry Accounts . 133 (6): 1488. doi : 10.1007/s00214-014-1488-3 . S2CID 120618516 . I.Shavitt in methods of computational Physics vol.2 Academic(1963) | https://en.wikipedia.org/wiki/Isaiah_Shavitt |
The Isay reaction also known as Gabriel-Isay condensation is an organic reaction in which certain diaminopyrimidines are transformed into pterins by condensation with a 1,2-dicarbonyl compound, such as 2,3-butanedione . [ 1 ] [ 2 ] The reaction is named after Oskar Isay .
This chemical reaction article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Isay_reaction |
The IscR stability element is a conserved secondary structure found in the intergenic regions of iscRSUA polycistronic mRNA . This secondary structure prevents the degradation of the iscR mRNA .
The iscRSUA operon encodes for the proteins required in iron–sulfur cluster biosynthesis where the expression of this operon is regulated by RyhB and iscR, a transcription repressor. [ 1 ] [ 2 ] [ 3 ] Under sufficient iron conditions RyhB binds to iscRSUA mRNA and promotes the degradation of the mRNA located downstream of iscR. Scanning the intergenic regions of this polycistronic mRNA and using Mfold software a secondary structure was predicted within the intergenic region between iscR and iscS and later confirmed by lead acetate probing. [ 4 ] Mutations that disrupt this secondary structure resulted in the degradation of iscR mRNA after RyhB binding. 3′ RACE analysis of the iscR mRNA fragment identified the intergenic RNA at the 3′ end. These results suggest that this intergenic RNA element acts as an iscR mRNA stability element by protecting iscR from exonuclease degradation. | https://en.wikipedia.org/wiki/IscR_stability_element |
The ischemic (ischaemic) cascade is a series of biochemical reactions that are initiated in the brain and other aerobic tissues after seconds to minutes of ischemia (inadequate blood supply). [ 1 ] This is typically secondary to stroke , injury, or cardiac arrest due to heart attack . Most ischemic neurons that die do so due to the activation of chemicals produced during and after ischemia. [ 2 ] The ischemic cascade usually goes on for two to three hours but can last for days, even after normal blood flow returns. [ 3 ]
A cascade is a series of events in which one event triggers the next, in a linear fashion. Thus "ischemic cascade" is actually a misnomer, since the events are not always linear: in some cases they are circular, and sometimes one event can cause or be caused by multiple events. [ 4 ] In addition, cells receiving different amounts of blood may go through different chemical processes. Despite these facts, the ischemic cascade can be generally characterized as follows: [ citation needed ]
The fact that the ischemic cascade involves a number of steps has led doctors to suspect that cerebroprotectants could be produced to interrupt the cascade at a single one of the steps, blocking the downstream effects. Over 150 cerebroprotectants have been tested in clinical trials, leading to the approval of tissue plasminogen activator (also known as tPA, t-PA, rtPA, Activase, or Alteplase or Actilyse) [ 7 ] in the US and other countries, and edaravone (Radicut) in Japan. [ 8 ] | https://en.wikipedia.org/wiki/Ischemic_cascade |
Ischemic cell death , or oncosis , is a form of accidental cell death. The process is characterized by an ATP depletion within the cell leading to impairment of ionic pumps, cell swelling, clearing of the cytosol , dilation of the endoplasmic reticulum and golgi apparatus , mitochondrial condensation, chromatin clumping, and cytoplasmic bleb formation. [ 1 ] Oncosis refers to a series of cellular reactions following injury that precedes cell death. The process of oncosis is divided into three stages. First, the cell becomes committed to oncosis as a result of damage incurred to the plasma membrane through toxicity or ischemia, resulting in the leak of ions and water due to ATP depletion. [ 1 ] The ionic imbalance that occurs subsequently causes the cell to swell without a concurrent change in membrane permeability to reverse the swelling. [ 1 ] In stage two, the reversibility threshold for the cell is passed and the cell becomes committed to cell death. During this stage the membrane becomes abnormally permeable to trypan blue and propidium iodide , indicating membrane compromise. [ 1 ] The final stage is cell death and removal of the cell via phagocytosis mediated by an inflammatory response. [ 2 ]
Although ischemic cell death is the accepted name of the process, the alternative name of oncosis was introduced as the process involves the affected cell(s) swelling to an abnormally large size in known models. This is thought to be caused by failure of the plasma membrane's ionic pumps. The name oncosis (derived from ónkos , meaning largeness, and ónkosis , meaning swelling) was first introduced in 1910 by pathologist Friedrich Daniel von Recklinghausen . [ 3 ]
Oncosis and apoptosis are distinct processes of cellular death. Oncosis is characterized by cellular swelling caused by a failure in ion transporter function. Apoptosis, or programmed cell death involves a series of cell shrinking processes, beginning with cell size reduction and pyknosis , followed by cell budding and karyorrhexis , and phagocytosis by macrophages or neighboring cells due to size decrease. [ 3 ] The phagocytic disposal of apoptotic cells prevents the release of cellular debris that could induce an inflammatory response in neighboring cells. In opposition, the leakage of cellular content associated with membrane disruption in oncosis often incites an inflammatory response in neighboring tissue, causing further cellular injury. [ 3 ] Additionally, apoptosis and the degradation of intracellular organelles is mediated by caspase activation, particularly caspase-3 . [ 4 ] Oligonuclosomal DNA fragmentation is initiated by caspase-activated deoxyribonuclease following caspase-3 mediated cleavage of the enzyme’s inhibitor, ICAD. [ 5 ] In contrast, the oncotic pathway has been shown to be caspase-3 independent. [ 1 ]
The primary determinant of cell death occurring via the oncotic or apoptotic pathway is cellular ATP levels. Apoptosis is contingent upon ATP levels to form the energy dependent apoptosome . A distinct biochemical event only seen in oncosis is the rapid depletion of intracellular ATP. [ 6 ] The lack of intracellular ATP results in a deactivation of sodium and potassium ATPase within the compromised cell membrane. The lack of ion transport at the cell membrane leads to an accumulation of sodium and chloride ions within the cell with a concurrent water influx, contributing to the hallmark cellular swelling of oncosis. [ 7 ] As with apoptosis, oncosis has been shown to be genetically programmed and dependent on expression levels of uncoupling protein-2 (UCP-2) in HeLa cells . An increase in UCP-2 levels leads to a rapid decrease in mitochondrial membrane potential, reducing mitochondrial NADH and intracellular ATP levels, initiating the oncotic pathway. The anti-apoptotic gene product Bcl-2 is not an active inhibitor of UCP-2 initiated cell death, further distinguishing oncosis and apoptosis as distinct cellular death mechanisms. [ 8 ] | https://en.wikipedia.org/wiki/Ischemic_cell_death |
The Ishango bone , discovered at the "Fisherman Settlement" of Ishango in the Democratic Republic of the Congo , is a bone tool and possible mathematical device that dates to the Upper Paleolithic era. [ 1 ] The curved bone is dark brown in color, about 10 centimeters in length, and features a sharp piece of quartz affixed to one end, perhaps for engraving. [ 1 ] Because the bone has been narrowed, scraped, polished, and engraved to a certain extent, it is no longer possible to determine what animal the bone belonged to, although it is assumed to have been a mammal. [ 2 ]
The ordered engravings have led many to speculate the meaning behind these marks, including interpretations like mathematical significance or astrological relevance. It is thought by some to be a tally stick , as it features a series of what has been interpreted as tally marks carved in three columns running the length of the tool, though it has also been suggested that the scratches might have been to create a better grip on the handle or for some other non-mathematical reason. Others argue that the marks on the object are non-random and that it was likely a kind of counting tool and used to perform simple mathematical procedures. [ 3 ] [ 4 ] Other speculations include the engravings on the bone serving as a lunar calendar. Dating to 20,000 years before present, it has been described as "the oldest mathematical tool of humankind", [ 1 ] though older engraved bones are also known, such as the approximately 26,000-year-old "Wolf Bone" from Dolni Vestonice in the Czech Republic , [ 5 ] [ 6 ] and the approximately 40,000-year-old Lebombo bone from southern Africa.
The Ishango bone was found in 1950 by Belgian Jean de Heinzelin de Braucourt while exploring what was then the Belgian Congo . [ 7 ] It was discovered in the area of Ishango near the Semliki River . Lake Edward empties into the Semliki, which forms part of the headwaters of the Nile River (now on the border between modern-day Uganda and D.R. Congo ). Some archaeologists believe the prior inhabitants of Ishango were a "pre- sapiens species". However, the most recent inhabitants, who gave the area its name, have no immediate connections with the primary settlement, which was "buried in a volcanic eruption". [ 8 ]
On an excavation, de Heinzelin discovered a bone about the "size of a pencil" amongst human remains and many stone tools in a small community that fished and gathered in this area of Africa. [ 8 ] Professor de Heinzelin brought the Ishango bone to Belgium , where it was stored in the treasure room of the Royal Belgian Institute of Natural Sciences in Brussels. [ 8 ] Several molds and copies were created from the petrified bone in order to preserve the delicate nature of the fragile artifact while being exported. [ 8 ] A written request to the museum was required to see the artifact, as it was no longer on display for the public eye. [ 8 ]
The artifact was first estimated to have originated between 9,000 BCE and 6,500 BCE, with numerous other analyses debating the bone to be as old as 44,000 years. [ 4 ] However, the dating of the site where it was discovered was re-evaluated, and it is now believed to be about 20,000 years old (dating from between 18,000 BCE and 20,000 BCE). [ 9 ] [ 10 ] The dating of this bone is widely debated in the archaeological community, as the ratio of carbon isotopes was upset by nearby volcanic activity. [ 8 ]
The 168 etchings on the bone are ordered in three parallel columns along the length of the bone, each marking with a varying orientation and length. [ 1 ] The first column, or central column along the most curved side of the bone, is referred to as the M column, from the French word milieu (middle). [ 1 ] The left and right columns are respectively referred to as G and D, or gauche (left) and droite (right) in French. [ 1 ] The parallel markings have led to various tantalizing hypotheses, such as that the implement indicates an understanding of decimals or prime numbers . Though these propositions have been questioned, it is considered likely by many scholars that the tool was used for mathematical purposes, perhaps including simple mathematical procedures or to construct a numeral system . [ 4 ]
Discoverer of the Ishango bone, de Heinzelin, suggested that the bone was evidence of knowledge of simple arithmetic, or at least that the markings were "deliberately planned". [ 1 ] [ 7 ] He based his interpretation on archaeological evidence, comparing "Ishango harpoon heads to those found in northern Sudan and ancient Egypt". [ 8 ] This comparison led to the suggestion of a link between arithmetic processes conducted at Ishango with the "commencement of mathematics in ancient Egypt." [ 8 ] The third column has been interpreted as a "table of prime numbers", as column G appears to illustrate prime numbers between 10 and 20, [ 1 ] but this may be a coincidence. [ 4 ] Historian of mathematics Peter S. Rudman argues that prime numbers were probably not understood until the early Greek period of about 500 BCE, and were dependent on the concept of division, which he dates to no earlier than 10,000 BCE. [ 11 ]
More recently, mathematicians Dirk Huylebrouck and Vladimir Pletser have proposed that the Ishango bone is a counting tool using the base 12 and sub-bases 3 and 4, and involving simple multiplication, somewhat comparable to a primitive slide rule . However, they have concluded that there is not sufficient evidence to confirm an understanding of prime numbers during this time period. [ 1 ] [ 2 ] [ 12 ]
Anthropologist Caleb Everett has also provided insight into interpretations of the bone, explaining that "the quantities evident in the groupings of marks are not random", and are likely evidence of prehistoric numerals. Everett suggests that the first column may reflect some "doubling pattern" and that the tool may have been used for counting and multiplication and also possibly as a "numeric reference table". [ 4 ]
Alexander Marshack , an archaeologist from Harvard University, speculated that the Ishango bone represents numeric notation of a six-month lunar calendar after conducting a "detailed microscopic examination" of the bone. [ 8 ] [ 1 ] [ 2 ] [ 9 ] This idea arose from the fact that the markings on the first two rows adds up to 60, corresponding with two lunar months, and the sum of the number of carvings on the last row being 48, or a month and a half. [ 8 ] Marshack generated a diagram comparing the different sizes and phases of the Moon with the notches of the Ishango bone. [ 8 ] There is some circumstantial evidence to support this alternate hypothesis, being that present day African societies utilize bones, strings, and other devices as calendars. [ 1 ] However, critics in the field of archaeology have concluded that Marshack's interpretation is flawed, describing that his analysis of the Ishango bone confines itself to a simple search for a pattern, rather than an actual test of his hypothesis. [ 9 ]
This has also led Claudia Zaslavsky to suggest that the creator of the tool may have been a woman, tracking the lunar phase in relation to the menstrual cycle . [ 13 ] [ 14 ]
Mathematician Olivier Keller warns against the urge to project modern culture's perception of numbers onto the Ishango bone. [ 2 ] Keller explains that this practice encourages observers to negate and possibly ignore alternative symbolic materials, those which are present in a range of media (on human remains, stones and cave art) from the Upper Paleolithic era and beyond which also deserve equitable investigation. [ 2 ] Dirk Huylebrouck, in a review of the research on the object, favors the idea that the Ishango bone had some advanced mathematical use, stating that "whatever the interpretation, the patterns surely show the bone was more than a simple tally stick." [ 1 ] [ 8 ] He also remarks that "to credit the computational and astronomical reading simultaneously would be far-fetched", quoting mathematician George Joseph , who stated that "a single bone may well collapse under the heavy weight of conjectures piled onto it." [ 8 ] Similarly, George Joseph, in "The Crest of the Peacock: Non-European Roots of Mathematics" also stated that the Ishango bone was "more than a simple tally." Moreover, he states that "certain underlying numerical patterns may be observed within each of the rows marked." [ 15 ] But, regarding various speculative theories of its exact mathematical use, concluded that several are plausible but uncertain. | https://en.wikipedia.org/wiki/Ishango_bone |
Ishikawa's reagent is a fluorinating reagent used in organic chemistry. It is used to convert alcohols into alkyl fluorides and carboxylic acids into acyl fluorides . Aldehydes and ketones do not react with it. The reagent consists of a mixture of N , N -diethyl-(1,1,2,3,3,3-hexafluoropropyl)amine and N , N -diethyl-( E )-pentafluoropropenylamine in varying proportions. The active species is the hexafluoropropylamine; any enamine is converted into this by the hydrogen fluoride byproduct as the reaction proceeds.
Ishikawa's reagent is a popular alternative to the DAST reagent, since it is shelf-stable and easily prepared from inexpensive and innocuous reagents. It is an improvement on Yarovenko's reagent , the adduct of chlorotrifluoroethylene and diethylamine , which must be prepared in a sealed vessel and once prepared keeps only for a few days, even in the refrigerator.
The reagent is mostly used to convert primary alcohols to alkyl fluorides under mild conditions with high yield. However, secondary and tertiary alcohols give a substantial amount of alkenes and ethers as side products.
The compound is prepared by adding hexafluoropropene to a solution of diethylamine in ether at 0 °C and distilling the product in vacuo . The amount of enamine in the product depends on temperature control during the reaction – the higher the temperature the more enamine. | https://en.wikipedia.org/wiki/Ishikawa_reagent |
The Ishimori equation is a partial differential equation proposed by the Japanese mathematician Ishimori (1984) . Its interest is as the first example of a nonlinear spin-one field model in the plane that is integrable ( Sattinger, Tracy & Venakides 1991 , p. 78).
The Ishimori equation has the form
The Lax representation
of the equation is given by
Here
the σ i {\displaystyle \sigma _{i}} are the Pauli matrices and I {\displaystyle I} is the identity matrix.
The Ishimori equation admits an important reduction:
in 1+1 dimensions it reduces to the continuous classical Heisenberg ferromagnet equation (CCHFE). The CCHFE is integrable.
The equivalent counterpart of the Ishimori equation is the Davey-Stewartson equation .
This condensed matter physics -related article is a stub . You can help Wikipedia by expanding it .
This electromagnetism -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Ishimori_equation |
The Ising model (or Lenz–Ising model ), named after the physicists Ernst Ising and Wilhelm Lenz , is a mathematical model of ferromagnetism in statistical mechanics . The model consists of discrete variables that represent magnetic dipole moments of atomic "spins" that can be in one of two states (+1 or −1). The spins are arranged in a graph , usually a lattice (where the local structure repeats periodically in all directions), allowing each spin to interact with its neighbors. Neighboring spins that agree have a lower energy than those that disagree; the system tends to the lowest energy but heat disturbs this tendency, thus creating the possibility of different structural phases. The model allows the identification of phase transitions as a simplified model of reality. The two-dimensional square-lattice Ising model is one of the simplest statistical models to show a phase transition . [ 1 ]
The Ising model was invented by the physicist Wilhelm Lenz ( 1920 ), who gave it as a problem to his student Ernst Ising. The one-dimensional Ising model was solved by Ising (1925) alone in his 1924 thesis; [ 2 ] it has no phase transition. The two-dimensional square-lattice Ising model is much harder and was only given an analytic description much later, by Lars Onsager ( 1944 ). It is usually solved by a transfer-matrix method , although there exists a very simple approach relating the model to a non-interacting fermionic quantum field theory . [ 3 ]
In dimensions greater than four, the phase transition of the Ising model is described by mean-field theory . The Ising model for greater dimensions was also explored with respect to various tree topologies in the late 1970s, culminating in an exact solution of the zero-field, time-independent Barth (1981) model for closed Cayley trees of arbitrary branching ratio, and thereby, arbitrarily large dimensionality within tree branches. The solution to this model exhibited a new, unusual phase transition behavior, along with non-vanishing long-range and nearest-neighbor spin-spin correlations, deemed relevant to large neural networks as one of its possible applications .
The Ising problem without an external field can be equivalently formulated as a graph maximum cut (Max-Cut) problem that can be solved via combinatorial optimization .
Consider a set Λ {\displaystyle \Lambda } of lattice sites, each with a set of adjacent sites (e.g. a graph ) forming a d {\displaystyle d} -dimensional lattice. For each lattice site k ∈ Λ {\displaystyle k\in \Lambda } there is a discrete variable σ k {\displaystyle \sigma _{k}} such that σ k ∈ { − 1 , + 1 } {\displaystyle \sigma _{k}\in \{-1,+1\}} , representing the site's spin. A spin configuration , σ = { σ k } k ∈ Λ {\displaystyle {\sigma }=\{\sigma _{k}\}_{k\in \Lambda }} is an assignment of spin value to each lattice site.
For any two adjacent sites i , j ∈ Λ {\displaystyle i,j\in \Lambda } there is an interaction J i j {\displaystyle J_{ij}} . Also a site j ∈ Λ {\displaystyle j\in \Lambda } has an external magnetic field h j {\displaystyle h_{j}} interacting with it. The energy of a configuration σ {\displaystyle {\sigma }} is given by the Hamiltonian function
H ( σ ) = − ∑ ⟨ i j ⟩ J i j σ i σ j − μ ∑ j h j σ j , {\displaystyle H(\sigma )=-\sum _{\langle ij\rangle }J_{ij}\sigma _{i}\sigma _{j}-\mu \sum _{j}h_{j}\sigma _{j},}
where the first sum is over pairs of adjacent spins (every pair is counted once). The notation ⟨ i j ⟩ {\displaystyle \langle ij\rangle } indicates that sites i {\displaystyle i} and j {\displaystyle j} are nearest neighbors. The magnetic moment is given by μ {\displaystyle \mu } . Note that the sign in the second term of the Hamiltonian above should actually be positive because the electron's magnetic moment is antiparallel to its spin, but the negative term is used conventionally. [ 4 ] The Ising Hamiltonian is an example of a pseudo-Boolean function ; tools from the analysis of Boolean functions can be applied to describe and study it.
The configuration probability is given by the Boltzmann distribution with inverse temperature β ≥ 0 {\displaystyle \beta \geq 0} :
P β ( σ ) = e − β H ( σ ) Z β , {\displaystyle P_{\beta }(\sigma )={\frac {e^{-\beta H(\sigma )}}{Z_{\beta }}},}
where β = 1 / ( k B T ) {\displaystyle \beta =1/(k_{\text{B}}T)} , and the normalization constant
Z β = ∑ σ e − β H ( σ ) {\displaystyle Z_{\beta }=\sum _{\sigma }e^{-\beta H(\sigma )}}
is the partition function . For a function f {\displaystyle f} of the spins ("observable"), one denotes by
⟨ f ⟩ β = ∑ σ f ( σ ) P β ( σ ) {\displaystyle \langle f\rangle _{\beta }=\sum _{\sigma }f(\sigma )P_{\beta }(\sigma )}
the expectation (mean) value of f {\displaystyle f} .
The configuration probabilities P β ( σ ) {\displaystyle P_{\beta }(\sigma )} represent the probability that (in equilibrium) the system is in a state with configuration σ {\displaystyle \sigma } .
The minus sign on each term of the Hamiltonian function H ( σ ) {\displaystyle H(\sigma )} is conventional. Using this sign convention, Ising models can be classified according to the sign of the interaction: if, for a pair i , j
The system is called ferromagnetic or antiferromagnetic if all interactions are ferromagnetic or all are antiferromagnetic. The original Ising models were ferromagnetic, and it is still often assumed that "Ising model" means a ferromagnetic Ising model.
In a ferromagnetic Ising model, spins desire to be aligned: the configurations in which adjacent spins are of the same sign have higher probability. In an antiferromagnetic model, adjacent spins tend to have opposite signs.
The sign convention of H (σ) also explains how a spin site j interacts with the external field. Namely, the spin site wants to line up with the external field. If:
Ising models are often examined without an external field interacting with the lattice, that is, h = 0 for all j in the lattice Λ. Using this simplification, the Hamiltonian becomes
H ( σ ) = − ∑ ⟨ i j ⟩ J i j σ i σ j . {\displaystyle H(\sigma )=-\sum _{\langle i~j\rangle }J_{ij}\sigma _{i}\sigma _{j}.}
When the external field is zero everywhere, h = 0, the Ising model is symmetric under switching the value of the spin in all the lattice sites; a nonzero field breaks this symmetry.
Another common simplification is to assume that all of the nearest neighbors ⟨ ij ⟩ have the same interaction strength. Then we can set J ij = J for all pairs i , j in Λ. In this case the Hamiltonian is further simplified to
H ( σ ) = − J ∑ ⟨ i j ⟩ σ i σ j . {\displaystyle H(\sigma )=-J\sum _{\langle i~j\rangle }\sigma _{i}\sigma _{j}.}
A subset S of the vertex set V(G) of a weighted undirected graph G determines a cut of the graph G into S and its complementary subset G\S. The size of the cut is the sum of the weights of the edges between S and G\S. A maximum cut size is at least the size of any other cut, varying S.
For the Ising model without an external field on a graph G, the Hamiltonian becomes the following sum over the graph edges E(G)
Here each vertex i of the graph is a spin site that takes a spin value σ i = ± 1 {\displaystyle \sigma _{i}=\pm 1} . A given spin configuration σ {\displaystyle \sigma } partitions the set of vertices V ( G ) {\displaystyle V(G)} into two σ {\displaystyle \sigma } -depended subsets, those with spin up V + {\displaystyle V^{+}} and those with spin down V − {\displaystyle V^{-}} . We denote by δ ( V + ) {\displaystyle \delta (V^{+})} the σ {\displaystyle \sigma } -depended set of edges that connects the two complementary vertex subsets V + {\displaystyle V^{+}} and V − {\displaystyle V^{-}} . The size | δ ( V + ) | {\displaystyle \left|\delta (V^{+})\right|} of the cut δ ( V + ) {\displaystyle \delta (V^{+})} to bipartite the weighted undirected graph G can be defined as
| δ ( V + ) | = 1 2 ∑ i j ∈ δ ( V + ) W i j , {\displaystyle \left|\delta (V^{+})\right|={\frac {1}{2}}\sum _{ij\in \delta (V^{+})}W_{ij},}
where W i j {\displaystyle W_{ij}} denotes a weight of the edge i j {\displaystyle ij} and the scaling 1/2 is introduced to compensate for double counting the same weights W i j = W j i {\displaystyle W_{ij}=W_{ji}} .
The identities
H ( σ ) = − ∑ i j ∈ E ( V + ) J i j − ∑ i j ∈ E ( V − ) J i j + ∑ i j ∈ δ ( V + ) J i j = − ∑ i j ∈ E ( G ) J i j + 2 ∑ i j ∈ δ ( V + ) J i j , {\displaystyle {\begin{aligned}H(\sigma )&=-\sum _{ij\in E(V^{+})}J_{ij}-\sum _{ij\in E(V^{-})}J_{ij}+\sum _{ij\in \delta (V^{+})}J_{ij}\\&=-\sum _{ij\in E(G)}J_{ij}+2\sum _{ij\in \delta (V^{+})}J_{ij},\end{aligned}}}
where the total sum in the first term does not depend on σ {\displaystyle \sigma } , imply that minimizing H ( σ ) {\displaystyle H(\sigma )} in σ {\displaystyle \sigma } is equivalent to minimizing ∑ i j ∈ δ ( V + ) J i j {\displaystyle \sum _{ij\in \delta (V^{+})}J_{ij}} . Defining the edge weight W i j = − J i j {\displaystyle W_{ij}=-J_{ij}} thus turns the Ising problem without an external field into a graph Max-Cut problem [ 5 ] maximizing the cut size | δ ( V + ) | {\displaystyle \left|\delta (V^{+})\right|} , which is related to the Ising Hamiltonian as follows,
H ( σ ) = ∑ i j ∈ E ( G ) W i j − 4 | δ ( V + ) | . {\displaystyle H(\sigma )=\sum _{ij\in E(G)}W_{ij}-4\left|\delta (V^{+})\right|.}
A significant number of statistical questions to ask about this model are in the limit of large numbers of spins:
The most studied case of the Ising model is the translation-invariant ferromagnetic zero-field model on a d -dimensional lattice, namely, Λ = Z d , J ij = 1, h = 0.
In his 1924 PhD thesis, Ising solved the model for the d = 1 case, which can be thought of as a linear horizontal lattice where each site only interacts with its left and right neighbor. In one dimension, the solution admits no phase transition . [ 6 ] Namely, for any positive β, the correlations ⟨σ i σ j ⟩ decay exponentially in | i − j |: ⟨ σ i σ j ⟩ β ≤ C exp ( − c ( β ) | i − j | ) , {\displaystyle \langle \sigma _{i}\sigma _{j}\rangle _{\beta }\leq C\exp \left(-c(\beta )|i-j|\right),}
and the system is disordered. On the basis of this result, he incorrectly concluded [ citation needed ] that this model does not exhibit phase behaviour in any dimension.
The Ising model undergoes a phase transition between an ordered and a disordered phase in 2 dimensions or more. Namely, the system is disordered for small β, whereas for large β the system exhibits ferromagnetic order:
⟨ σ i σ j ⟩ β ≥ c ( β ) > 0. {\displaystyle \langle \sigma _{i}\sigma _{j}\rangle _{\beta }\geq c(\beta )>0.}
This was first proven by Rudolf Peierls in 1936, [ 7 ] using what is now called a Peierls argument .
The Ising model on a two-dimensional square lattice with no magnetic field was analytically solved by Lars Onsager ( 1944 ). Onsager obtained the correlation functions and free energy of the Ising model and announced the formula for the spontaneous magnetization for the 2-dimensional model in 1949 but did not give a derivation. Yang (1952) gave the first published proof of this formula, using a limit formula for Fredholm determinants , proved in 1951 by Szegő in direct response to Onsager's work. [ 8 ]
A number of correlation inequalities have been derived rigorously for the Ising spin correlations (for general lattice structures), which have enabled mathematicians to study the Ising model both on and off criticality.
Given any subset of spins σ A {\displaystyle \sigma _{A}} and σ B {\displaystyle \sigma _{B}} on the lattice, the following inequality holds,
⟨ σ A σ B ⟩ ≥ ⟨ σ A ⟩ ⟨ σ B ⟩ , {\displaystyle \langle \sigma _{A}\sigma _{B}\rangle \geq \langle \sigma _{A}\rangle \langle \sigma _{B}\rangle ,}
where ⟨ σ A ⟩ = ⟨ ∏ j ∈ A σ j ⟩ {\displaystyle \langle \sigma _{A}\rangle =\langle \prod _{j\in A}\sigma _{j}\rangle } .
With B = ∅ {\displaystyle B=\emptyset } , the special case ⟨ σ A ⟩ ≥ 0 {\displaystyle \langle \sigma _{A}\rangle \geq 0} results.
This means that spins are positively correlated on the Ising ferromagnet. An immediate application of this is that the magnetization of any set of spins ⟨ σ A ⟩ {\displaystyle \langle \sigma _{A}\rangle } is increasing with respect to any set of coupling constants J B {\displaystyle J_{B}} .
The Simon-Lieb inequality [ 9 ] states that for any set S {\displaystyle S} disconnecting x {\displaystyle x} from y {\displaystyle y} (e.g. the boundary of a box with x {\displaystyle x} being inside the box and y {\displaystyle y} being outside),
⟨ σ x σ y ⟩ ≤ ∑ z ∈ S ⟨ σ x σ z ⟩ ⟨ σ z σ y ⟩ . {\displaystyle \langle \sigma _{x}\sigma _{y}\rangle \leq \sum _{z\in S}\langle \sigma _{x}\sigma _{z}\rangle \langle \sigma _{z}\sigma _{y}\rangle .}
This inequality can be used to establish the sharpness of phase transition for the Ising model. [ 10 ]
This inequality is proven first for a type of positively-correlated percolation model , of which includes a representation of the Ising model. It is used to determine the critical temperatures of planar Potts model using percolation arguments (which includes the Ising model as a special case). [ 11 ]
One of Democritus ' arguments in support of atomism was that atoms naturally explain the sharp phase boundaries observed in materials [ citation needed ] , as when ice melts to water or water turns to steam. His idea was that small changes in atomic-scale properties would lead to big changes in the aggregate behavior. Others believed that matter is inherently continuous, not atomic, and that the large-scale properties of matter are not reducible to basic atomic properties.
While the laws of chemical bonding made it clear to nineteenth century chemists that atoms were real, among physicists the debate continued well into the early twentieth century. Atomists, notably James Clerk Maxwell and Ludwig Boltzmann , applied Hamilton's formulation of Newton's laws to large systems, and found that the statistical behavior of the atoms correctly describes room temperature gases. But classical statistical mechanics did not account for all of the properties of liquids and solids, nor of gases at low temperature.
Once modern quantum mechanics was formulated, atomism was no longer in conflict with experiment, but this did not lead to a universal acceptance of statistical mechanics, which went beyond atomism. Josiah Willard Gibbs had given a complete formalism to reproduce the laws of thermodynamics from the laws of mechanics. But many faulty arguments survived from the 19th century, when statistical mechanics was considered dubious. The lapses in intuition mostly stemmed from the fact that the limit of an infinite statistical system has many zero-one laws which are absent in finite systems: an infinitesimal change in a parameter can lead to big differences in the overall, aggregate behavior, as Democritus expected.
In the early part of the twentieth century, some believed that the partition function could never describe a phase transition, based on the following argument:
This argument works for a finite sum of exponentials, and correctly establishes that there are no singularities in the free energy of a system of a finite size. For systems which are in the thermodynamic limit (that is, for infinite systems) the infinite sum can lead to singularities. The convergence to the thermodynamic limit is fast, so that the phase behavior is apparent already on a relatively small lattice, even though the singularities are smoothed out by the system's finite size.
This was first established by Rudolf Peierls in the Ising model.
Shortly after Lenz and Ising constructed the Ising model, Peierls was able to explicitly show that a phase transition occurs in two dimensions.
To do this, he compared the high-temperature and low-temperature limits. At infinite temperature (β = 0) all configurations have equal probability. Each spin is completely independent of any other, and if typical configurations at infinite temperature are plotted so that plus/minus are represented by black and white, they look like television snow . For high, but not infinite temperature, there are small correlations between neighboring positions, the snow tends to clump a little bit, but the screen stays randomly looking, and there is no net excess of black or white.
A quantitative measure of the excess is the magnetization , which is the average value of the spin:
M = 1 N ∑ i = 1 N σ i . {\displaystyle M={\frac {1}{N}}\sum _{i=1}^{N}\sigma _{i}.}
A bogus argument analogous to the argument in the last section now establishes that the average magnetization in the Ising model is always zero.
As before, this only proves that the average magnetization is zero at any finite volume. For an infinite system, fluctuations might not be able to push the system from a mostly plus state to a mostly minus with a nonzero probability.
For very high temperatures, the magnetization is zero, as it is at infinite temperature. To see this, note that if spin A has only a small correlation ε with spin B, and B is only weakly correlated with C, but C is otherwise independent of A, the amount of correlation of A and C goes like ε 2 . For two spins separated by distance L , the amount of correlation goes as ε L , but if there is more than one path by which the correlations can travel, this amount is enhanced by the number of paths.
The number of paths of length L on a square lattice in d dimensions is N ( L ) = ( 2 d ) L , {\displaystyle N(L)=(2d)^{L},} since there are 2 d choices for where to go at each step.
A bound on the total correlation is given by the contribution to the correlation by summing over all paths linking two points, which is bounded above by the sum over all paths of length L divided by ∑ L ( 2 d ) L ε L , {\displaystyle \sum _{L}(2d)^{L}\varepsilon ^{L},} which goes to zero when ε is small.
At low temperatures (β ≫ 1) the configurations are near the lowest-energy configuration, the one where all the spins are plus or all the spins are minus. Peierls asked whether it is statistically possible at low temperature, starting with all the spins minus, to fluctuate to a state where most of the spins are plus. For this to happen, droplets of plus spin must be able to congeal to make the plus state.
The energy of a droplet of plus spins in a minus background is proportional to the perimeter of the droplet L, where plus spins and minus spins neighbor each other. For a droplet with perimeter L , the area is somewhere between ( L − 2)/2 (the straight line) and ( L /4) 2 (the square box). The probability cost for introducing a droplet has the factor e −β L , but this contributes to the partition function multiplied by the total number of droplets with perimeter L , which is less than the total number of paths of length L : N ( L ) < 4 2 L . {\displaystyle N(L)<4^{2L}.} So that the total spin contribution from droplets, even overcounting by allowing each site to have a separate droplet, is bounded above by ∑ L L 2 4 2 L e − 4 β L , {\displaystyle \sum _{L}L^{2}4^{2L}e^{-4\beta L},}
which goes to zero at large β. For β sufficiently large, this exponentially suppresses long loops, so that they cannot occur, and the magnetization never fluctuates too far from −1.
So Peierls established that the magnetization in the Ising model eventually defines superselection sectors , separated domains not linked by finite fluctuations.
Kramers and Wannier were able to show that the high-temperature expansion and the low-temperature expansion of the model are equal up to an overall rescaling of the free energy. This allowed the phase-transition point in the two-dimensional model to be determined exactly (under the assumption that there is a unique critical point).
After Onsager's solution, Yang and Lee investigated the way in which the partition function becomes singular as the temperature approaches the critical temperature.
The original motivation for the model was the phenomenon of ferromagnetism . Iron is magnetic; once it is magnetized it stays magnetized for a long time compared to any atomic time.
In the 19th century, it was thought that magnetic fields are due to currents in matter, and Ampère postulated that permanent magnets are caused by permanent atomic currents. The motion of classical charged particles could not explain permanent currents though, as shown by Larmor . In order to have ferromagnetism, the atoms must have permanent magnetic moments which are not due to the motion of classical charges.
Once the electron's spin was discovered, it was clear that the magnetism should be due to a large number of electron spins all oriented in the same direction. It was natural to ask how the electrons' spins all know which direction to point in, because the electrons on one side of a magnet don't directly interact with the electrons on the other side. They can only influence their neighbors. The Ising model was designed to investigate whether a large fraction of the electron spins could be oriented in the same direction using only local forces.
The Ising model can be reinterpreted as a statistical model for the motion of atoms. Since the kinetic energy depends only on momentum and not on position, while the statistics of the positions only depends on the potential energy, the thermodynamics of the gas only depends on the potential energy for each configuration of atoms.
A coarse model is to make space-time a lattice and imagine that each position either contains an atom or it doesn't. The space of configuration is that of independent bits B i , where each bit is either 0 or 1 depending on whether the position is occupied or not. An attractive interaction reduces the energy of two nearby atoms. If the attraction is only between nearest neighbors, the energy is reduced by −4 JB i B j for each occupied neighboring pair.
The density of the atoms can be controlled by adding a chemical potential , which is a multiplicative probability cost for adding one more atom. A multiplicative factor in probability can be reinterpreted as an additive term in the logarithm – the energy. The extra energy of a configuration with N atoms is changed by μN . The probability cost of one more atom is a factor of exp(− βμ ).
So the energy of the lattice gas is: E = − 1 2 ∑ ⟨ i , j ⟩ 4 J B i B j + ∑ i μ B i . {\displaystyle E=-{\frac {1}{2}}\sum _{\langle i,j\rangle }4JB_{i}B_{j}+\sum _{i}\mu B_{i}.}
Rewriting the bits in terms of spins, B i = ( S i + 1 ) / 2. {\displaystyle B_{i}=(S_{i}+1)/2.} E = − 1 2 ∑ ⟨ i , j ⟩ J S i S j − 1 2 ∑ i ( 4 J − μ ) S i . {\displaystyle E=-{\frac {1}{2}}\sum _{\langle i,j\rangle }JS_{i}S_{j}-{\frac {1}{2}}\sum _{i}(4J-\mu )S_{i}.}
For lattices where every site has an equal number of neighbors, this is the Ising model with a magnetic field h = ( zJ − μ )/2, where z is the number of neighbors.
In biological systems, modified versions of the lattice gas model have been used to understand a range of binding behaviors. These include the binding of ligands to receptors in the cell surface, [ 12 ] the binding of chemotaxis proteins to the flagellar motor, [ 13 ] and the condensation of DNA. [ 14 ]
The activity of neurons in the brain can be modelled statistically. Each neuron at any time is either active + or inactive −. The active neurons are those that send an action potential down the axon in any given time window, and the inactive ones are those that do not.
Following the general approach of Jaynes, [ 15 ] [ 16 ] a later interpretation of Schneidman, Berry, Segev and Bialek, [ 17 ] is that the Ising model is useful for any model of neural function, because a statistical model for neural activity should be chosen using the principle of maximum entropy . Given a collection of neurons, a statistical model which can reproduce the average firing rate for each neuron introduces a Lagrange multiplier for each neuron: E = − ∑ i h i S i {\displaystyle E=-\sum _{i}h_{i}S_{i}} But the activity of each neuron in this model is statistically independent. To allow for pair correlations, when one neuron tends to fire (or not to fire) along with another, introduce pair-wise lagrange multipliers: E = − 1 2 ∑ i j J i j S i S j − ∑ i h i S i {\displaystyle E=-{\tfrac {1}{2}}\sum _{ij}J_{ij}S_{i}S_{j}-\sum _{i}h_{i}S_{i}} where J i j {\displaystyle J_{ij}} are not restricted to neighbors. Note that this generalization of Ising model is sometimes called the quadratic exponential binary distribution in statistics.
This energy function only introduces probability biases for a spin having a value and for a pair of spins having the same value. Higher order correlations are unconstrained by the multipliers. An activity pattern sampled from this distribution requires the largest number of bits to store in a computer, in the most efficient coding scheme imaginable, as compared with any other distribution with the same average activity and pairwise correlations. This means that Ising models are relevant to any system which is described by bits which are as random as possible, with constraints on the pairwise correlations and the average number of 1s, which frequently occurs in both the physical and social sciences.
With the Ising model the so-called spin glasses can also be described, by the usual Hamiltonian H = − 1 2 ∑ J i , k S i S k , {\textstyle H=-{\frac {1}{2}}\,\sum J_{i,k}\,S_{i}\,S_{k},} where the S -variables describe the Ising spins, while the J i,k are taken from a random distribution. For spin glasses a typical distribution chooses antiferromagnetic bonds with probability p and ferromagnetic bonds with probability 1 − p (also known as the random-bond Ising model). These bonds stay fixed or "quenched" even in the presence of thermal fluctuations. When p = 0 we have the original Ising model. This system deserves interest in its own; particularly one has "non-ergodic" properties leading to strange relaxation behaviour. Much attention has been also attracted by the related bond and site dilute Ising model, especially in two dimensions, leading to intriguing critical behavior. [ 18 ]
Ising model was instrumental in the development of the Hopfield network . The original Ising model is a model for equilibrium. Roy J. Glauber in 1963 studied the Ising model evolving in time, as a process towards thermal equilibrium ( Glauber dynamics ), adding in the component of time. [ 19 ] (Kaoru Nakano, 1971) [ 20 ] [ 21 ] and ( Shun'ichi Amari , 1972), [ 22 ] proposed to modify the weights of an Ising model by Hebbian learning rule as a model of associative memory. The same idea was published by ( William A. Little [ de ] , 1974), [ 23 ] who was cited by Hopfield in his 1982 paper.
The Sherrington–Kirkpatrick model of spin glass, published in 1975, [ 24 ] is the Hopfield network with random initialization. Sherrington and Kirkpatrick found that it is highly likely for the energy function of the SK model to have many local minima. In the 1982 paper, Hopfield applied this recently developed theory to study the Hopfield network with binary activation functions. [ 25 ] In a 1984 paper he extended this to continuous activation functions. [ 26 ] It became a standard model for the study of neural networks through statistical mechanics. [ 27 ] [ 28 ]
The melt pond can be modelled by the Ising model; sea ice topography data bears rather heavily on the results. The state variable is binary for a simple 2D approximation, being either water or ice. [ 29 ]
In order to investigate an Ising model with potential relevance for large (e.g. with 10 4 {\displaystyle 10^{4}} or 10 5 {\displaystyle 10^{5}} interactions per node) neural nets, at the suggestion of Krizan in 1979, Barth (1981) obtained the exact analytical expression for the free energy of the Ising model on the closed Cayley tree (with an arbitrarily large branching ratio) for a zero-external magnetic field (in the thermodynamic limit) by applying the methodologies of Glasser (1970) and Jellito (1979)
− β f = ln 2 + 2 γ ( γ + 1 ) ln ( cosh J ) + γ ( γ − 1 ) ( γ + 1 ) ∑ i = 2 z 1 γ i ln J i ( τ ) {\displaystyle -\beta f=\ln 2+{\frac {2\gamma }{(\gamma +1)}}\ln(\cosh J)+{\frac {\gamma (\gamma -1)}{(\gamma +1)}}\sum _{i=2}^{z}{\frac {1}{\gamma ^{i}}}\ln J_{i}(\tau )}
where γ {\displaystyle \gamma } is an arbitrary branching ratio (greater than or equal to 2), t ≡ tanh J {\displaystyle t\equiv \tanh J} , τ ≡ t 2 {\displaystyle \tau \equiv t^{2}} , J ≡ β ϵ {\displaystyle J\equiv \beta \epsilon } (with ϵ {\displaystyle \epsilon } representing the nearest-neighbor interaction energy) and there are k (→ ∞ in the thermodynamic limit) generations in each of the tree branches (forming the closed tree architecture as shown in the given closed Cayley tree diagram.) The sum in the last term can be shown to converge uniformly and rapidly (i.e. for z → ∞, it remains finite) yielding a continuous and monotonous function, establishing that, for γ {\displaystyle \gamma } greater than or equal to 2, the free energy is a continuous function of temperature T. Further analysis of the free energy indicates that it exhibits an unusual discontinuous first derivative at the critical temperature ( Krizan, Barth & Glasser (1983) , Glasser & Goldberg (1983) .)
The spin-spin correlation between sites (in general, m and n) on the tree was found to have a transition point when considered at the vertices (e.g. A and Ā, its reflection), their respective neighboring sites (such as B and its reflection), and between sites adjacent to the top and bottom extreme vertices of the two trees (e.g. A and B), as may be determined from ⟨ s m s n ⟩ = Z N − 1 ( 0 , T ) [ cosh J ] N b 2 N ∑ l = 1 z g m n ( l ) t l {\displaystyle \langle s_{m}s_{n}\rangle ={Z_{N}}^{-1}(0,T)[\cosh J]^{N_{b}}2^{N}\sum _{l=1}^{z}g_{mn}(l)t^{l}} where N b {\displaystyle N_{b}} is equal to the number of bonds, g m n ( l ) t l {\displaystyle g_{mn}(l)t^{l}} is the number of graphs counted for odd vertices with even intermediate sites (see cited methodologies and references for detailed calculations), 2 N {\displaystyle 2^{N}} is the multiplicity resulting from two-valued spin possibilities and the partition function Z N {\displaystyle {Z_{N}}} is derived from ∑ { s } e − β H {\displaystyle \sum _{\{s\}}e^{-\beta H}} . (Note: s i {\displaystyle s_{i}} is consistent with the referenced literature in this section and is equivalent to S i {\displaystyle S_{i}} or σ i {\displaystyle \sigma _{i}} utilized above and in earlier sections; it is valued at ± 1 {\displaystyle \pm 1} .) The critical temperature T C {\displaystyle T_{C}} is given by T C = 2 ϵ k B [ ln ( γ + 1 ) − ln ( γ − 1 ) ] . {\displaystyle T_{C}={\frac {2\epsilon }{k_{\text{B}}[\ln({\sqrt {\gamma }}+1)-\ln({\sqrt {\gamma }}-1)]}}.}
The critical temperature for this model is only determined by the branching ratio γ {\displaystyle \gamma } and the site-to-site interaction energy ϵ {\displaystyle \epsilon } , a fact which may have direct implications associated with neural structure vs. its function (in that it relates the energies of interaction and branching ratio to its transitional behavior.) For example, a relationship between the transition behavior of activities of neural networks between sleeping and wakeful states (which may correlate with a spin-spin type of phase transition) in terms of changes in neural interconnectivity ( γ {\displaystyle \gamma } ) and/or neighbor-to-neighbor interactions ( ϵ {\displaystyle \epsilon } ), over time, is just one possible avenue suggested for further experimental investigation into such a phenomenon. In any case, for this Ising model it was established, that “the stability of the long-range correlation increases with increasing γ {\displaystyle \gamma } or increasing ϵ {\displaystyle \epsilon } .”
For this topology, the spin-spin correlation was found to be zero between the extreme vertices and the central sites at which the two trees (or branches) are joined (i.e. between A and individually C, D, or E.) This behavior is explained to be due to the fact that, as k increases, the number of links increases exponentially (between the extreme vertices) and so even though the contribution to spin correlations decrease exponentially, the correlation between sites such as the extreme vertex (A) in one tree and the extreme vertex in the joined tree (Ā) remains finite (above the critical temperature.) In addition, A and B also exhibit a non-vanishing correlation (as do their reflections) thus lending itself to, for B level sites (with A level), being considered “clusters” which tend to exhibit synchronization of firing.
Based upon a review of other classical network models as a comparison, the Ising model on a closed Cayley tree was determined to be the first classical statistical mechanical model to demonstrate both local and long-range sites with non-vanishing spin-spin correlations, while at the same time exhibiting intermediate sites with zero correlation, which indeed was a relevant matter for large neural networks at the time of its consideration. The model's behavior is also of relevance for any other divergent-convergent tree physical (or biological) system exhibiting a closed Cayley tree topology with an Ising-type of interaction. This topology should not be ignored since its behavior for Ising models has been solved exactly, and presumably nature will have found a way of taking advantage of such simple symmetries at many levels of its designs.
Barth (1981) early on noted the possibility of interrelationships between (1) the classical large neural network model (with similar coupled divergent-convergent topologies) with (2) an underlying statistical quantum mechanical model (independent of topology and with persistence in fundamental quantum states):
The most significant result obtained from the closed Cayley tree model involves the occurrence of long-range correlation in the absence of intermediate-range correlation. This result has not been demonstrated by other classical models. The failure of the classical view of impulse transmission to account for this phenomenon has been cited by numerous investigators (Ricciiardi and Umezawa, 1967, Hokkyo 1972, Stuart, Takahashi and Umezawa 1978, 1979) as significant enough to warrant radically new assumptions on a very fundamental level and have suggested the existence of quantum cooperative modes within the brain…In addition, it is interesting to note that the (modeling) of…Goldstone particles or bosons (as per Umezawa, et al)…within the brain, demonstrates the long-range correlation of quantum numbers preserved in the ground state…In the closed Cayley tree model ground states of pairs of sites, as well as the state variable of individual sites, (can) exhibit long-range correlation.
It was a natural and common belief among early neurophysicists (e.g. Umezawa, Krizan, Barth, etc.) that classical neural models (including those with statistical mechanical aspects) will one day have to be integrated with quantum physics (with quantum statistical aspects), similar perhaps to how the domain of chemistry has historically integrated itself into quantum physics via quantum chemistry.
Several additional statistical mechanical problems of interest remain to be solved for the closed Cayley tree, including the time-dependent case and the external field situation, as well as theoretical efforts aimed at understanding interrelationships with underlying quantum constituents and their physics.
The Ising model can often be difficult to evaluate numerically if there are many states in the system. Consider an Ising model with
Since every spin site has ±1 spin, there are 2 L different states that are possible. [ 30 ] This motivates the reason for the Ising model to be simulated using Monte Carlo methods . [ 30 ]
The Hamiltonian that is commonly used to represent the energy of the model when using Monte Carlo methods is:
H ( σ ) = − J ∑ ⟨ i j ⟩ σ i σ j − h ∑ j σ j . {\displaystyle H(\sigma )=-J\sum _{\langle i~j\rangle }\sigma _{i}\sigma _{j}-h\sum _{j}\sigma _{j}.}
Furthermore, the Hamiltonian is further simplified by assuming zero external field h , since many questions that are posed to be solved using the model can be answered in absence of an external field. This leads us to the following energy equation for state σ:
H ( σ ) = − J ∑ ⟨ i j ⟩ σ i σ j . {\displaystyle H(\sigma )=-J\sum _{\langle i~j\rangle }\sigma _{i}\sigma _{j}.}
Given this Hamiltonian, quantities of interest such as the specific heat or the magnetization of the magnet at a given temperature can be calculated. [ 30 ]
The Metropolis–Hastings algorithm is the most commonly used Monte Carlo algorithm to calculate Ising model estimations. [ 30 ] The algorithm first chooses selection probabilities g (μ, ν), which represent the probability that state ν is selected by the algorithm out of all states, given that one is in state μ. It then uses acceptance probabilities A (μ, ν) so that detailed balance is satisfied. If the new state ν is accepted, then we move to that state and repeat with selecting a new state and deciding to accept it. If ν is not accepted then we stay in μ. This process is repeated until some stopping criterion is met, which for the Ising model is often when the lattice becomes ferromagnetic , meaning all of the sites point in the same direction. [ 30 ]
When implementing the algorithm, one must ensure that g (μ, ν) is selected such that ergodicity is met. In thermal equilibrium a system's energy only fluctuates within a small range. [ 30 ] This is the motivation behind the concept of single-spin-flip dynamics , [ 31 ] which states that in each transition, we will only change one of the spin sites on the lattice. [ 30 ] Furthermore, by using single- spin-flip dynamics, one can get from any state to any other state by flipping each site that differs between the two states one at a time. The maximum amount of change between the energy of the present state, H μ and any possible new state's energy H ν (using single-spin-flip dynamics) is 2 J between the spin we choose to "flip" to move to the new state and that spin's neighbor. [ 30 ] Thus, in a 1D Ising model, where each site has two neighbors (left and right), the maximum difference in energy would be 4 J . Let c represent the lattice coordination number ; the number of nearest neighbors that any lattice site has. We assume that all sites have the same number of neighbors due to periodic boundary conditions . [ 30 ] It is important to note that the Metropolis–Hastings algorithm does not perform well around the critical point due to critical slowing down. Other techniques such as multigrid methods, Niedermayer's algorithm, Swendsen–Wang algorithm , or the Wolff algorithm are required in order to resolve the model near the critical point; a requirement for determining the critical exponents of the system.
Specifically for the Ising model and using single-spin-flip dynamics, one can establish the following. Since there are L total sites on the lattice, using single-spin-flip as the only way we transition to another state, we can see that there are a total of L new states ν from our present state μ. The algorithm assumes that the selection probabilities are equal to the L states: g (μ, ν) = 1/ L . Detailed balance tells us that the following equation must hold:
P ( μ , ν ) P ( ν , μ ) = g ( μ , ν ) A ( μ , ν ) g ( ν , μ ) A ( ν , μ ) = A ( μ , ν ) A ( ν , μ ) = P β ( ν ) P β ( μ ) = 1 Z e − β ( H ν ) 1 Z e − β ( H μ ) = e − β ( H ν − H μ ) . {\displaystyle {\frac {P(\mu ,\nu )}{P(\nu ,\mu )}}={\frac {g(\mu ,\nu )A(\mu ,\nu )}{g(\nu ,\mu )A(\nu ,\mu )}}={\frac {A(\mu ,\nu )}{A(\nu ,\mu )}}={\frac {P_{\beta }(\nu )}{P_{\beta }(\mu )}}={\frac {{\frac {1}{Z}}e^{-\beta (H_{\nu })}}{{\frac {1}{Z}}e^{-\beta (H_{\mu })}}}=e^{-\beta (H_{\nu }-H_{\mu })}.}
Thus, we want to select the acceptance probability for our algorithm to satisfy
A ( μ , ν ) A ( ν , μ ) = e − β ( H ν − H μ ) . {\displaystyle {\frac {A(\mu ,\nu )}{A(\nu ,\mu )}}=e^{-\beta (H_{\nu }-H_{\mu })}.}
If H ν > H μ , then A (ν, μ) > A (μ, ν). Metropolis sets the larger of A (μ, ν) or A (ν, μ) to be 1. By this reasoning the acceptance algorithm is: [ 30 ]
A ( μ , ν ) = { e − β ( H ν − H μ ) , if H ν − H μ > 0 , 1 otherwise . {\displaystyle A(\mu ,\nu )={\begin{cases}e^{-\beta (H_{\nu }-H_{\mu })},&{\text{if }}H_{\nu }-H_{\mu }>0,\\1&{\text{otherwise}}.\end{cases}}}
The basic form of the algorithm is as follows:
The change in energy H ν − H μ only depends on the value of the spin and its nearest graph neighbors. So if the graph is not too connected, the algorithm is fast. This process will eventually produce a pick from the distribution.
It is possible to view the Ising model as a Markov chain , as the immediate probability P β (ν) of transitioning to a future state ν only depends on the present state μ. The Metropolis algorithm is actually a version of a Markov chain Monte Carlo simulation, and since we use single-spin-flip dynamics in the Metropolis algorithm, every state can be viewed as having links to exactly L other states, where each transition corresponds to flipping a single spin site to the opposite value. [ 32 ] Furthermore, since the energy equation H σ change only depends on the nearest-neighbor interaction strength J , the Ising model and its variants such the Sznajd model can be seen as a form of a voter model for opinion dynamics.
The thermodynamic limit exists as long as the interaction decay is J i j ∼ | i − j | − α {\displaystyle J_{ij}\sim |i-j|^{-\alpha }} with α > 1. [ 33 ]
In the nearest neighbor case (with periodic or free boundary conditions) an exact solution is available. The Hamiltonian of the one-dimensional Ising model on a lattice of L sites with free boundary conditions is H ( σ ) = − J ∑ i = 1 , … , L − 1 σ i σ i + 1 − h ∑ i σ i , {\displaystyle H(\sigma )=-J\sum _{i=1,\ldots ,L-1}\sigma _{i}\sigma _{i+1}-h\sum _{i}\sigma _{i},} where J and h can be any number, since in this simplified case J is a constant representing the interaction strength between the nearest neighbors and h is the constant external magnetic field applied to lattice sites. Then the free energy is f ( β , h ) = − lim L → ∞ 1 β L ln Z ( β ) = − 1 β ln ( e β J cosh β h + e 2 β J ( sinh β h ) 2 + e − 2 β J ) , {\displaystyle f(\beta ,h)=-\lim _{L\to \infty }{\frac {1}{\beta L}}\ln Z(\beta )=-{\frac {1}{\beta }}\ln \left(e^{\beta J}\cosh \beta h+{\sqrt {e^{2\beta J}(\sinh \beta h)^{2}+e^{-2\beta J}}}\right),} and the spin-spin correlation (i.e. the covariance) is ⟨ σ i σ j ⟩ − ⟨ σ i ⟩ ⟨ σ j ⟩ = C ( β ) e − c ( β ) | i − j | , {\displaystyle \langle \sigma _{i}\sigma _{j}\rangle -\langle \sigma _{i}\rangle \langle \sigma _{j}\rangle =C(\beta )e^{-c(\beta )|i-j|},} where C (β) and c (β) are positive functions for T > 0. For T → 0, though, the inverse correlation length c (β) vanishes.
The proof of this result is a simple computation.
If h = 0, it is very easy to obtain the free energy in the case of free boundary condition, i.e. when H ( σ ) = − J ( σ 1 σ 2 + ⋯ + σ L − 1 σ L ) . {\displaystyle H(\sigma )=-J\left(\sigma _{1}\sigma _{2}+\cdots +\sigma _{L-1}\sigma _{L}\right).} Then the model factorizes under the change of variables σ j ′ = σ j σ j − 1 , j ≥ 2. {\displaystyle \sigma '_{j}=\sigma _{j}\sigma _{j-1},\quad j\geq 2.}
This gives Z ( β ) = ∑ σ 1 , … , σ L e β J σ 1 σ 2 e β J σ 2 σ 3 ⋯ e β J σ L − 1 σ L = 2 ∏ j = 2 L ∑ σ j ′ e β J σ j ′ = 2 [ e β J + e − β J ] L − 1 . {\displaystyle Z(\beta )=\sum _{\sigma _{1},\ldots ,\sigma _{L}}e^{\beta J\sigma _{1}\sigma _{2}}e^{\beta J\sigma _{2}\sigma _{3}}\cdots e^{\beta J\sigma _{L-1}\sigma _{L}}=2\prod _{j=2}^{L}\sum _{\sigma '_{j}}e^{\beta J\sigma '_{j}}=2\left[e^{\beta J}+e^{-\beta J}\right]^{L-1}.}
Therefore, the free energy is
f ( β , 0 ) = − 1 β ln [ e β J + e − β J ] . {\displaystyle f(\beta ,0)=-{\frac {1}{\beta }}\ln \left[e^{\beta J}+e^{-\beta J}\right].}
With the same change of variables
⟨ σ j σ j + N ⟩ = [ e β J − e − β J e β J + e − β J ] N , {\displaystyle \langle \sigma _{j}\sigma _{j+N}\rangle =\left[{\frac {e^{\beta J}-e^{-\beta J}}{e^{\beta J}+e^{-\beta J}}}\right]^{N},}
hence it decays exponentially as soon as T ≠ 0; but for T = 0, i.e. in the limit β → ∞ there is no decay.
If h ≠ 0 we need the transfer matrix method. For the periodic boundary conditions case is the following. The partition function is Z ( β ) = ∑ σ 1 , … , σ L e β h σ 1 e β J σ 1 σ 2 e β h σ 2 e β J σ 2 σ 3 ⋯ e β h σ L e β J σ L σ 1 = ∑ σ 1 , … , σ L V σ 1 , σ 2 V σ 2 , σ 3 ⋯ V σ L , σ 1 . {\displaystyle Z(\beta )=\sum _{\sigma _{1},\ldots ,\sigma _{L}}e^{\beta h\sigma _{1}}e^{\beta J\sigma _{1}\sigma _{2}}e^{\beta h\sigma _{2}}e^{\beta J\sigma _{2}\sigma _{3}}\cdots e^{\beta h\sigma _{L}}e^{\beta J\sigma _{L}\sigma _{1}}=\sum _{\sigma _{1},\ldots ,\sigma _{L}}V_{\sigma _{1},\sigma _{2}}V_{\sigma _{2},\sigma _{3}}\cdots V_{\sigma _{L},\sigma _{1}}.} The coefficients V σ , σ ′ {\displaystyle V_{\sigma ,\sigma '}} can be seen as the entries of a matrix. There are different possible choices: a convenient one (because the matrix is symmetric) is V σ , σ ′ = e β h 2 σ e β J σ σ ′ e β h 2 σ ′ {\displaystyle V_{\sigma ,\sigma '}=e^{{\frac {\beta h}{2}}\sigma }e^{\beta J\sigma \sigma '}e^{{\frac {\beta h}{2}}\sigma '}} or V = [ e β ( h + J ) e − β J e − β J e − β ( h − J ) ] . {\displaystyle V={\begin{bmatrix}e^{\beta (h+J)}&e^{-\beta J}\\e^{-\beta J}&e^{-\beta (h-J)}\end{bmatrix}}.} In matrix formalism Z ( β ) = Tr ( V L ) = λ 1 L + λ 2 L = λ 1 L [ 1 + ( λ 2 λ 1 ) L ] , {\displaystyle Z(\beta )=\operatorname {Tr} \left(V^{L}\right)=\lambda _{1}^{L}+\lambda _{2}^{L}=\lambda _{1}^{L}\left[1+\left({\frac {\lambda _{2}}{\lambda _{1}}}\right)^{L}\right],} where λ 1 is the highest eigenvalue of V , while λ 2 is the other eigenvalue: λ 1 = e β J cosh β h + e 2 β J ( cosh β h ) 2 − 2 sinh 2 β J = e β J cosh β h + e 2 β J ( sinh β h ) 2 + e − 2 β J , {\displaystyle \lambda _{1}=e^{\beta J}\cosh \beta h+{\sqrt {e^{2\beta J}(\cosh \beta h)^{2}-2\sinh 2\beta J}}=e^{\beta J}\cosh \beta h+{\sqrt {e^{2\beta J}(\sinh \beta h)^{2}+e^{-2\beta J}}},} and λ 2 < λ 1 . This gives the formula of the free energy above. In the thermodynamics limit for the non-interaction case (J = 0), we got Z N → ( λ 1 ) N = ( 2 cosh β h ) N , {\displaystyle Z_{N}\to (\lambda _{1})^{N}=(2\cosh \beta h)^{N},} as the answer for the open-boundary Ising model.
The energy of the lowest state is − JL , when all the spins are the same. For any other configuration, the extra energy is equal to 2 J times the number of sign changes that are encountered when scanning the configuration from left to right.
If we designate the number of sign changes in a configuration as k , the difference in energy from the lowest energy state is 2 k . Since the energy is additive in the number of flips, the probability p of having a spin-flip at each position is independent. The ratio of the probability of finding a flip to the probability of not finding one is the Boltzmann factor:
p 1 − p = e − 2 β J . {\displaystyle {\frac {p}{1-p}}=e^{-2\beta J}.}
The problem is reduced to independent biased coin tosses . This essentially completes the mathematical description.
From the description in terms of independent tosses, the statistics of the model for long lines can be understood. The line splits into domains. Each domain is of average length exp(2β). The length of a domain is distributed exponentially, since there is a constant probability at any step of encountering a flip. The domains never become infinite, so a long system is never magnetized. Each step reduces the correlation between a spin and its neighbor by an amount proportional to p , so the correlations fall off exponentially.
⟨ S i S j ⟩ ∝ e − p | i − j | . {\displaystyle \langle S_{i}S_{j}\rangle \propto e^{-p|i-j|}.}
The partition function is the volume of configurations, each configuration weighted by its Boltzmann weight. Since each configuration is described by the sign-changes, the partition function factorizes:
Z = ∑ configs e ∑ k S k = ∏ k ( 1 + p ) = ( 1 + p ) L . {\displaystyle Z=\sum _{\text{configs}}e^{\sum _{k}S_{k}}=\prod _{k}(1+p)=(1+p)^{L}.}
The logarithm divided by L is the free energy density:
β f = log ( 1 + p ) = log ( 1 + e − 2 β J 1 + e − 2 β J ) , {\displaystyle \beta f=\log(1+p)=\log \left(1+{\frac {e^{-2\beta J}}{1+e^{-2\beta J}}}\right),}
which is analytic away from β = ∞. A sign of a phase transition is a non-analytic free energy, so the one-dimensional model does not have a phase transition.
To express the Ising Hamiltonian using a quantum mechanical description of spins, we replace the spin variables with their respective Pauli matrices . However, depending on the direction of the magnetic field, we can create a transverse-field or longitudinal-field Hamiltonian. The transverse-field Hamiltonian is given by
H ( σ ) = − J ∑ i = 1 , … , L σ i z σ i + 1 z − h ∑ i σ i x . {\displaystyle H(\sigma )=-J\sum _{i=1,\ldots ,L}\sigma _{i}^{z}\sigma _{i+1}^{z}-h\sum _{i}\sigma _{i}^{x}.}
The transverse-field model experiences a phase transition between an ordered and disordered regime at J ~ h . This can be shown by a mapping of Pauli matrices
σ n z = ∏ i = 1 n T i x , {\displaystyle \sigma _{n}^{z}=\prod _{i=1}^{n}T_{i}^{x},}
σ n x = T n z T n + 1 z . {\displaystyle \sigma _{n}^{x}=T_{n}^{z}T_{n+1}^{z}.}
Upon rewriting the Hamiltonian in terms of this change-of-basis matrices, we obtain
H ( σ ) = − h ∑ i = 1 , … , L T i z T i + 1 z − J ∑ i T i x . {\displaystyle H(\sigma )=-h\sum _{i=1,\ldots ,L}T_{i}^{z}T_{i+1}^{z}-J\sum _{i}T_{i}^{x}.}
Since the roles of h and J are switched, the Hamiltonian undergoes a transition at J = h . [ 37 ]
When there is no external field, we can derive a functional equation that f ( β , 0 ) = f ( β ) {\displaystyle f(\beta ,0)=f(\beta )} satisfies using renormalization. [ 38 ] Specifically, let Z N ( β , J ) {\displaystyle Z_{N}(\beta ,J)} be the partition function with N {\displaystyle N} sites. Now we have: Z N ( β , J ) = ∑ σ e K σ 2 ( σ 1 + σ 3 ) e K σ 4 ( σ 3 + σ 5 ) ⋯ {\displaystyle Z_{N}(\beta ,J)=\sum _{\sigma }e^{K\sigma _{2}(\sigma _{1}+\sigma _{3})}e^{K\sigma _{4}(\sigma _{3}+\sigma _{5})}\cdots } where K := β J {\displaystyle K:=\beta J} . We sum over each of σ 2 , σ 4 , ⋯ {\displaystyle \sigma _{2},\sigma _{4},\cdots } , to obtain Z N ( β , J ) = ∑ σ ( 2 cosh ( K ( σ 1 + σ 3 ) ) ) ⋅ ( 2 cosh ( K ( σ 3 + σ 5 ) ) ) ⋯ {\displaystyle Z_{N}(\beta ,J)=\sum _{\sigma }(2\cosh(K(\sigma _{1}+\sigma _{3})))\cdot (2\cosh(K(\sigma _{3}+\sigma _{5})))\cdots } Now, since the cosh function is even, we can solve A e K ′ σ 1 σ 3 = 2 cosh ( K ( σ 1 + σ 3 ) ) {\displaystyle Ae^{K'\sigma _{1}\sigma _{3}}=2\cosh(K(\sigma _{1}+\sigma _{3}))} as A = 2 cosh ( 2 K ) , K ′ = 1 2 ln cosh ( 2 K ) {\textstyle A=2{\sqrt {\cosh(2K)}},K'={\frac {1}{2}}\ln \cosh(2K)} . Now we have a self-similarity relation: 1 N ln Z N ( K ) = 1 2 ln ( 2 cosh ( 2 K ) ) + 1 2 1 N / 2 ln Z N / 2 ( K ′ ) {\displaystyle {\frac {1}{N}}\ln Z_{N}(K)={\frac {1}{2}}\ln \left(2{\sqrt {\cosh(2K)}}\right)+{\frac {1}{2}}{\frac {1}{N/2}}\ln Z_{N/2}(K')} Taking the limit, we obtain f ( β ) = 1 2 ln ( 2 cosh ( 2 K ) ) + 1 2 f ( β ′ ) {\displaystyle f(\beta )={\frac {1}{2}}\ln \left(2{\sqrt {\cosh(2K)}}\right)+{\frac {1}{2}}f(\beta ')} where β ′ J = 1 2 ln cosh ( 2 β J ) {\displaystyle \beta 'J={\frac {1}{2}}\ln \cosh(2\beta J)} .
When β {\displaystyle \beta } is small, we have f ( β ) ≈ ln 2 {\displaystyle f(\beta )\approx \ln 2} , so we can numerically evaluate f ( β ) {\displaystyle f(\beta )} by iterating the functional equation until K {\displaystyle K} is small.
Onsager (1944) obtained the following analytical expression for the free energy of the Ising model on the anisotropic square lattice when the magnetic field h = 0 {\displaystyle h=0} in the thermodynamic limit as a function of temperature and the horizontal and vertical interaction energies J 1 {\displaystyle J_{1}} and J 2 {\displaystyle J_{2}} , respectively
− β f = ln 2 + 1 8 π 2 ∫ 0 2 π d θ 1 ∫ 0 2 π d θ 2 ln [ cosh ( 2 β J 1 ) cosh ( 2 β J 2 ) − sinh ( 2 β J 1 ) cos ( θ 1 ) − sinh ( 2 β J 2 ) cos ( θ 2 ) ] . {\displaystyle -\beta f=\ln 2+{\frac {1}{8\pi ^{2}}}\int _{0}^{2\pi }d\theta _{1}\int _{0}^{2\pi }d\theta _{2}\ln[\cosh(2\beta J_{1})\cosh(2\beta J_{2})-\sinh(2\beta J_{1})\cos(\theta _{1})-\sinh(2\beta J_{2})\cos(\theta _{2})].}
From this expression for the free energy, all thermodynamic functions of the model can be calculated by using an appropriate derivative. The 2D Ising model was the first model to exhibit a continuous phase transition at a positive temperature. It occurs at the temperature T c {\displaystyle T_{c}} which solves the equation
sinh ( 2 J 1 k T c ) sinh ( 2 J 2 k T c ) = 1. {\displaystyle \sinh \left({\frac {2J_{1}}{kT_{c}}}\right)\sinh \left({\frac {2J_{2}}{kT_{c}}}\right)=1.}
In the isotropic case when the horizontal and vertical interaction energies are equal J 1 = J 2 = J {\displaystyle J_{1}=J_{2}=J} , the critical temperature T c {\displaystyle T_{c}} occurs at the following point
T c = 2 J k ln ( 1 + 2 ) = ( 2.269185 ⋯ ) J k {\displaystyle T_{c}={\frac {2J}{k\ln(1+{\sqrt {2}})}}=(2.269185\cdots ){\frac {J}{k}}}
When the interaction energies J 1 {\displaystyle J_{1}} , J 2 {\displaystyle J_{2}} are both negative, the Ising model becomes an antiferromagnet. Since the square lattice is bi-partite, it is invariant under this change when the magnetic field h = 0 {\displaystyle h=0} , so the free energy and critical temperature are the same for the antiferromagnetic case. For the triangular lattice, which is not bi-partite, the ferromagnetic and antiferromagnetic Ising model behave notably differently. Specifically, around a triangle, it is impossible to make all 3 spin-pairs antiparallel, so the antiferromagnetic Ising model cannot reach the minimal energy state. This is an example of geometric frustration .
Start with an analogy with quantum mechanics. The Ising model on a long periodic lattice has a partition function
∑ { S } exp ( ∑ i j S i , j ( S i , j + 1 + S i + 1 , j ) ) . {\displaystyle \sum _{\{S\}}\exp {\biggl (}\sum _{ij}S_{i,j}\left(S_{i,j+1}+S_{i+1,j}\right){\biggr )}.}
Think of the i direction as space , and the j direction as time . This is an independent sum over all the values that the spins can take at each time slice. This is a type of path integral , it is the sum over all spin histories.
A path integral can be rewritten as a Hamiltonian evolution. The Hamiltonian steps through time by performing a unitary rotation between time t and time t + Δ t : U = e i H Δ t {\displaystyle U=e^{iH\Delta t}}
The product of the U matrices, one after the other, is the total time evolution operator, which is the path integral we started with.
U N = ( e i H Δ t ) N = ∫ D X e i L {\displaystyle U^{N}=(e^{iH\Delta t})^{N}=\int DXe^{iL}}
where N is the number of time slices. The sum over all paths is given by a product of matrices, each matrix element is the transition probability from one slice to the next.
Similarly, one can divide the sum over all partition function configurations into slices, where each slice is the one-dimensional configuration at time 1. This defines the transfer matrix : T C 1 C 2 . {\displaystyle T_{C_{1}C_{2}}.}
The configuration in each slice is a one-dimensional collection of spins. At each time slice, T has matrix elements between two configurations of spins, one in the immediate future and one in the immediate past. These two configurations are C 1 and C 2 , and they are all one-dimensional spin configurations. We can think of the vector space that T acts on as all complex linear combinations of these. Using quantum mechanical notation: | A ⟩ = ∑ S A ( S ) | S ⟩ {\displaystyle |A\rangle =\sum _{S}A(S)|S\rangle }
where each basis vector | S ⟩ {\displaystyle |S\rangle } is a spin configuration of a one-dimensional Ising model.
Like the Hamiltonian, the transfer matrix acts on all linear combinations of states. The partition function is a matrix function of T, which is defined by the sum over all histories which come back to the original configuration after N steps: Z = t r ( T N ) . {\displaystyle Z=\mathrm {tr} (T^{N}).}
Since this is a matrix equation, it can be evaluated in any basis. So if we can diagonalize the matrix T , we can find Z .
The contribution to the partition function for each past/future pair of configurations on a slice is the sum of two terms. There is the number of spin flips in the past slice and there is the number of spin flips between the past and future slice. Define an operator on configurations which flips the spin at site i:
σ i x . {\displaystyle \sigma _{i}^{x}.}
In the usual Ising basis, acting on any linear combination of past configurations, it produces the same linear combination but with the spin at position i of each basis vector flipped.
Define a second operator which multiplies the basis vector by +1 and −1 according to the spin at position i :
σ i z . {\displaystyle \sigma _{i}^{z}.}
T can be written in terms of these:
∑ i A σ i x + B σ i z σ i + 1 z {\displaystyle \sum _{i}A\sigma _{i}^{x}+B\sigma _{i}^{z}\sigma _{i+1}^{z}}
where A and B are constants which are to be determined so as to reproduce the partition function. The interpretation is that the statistical configuration at this slice contributes according to both the number of spin flips in the slice, and whether or not the spin at position i has flipped.
Just as in the one-dimensional case, we will shift attention from the spins to the spin-flips. The σ z term in T counts the number of spin flips, which we can write in terms of spin-flip creation and annihilation operators:
∑ C ψ i † ψ i . {\displaystyle \sum C\psi _{i}^{\dagger }\psi _{i}.\,}
The first term flips a spin, so depending on the basis state it either:
Writing this out in terms of creation and annihilation operators: σ i x = D ψ † i ψ i + 1 + D ∗ ψ † i ψ i − 1 + C ψ i ψ i + 1 + C ∗ ψ † i ψ † i + 1 . {\displaystyle \sigma _{i}^{x}=D{\psi ^{\dagger }}_{i}\psi _{i+1}+D^{*}{\psi ^{\dagger }}_{i}\psi _{i-1}+C\psi _{i}\psi _{i+1}+C^{*}{\psi ^{\dagger }}_{i}{\psi ^{\dagger }}_{i+1}.}
Ignore the constant coefficients, and focus attention on the form. They are all quadratic. Since the coefficients are constant, this means that the T matrix can be diagonalized by Fourier transforms.
Carrying out the diagonalization produces the Onsager free energy.
Onsager famously announced the following expression for the spontaneous magnetization M of a two-dimensional Ising ferromagnet on the square lattice at two different conferences in 1948, though without proof [ 8 ]
M = ( 1 − [ sinh 2 β J 1 sinh 2 β J 2 ] − 2 ) 1 8 {\displaystyle M=\left(1-\left[\sinh 2\beta J_{1}\sinh 2\beta J_{2}\right]^{-2}\right)^{\frac {1}{8}}}
where J 1 {\displaystyle J_{1}} and J 2 {\displaystyle J_{2}} are horizontal and vertical interaction energies.
A complete derivation was only given in 1951 by Yang (1952) using a limiting process of transfer matrix eigenvalues. The proof was subsequently greatly simplified in 1963 by Montroll, Potts, and Ward [ 8 ] using Szegő 's limit formula for Toeplitz determinants by treating the magnetization as the limit of correlation functions.
At the critical point, the two-dimensional Ising model is a two-dimensional conformal field theory . The spin and energy correlation functions are described by a minimal model , which has been exactly solved.
In three as in two dimensions, the most studied case of the Ising model is the translation-invariant model on a cubic lattice with nearest-neighbor coupling in the zero magnetic field. Many theoreticians searched for an analytical three-dimensional solution for many decades, which would be analogous to Onsager's solution in the two-dimensional case. [ 39 ] [ 40 ] Such a solution has not been found until now, although there is no proof that it may not exist. In three dimensions, the Ising model was shown to have a representation in terms of non-interacting fermionic strings by Alexander Polyakov and Vladimir Dotsenko . This construction has been carried on the lattice, and the continuum limit , conjecturally describing the critical point, is unknown.
In three as in two dimensions, Peierls' argument shows that there is a phase transition. This phase transition is rigorously known to be continuous (in the sense that correlation length diverges and the magnetization goes to zero), and is called the critical point . It is believed that the critical point can be described by a renormalization group fixed point of the Wilson-Kadanoff renormalization group transformation. It is also believed that the phase transition can be described by a three-dimensional unitary conformal field theory, as evidenced by Monte Carlo simulations, [ 41 ] [ 42 ] exact diagonalization results in quantum models, [ 43 ] and quantum field theoretical arguments. [ 44 ] Although it is an open problem to establish rigorously the renormalization group picture or the conformal field theory picture, theoretical physicists have used these two methods to compute the critical exponents of the phase transition, which agree with the experiments and with the Monte Carlo simulations. This conformal field theory describing the three-dimensional Ising critical point is under active investigation using the method of the conformal bootstrap . [ 45 ] [ 46 ] [ 47 ] [ 48 ] This method currently yields the most precise information about the structure of the critical theory (see Ising critical exponents ).
In 2000, Sorin Istrail of Sandia National Laboratories proved that the spin glass Ising model on a nonplanar lattice is NP-complete . That is, assuming P ≠ NP, the general spin glass Ising model is exactly solvable only in planar cases, so solutions for dimensions higher than two are also intractable. [ 49 ] Istrail's result only concerns the spin glass model with spatially varying couplings, and tells nothing about Ising's original ferromagnetic model with equal couplings.
In any dimension, the Ising model can be productively described by a locally varying mean field. The field is defined as the average spin value over a large region, but not so large so as to include the entire system. The field still has slow variations from point to point, as the averaging volume moves. These fluctuations in the field are described by a continuum field theory in the infinite system limit.
The field H is defined as the long wavelength Fourier components of the spin variable, in the limit that the wavelengths are long. There are many ways to take the long wavelength average, depending on the details of how high wavelengths are cut off. The details are not too important, since the goal is to find the statistics of H and not the spins. Once the correlations in H are known, the long-distance correlations between the spins will be proportional to the long-distance correlations in H .
For any value of the slowly varying field H , the free energy (log-probability) is a local analytic function of H and its gradients. The free energy F ( H ) is defined to be the sum over all Ising configurations which are consistent with the long wavelength field. Since H is a coarse description, there are many Ising configurations consistent with each value of H , so long as not too much exactness is required for the match.
Since the allowed range of values of the spin in any region only depends on the values of H within one averaging volume from that region, the free energy contribution from each region only depends on the value of H there and in the neighboring regions. So F is a sum over all regions of a local contribution, which only depends on H and its derivatives.
By symmetry in H , only even powers contribute. By reflection symmetry on a square lattice, only even powers of gradients contribute. Writing out the first few terms in the free energy:
β F = ∫ d d x [ A H 2 + ∑ i = 1 d Z i ( ∂ i H ) 2 + λ H 4 + ⋯ ] . {\displaystyle \beta F=\int d^{d}x\left[AH^{2}+\sum _{i=1}^{d}Z_{i}(\partial _{i}H)^{2}+\lambda H^{4}+\cdots \right].}
On a square lattice, symmetries guarantee that the coefficients Z i of the derivative terms are all equal. But even for an anisotropic Ising model, where the Z i ' s in different directions are different, the fluctuations in H are isotropic in a coordinate system where the different directions of space are rescaled.
On any lattice, the derivative term Z i j ∂ i H ∂ j H {\displaystyle Z_{ij}\,\partial _{i}H\,\partial _{j}H} is a positive definite quadratic form , and can be used to define the metric for space. So any translationally invariant Ising model is rotationally invariant at long distances, in coordinates that make Z ij = δ ij . Rotational symmetry emerges spontaneously at large distances just because there aren't very many low order terms. At higher order multicritical points, this accidental symmetry is lost.
Since β F is a function of a slowly spatially varying field, the probability of any field configuration is (omitting higher-order terms):
P ( H ) ∝ e − ∫ d d x [ A H 2 + Z | ∇ H | 2 + λ H 4 ] = e − β F [ H ] . {\displaystyle P(H)\propto e^{-\int d^{d}x\left[AH^{2}+Z|\nabla H|^{2}+\lambda H^{4}\right]}=e^{-\beta F[H]}.}
The statistical average of any product of H terms is equal to:
⟨ H ( x 1 ) H ( x 2 ) ⋯ H ( x n ) ⟩ = ∫ D H e − ∫ d d x [ A H 2 + Z | ∇ H | 2 + λ H 4 ] H ( x 1 ) H ( x 2 ) ⋯ H ( x n ) ∫ D H e − ∫ d d x [ A H 2 + Z | ∇ H | 2 + λ H 4 ] . {\displaystyle \langle H(x_{1})H(x_{2})\cdots H(x_{n})\rangle ={\int DH\,e^{-\int d^{d}x\left[AH^{2}+Z|\nabla H|^{2}+\lambda H^{4}\right]}H(x_{1})H(x_{2})\cdots H(x_{n}) \over \int DH\,e^{-\int d^{d}x\left[AH^{2}+Z|\nabla H|^{2}+\lambda H^{4}\right]}}.}
The denominator in this expression is called the partition function : Z = ∫ D H e − ∫ d d x [ A H 2 + Z | ∇ H | 2 + λ H 4 ] {\displaystyle Z=\int DH\,e^{-\int d^{d}x\left[AH^{2}+Z|\nabla H|^{2}+\lambda H^{4}\right]}} and the integral over all possible values of H is a statistical path integral. It integrates exp(β F ) over all values of H , over all the long wavelength fourier components of the spins. F is a "Euclidean" Lagrangian for the field H . It is similar to the Lagrangian in of a scalar field in quantum field theory , the difference being that all the derivative terms enter with a positive sign, and there is no overall factor of i (thus "Euclidean").
The form of F can be used to predict which terms are most important by dimensional analysis. Dimensional analysis is not completely straightforward, because the scaling of H needs to be determined.
In the generic case, choosing the scaling law for H is easy, since the only term that contributes is the first one,
F = ∫ d d x A H 2 . {\displaystyle F=\int d^{d}x\,AH^{2}.}
This term is the most significant, but it gives trivial behavior. This form of the free energy is ultralocal, meaning that it is a sum of an independent contribution from each point. This is like the spin-flips in the one-dimensional Ising model. Every value of H at any point fluctuates completely independently of the value at any other point.
The scale of the field can be redefined to absorb the coefficient A , and then it is clear that A only determines the overall scale of fluctuations. The ultralocal model describes the long wavelength high temperature behavior of the Ising model, since in this limit the fluctuation averages are independent from point to point.
To find the critical point, lower the temperature. As the temperature goes down, the fluctuations in H go up because the fluctuations are more correlated. This means that the average of a large number of spins does not become small as quickly as if they were uncorrelated, because they tend to be the same. This corresponds to decreasing A in the system of units where H does not absorb A . The phase transition can only happen when the subleading terms in F can contribute, but since the first term dominates at long distances, the coefficient A must be tuned to zero. This is the location of the critical point:
F = ∫ d d x [ t H 2 + λ H 4 + Z ( ∇ H ) 2 ] , {\displaystyle F=\int d^{d}x\left[tH^{2}+\lambda H^{4}+Z(\nabla H)^{2}\right],}
where t is a parameter which goes through zero at the transition.
Since t is vanishing, fixing the scale of the field using this term makes the other terms blow up. Once t is small, the scale of the field can either be set to fix the coefficient of the H 4 term or the (∇ H ) 2 term to 1.
To find the magnetization, fix the scaling of H so that λ is one. Now the field H has dimension − d /4, so that H 4 d d x is dimensionless, and Z has dimension 2 − d /2. In this scaling, the gradient term is only important at long distances for d ≤ 4. Above four dimensions, at long wavelengths, the overall magnetization is only affected by the ultralocal terms.
There is one subtle point. The field H is fluctuating statistically, and the fluctuations can shift the zero point of t . To see how, consider H 4 split in the following way:
H ( x ) 4 = − ⟨ H ( x ) 2 ⟩ 2 + 2 ⟨ H ( x ) 2 ⟩ H ( x ) 2 + ( H ( x ) 2 − ⟨ H ( x ) 2 ⟩ ) 2 {\displaystyle H(x)^{4}=-\langle H(x)^{2}\rangle ^{2}+2\langle H(x)^{2}\rangle H(x)^{2}+\left(H(x)^{2}-\langle H(x)^{2}\rangle \right)^{2}}
The first term is a constant contribution to the free energy, and can be ignored. The second term is a finite shift in t . The third term is a quantity that scales to zero at long distances. This means that when analyzing the scaling of t by dimensional analysis, it is the shifted t that is important. This was historically very confusing, because the shift in t at any finite λ is finite, but near the transition t is very small. The fractional change in t is very large, and in units where t is fixed the shift looks infinite.
The magnetization is at the minimum of the free energy, and this is an analytic equation. In terms of the shifted t ,
∂ ∂ H ( t H 2 + λ H 4 ) = 2 t H + 4 λ H 3 = 0 {\displaystyle {\partial \over \partial H}\left(tH^{2}+\lambda H^{4}\right)=2tH+4\lambda H^{3}=0}
For t < 0, the minima are at H proportional to the square root of t . So Landau's catastrophe argument is correct in dimensions larger than 5. The magnetization exponent in dimensions higher than 5 is equal to the mean-field value.
When t is negative, the fluctuations about the new minimum are described by a new positive quadratic coefficient. Since this term always dominates, at temperatures below the transition the fluctuations again become ultralocal at long distances.
To find the behavior of fluctuations, rescale the field to fix the gradient term. Then the length scaling dimension of the field is 1 − d /2. Now the field has constant quadratic spatial fluctuations at all temperatures. The scale dimension of the H 2 term is 2, while the scale dimension of the H 4 term is 4 − d . For d < 4, the H 4 term has positive scale dimension. In dimensions higher than 4 it has negative scale dimensions.
This is an essential difference. In dimensions higher than 4, fixing the scale of the gradient term means that the coefficient of the H 4 term is less and less important at longer and longer wavelengths. The dimension at which nonquadratic contributions begin to contribute is known as the critical dimension. In the Ising model, the critical dimension is 4.
In dimensions above 4, the critical fluctuations are described by a purely quadratic free energy at long wavelengths. This means that the correlation functions are all computable from as Gaussian averages:
⟨ S ( x ) S ( y ) ⟩ ∝ ⟨ H ( x ) H ( y ) ⟩ = G ( x − y ) = ∫ d k ( 2 π ) d e i k ( x − y ) k 2 + t {\displaystyle \langle S(x)S(y)\rangle \propto \langle H(x)H(y)\rangle =G(x-y)=\int {dk \over (2\pi )^{d}}{e^{ik(x-y)} \over k^{2}+t}}
valid when x − y is large. The function G ( x − y ) is the analytic continuation to imaginary time of the Feynman propagator , since the free energy is the analytic continuation of the quantum field action for a free scalar field. For dimensions 5 and higher, all the other correlation functions at long distances are then determined by Wick's theorem . All the odd moments are zero, by ± symmetry. The even moments are the sum over all partition into pairs of the product of G ( x − y ) for each pair.
⟨ S ( x 1 ) S ( x 2 ) ⋯ S ( x 2 n ) ⟩ = C n ∑ G ( x i 1 , x j 1 ) G ( x i 2 , x j 2 ) … G ( x i n , x j n ) {\displaystyle \langle S(x_{1})S(x_{2})\cdots S(x_{2n})\rangle =C^{n}\sum G(x_{i1},x_{j1})G(x_{i2},x_{j2})\ldots G(x_{in},x_{jn})}
where C is the proportionality constant. So knowing G is enough. It determines all the multipoint correlations of the field.
To determine the form of G , consider that the fields in a path integral obey the classical equations of motion derived by varying the free energy:
( − ∇ x 2 + t ) ⟨ H ( x ) H ( y ) ⟩ = 0 → ∇ 2 G ( x ) + t G ( x ) = 0 {\displaystyle {\begin{aligned}&&\left(-\nabla _{x}^{2}+t\right)\langle H(x)H(y)\rangle &=0\\\rightarrow {}&&\nabla ^{2}G(x)+tG(x)&=0\end{aligned}}}
This is valid at noncoincident points only, since the correlations of H are singular when points collide. H obeys classical equations of motion for the same reason that quantum mechanical operators obey them—its fluctuations are defined by a path integral.
At the critical point t = 0, this is Laplace's equation , which can be solved by Gauss's method from electrostatics. Define an electric field analog by
E = ∇ G {\displaystyle E=\nabla G}
Away from the origin:
∇ ⋅ E = 0 {\displaystyle \nabla \cdot E=0}
since G is spherically symmetric in d dimensions, and E is the radial gradient of G . Integrating over a large d − 1 dimensional sphere,
∫ d d − 1 S E r = c o n s t a n t {\displaystyle \int d^{d-1}SE_{r}=\mathrm {constant} }
This gives:
E = C r d − 1 {\displaystyle E={C \over r^{d-1}}}
and G can be found by integrating with respect to r .
G ( r ) = C r d − 2 {\displaystyle G(r)={C \over r^{d-2}}}
The constant C fixes the overall normalization of the field.
When t does not equal zero, so that H is fluctuating at a temperature slightly away from critical, the two point function decays at long distances. The equation it obeys is altered:
∇ 2 G + t G = 0 → 1 r d − 1 d d r ( r d − 1 d G d r ) + t G ( r ) = 0 {\displaystyle \nabla ^{2}G+tG=0\to {1 \over r^{d-1}}{d \over dr}\left(r^{d-1}{dG \over dr}\right)+tG(r)=0}
For r small compared with t {\displaystyle {\sqrt {t}}} , the solution diverges exactly the same way as in the critical case, but the long distance behavior is modified.
To see how, it is convenient to represent the two point function as an integral, introduced by Schwinger in the quantum field theory context:
G ( x ) = ∫ d τ 1 ( 2 π τ ) d e − x 2 4 τ − t τ {\displaystyle G(x)=\int d\tau {1 \over \left({\sqrt {2\pi \tau }}\right)^{d}}e^{-{x^{2} \over 4\tau }-t\tau }}
This is G , since the Fourier transform of this integral is easy. Each fixed τ contribution is a Gaussian in x , whose Fourier transform is another Gaussian of reciprocal width in k .
G ( k ) = ∫ d τ e − ( k 2 − t ) τ = 1 k 2 − t {\displaystyle G(k)=\int d\tau e^{-(k^{2}-t)\tau }={1 \over k^{2}-t}}
This is the inverse of the operator ∇ 2 − t in k -space, acting on the unit function in k -space, which is the Fourier transform of a delta function source localized at the origin. So it satisfies the same equation as G with the same boundary conditions that determine the strength of the divergence at 0.
The interpretation of the integral representation over the proper time τ is that the two point function is the sum over all random walk paths that link position 0 to position x over time τ. The density of these paths at time τ at position x is Gaussian, but the random walkers disappear at a steady rate proportional to t so that the Gaussian at time τ is diminished in height by a factor that decreases steadily exponentially. In the quantum field theory context, these are the paths of relativistically localized quanta in a formalism that follows the paths of individual particles. In the pure statistical context, these paths still appear by the mathematical correspondence with quantum fields, but their interpretation is less directly physical.
The integral representation immediately shows that G ( r ) is positive, since it is represented as a weighted sum of positive Gaussians. It also gives the rate of decay at large r, since the proper time for a random walk to reach position τ is r 2 and in this time, the Gaussian height has decayed by e − t τ = e − t r 2 {\displaystyle e^{-t\tau }=e^{-tr^{2}}} . The decay factor appropriate for position r is therefore e − t r {\displaystyle e^{-{\sqrt {t}}r}} .
A heuristic approximation for G ( r ) is:
G ( r ) ≈ e − t r r d − 2 {\displaystyle G(r)\approx {e^{-{\sqrt {t}}r} \over r^{d-2}}}
This is not an exact form, except in three dimensions, where interactions between paths become important. The exact forms in high dimensions are variants of Bessel functions .
The interpretation of the correlations as fixed size quanta travelling along random walks gives a way of understanding why the critical dimension of the H 4 interaction is 4. The term H 4 can be thought of as the square of the density of the random walkers at any point. In order for such a term to alter the finite order correlation functions, which only introduce a few new random walks into the fluctuating environment, the new paths must intersect. Otherwise, the square of the density is just proportional to the density and only shifts the H 2 coefficient by a constant. But the intersection probability of random walks depends on the dimension, and random walks in dimension higher than 4 do not intersect.
The fractal dimension of an ordinary random walk is 2. The number of balls of size ε required to cover the path increase as ε −2 . Two objects of fractal dimension 2 will intersect with reasonable probability only in a space of dimension 4 or less, the same condition as for a generic pair of planes. Kurt Symanzik argued that this implies that the critical Ising fluctuations in dimensions higher than 4 should be described by a free field. This argument eventually became a mathematical proof.
The Ising model in four dimensions is described by a fluctuating field, but now the fluctuations are interacting. In the polymer representation, intersections of random walks are marginally possible. In the quantum field continuation, the quanta interact.
The negative logarithm of the probability of any field configuration H is the free energy function
F = ∫ d 4 x [ Z 2 | ∇ H | 2 + t 2 H 2 + λ 4 ! H 4 ] {\displaystyle F=\int d^{4}x\left[{Z \over 2}|\nabla H|^{2}+{t \over 2}H^{2}+{\lambda \over 4!}H^{4}\right]\,}
The numerical factors are there to simplify the equations of motion. The goal is to understand the statistical fluctuations. Like any other non-quadratic path integral, the correlation functions have a Feynman expansion as particles travelling along random walks, splitting and rejoining at vertices. The interaction strength is parametrized by the classically dimensionless quantity λ.
Although dimensional analysis shows that both λ and Z are dimensionless, this is misleading. The long wavelength statistical fluctuations are not exactly scale invariant, and only become scale invariant when the interaction strength vanishes.
The reason is that there is a cutoff used to define H , and the cutoff defines the shortest wavelength. Fluctuations of H at wavelengths near the cutoff can affect the longer-wavelength fluctuations. If the system is scaled along with the cutoff, the parameters will scale by dimensional analysis, but then comparing parameters doesn't compare behavior because the rescaled system has more modes. If the system is rescaled in such a way that the short wavelength cutoff remains fixed, the long-wavelength fluctuations are modified.
A quick heuristic way of studying the scaling is to cut off the H wavenumbers at a point λ. Fourier modes of H with wavenumbers larger than λ are not allowed to fluctuate. A rescaling of length that make the whole system smaller increases all wavenumbers, and moves some fluctuations above the cutoff.
To restore the old cutoff, perform a partial integration over all the wavenumbers which used to be forbidden, but are now fluctuating. In Feynman diagrams, integrating over a fluctuating mode at wavenumber k links up lines carrying momentum k in a correlation function in pairs, with a factor of the inverse propagator.
Under rescaling, when the system is shrunk by a factor of (1+ b ), the t coefficient scales up by a factor (1+ b ) 2 by dimensional analysis. The change in t for infinitesimal b is 2 bt . The other two coefficients are dimensionless and do not change at all.
The lowest order effect of integrating out can be calculated from the equations of motion:
∇ 2 H + t H = − λ 6 H 3 . {\displaystyle \nabla ^{2}H+tH=-{\lambda \over 6}H^{3}.}
This equation is an identity inside any correlation function away from other insertions. After integrating out the modes with Λ < k < (1+ b )Λ, it will be a slightly different identity.
Since the form of the equation will be preserved, to find the change in coefficients it is sufficient to analyze the change in the H 3 term. In a Feynman diagram expansion, the H 3 term in a correlation function inside a correlation has three dangling lines. Joining two of them at large wavenumber k gives a change H 3 with one dangling line, so proportional to H :
δ H 3 = 3 H ∫ Λ < | k | < ( 1 + b ) Λ d 4 k ( 2 π ) 4 1 ( k 2 + t ) {\displaystyle \delta H^{3}=3H\int _{\Lambda <|k|<(1+b)\Lambda }{d^{4}k \over (2\pi )^{4}}{1 \over (k^{2}+t)}}
The factor of 3 comes from the fact that the loop can be closed in three different ways.
The integral should be split into two parts:
∫ d k 1 k 2 − t ∫ d k 1 k 2 ( k 2 + t ) = A Λ 2 b + B b t {\displaystyle \int dk{1 \over k^{2}}-t\int dk{1 \over k^{2}(k^{2}+t)}=A\Lambda ^{2}b+Bbt}
The first part is not proportional to t , and in the equation of motion it can be absorbed by a constant shift in t . It is caused by the fact that the H 3 term has a linear part. Only the second term, which varies from t to t , contributes to the critical scaling.
This new linear term adds to the first term on the left hand side, changing t by an amount proportional to t . The total change in t is the sum of the term from dimensional analysis and this second term from operator products :
δ t = ( 2 − B λ 2 ) b t {\displaystyle \delta t=\left(2-{B\lambda \over 2}\right)bt}
So t is rescaled, but its dimension is anomalous , it is changed by an amount proportional to the value of λ.
But λ also changes. The change in λ requires considering the lines splitting and then quickly rejoining. The lowest order process is one where one of the three lines from H 3 splits into three, which quickly joins with one of the other lines from the same vertex. The correction to the vertex is
δ λ = − 3 λ 2 2 ∫ k d k 1 ( k 2 + t ) 2 = − 3 λ 2 2 b {\displaystyle \delta \lambda =-{3\lambda ^{2} \over 2}\int _{k}dk{1 \over (k^{2}+t)^{2}}=-{3\lambda ^{2} \over 2}b}
The numerical factor is three times bigger because there is an extra factor of three in choosing which of the three new lines to contract. So
δ λ = − 3 B λ 2 b {\displaystyle \delta \lambda =-3B\lambda ^{2}b}
These two equations together define the renormalization group equations in four dimensions:
d t t = ( 2 − B λ 2 ) b d λ λ = − 3 B λ 2 b {\displaystyle {\begin{aligned}{dt \over t}&=\left(2-{B\lambda \over 2}\right)b\\{d\lambda \over \lambda }&={-3B\lambda \over 2}b\end{aligned}}}
The coefficient B is determined by the formula B b = ∫ Λ < | k | < ( 1 + b ) Λ d 4 k ( 2 π ) 4 1 k 4 {\displaystyle Bb=\int _{\Lambda <|k|<(1+b)\Lambda }{d^{4}k \over (2\pi )^{4}}{1 \over k^{4}}}
and is proportional to the area of a three-dimensional sphere of radius λ, times the width of the integration region b Λ divided by Λ 4 : B = ( 2 π 2 Λ 3 ) 1 ( 2 π ) 4 b Λ 1 b Λ 4 = 1 8 π 2 {\displaystyle B=(2\pi ^{2}\Lambda ^{3}){1 \over (2\pi )^{4}}{b\Lambda }{1 \over b\Lambda ^{4}}={1 \over 8\pi ^{2}}}
In other dimensions, the constant B changes, but the same constant appears both in the t flow and in the coupling flow. The reason is that the derivative with respect to t of the closed loop with a single vertex is a closed loop with two vertices. This means that the only difference between the scaling of the coupling and the t is the combinatorial factors from joining and splitting.
To investigate three dimensions starting from the four-dimensional theory should be possible, because the intersection probabilities of random walks depend continuously on the dimensionality of the space. In the language of Feynman graphs, the coupling does not change very much when the dimension is changed.
The process of continuing away from dimension 4 is not completely well defined without a prescription for how to do it. The prescription is only well defined on diagrams. It replaces the Schwinger representation in dimension 4 with the Schwinger representation in dimension 4 − ε defined by: G ( x − y ) = ∫ d τ 1 t d 2 e x 2 2 τ + t τ {\displaystyle G(x-y)=\int d\tau {1 \over t^{d \over 2}}e^{{x^{2} \over 2\tau }+t\tau }}
In dimension 4 − ε, the coupling λ has positive scale dimension ε, and this must be added to the flow.
d λ λ = ε − 3 B λ d t t = 2 − λ B {\displaystyle {\begin{aligned}{d\lambda \over \lambda }&=\varepsilon -3B\lambda \\{dt \over t}&=2-\lambda B\end{aligned}}}
The coefficient B is dimension dependent, but it will cancel. The fixed point for λ is no longer zero, but at: λ = ε 3 B {\displaystyle \lambda ={\varepsilon \over 3B}} where the scale dimensions of t is altered by an amount λ B = ε/3.
The magnetization exponent is altered proportionately to: 1 2 ( 1 − ε 3 ) {\displaystyle {\tfrac {1}{2}}\left(1-{\varepsilon \over 3}\right)}
which is .333 in 3 dimensions (ε = 1) and .166 in 2 dimensions (ε = 2). This is not so far off from the measured exponent .308 and the Onsager two dimensional exponent .125.
The behavior of an Ising model on a fully connected graph may be completely understood by mean-field theory . This type of description is appropriate to very-high-dimensional square lattices, because then each site has a very large number of neighbors.
The idea is that if each spin is connected to a large number of spins, only the average ratio of + spins to − spins is important, since the fluctuations about this mean will be small. The mean field H is the average fraction of spins which are + minus the average fraction of spins which are −. The energy cost of flipping a single spin in the mean field H is ±2 JNH . It is convenient to redefine J to absorb the factor N , so that the limit N → ∞ is smooth. In terms of the new J , the energy cost for flipping a spin is ±2 JH .
This energy cost gives the ratio of probability p that the spin is + to the probability 1− p that the spin is −. This ratio is the Boltzmann factor: p 1 − p = e 2 β J H {\displaystyle {p \over 1-p}=e^{2\beta JH}}
so that p = 1 1 + e − 2 β J H {\displaystyle p={1 \over 1+e^{-2\beta JH}}}
The mean value of the spin is given by averaging 1 and −1 with the weights p and 1 − p , so the mean value is 2 p − 1. But this average is the same for all spins, and is therefore equal to H . H = 2 p − 1 = 1 − e − 2 β J H 1 + e − 2 β J H = tanh ( β J H ) {\displaystyle H=2p-1={1-e^{-2\beta JH} \over 1+e^{-2\beta JH}}=\tanh(\beta JH)}
The solutions to this equation are the possible consistent mean fields. For β J < 1 there is only the one solution at H = 0. For bigger values of β there are three solutions, and the solution at H = 0 is unstable.
The instability means that increasing the mean field above zero a little bit produces a statistical fraction of spins which are + which is bigger than the value of the mean field. So a mean field which fluctuates above zero will produce an even greater mean field, and will eventually settle at the stable solution. This means that for temperatures below the critical value β J = 1 the mean-field Ising model undergoes a phase transition in the limit of large N .
Above the critical temperature, fluctuations in H are damped because the mean field restores the fluctuation to zero field. Below the critical temperature, the mean field is driven to a new equilibrium value, which is either the positive H or negative H solution to the equation.
For β J = 1 + ε, just below the critical temperature, the value of H can be calculated from the Taylor expansion of the hyperbolic tangent: H = tanh ( β J H ) ≈ ( 1 + ε ) H − ( 1 + ε ) 3 H 3 3 {\displaystyle H=\tanh(\beta JH)\approx (1+\varepsilon )H-{(1+\varepsilon )^{3}H^{3} \over 3}}
Dividing by H to discard the unstable solution at H = 0, the stable solutions are: H = 3 ε {\displaystyle H={\sqrt {3\varepsilon }}}
The spontaneous magnetization H grows near the critical point as the square root of the change in temperature. This is true whenever H can be calculated from the solution of an analytic equation which is symmetric between positive and negative values, which led Landau to suspect that all Ising type phase transitions in all dimensions should follow this law.
The mean-field exponent is universal because changes in the character of solutions of analytic equations are always described by catastrophes in the Taylor series , which is a polynomial equation. By symmetry, the equation for H must only have odd powers of H on the right hand side. Changing β should only smoothly change the coefficients. The transition happens when the coefficient of H on the right hand side is 1. Near the transition: H = ∂ ( β F ) ∂ h = ( 1 + A ε ) H + B H 3 + ⋯ {\displaystyle H={\partial (\beta F) \over \partial h}=(1+A\varepsilon )H+BH^{3}+\cdots }
Whatever A and B are, so long as neither of them is tuned to zero, the spontaneous magnetization will grow as the square root of ε. This argument can only fail if the free energy β F is either non-analytic or non-generic at the exact β where the transition occurs.
But the spontaneous magnetization in magnetic systems and the density in gasses near the critical point are measured very accurately. The density and the magnetization in three dimensions have the same power-law dependence on the temperature near the critical point, but the behavior from experiments is: H ∝ ε 0.308 {\displaystyle H\propto \varepsilon ^{0.308}}
The exponent is also universal, since it is the same in the Ising model as in the experimental magnet and gas, but it is not equal to the mean-field value. This was a great surprise.
This is also true in two dimensions, where H ∝ ε 0.125 {\displaystyle H\propto \varepsilon ^{0.125}}
But there it was not a surprise, because it was predicted by Onsager .
In three dimensions, the perturbative series from the field theory is an expansion in a coupling constant λ which is not particularly small. The effective size of the coupling at the fixed point is one over the branching factor of the particle paths, so the expansion parameter is about 1/3. In two dimensions, the perturbative expansion parameter is 2/3.
But renormalization can also be productively applied to the spins directly, without passing to an average field. Historically, this approach is due to Leo Kadanoff and predated the perturbative ε expansion.
The idea is to integrate out lattice spins iteratively, generating a flow in couplings. But now the couplings are lattice energy coefficients. The fact that a continuum description exists guarantees that this iteration will converge to a fixed point when the temperature is tuned to criticality.
Write the two-dimensional Ising model with an infinite number of possible higher order interactions. To keep spin reflection symmetry, only even powers contribute: E = ∑ i j J i j S i S j + ∑ J i j k l S i S j S k S l … . {\displaystyle E=\sum _{ij}J_{ij}S_{i}S_{j}+\sum J_{ijkl}S_{i}S_{j}S_{k}S_{l}\ldots .}
By translation invariance, J ij is only a function of i-j. By the accidental rotational symmetry, at large i and j its size only depends on the magnitude of the two-dimensional vector i − j . The higher order coefficients are also similarly restricted.
The renormalization iteration divides the lattice into two parts – even spins and odd spins. The odd spins live on the odd-checkerboard lattice positions, and the even ones on the even-checkerboard. When the spins are indexed by the position ( i , j ), the odd sites are those with i + j odd and the even sites those with i + j even, and even sites are only connected to odd sites.
The two possible values of the odd spins will be integrated out, by summing over both possible values. This will produce a new free energy function for the remaining even spins, with new adjusted couplings. The even spins are again in a lattice, with axes tilted at 45 degrees to the old ones. Unrotating the system restores the old configuration, but with new parameters. These parameters describe the interaction between spins at distances 2 {\textstyle {\sqrt {2}}} larger.
Starting from the Ising model and repeating this iteration eventually changes all the couplings. When the temperature is higher than the critical temperature, the couplings will converge to zero, since the spins at large distances are uncorrelated. But when the temperature is critical, there will be nonzero coefficients linking spins at all orders. The flow can be approximated by only considering the first few terms. This truncated flow will produce better and better approximations to the critical exponents when more terms are included.
The simplest approximation is to keep only the usual J term, and discard everything else. This will generate a flow in J , analogous to the flow in t at the fixed point of λ in the ε expansion.
To find the change in J , consider the four neighbors of an odd site. These are the only spins which interact with it. The multiplicative contribution to the partition function from the sum over the two values of the spin at the odd site is: e J ( N + − N − ) + e J ( N − − N + ) = 2 cosh ( J [ N + − N − ] ) {\displaystyle e^{J(N_{+}-N_{-})}+e^{J(N_{-}-N_{+})}=2\cosh(J[N_{+}-N_{-}])}
where N ± is the number of neighbors which are ±. Ignoring the factor of 2, the free energy contribution from this odd site is: F = log ( cosh [ J ( N + − N − ) ] ) . {\displaystyle F=\log(\cosh[J(N_{+}-N_{-})]).}
This includes nearest neighbor and next-nearest neighbor interactions, as expected, but also a four-spin interaction which is to be discarded. To truncate to nearest neighbor interactions, consider that the difference in energy between all spins the same and equal numbers + and – is: Δ F = ln ( cosh [ 4 J ] ) . {\displaystyle \Delta F=\ln(\cosh[4J]).}
From nearest neighbor couplings, the difference in energy between all spins equal and staggered spins is 8 J . The difference in energy between all spins equal and nonstaggered but net zero spin is 4 J . Ignoring four-spin interactions, a reasonable truncation is the average of these two energies or 6 J . Since each link will contribute to two odd spins, the right value to compare with the previous one is half that: 3 J ′ = ln ( cosh [ 4 J ] ) . {\displaystyle 3J'=\ln(\cosh[4J]).}
For small J , this quickly flows to zero coupling. Large J' s flow to large couplings. The magnetization exponent is determined from the slope of the equation at the fixed point.
Variants of this method produce good numerical approximations for the critical exponents when many terms are included, in both two and three dimensions. | https://en.wikipedia.org/wiki/Ising_model |
Islam A. Siddiqui ( Hindi : इस्लाम सिद्दिक़ी ) is an Indian-American scientist, and government official, and lobbyist who served as the Chief Agricultural Negotiator in the Office of the United States Trade Representative . Prior to this, he was Vice President for Science and Regulatory Affairs at CropLife America , and a career official in the California Department of Food and Agriculture .
Siddiqui earned a Bachelor of Science degree in plant protection from G. B. Pant University of Agriculture and Technology in Pantnagar , India, and M.S. and Ph.D. degrees in plant pathology, both from the University of Illinois Urbana-Champaign . [ 2 ] [ 3 ]
Siddiqui served the Clinton Administration in several capacities from 1997 to 2001. At the United States Department of Agriculture , Siddiqui was Undersecretary for Marketing and Regulatory Programs, Senior Trade Advisor to Secretary Dan Glickman , and Deputy Undersecretary for Marketing and Regulatory Programs. Before joining USDA, Siddiqui spent 28 years with the California Department of Food and Agriculture . [ 4 ]
From 2004 to 2009, Dr. Siddiqui served on the United States Department of Commerce 's Industry Trade Advisory Committee on Chemicals, Pharmaceuticals, and Health/Science Products and Services, which advises the United States Secretary of Commerce and United States Trade Representative on international trade issues related to these sectors. From 2001 and 2003, Siddiqui was appointed as Senior Associate at the Center for Strategic and International Studies , where he focused on agricultural biotechnology and food security issues.
From 2001 to 2008, Siddiqui was a registered lobbyist with CropLife America, representing biotechnology companies including BASF , Bayer CropScience , Dow AgroSciences , DuPont , FMC Corp. , Monsanto , Sumitomo , and Syngenta .
On April 2, 2010, President Barack Obama named Siddiqui to the post of Chief Agricultural Negotiator in a recess appointment . Siddiqui's previous nomination to the position remained on the Senate docket for more than a year and a half. His nomination was reported to the Senate floor from the United States Senate Committee on Finance on October 11, 2011, and senators finally voted to confirm Siddiqui as part of an en bloc group of nominations confirmed early in the morning hours of October 21, 2011. [ 5 ] [ 6 ] [ 7 ] Siddiqui submitted his resignation December 12, 2013. [ 8 ]
Siddiqui is a supporter of genetically modified foods for human consumption, and repudiates their potential health risks . In 1999, he worked against the mandatory labeling of genetically modified foods in Japan, stating that such labeling "would suggest a health risk where there is none." [ 9 ] In 2003, he criticized the European Union 's precautionary rejection of the importation of genetically modified foods, stating that the ban was tantamount to "denying food to starving people." [ 10 ] In 2009 he called for a "second green revolution " employing biotechnology and genetic engineering . [ 11 ]
In 1998, as Under Secretary for Marketing and Regulatory Programs at the United States Department of Agriculture , Siddiqui oversaw the release of the National Organic Program 's standards for organic food labeling. The standards permitted both irradiated and genetically modified foods to be labeled as organic. [ 12 ] (The standards were subsequently revised in response to public opposition.)
In 2005, speaking on behalf of CropLife America, Siddiqui stated his satisfaction with the defeat of local propositions in California that would have banned cultivation of genetically modified crops . [ 13 ] | https://en.wikipedia.org/wiki/Islam_A._Siddiqui |
The Islamic Association of Engineers ( Persian : انجمن اسلامی مهندسین , romanized : anǰoman-e eslāmī-ye mohandesīn ) is a civic [ 2 ] and professional association in Iran founded in 1957. [ 3 ]
The organization is a platform for Islamic modernist activists and a forum for debating key issues among them. It holds regular meetings, lectures and research and turns them into books. [ 3 ]
Mehdi Bazargan and Ezzatollah Sahabi were among its founders. [ 2 ] Alongside Islamic Association of Students , the organization was active against outreach of Marxist ideology before Iranian Revolution [ 2 ] and was one of the professional bodies that served as a platform for religious activism, playing an important role in shaping the Islamic ideology of the revolution . [ 3 ] Ali Shariati was among occasional lecturers at the organization. [ 4 ] A number of leading members in the association held government portfolios during Interim Government of Iran . [ 5 ]
This article about an organization in Iran is a stub . You can help Wikipedia by expanding it .
This article about an Islamic organization is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Islamic_Association_of_Engineers |
Islamic Association of Engineers of Iran ( Persian : انجمن اسلامی مهندسان ایران , romanized : anǰoman-e eslāmī-ye mohandisān-e Īrān ) is an Iranian political party of engineers affiliated with the Council for Coordinating the Reforms Front . [ 3 ]
This article about an Iranian political party is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Islamic_Association_of_Engineers_of_Iran |
The Islamic Society of Engineers (ISE) ( Persian : جامعهٔ اسلامی مهندسین , Jāme'-e eslāmī-ye mohandisīn ) is a principlist political organization of engineers in Iran . Formerly one of the parties aligned with the Combatant Clergy Association , [ 1 ] it is close to the Islamic Coalition Party , whose decisions it mostly follows. It is questionable whether it is an independent and strong party. [ 3 ]
The Society was formed at the end of the Iran–Iraq War (1988) with the objective of elevating the Islamic, political, scientific and technical knowledge of the Muslim people of Iran, defending major freedoms such as freedom of expression and gatherings, as well as continued campaigning against foreign cultural agents whether Eastern or Western materialism. [ 1 ]
This article about an Iranian political party is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Islamic_Society_of_Engineers |
Purity ( Arabic : طهارة , romanized : ṭahārah ) [ 1 ] is an essential aspect of Islam . It is the opposite of najāsa , the state of being ritually impure. It is achieved by first removing physical impurities (for example, urine) from the body, and then removing ritual impurity through wudu (usually) or ghusl .
The Quran says: "In it there are men who love to observe purity and Allah loves those who maintain purity." [ Quran 9:108 ] and there is one verse which concerned with taharah or purity, and impurity of humans: "O you who have believed, indeed the polytheists are unclean, so let them not approach al-Masjid al-Haram after this, their [final] year. And if you fear privation, Allah will enrich you from His bounty if He wills. Indeed, Allah is knowing and wise." [ Quran 9:28 ]
Ayatollah Ali al-Sistani does not believe in the impurity of People of the Book (Jews, Christians, and Zoroastrians ). [ 2 ]
Some scholars such as Mohsen Fayz Kashani (d. 1680) and Sulayman ibn Abdullah Mahuzi (d. 1708) did not believe in the impurity of non-believers, and particularly non-People of the Book. Kashani believes that the impurity of kuffar is spiritual and internal, so there is no need to wash after touching them. This group believes in the purity of non-Muslims and of all humans. Mohammad Ebrahim Jannaati , Mohammad Hussein Fadlallah (d. 2010), Mostafa Mohaghegh Damad , Kamal Haydari , and Reza Hosseini Nassab are part of this group. [ 3 ]
Ayatollah Ruhollah Khomeini said that all non-Muslims, including People of the Book, are impure. [ 4 ]
Sunni Islam has its own hygienical jurisprudence. It is preferable for a Sunni Muslim to remove the hair directly below the navel and under the arms also as trimming the nails once a week. Leaving hair and nails is permissible after 15 days and disliked after 40 days. [ 5 ] The best day for removing needless hair and cutting nails is Friday. It is permissible to use shaving cream to remove needless hair. Needless hair and nails should be buried to prevent illnesses from spreading. Cutting eyebrows is permissible if they are too long. Sunni women should put their nails and hair removed from below the navel, and under the arms in a place where no non-permissible men can see it. [ 6 ]
Personal grooming is also a matter of focus in Islam, and comprises all the ritual purity practices of prophets known as fitra . Allowing a beard to grow while trimming the moustache is emphasized with it being seen as mandatory by some respected Sunni scholars from the 4 major Sunni schools of jurisprudence .
Islamic hygienical jurisprudence includes a number of regulations involving cleanliness during salat (obligatory prayer) through wudu (partial ablution) and ghusl (full ablution), as well as dietary laws and toilet etiquette for Muslims . The fiqh (Islamic jurisprudence) is based on admonitions in the Quran for Muslims to be ritually clean whenever possible, [ citation needed ] as well as in hadith literature (words, actions, or habits of the Islamic prophet Muhammad ).
Cleanliness is an important part of Islam, including Quranic verses that teach how to achieve ritual cleanliness . [ citation needed ] Keeping oral hygiene through cleaning the teeth with the use of a form of toothbrush called miswak is considered sunnah , the way of Muhammad. Ritual ablution is also very important, as observed by the practices of wudu , ghusl , and tayammum (water-free alternative using any natural surface such as rock, sand, or dust). [ citation needed ]
In Muslim-majority countries , bathrooms are often equipped with a bidet . This ablution is required in order to maintain ritual cleanliness. The common Muslims practice of taking off shoes when entering mosques and homes is also based on ritual cleanliness. [ 7 ]
Islamic dietary laws provide a set of rules as to what Muslims eat in their diet. These rules specify the food that is halāl , meaning lawful. They are found in the Quran, usually detailing what is unlawful, or harām . [ 8 ]
Removal of pubic hair and armpit hair is prescribed by the sunnah , and is listed among the ritual purity practices known as fitra .
Urine is forbidden to be on a Muslim during prayer times, as it is considered impure. The foreskin is a possible spot where urine and other impurities ( smegma ) can accumulate. Circumcision is used to prevent this. [ 9 ] [ 10 ]
The Islamic faith has particular rules regarding personal hygiene when going to the toilet . This code is known as Qaḍāʾ al-Ḥājah ( قضاء الحاجة ). [ 11 ] [ 12 ]
Issues of laterality, such as whether one uses the left or right hand and the foot used to step into or out of toilet areas, are derived from hadith sources. [ 13 ] The only issue which the Qur'an mentions is the one of washing one's hands especially after using the toilet which is mentioned in Quran 5:6 .
Examples of these rules include, but are not limited to:
Sexual hygiene in Islam is a prominent topic in Islamic jurisprudence ( fiqh ) due to its everyday nature. Ibn Abidin , a 13th century Hanafi Islamic scholar explains: [ 15 ]
When there is discharge of thick, cloudy white fluid (wady) (that exits before or after urinating) or unlustful discharge of thin, sticky, white fluid (madhy) caused by play or kissing, it requires washing the private parts and wudu .
Regarding things that necessitates ghusl:
After partaking in sexual activity where penetration or ejaculation occurs, both men and women are required to complete a full-body ritual ablution known as ghusl in order to re-establish ritual purity before prayer. [ 17 ] Ghusl requires clean, odorless water that has not been used for a previous ritual and begins with the declaration of the intention of purity and worship. [ 18 ] A Muslim performing complete ablution then washes every part of his or her body. [ 18 ] | https://en.wikipedia.org/wiki/Islamic_hygienical_jurisprudence |
Islamic toilet etiquette is a set of personal hygiene rules in Islam that concerns going to the toilet . This code of Islamic hygienical jurisprudence is called Qaḍāʾ al-Ḥāǧa ( Arabic : قضاء الحاجة ).
Personal hygiene is mentioned in a single verse of the Quran in the context of ritual purification from a minor source of impurity, known as the Wuḍūʾ verse; its interpretation is contentious between different legal schools and sects of Islam. [ 1 ] Further requirements with regard to personal hygiene are derived from a Hadith , and these requirements also differ between sects. [ 2 ] [ 3 ]
A Muslim must first find an acceptable place away from standing water, people's pathways, or shade. [ 4 ] It is advised that it is better to enter the area with the left foot, [ 5 ] [ failed verification ] and it is prohibited to face directly towards the Qibla (direction of prayer towards Mecca ) or directly opposite from it. [ 6 ] It is reported in the collection of hadith, Sahih al-Bukhari , that just before entering the toilet, Muhammad said: ( Arabic : اللَّهُمَّ إِنِّي أَعُوذُ بِكَ مِنَ الْخُبُثِ وَالْخَبَائِثِ , romanized : Allāhumma ʾinnī ʾaʿuḏu bika mina al-Ḫubuṯi wa-al-Ḫabāʾiṯi , lit. '"Oh God, I seek refuge in You from that which is evil (m.) and that which is evil (f.)")'. [ 7 ] Following his example, Muslims are advised to say this Dua before entering into the toilet.
While on the toilet, one must remain silent. Talking and initiating or answering greetings are strongly discouraged. [ 8 ] When defecating together, two men cannot converse, nor look at each other's genitals. [ 9 ] Eating any food while on the toilet is forbidden. [ 8 ]
After defecating, the anus must be washed with water [ citation needed ] using the left hand, or an odd number of smooth stones or pebbles called jamrah or hijaarah (Sahih Al-Bukhari 161, Book 4, Hadith 27). Many jurists agree that toilet paper suffices in place of these stones. [ 10 ] Similarly, the penis or vulva should be washed with water using the left hand after urinating, a procedure called istinja . It is commonly done using a vessel known as a Aftabeh , Lota , or bodna .
When leaving the toilet, one is advised to exit with the right foot [ 5 ] [ failed verification ] and say the Dua for leaving bathroom/toilet: "'الحمد لله الذي أذهب عني الأذى وعافاني'Alhamdu lillahil lazi azha-ba annill Aza Wa AA Fani. [ 11 ] "Praise be to Allah who relieved me of the filth and gave me relief." [ 8 ] | https://en.wikipedia.org/wiki/Islamic_toilet_etiquette |
Island Conservation is a non-profit organization with the mission to "restore islands for nature and people worldwide" and has therefore focused its efforts on islands with species categorized as Critically Endangered and Endangered on the IUCN's Red List . [ 4 ] Working in partnership with local communities, government management agencies, and conservation organizations, Island Conservation develops plans and implements the removal of invasive alien species, [ 5 ] and conducts field research to document the benefits of the work and to inform future projects.
Island Conservation's approach is now being shown to have a wider beneficial effect on the marine systems surrounding its project areas. [ 6 ] [ 7 ] [ 8 ] In addition, invasive vertebrate eradication has now been shown to have many benefits besides conservation of species. Specifically, the approach has been found to align with 13 UN Sustainable Development Goals and 42 associated targets encompassing marine and terrestrial biodiversity conservation, promotion of local and global partnerships, economic development, climate change mitigation , human health and sanitation and sustainable production and consumption. [ 9 ] [ 10 ]
To date Island Conservation has deployed teams to protect 1,195 populations of 487 species and subspecies on 64 islands. [ 11 ]
The work of Island Conservation is not without controversy, This is documented in the book Battle at the End of Eden . [ 12 ] Restoring islands requires removing whole populations of an invasive species. There is an ethical question of whether humankind has the right to remove one species to save others. However, a 2019 study suggests that if eradications of invasive animals were conducted on just 169 islands, the survival prospects of 9.4% of the Earth's most highly threatened terrestrial insular vertebrates would be improved. [ 13 ] [ 14 ]
Island Conservation was founded by Bernie Tershy and Don Croll, both Professors at UCSC's Long Marine Lab . These scientists learned about the story of Clipperton Island which had been visited by ornithologist Ken Stager of the Los Angeles County Museum in 1958. Appalled at the depredations visited by feral pigs upon the island's brown booby and masked booby colonies (reduced to 500 and 150 birds, respectively), Stager procured a shotgun and removed all 58 pigs. By 2003, the colonies numbered 25,000 brown boobies and 112,000 masked boobies, the world's second-largest brown booby colony and largest masked booby colony. [ 15 ]
Much of organization's early focus was working in Mexico in conjunction with its sister organization, Grupo de Ecología y Conservación de Islas, in the Gulf of California and off the Pacific Coast. [ 16 ] [ 17 ] Subsequently, Island Conservation expanded its geographic scope to the Channel Islands of California , Pacific Coast of Canada , The Aleutians Islands , Hawaiian Islands , and finally to the Pacific , Caribbean , and South America .
Island Conservation has a strong scientific grounding. Over 160 peer-reviewed publications in major journals such as Biological Conservation , Conservation Biology and Proceedings of the National Academy of Sciences have been authored or co-authored by Island Conservation staff and contractors. [ 18 ]
As Island Conservation does not have management responsibility over any islands itself, all projects are in partnership with the island owner/manager, island users, local communities and regulatory authorities. Since its founding in 1994, the organization has developed partnerships with over 100 organizations. [ 19 ] Partners include conservation organizations, government agencies, regulatory agencies, scientific institutions, and international conservation consortiums. Island Conservation is a member of the International Union for Conservation of Nature (IUCN) , Alliance for Zero Extinction , [ 20 ] and has a Memorandum of Understanding with the US Fish & Wildlife Service , [ 21 ] and BirdLife International , [ 22 ] amongst others.
The organization's founding advisory board [ 23 ] is composed of prominent scientists, practitioners, and authors in the fields of conservation biology and invasive species including Paul Ehrlich , José Sarukhán Kermez, Russell Mittermeier , Harold Mooney , David Quammen , Peter Raven , Michael Soulé , and Edward O. Wilson .
In this region, Island Conservation currently works in the United States and Canada . In the United States, the Anacapa Island Restoration Project [ 24 ] [ 25 ] [ 26 ] was completed in 2002 and benefited the Scripps's murrelet , Cassin's auklet , and Anacapa Deer Mouse. The Lehua Island Restoration Project was completed in 2006 which benefited Newell's shearwater and black-footed albatross . [ 27 ] [ 28 ] Subsequently, projects completed include the Hawadax Island Restoration Project [ 29 ] [ 30 ] [ 31 ] in 2008, the San Nicolas Island Project [ 32 ] [ 33 ] [ 34 ] in 2010, and the Palmyra Island Restoration Project [ 35 ] in 2011.
Key federal government partnerships in North America include in the US Department of Interior , USFWS , NPS , the US Department of Agriculture-APHIS , National Wildlife Research Center, NOAA , Parks Canada Agency , and Environment and Climate Change Canada . Island Conservation is working with the following non-governmental organizations: Coastal Conservation Association (CA) , Bird Studies Canada , American Bird Conservancy , The Nature Conservancy , and Grupo de Ecología y Conservación de Islas.
Since 2010, Island Conservation has contributed to the development and implementation of island restoration projects in Australia ( Lord Howe Island [ 36 ] and Norfolk Island ), French Polynesia ( Tetiꞌaroa Restoration Project in 2022, [ 37 ] Acteon-Gambier Archipelago Restoration Project [ 38 ] in 2015), Tonga ( Late Island and numerous small islets), Republic of Palau (including within the Rock Islands Southern Lagoon World Heritage Area [ 39 ] ), Federated States of Micronesia (Ulithi Lagoon), and New Caledonia (Walpole Island). Island Conservation is an active member of the Pacific Invasives Partnership. [ 40 ] Other key partnerships include Invasive Species Council, [ 41 ] BirdLife International , New Zealand Department of Conservation , SPREP and the Ornithological Society of French Polynesia .
In this region, Island Conservation works primarily in Puerto Rico , The Commonwealth of The Bahamas , and the Dominican Republic . In May 2012, Island Conservation and the Bahamas National Trust worked together to remove invasive house mice from Allen Cay to protect native species including the Allen Cays rock iguana and Sargasso shearwater . [ 42 ] Since 2008, Island Conservation and the US Fish and Wildlife Service (USFWS) have worked together to remove invasive vertebrates from Desecheo National Wildlife Refuge in Puerto Rico, primarily benefiting the Higo Chumbo cactus , three endemic reptiles, two endemic invertebrates, and to recover globally significant seabird colonies of brown boobies , red footed boobies , and bridled terns . [ 43 ] Future work will focus on important seabird populations, key reptile groups including West Indian Rock Iguanas, and the restoration of Mona Island , [ 44 ] Alto Velo, and offshore cays in the Puerto Rican Bank and The Bahamas. Key partnerships include the USFWS, Puerto Rico DNER , the Bahamas National Trust , and the Dominican Republic Ministry of Environment and Natural Resources .
In this region, Island Conservation works primarily in Ecuador and Chile . In Ecuador, the Rábida Island Restoration Project was completed in 2010. A gecko (Phyllodactylus sp.) found during monitoring in late 2012 was only recorded from subfossils estimated at more than 5,700 years old. Live Rábida Island endemic land snails (Bulimulus (Naesiotus) rabidensis), not seen since collected over 100 years ago, were also collected in late 2012. [ 45 ] This was followed in 2012 by the Pinzon and Plaza Sur Island Restoration Project primarily benefiting the Pinzón giant tortoise , Opuntia galapageia , Galápagos land iguana . As a result of the project, Pinzon Giant Tortoise hatched from eggs and were surviving in the wild for the first time in more than 150 years [ 46 ] [ 47 ] [ 48 ] [ 49 ] In 2019, The Directorate of Galápagos National Park with Island Conservation used drones to eradicate invasive rats from North Seymour Island —this was the first time such an approach has been used on vertebrates in the wild. The expectation is that this innovation will pave the way for cheaper invasive species eradications in the future on small and mid-sized islands. [ 50 ] [ 51 ] [ 52 ] [ 53 ] The current focus in Ecuador is Floreana Island with 55 IUCN threatened species present and 13 extirpated species that could be reintroduced after invasive mammals are eradicated. Partners include: The Leona M. and Harry B. Helmsley Charitable Trust , Ministry of Environment (Galápagos National Park Directorate, Galápagos Biosecurity Agency), the Ministry of Agriculture, the Floreana Parish Council and the Galapagos Government Council.
In 2009 Chile, Island Conservation initiated formal collaborations with CONAF , the country's protected areas agency, to further restoration of islands under their administration. In January 2014, the Choros Island Restoration Project was completed benefiting the Humboldt penguin , Peruvian diving petrel , and the local eco-tourism industry. [ 54 ] [ 55 ] The focus of future work includes the Humboldt Penguin National Reserve and the Juan Fernández Archipelago , where technology developed by Wildlife Drones is being used to support conservation efforts. This includes tracking endangered species and collecting ecological data across challenging terrains.
From its earliest days, Island Conservation has prided itself on innovating its tools and approach to eradication projects. Island Conservation implemented its first helicopter-based aerial broadcast eradication on Anacapa Island in 2001 refining technology developed in New Zealand for agriculture and pest control, this has been replicated on more than 10 international island restoration projects since. [ 56 ] Island Conservation has developed practices for holding native species in captivity for re-release and mitigating risks to species, including the successful capture and release of endemic mice on Anacapa and hawks on Pinzon. [ 57 ]
In 2010, Island Conservation partnered with the U.S. Humane Society to remove feral cats from San Nicolas Island [ 58 ] for relocation to a sanctuary on the mainland California. New tools including a remote trap monitoring system, digital data collection system, [ 59 ] and statistical decision support tools [ 60 ] [ 61 ] improved the humanness of removal methods, reduced project cost, and reduced time to declare success. [ 62 ]
Following a series of failed eradication attempts in 2012, Island Conservation led a group of international experts to identify challenges on tropical islands [ 63 ] resulting in recommend practices for tropical rodent eradications. [ 64 ] Applying these lessons [ 65 ] following a failed attempt on Desecheo island 2017 resulted in success.
Island Conservation led a horizon scan in 2015 [ 66 ] that identified drones, [ 67 ] genetic biocontrol, and conflict transformation as critical innovations to increase the scale, scope, and pace of rodent eradications. Since this exercise, Island Conservation formed the Genetic Biocontrol for Invasive Rodents (GBIRd) partnership to cautiously explore the development of safe and ethical genetic technologies [ 68 ] to prevent extinctions, supported sustainable community-driven approaches [ 69 ] to conservation projects, and implemented the world's first drone-powered rat eradication. The current focus of the Conservation Innovation program is to advance methods that increase safety, reduce cost, and improve the feasibility of eradicating invasive vertebrates from islands. | https://en.wikipedia.org/wiki/Island_Conservation |
Island ecology is the study of island organisms and their interactions with each other and the environment. Islands account for nearly 1/6 of earth’s total land area, [ 1 ] yet the ecology of island ecosystems is vastly different from that of mainland communities. Their isolation and high availability of empty niches lead to increased speciation . As a result, island ecosystems comprise 30% of the world’s biodiversity hotspots , 50% of marine tropical diversity, and some of the most unusual and rare species. [ 2 ] Many species still remain unknown.
The diversity of species on islands is highly impacted by human activities such as deforestation and introduction of the exotic species . In response, ecologists and managers are directing attention towards conservation and restoration of island species. Because they are simple systems, islands provide an opportunity to study processes of extinction that can be extrapolated to larger ecosystems.
Islands are attractive sites for ecological research because they provide clear examples of evolution in action. They show interesting patterns of colonization, adaptation, and speciation.
Islands are surrounded by water, and may or may not exist as part of a continental land mass. Oceanic islands arise due to volcanic activity or reef growth, and usually subside over time due to erosion and changing sea levels. [ 1 ] When islands emerge, they undergo the process of ecological succession as species colonize the island (see theory of island biogeography ). New species cannot immigrate via land, and instead must arrive via air, water, or wind. As a result, organisms with high dispersal capabilities, such as plants and birds, are much more common on islands than are poorly dispersing taxa like mammals. [ 1 ] However, some mammals are present on islands, presumably from swimming or riding on natural “rafts” that are washed away from the mainland.
Of the species that arrive, only some will be able to survive and establish populations. As a result, islands have fewer species than mainland habitats. Island populations are small and exhibit low genetic variability (see founder effect ), but are isolated from the predators and competitors that they initially evolved with. This can lead to a process called ecological release , where a species is released from its ancestral community interactions and then colonizes new niches.
In response to these changing ecological pressures, island species can become much more docile than their mainland counterparts, and may grow larger (see island gigantism ) or smaller (see island dwarfism ). Some of these unique adaptations are reflected in charismatic island species such as the Malagasy hippopotamus , Komodo dragon , or pygmy mammoths . Although, the giant tortoises of the Galápagos Islands and the Seychelles (the Galápagos tortoise and Aldabrachelys respectively) are sometimes given as examples of insular gigantism, [ 3 ] they are now thought to represent the last remaining populations of historically widespread giant tortoises i.e. gigantism is an ancestral trait that occurred in the absence of insular selection pressures. The collection of differences in morphology , ecology , physiology and behaviour of insular species compared to their continental counterparts is termed Island syndrome . [ 4 ] [ 5 ]
After immigration, birds, and some reptiles or mammals, tend to become larger and predatory, [ 6 ] showing relaxed intraspecific competition . [ 7 ] For mammals, small species will increase in size and large species will decrease in size. [ 8 ] This is referred to as the “island rule,” and is suggested to minimize energy expenditure. [ 9 ]
Other adaptations to life on islands include increased poikilothermy , [ 9 ] relaxed anti-predator behavior, [ 10 ] [ 11 ] and reduced sexual selection [ 12 ] in animals, and loss of herbivore defenses [ 13 ] and reduced dispersal [ 14 ] in plants.
The formation of new islands and their isolation from the mainland provides many unoccupied niches for species to adapt to. Since immigration of predators and competitors is limited, many organisms are able to persist in these new niches. This results in a high occurrence of endemism , where species are unique to a localized area. For example, 50% of endemic bird areas are found on islands. [ 2 ]
Endemism is often the result of adaptive radiation . [ 1 ] Adaptive radiation is when a single species colonizes an area and rapidly diversifies to fill all of the available niches. A common example is the assemblage of finch species documented by Charles Darwin in the Galapagos Islands . Darwin’s finches exhibited adaptive radiation by evolving different beak sizes to exploit the diversity of seeds present on the different islands.
Because the distributions of these populations are limited by their island habitats, they tend to have fewer individuals than their mainland counterparts and lower genetic variation. This, along with the behavioral and ecological factors mentioned above, makes island species more vulnerable to extinction. [ 1 ]
The continued survival of species on islands depends on factors such as natural selection , genetic variation, natural disturbances (hurricanes, volcanic eruptions) and human-caused disturbances (introduced species, habitat loss ). Human-caused disturbances tend to be the greatest cause of mortality, and understanding the causes of extinction facilitates conservation efforts.
The movement of humans to islands has led to rapid extinction of native island species either from hunting, habitat destruction , or introduced species .
Many large animals on islands have been hunted to extinction by humans. A well-known example is the dodo , once found on the island of Mauritius . [ 15 ] It evolved to become large, flightless and docile, and was subsequently driven to extinction by humans and introduced predators.
The depletion of natural resources can have dramatic effects on island ecology. On Easter Island , the depletion of the forest by humans not only resulted in widespread loss of species, but also the collapse of the island civilization. [ 16 ]
Today there are over 500 million people on islands, all dependent on local resources either directly (traditional use) or indirectly (ecotourism revenue). Population growth and development result in heavy deforestation , pollution , and over-exploitation . Overharvesting of ocean fauna is particularly troubling as yields of coral reef fish species are an important food source for island populations.
Humans have contributed to globalization and decreased effective isolation of island communities, allowing for invasion of exotic species. This can have a profound effect on the native species. In Guam , the introduced brown tree snake ate nearly all of the native vertebrate species to extinction. Feral cats and dogs have also greatly diminished native vertebrate populations on islands, through both predation and disease. Introduced ungulates are another major threat, as they graze on native vegetation and can destroy entire forests. [ 17 ] Exotic grasses can out-compete native understory species and increase the risk of fire. [ 18 ] Lastly, social insects such as ants also cause major problems. [ 19 ]
Nonnative species introduced onto islands can have profound effects on an island's ecosystem, more so than nonnative species introduced to continental land (Platenberg). The higher impact of introduced and nonnative species on islands is largely a result of lower biodiversity levels (Platenburg et al.). Biodiversity on islands is especially threatened by logging, hunting, fishing and plant gathering. However, islands’ vulnerability to introduced species is also due to agricultural, economic, and health differences as compared to continental land (Russel et al.).
The smaller land area and population sizes of islands compared to continents create greater vulnerability to the impacts of introduced species (Russel et al.). Introduced species negatively impact ecosystems through altered predator-prey interactions that can cause harm or even local extinction to native species populations (Towns et al.). There are many examples of animal species such as birds, reptiles, and aquatic insects being harmed by the introduction of predators such as rats, cats, and ants. For example, seabirds on islands in Hawaii are impacted by non-native predators like barn owls and ants. At a colony in Hawaii, at least 20% of wedge-tailed shearwater eggs were taken by mynas, dark-plumaged birds of the starling family (Towns et al.). Also in Hawaii, more than forty four introduced ant species, especially tropical fire ants, caused detriments to the growth of shearwater chicks, such as loss of tissue in their feet (Towns et al.).
Other examples of high-impact species to island ecosystems are the Cuban treefrog and cane toad, which were introduced to the US Virgin Islands under various circumstances (Platenberg). The Cuban treefrog has been present in the USVI since arriving unintentionally on a cargo ship in the 1970s (Platenberg). The Cuban tree frog is known for its ability to survive under harsh conditions, and it is highly adaptable, as it will eat a wide variety of organisms (Platenberg). Native frog and anole lizard populations have declined, likely due to Cuban tree frog interference (Platenberg). In contrast to the accidental introduction of the Cuban treefrog, the cane toad was deliberately introduced to control agricultural pests (Platenberg). Similar to the Cuban treefrog, the cane toad is also omnivorous. Cane toad tadpoles compete for limited freshwater resources with the white-lipped frog, a native species, thus limiting their resources (Platenberg). In general, when the introduction of a nonnative species results in extinction, the ecosystem experiences losses in some trophic levels (Platenberg). For example, vertebrate herbivores that are prone to extinction change the ecosystem function in plant communities. This phenomenon is seen in New Zealand, where the loss of bird species may have changed dynamics in avian-induced vegetation communities and impacted abundances of forest plants (Platenberg).
Also in New Zealand, small mammalian predators such as rodents have little direct effect on vegetation but have greater effect on island faunas through extinction and displacement (Wood et al.). Pacific rats, for example, were thought to be causing the local extinction of large, nocturnal ground-dwelling lizards, and they were assumed to have minimal effect on diurnal species, those that sleep at night, such as shore skinks (Wood et al.). In places where Pacific rats were removed, however, shore skink populations rapidly changed, indicating that the rats’ impact has been underestimated (Wood et al.).
The loss of a keystone species, a species that all other species in the ecosystem depend on such as seabirds, can also have significant effects (Towns). Seabirds are essential to the structure of the ecosystem because they transport large amounts of nutrients into ecosystems and burrow into soils, helping vegetation (Towns). However, since human settlement, seabird communities have been severely impacted on islands across the globe (Towns). While some exotic species may perform ecological roles similar to those of extinct species, there are many roles that cannot be fulfilled by other species. Therefore, similar exotic species do not offer complete replacement for extinct species in the community (Towns). Even if the number of species introduced to an island is roughly the same as the number of extinct ones, the ecological traits are not comparable enough to make up for losses (Towns).
Global warming is emerging as a strong cause of species loss on islands. This can be due to sea level rise , the intrusion of salt water into freshwater habitats, or species inability to adapt to increasing temperatures and extreme weather events. Plant species are particularly susceptible. [ 20 ] In more isolated areas, such as the Southern Ocean Islands, indirect effects such as invasive species and global warming can play a greater role in influencing populations than overexploitation , pollution and habitat loss . [ 21 ]
Human activities and the introduction of non-native species often cause trophic cascades , where direct effects on one species result in indirect effects on other species in the food web. An example is on Santa Cruz Island of the California Channel Islands , where DDT poisoning reduced bald eagle populations. This, along with an abundance of introduced feral pigs for prey, allowed golden eagles to colonize the island and replace bald eagles. However, the golden eagles also ate native island foxes . Fox population levels decreased to near extinction, while skunk populations increased due to relaxed competition with foxes.
Since island ecosystems are self-contained, it should be possible to mitigate many of the threats to species. Ecologists and managers are working together to prioritize areas for conservation and to quickly design and implement action plans. Not everything can be put into a reserve, so it is important to first compile pertinent information and prioritize areas of concern. [ 22 ] Once an area has been chosen, managers must then acquire ownership and gain support. Local experts and indigenous populations should also be involved in this process. [ 22 ] Having clearly defined goals will facilitate the many necessary interactions between people and agencies. [ 22 ] Once a reserve is in place, managers can then practice adaptive management and do continued community education.
On land, island conservation focuses on the protection of species and their habitat. In some cases, conservation can be integrated with agricultural production. For example, the Acacia koa plantations and wooded pastures in Hawaii are anthropogenically altered ecosystems, yet allow connectivity between forest fragments and thus maintain higher diversity than would open pasture. [ 23 ] Other directions include habitat restoration, and eradication of introduced predators, ungulates, and exotic plants (via hunting, removal or biological control ).
In marine ecosystems, there has been an increasing establishment of “no-take” reserves. This allows for the reestablishment of native species, and also the augmentation of commercially harvested species. [ 24 ] However, in both terrestrial and marine systems, these actions are expensive and do not always result in the desired outcomes. For example, some non-natives become keystone species and their removal can cause more harm than good to the ecosystem. To be more effective, managers of island ecosystems should share information and learn from each other’s mistakes. [ 25 ]
Island conservation tends to focus on preservation of individual species and their habitats. However, many ecologists caution that ecological and evolutionary processes should be conserved as well. [ 25 ] The conservation of island communities as a whole is closely linked to restoration .
Active restoration on islands can be done for both animal species (translocations, induced breeding) and plant species (reforestation). Creating goals for restoration can be challenging because it is often impossible to restore the ecosystem to its “historic” or “normal” state, if that state can even be clearly defined. Restoration is never complete, as ecological communities are always in a state of change.
As resource depletion is a major issue on islands, the needs of human populations must also be taken into account. On many islands, scientists and managers are studying traditional practices of indigenous populations as potential conservation solutions. In some cases, limited-take systems that serve the community may provide a better alternative to fully closed protected areas, if there are not enough resources for proper enforcement. [ 26 ] Public education plays an important role.
A significant advancement in the field is the shift from 2-D to 3-D science in ecology. This approach offers a comprehensive understanding of ecological dynamics and human impacts on both terrestrial and marine environments. The adoption of 3-D models supports better natural resource management and informs conservation and management plans. This transition also affects how policymakers evaluate regulations, providing a more dynamic perspective on ecological and environmental challenges. [ 27 ] | https://en.wikipedia.org/wiki/Island_ecology |
Island gigantism , or insular gigantism , is a biological phenomenon in which the size of an animal species isolated on an island increases dramatically in comparison to its mainland relatives. Island gigantism is one aspect of the more general "island effect" or "Foster's rule" , which posits that when mainland animals colonize islands, small species tend to evolve larger bodies, and large species tend to evolve smaller bodies ( insular dwarfism ). This is itself one aspect of the more general phenomenon of island syndrome which describes the differences in morphology , ecology , physiology and behaviour of insular species compared to their continental counterparts. Following the arrival of humans and associated introduced predators (dogs, cats, rats, pigs), many giant as well as other island endemics have become extinct (e.g. the dodo and Rodrigues solitaire , giant flightless pigeons related to the Nicobar pigeon ). A similar size increase, as well as increased woodiness, has been observed in some insular plants such as the Mapou tree ( Cyphostemma mappia ) in Mauritius which is also known as the "Mauritian baobab" although it is member of the grape family ( Vitaceae ).
Large mammalian carnivores are often absent on islands because of insufficient range or difficulties in over-water dispersal . In their absence, the ecological niches for large predators may be occupied by birds, reptiles or smaller carnivorans, which can then grow to larger-than-normal size. For example, on prehistoric Gargano Island in the Miocene - Pliocene Mediterranean , on islands in the Caribbean like Cuba , and on Madagascar and New Zealand , some or all apex predators were birds like eagles , falcons and owls , including some of the largest known examples of these groups. However, birds and reptiles generally make less efficient large predators than advanced carnivorans .
Since small size usually makes it easier for herbivores to escape or hide from predators, the decreased predation pressure on islands can allow them to grow larger. [ 1 ] [ a ] Small herbivores may also benefit from the absence of competition from missing types of large herbivores.
Benefits of large size that have been suggested for island tortoises include decreased vulnerability to scarcity of food and/or water, through ability to survive for longer intervals without them, or ability to travel longer distances to obtain them. Periods of such scarcity may be a greater threat on oceanic islands than on the mainland. [ 4 ]
Thus, island gigantism is usually an evolutionary trend resulting from the removal of constraints on the size of small animals related to predation and/or competition. [ 5 ] Such constraints can operate differently depending on the size of the animal, however; for example, while small herbivores may escape predation by hiding, large herbivores may deter predators by intimidation. As a result, the complementary phenomenon of island dwarfism can also result from the removal of constraints related to predation and/or competition on the size of large herbivores. [ 6 ] In contrast, insular dwarfism among predators more commonly results from the imposition of constraints associated with the limited prey resources available on islands. [ 6 ] As opposed to island dwarfism, island gigantism is found in most major vertebrate groups and in invertebrates .
Territorialism may favor the evolution of island gigantism. A study on Anaho Island in Nevada determined that reptile species that were territorial tended to be larger on the island compared to the mainland, particularly in the smaller species. In territorial species, larger size makes individuals better able to compete to defend their territory. This gives additional impetus to evolution toward larger size in an insular population. [ 7 ]
A further means of establishing island gigantism may be a founder effect operative when larger members of a mainland population are superior in their ability to colonize islands. [ 8 ]
Island size plays a role in determining the extent of gigantism. Smaller islands generally accelerate the rate of evolution of changes in organism size, and organisms there evolve greater extremes in size. [ 9 ]
Examples of island gigantism include:
Many rodents grow larger on islands, whereas carnivorans , proboscideans and artiodactyls usually become smaller.
In addition to size increase, island plants may also exhibit "insular woodiness". [ 49 ] The most notable examples are the megaherbs of New Zealand 's subantarctic islands . [ citation needed ] Increased leaf and seed size was also reported in some island species regardless of growth form (herbaceous, bush , or tree ). [ 50 ] | https://en.wikipedia.org/wiki/Island_gigantism |
An island of inversion is a region of the chart of nuclides where isotopes have enhanced stability in a sea of mostly very unstable nuclei at the edge of the nuclear map. Each island contains isotopes with a non-standard ordering of single particle levels in the nuclear shell model . Such an area was first described in 1975 by French physicists carrying out spectroscopic mass measurements of exotic isotopes of lithium and sodium . [ 1 ] Since then further studies have shown that at least five such regions exist. These are centered on five neutron-rich nuclides: 11 Li , 20 C , 31 Na , 42 Si , and 64 Cr . [ 2 ] Because there are five known islands of inversion, physicists have suggested renaming the phenomenon "archipelago of islands of shell breaking". [ 2 ] Studies with the purpose of defining the edges of this region are still ongoing.
This nuclear physics or atomic physics –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Island_of_inversion |
Foster's rule , also known as the island rule or the island effect , is an ecogeographical rule in evolutionary biology stating that members of a species get smaller or bigger depending on the resources available in the environment. For example, it is known that pygmy mammoths evolved from normal mammoths on small islands . Similar evolutionary paths have been observed in elephants , hippopotamuses , boas , sloths , deer (such as Key deer ) and humans . [ 1 ] [ 2 ] It is part of the more general phenomenon of island syndrome which describes the differences in morphology , ecology , physiology and behaviour of insular species compared to their continental counterparts.
The rule was first formulated by Leigh Van Valen in 1973 [ 3 ] [ 4 ] based on the study by mammalogist J. Bristol Foster in 1964. [ 5 ] [ 6 ] In it, Foster compared 116 island species to their mainland varieties. Foster proposed that certain island creatures evolved larger body size ( insular gigantism ) while others became smaller ( insular dwarfism ). Foster proposed the simple explanation that smaller creatures get larger when predation pressure is relaxed because of the absence of some of the predators of the mainland, and larger creatures become smaller when food resources are limited because of land area constraints. [ 7 ]
The idea was expanded upon in The Theory of Island Biogeography , by Robert MacArthur and Edward O. Wilson . In 1978, Ted J. Case published a longer paper on the topic in the journal Ecology . [ 8 ]
Recent literature has also applied the island rule to plants. [ 9 ]
There are some cases that do not neatly fit the rule; for example, artiodactyls have on several islands evolved into both dwarf and giant forms. [ 10 ] [ 11 ]
The Island Rule is a contested topic in evolutionary biology. Some argue that, since body size is a trait that is affected by multiple factors, and not just by organisms moving to an island, genetic variations across all populations could also cause the body mass differences between mainland and island populations. [ 12 ] | https://en.wikipedia.org/wiki/Island_rule |
Island syndrome describes the differences in morphology , ecology , physiology and behaviour of insular species compared to their continental counterparts. These differences evolve due to the different ecological pressures affecting insular species, including a paucity of large predators and herbivores as well as a consistently mild climate . [ 2 ] [ 3 ]
Interspecific competition between continental species drives divergence of body size so that species may avoid high levels of competition by occupying distinct niches . Reduced interspecific competition between insular species reduces this selection pressure for species to occupy distinct niches. [ 6 ] As a result, there is less diversity in the body size of insular species. Typically small mammals increase in size (for example fossa are a larger insular relative of the mongoose ) while typically large mammals decrease in size (for example the Malagasy hippopotamuses are smaller insular relatives of continental hippopotamuses ). These are examples of insular gigantism and insular dwarfism respectively. This observed effect is called Foster's rule . Conversely, birds and reptiles tend to exhibit insular gigantism, exemplified by the moa , cassowary and Komodo dragon .
Although the giant tortoises of the Galápagos Islands and the Seychelles (the Galápagos tortoise and Aldabrachelys respectively) are sometimes given as examples of insular gigantism, [ 2 ] they are now thought to represent the last remaining populations of historically widespread giant tortoises. The remains of tortoises of similar or larger size have been found in Australia ( Meiolania ), southern Asia ( Megalochelys ), Madagascar ( Aldabrachelys ), North America [ 7 ] ( Hesperotestudo ) and South America [ 8 ] ( Chelonoidis ). The extant giant tortoises are thought to persist only in a few remote archipelagos because humans arrived there relatively late and have not heavily predated them, suggesting that these tortoise populations have been less subjected to overexploitation .
Since insular prey species experience a reduced risk of predation, they often lose or reduce morphologies utilised in predator evasion. For example, the wings of weevils , rails and pigeons have become so reduced in insular species that many have lost the ability to fly. [ 2 ] This has occurred in several ratites including the kiwi and the cassowary as well as in the dodo and the kākāpō after invading island habitats. The extinct moa of New Zealand exhibit the most extreme known example of insular wing reduction; there is no osseous evidence of even vestigial wings and the pectoral girdle is reduced to a scapulocoracoideum which would be unable to bear a forelimb as it lacks a glenoid fossa . [ 9 ] Therefore, it is the only bird known to have completely lost its wings after a shift to insularity. Loss of flight allows birds to eliminate the costs of maintaining large flight-enabling muscles like the pectoral muscles and allows the skeleton to become heavier and stronger. [ 10 ] Insular populations of barn owl have shorter wings, representing a transitional stage in which their capacity for flight is being reduced. [ 11 ]
Due to the reduced sexual selection of insular species, they tend to exhibit reduced sexual coloration so as to conserve the energy that this demands. Additionally, the low biodiversity of insular ecosystems makes species recognition less important so species-specific coloration is under less selection. [ 5 ] As a result, insular bird species often exhibit duller, sexually monomorphic plumage. [ 5 ]
Several insular species acquire increased melanin colouration. Male white-winged fairywrens living on mainland Australia exhibit a blue nuptial plumage, whereas two island subspecies ( Malurus leucopterus leucopterus from Dirk Hartog Island and Malurus leucopterus edouardi from Barrow Island ) exhibit a black nuptial plumage. [ 12 ] A subspecies of the chestnut-bellied monarch endemic to the Solomon Islands , Monarcha castaneiventris obscurior , exhibits polymorphism in plumage color: some birds are black with a chestnut-colored belly while others are completely melanic. The frequency of the melanic phenotype increases on smaller islands, even when the relative proximity of the islands is accounted for. [ 13 ]
High levels of intraspecific competition between offspring selects for the very fittest individuals. As a result, insular parents tend to produce fewer offspring so that each offspring receives greater parental investment , maximising their fitness . [ 2 ] Lizards endemic to island ecosystems lay smaller clutches that give larger offspring compared to continental lizards of a similar size. Because of increased frequency of laying in insular lizards, continental and insular lizards produced offspring at a comparable rate. [ 14 ]
The expensive tissue hypothesis suggests that tissues with a high metabolic demand like the brain will become reduced if they confer little selective advantage and so do not help to increase food intake. The paucity of large predators means that insular species can afford to become slower and less alert without suffering from massively increased predation risk. As such, reduction in relative brain size is often seen in insular species as this reduces basal metabolic rate [ 15 ] without increases in predation risk. For example, the endocranial volume of the extinct Malagasy dwarf hippos is 30% less than that of an equally sized continental ancestor. [ 16 ] Similarly, the early human , Homo floresiensis , had a brain of similar size to that of the significantly earlier Australopithecus specimens from mainland Africa [ 17 ] [ 18 ] and 3.4 times smaller than that of Homo sapiens which evolved later (see Evolution of human brain size ).
Due to low predation risk, insular prey species can afford to reduce their basal metabolic rate by adopting poikilothermy without any significant increase in predation risk. As a result, poikilothermy is far more common in island species. [ 10 ]
Due to lack of predation, insular species tend to become more docile and less territorial than their continental counterparts (sometimes referred to as island tameness ). [ 2 ] [ 19 ] Deer mice , song sparrows and bronze anoles all have smaller territories with greater overlap compared to their mainland conspecifics. They are also more tolerant to intruders. Falkland Island foxes and Tammar wallabies have both lost an innate fear of large predators including humans. [ 2 ]
The nematode parasite Heligmosomoides polygyrus underwent niche expansion (by invading new host species) and a reduction in genetic diversity after invading ecosystems in seven western Mediterranean islands . The loss of genetic diversity was related to the distance between the contemporal population and the mainland origin. [ 20 ]
Plant stature and leaf area both follow the pattern of insular mammals, with small species becoming larger and large species becoming smaller in island populations. [ 2 ] [ 6 ] This may be due to reduced interspecific competition which would decrease the ecological drive for plants to occupy separate niches. Due to reduced biomass of large herbivores, several island plants lose protective spines and thorns as well as decreasing the amounts of defensive chemicals produced. The improbability of island fires also results in a loss of fire-resistance in bark, fruits and cones. Insular woodiness, the evolutionary transition from herbaceousness toward woodiness , is a very common phenomenon among island floras. [ 21 ]
Due to a lack of dedicated pollinators on remote islands, insular plants often use small, inconspicuously colored and easily accessible flowers to attract a range of alternative pollinator species. Self-pollination is also more commonly used by insular plant species, as pollen does not have to travel so far to reach a receptive ovule or stigma .
Seeds exhibit insular gigantism , becoming predominantly larger than mainland seeds, which is thought to improve mortality at sea during dispersal . [ 2 ] [ 6 ]
The relaxed predation risk in island ecosystems has resulted in the loss of several adaptations and behaviours that act to evade or discourage predation. This makes insular species particularly vulnerable to exploitation by alien species . For example, when humans first introduced dogs, pigs, cats, rats, and crab-eating macaques to the island of Mauritius in the 17th century, they plundered dodo nests and increased interspecies competition for the limited food resources. [ 22 ] This ultimately resulted in the dodo's extinction. The limited resources in island ecosystems are also vulnerable to overexploitation if they are not managed sustainably .
Hațeg Island was a large offshore island in the Tethys Sea of the Late Cretaceous [ 23 ] and is often called "The Island of the Dwarf Dinosaurs" on account of the extensive fossil evidence that its native dinosaurs exhibited island dwarfism . The island's native titanosaur , Magyarosaurus dacus , had a body mass of only 900 kilograms (2,000 lb) [ 24 ] [ 25 ] while mainland titanosaurs like Patagotitan could reach up to 69 tonnes (76 tons). The pterosaur Hatzegopteryx took over the position of apex predator of Hațeg Island in the absence of any hypercarnivorous dinosaurs and likely hunted juvenile dwarf dinosaurs or even adults of the smaller species. Based on its robust jaw and cervical vertebrae, Hatzegopteryx is thought to have hunted in a similar manner to modern storks by attacking prey that are too large to swallow whole. [ 26 ] Its wingspan is estimated to have reached up to 10 to 12 metres (33 to 39 ft), making it one of the largest pterosaurs to have ever lived. As such, it is a potent example of island gigantism , in this case to fill the otherwise empty niche of apex predator . Balaur bondoc was originally classified as a dromaeosaurid dinosaur based on its retractable toe claws. Its forelimbs appeared to be too short and stocky for it to be a basal avialan , however, phylogenetic analysis later confirmed that Balaur was indeed a basal member of Avialae , a clade that includes modern birds . Its limbs were clearly incapable of powered flight and so Balaur is yet another example of the secondary loss of flight after invading an island niche, similar to ratites as well as the extinct moa and the dodo (See Insular reduction in flight capacity ).
The term "reversed island syndrome" (RIS) was first used by Pasquale Raia in 2010 to describe the differences in morphology , ecology , physiology and behaviour observed in insular species when population density is either low or fluctuating. [ 27 ] This results in stronger natural selection and weaker intraspecific selection, leading to different phenotypes compared to the standard island syndrome.
RIS was first described in a population of Italian wall lizard endemic to the Licosa Islet where the unpredictable environmental conditions and highly fluctuating population density have selected for aggressive behaviour and increased reproductive effort. [ 28 ] The male lizards exhibit elevated α-MSH levels relative to mainland populations, which increases the basal metabolic rate, strengthens immune responses, [ 29 ] produces darker blue coloration and raises 5α-dihydrotestosterone levels. [ 28 ] The latter improves male reproductive success by increasing the likelihood of winning sexual conflicts over females and augmenting sperm quality. [ 28 ] Females produce similar numbers of eggs compared to mainland populations but the eggs of insular females are significantly heavier, reflecting increased reproductive effort. The unpredictable conditions produce high mortality rates so adults invest more effort into current broods since they are less likely to survive to produce subsequent broods i.e. there is low interbrood conflict . | https://en.wikipedia.org/wiki/Island_syndrome |
In engineering, iso-elastic refers to a system of elastic and tensile parts (springs and pulleys) which are arranged in a configuration which isolates physical motion at one end in order to minimize or prevent similar motion from occurring at the other end.
This type of device must be able to maintain angular direction and load-bearing over a large range of motion.
The most prominent use of an iso-elastic system is in the supporting armature of a Steadicam , used to isolate a film or video camera from the operator's movements.
Steadicam arms all work in a fashion similar to a spring lamp since each arm has two sections (similar to and labelled like a human arm); both the upper and fore-arm sections consist of a parallelogram with a diagonal iso-elastic cable-pulley-spring system. The iso-elastic system is tensioned to counteract the weight of the camera and steadicam sled. This tensioning allows the camera and operator to move vertically and independently of each other. For example, as the operator runs, the bouncing of his body is absorbed by the springs, keeping the camera steady. The arm also has unsprung hinges at both ends of each arm allowing it to bend in the horizontal plane (just like your elbow, not like a spring lamp).
To understand how an iso-elastic system works, we must first understand how springs work. The tension (elastic force) in a spring is proportional to its extension according to Hooke's law . This means that if a weight is hung on a spring it will oscillate with simple harmonic motion about its balance point; when the weight is above the balance point the spring's tension is reduced so the weight falls due to gravity, and when the weight is below the balance point the spring's tension will pull it back upwards.
If a simple spring system were used in a steadicam, then as the operator moved vertically, the camera would be subject to simple harmonic motion, and bounce up and down. To counteract this tendency, an iso-elastic system is employed.
The springs used are large, stiff springs with a high modulus of elasticity , and they are highly tensioned. A compound pulley system is then used so that the large force exerted by the spring can be divided by a factor of five, for example, so the cable exiting the pulley system will have only moderate tension. Most importantly, however, when the cable is drawn in or out the extension of the spring changes by only a fifth of that distance, so that the tension force of the spring will not change much. The result is that the spring-pulley system can produce a fairly constant tension in the cable over a large range of movement.
The almost constant force exerted by an iso-elastic system is employed in the armature of a steadicam, to counteract the constant force of gravity on the camera's and mount's mass . The result is that the weight of the camera is almost exactly balanced by the tension force throughout the entire range of vertical movement, so even when the operator jumps vertically, the camera will retain its vertical position due to inertia , but remain balanced, just with the armature at a different angle.
As a result, the camera doesn't bounce up to the 'balanced' position after a move, for example when the operator steps up onto a curb from the road. This allows the camera to be more isolated and independent of the operator's moves. The operator can of course deliberately move the camera up or down, if desired. In reality however camera operators find it preferable for the arm to not be perfectly iso-elastic so that the camera will naturally rise to a comfortable operating height; the springs will be tensioned so this only happens very slowly and without bouncing so as to maintain the smoothness of the camera's motion." [ 1 ] | https://en.wikipedia.org/wiki/Iso-elastic |
IsoBase is a database identifying functionally related proteins integrating sequence data and protein–protein interaction networks. [ 1 ]
This Biological database -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/IsoBase |
Isoantibodies , formerly called alloantibodies , are antibodies produced by an individual against isoantigens produced by members of the same species . In the case of the species Homo sapiens , for example, there are a significant number of antigens that are different in every individual. When antigens from another individual are introduced into another's body, these isoantibodies immediately bind to and destroy them.
One common example is the isohaemagglutinins , which are responsible for blood transfusion reactions. [ 1 ] This may subjectively differ from the term 'natural' antibodies, or simply 'antibodies', as the former seem to arise from genetic control without apparent antigenic stimulation whereas the latter arise due to antigenic stimulation.
A protein or other substance, such as histocompatibility or red blood cell antigens, that is present in only some members of a species and therefore able to stimulate isoantibody production in other members of the same species who lack it. When injected into another animal, they trigger an immune response aimed at eliminating them. Therefore, it can be thought of as an antigen that is present in some members of the same species, but is not common to all members of that species. If an alloantigen is presented to a member of the same species that does not have the alloantigen, it will be recognized as foreign. They are the products of polymorphic genes . [ 2 ]
Isoantibodies are seen in people with different blood groups . The anti-A or anti-B isoantibodies or both (also called isohaemagglutinins ) are produced by an individual against the antigens (A or B) on the RBCs of other blood groups. In a person with A blood group, the plasma will contain isoantibodies against B antigens, so immediately after transfusion of blood from B group the anti-B isohemagglutinins agglutinate the foreign red blood cells.
Anti-A and anti-B antibodies (called isohaemagglutinins ), which are not present in human babies, appear in the first years of life. It is possible that food and environmental antigens (bacterial, viral or plant antigens) have epitopes similar enough to A and B glycoprotein antigens. [ 3 ] The antibodies created against these environmental antigens in the first years of life can cross react with ABO-incompatible red blood cells when it comes in contact with during blood transfusion later in life. Anti-A and anti-B antibodies are usually IgM type. O-type individuals can produce IgG-type ABO antibodies. | https://en.wikipedia.org/wiki/Isoantibodies |
Isoaspartic acid ( isoaspartate , isoaspartyl , β-aspartate ) is an aspartic acid residue isomeric to the typical α peptide linkage. It is a β-amino acid, with the side chain carboxyl moved to the backbone. Such a change is caused by a chemical reaction in which the nitrogen atom on the N+1 following peptide bond (in black at top right of Figure 1) nucleophilically attacks the γ-carbon of the side chain of an asparagine or aspartic acid residue, forming a succinimide intermediate (in red). Hydrolysis of the intermediate results in two products, either aspartic acid (in black at left) or isoaspartic acid, which is a β-amino acid (in green at bottom right). [ 1 ] The reaction also results in the deamidation of the asparagine residue. Racemization may occur leading to the formation of D-aminoacids. [ 2 ]
Isoaspartyl formation reactions have been conjectured to be one of the factors that limit the useful lifetime of proteins . [ 3 ]
Isoaspartyl formation proceeds much more quickly if the asparagine is followed by a small, flexible residue (such as Gly) that leaves the peptide group open for attack. These reactions also proceed much more quickly at elevated pH (>10) and temperatures.
L-isoaspartyl methyltransferase repairs isoaspartate and D-aspartate residues by sticking a methyl group onto the side chain carboxyl group in the residue, creating an ester. The ester rapidly and spontaneously turns into the succinimide (red), and randomly turns back into normal aspartic acid (black) or isoaspartate again (green) for another attempt. [ 4 ] | https://en.wikipedia.org/wiki/Isoaspartate |
The isoazimuth is the locus of the points on the Earth's surface whose initial orthodromic course with respect to a fixed point is constant. [ 1 ]
That is, if the initial orthodromic course Z from the starting point S to the fixed point X is 80 degrees , the associated isoazimuth is formed by all points whose initial orthodromic course with respect to point X is 80° (with respect to true north). The isoazimuth is written using the notation isoz(X, Z) [ according to whom? ] .
The isoazimuth is of use when navigating with respect to an object of known location, such as a radio beacon. A straight line called the azimuth line of position is drawn on a map, and on most common map projections this is a close enough approximation to the isoazimuth. On the Littrow projection , the correspondence is exact. This line is then crossed with an astronomical observation called a Sumner line , and the result gives an estimate of the navigator's position.
Let X be a fixed point on the Earth of coordinates latitude: B 2 {\displaystyle B_{2}} , and longitude: L 2 {\displaystyle L_{2}} . In a terrestrial spherical model, the equation of isoazimuth curve with initial course C passing through point S( B , L ) is: tan ( B 2 ) cos ( B ) = sin ( B ) cos ( L 2 − L ) + sin ( L 2 − L ) / tan ( C ) {\displaystyle \tan(B_{2})\cos(B)=\sin(B)\cos(L_{2}-L)+\sin(L_{2}-L)/\tan(C)\;}
In this case the X point is the illuminating pole of the observed star, and the angle Z is its azimuth . The equation of the isoazimuthal [ 2 ] curve for a star with coordinates ( Dec, GHA ), - Declination and Greenwich hour angle -, observed under an azimuth Z is given by:
where LHA is the local hour angle , and all points with latitude B and longitude L , they define the curve. | https://en.wikipedia.org/wiki/Isoazimuth |
Isobars are atoms ( nuclides ) of different chemical elements that have the same number of nucleons . Correspondingly, isobars differ in atomic number (or number of protons ) but have the same mass number . An example of a series of isobars is 40 S , 40 Cl , 40 Ar , 40 K , and 40 Ca . While the nuclei of these nuclides all contain 40 nucleons, they contain varying numbers of protons and neutrons. [ 1 ]
The term "isobars" (originally "isobares") for nuclides was suggested by British chemist Alfred Walter Stewart in 1918. [ 2 ] It is derived from Greek ἴσος (isos) ' equal ' and βάρος (baros) ' weight ' . [ 3 ]
The same mass number implies neither the same mass of nuclei , nor equal atomic masses of corresponding nuclides. From the Weizsäcker formula for the mass of a nucleus:
where mass number A equals to the sum of atomic number Z and number of neutrons N , and m p , m n , a V , a S , a C , a A are constants, one can see that the mass depends on Z and N non-linearly, even for a constant mass number. For odd A , it is admitted that δ = 0 and the mass dependence on Z is convex (or on N or N − Z , it does not matter for a constant A ). This explains that beta decay is energetically favorable for neutron-rich nuclides, and positron decay is favorable for strongly neutron-deficient nuclides. Both decay modes do not change the mass number, hence an original nucleus and its daughter nucleus are isobars. In both aforementioned cases, a heavier nucleus decays to its lighter isobar.
For even A the δ term has the form:
where a P is another constant. This term, subtracted from the mass expression above, is positive for even-even nuclei and negative for odd-odd nuclei. This means that even-even nuclei, which do not have a strong neutron excess or neutron deficiency, have higher binding energy than their odd-odd isobar neighbors. It implies that even-even nuclei are (relatively) lighter and more stable. The difference is especially strong for small A . This effect is also predicted (qualitatively) by other nuclear models and has important consequences.
The Mattauch isobar rule states that if two adjacent elements on the periodic table have isotopes of the same mass number, at least one of these isobars must be a radionuclide (radioactive). In cases of three isobars of sequential elements where the first and last are stable (this is often the case for even-even nuclides, see above ), branched decay of the middle isobar may occur. For instance, radioactive iodine-126 has almost equal probabilities for two decay modes: positron emission , leading to tellurium-126 , and beta emission , leading to xenon-126 .
No observationally stable isobars exist for mass numbers 5 (decays to helium-4 plus a proton or neutron ), 8 (decays to two helium-4 nuclei), 147, 151, as well as for 209 and above (noting primordial but not stable 147 Sm, 151 Eu, and 209 Bi). Two observationally stable isobars exist for 36, 40, 46, 50, 54, 58, 64, 70, 74, 80, 84, 86, 92, 94, 96, 98, 102, 104, 106, 108, 110, 112, 114, 120, 122, 123, 124, 126, 132, 134, 136, 138, 142, 154, 156, 158, 160, 162, 164, 168, 170, 176, 180 (including a meta state), 192, 196, 198 and 204. [ 4 ]
In theory, no two stable nuclides have the same mass number (since no two nuclides that have the same mass number are both stable to beta decay and double beta decay ), and no stable nuclides exist for mass numbers 5, 8, 143–155, 160–162, and ≥ 165, since in theory, the beta-decay stable nuclides for these mass numbers can undergo alpha decay .
Sprawls, Perry (1993). "5 – Characteristics and Structure of Matter". Physical Principles of Medical Imaging (2 ed.). Madison, WI : Medical Physics Publishing. ISBN 0-8342-0309-X . Retrieved 28 April 2010 . | https://en.wikipedia.org/wiki/Isobar_(nuclide) |
Isobornyl acetate is an organic compound consisting of the acetate ester or the terpenoid isoborneol . It is a colorless liquid with a pleasant pine -like scent , and it is produced on a multi-ton scale for this purpose. The compound is prepared by reaction of camphene with acetic acid in the presence of a strongly acidic catalyst such as sulfuric acid . Hydrolysis of isobornyl acetate gives isoborneol, a precursor to camphor . [ 1 ]
Like many plant exudates , isobornyl acetate appears to have antifeedant properties. [ 2 ]
This organic chemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Isobornyl_acetate |
This page provides supplementary chemical data on isobutane .
The handling of this chemical may incur notable safety precautions. It is highly recommend that you seek the Material Safety Datasheet ( MSDS ) for this chemical from a reliable source such as SIRI , and follow its directions.
Table data obtained from CRC Handbook of Chemistry and Physics 44th ed. | https://en.wikipedia.org/wiki/Isobutane_(data_page) |
Isobutyric anhydride is an organic compound with the formula ((CH 3 ) 2 CHCO) 2 O . It is an acyclic carboxylic anhydride of isobutyric acid . [ 2 ] It is classified as an organic acid anhydride , being derived from dehydration of isobutyric acid. It is a colorless liquid with a strong, pungent odor. [ 1 ] [ 3 ]
Isobutyric anhydride is a reagent in the production of the ester of cyclohexanone oxime . [ 4 ]
Isobutyric anhydride is used as an acylating agent in organic synthesis. Its primary application is in the production of esters , such as cyclohexanone oxime . [ 4 ] Isobutyric anhydride is used in the synthesis of various dyes . [ 5 ] It is also used in the production of cellulose derivatives, such as cellulose isobutyrate and cellulose acetate isobutyrate . [ 6 ] [ 7 ] Another application of isobutyric anhydride is in the synthesis of various chemical derivatives. For example, it is used to produce 4- O -isobutyryl derivatives of monosaccharides. [ 8 ] | https://en.wikipedia.org/wiki/Isobutyric_anhydride |
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