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A radiogenic nuclide is a nuclide that is produced by a process of radioactive decay . It may itself be radioactive (a radionuclide ) or stable (a stable nuclide ).
Radiogenic nuclides (more commonly referred to as radiogenic isotopes ) form some of the most important tools in geology. They are used in two principal ways:
Some naturally occurring isotopes are entirely radiogenic, but all those are radioactive isotopes, with half-lives too short to have occurred primordially and still exist today. Thus, they are only present as radiogenic daughters of either ongoing decay processes, or else cosmogenic (cosmic ray induced) processes that produce them in nature freshly. A few others are naturally produced by nucleogenic processes (natural nuclear reactions of other types, such as neutron absorption).
For radiogenic isotopes that decay slowly enough, or that are stable isotopes , a primordial fraction is always present, since all sufficiently long-lived and stable isotopes do in fact naturally occur primordially. An additional fraction of some of these isotopes may also occur radiogenically.
Lead is perhaps the best example of a partly radiogenic substance, as all four of its stable isotopes ( 204 Pb, 206 Pb, 207 Pb, and 208 Pb) are present primordially, in known and fixed ratios. However, 204 Pb is only present primordially, while the other three isotopes may also occur as radiogenic decay products of uranium and thorium . Specifically, 206 Pb is formed from 238 U, 207 Pb from 235 U, and 208 Pb from 232 Th. In rocks that contain uranium and thorium, the excess amounts of the three heavier lead isotopes allows the rocks to be "dated", thus providing a time estimate for when the rock solidified and the mineral held the ratio of isotopes fixed and in place.
Another notable radiogenic nuclide is argon -40, formed from radioactive potassium . Almost all the argon in the Earth's atmosphere is radiogenic, whereas primordial argon is argon-36.
Some nitrogen -14 is radiogenic, coming from the decay of carbon-14 (half-life around 5700 years), but the carbon-14 was formed some time earlier from nitrogen-14 by the action of cosmic rays.
Other important examples of radiogenic elements are radon and helium , both of which form during the decay of heavier elements in bedrock. Radon is entirely radiogenic, since it has too short a half-life to have occurred primordially. Helium, however, occurs in the crust of the Earth primordially, since both helium-3 and helium-4 are stable, and small amounts were trapped in the crust of the Earth as it formed. Helium-3 is almost entirely primordial (a small amount is formed by natural nuclear reactions in the crust). Helium-3 can also be produced as the decay product of tritium ( 3 H) which is a product of some nuclear reactions, including ternary fission . The global supply of helium (which occurs in gas wells as well as the atmosphere) is mainly (about 90%–99%) radiogenic, as shown by its factor of 10 to 100 times enrichment in radiogenic helium-4 relative to the primordial ratio of helium-4 to helium-3. This latter ratio is known from extraterrestrial sources, such as some Moon rocks and meteorites, which are relatively free of parental sources for helium-3 and helium-4.
As noted in the case of lead-204, a radiogenic nuclide is often not radioactive. In this case, if its precursor nuclide has a half-life too short to have survived from primordial times, then the parent nuclide will be gone, and known now entirely by a relative excess of its stable daughter. In practice, this occurs for all radionuclides with half lives less than about 50 to 100 million years. Such nuclides are formed in supernovas , but are known as extinct radionuclides , since they are not seen directly on the Earth today.
An example of an extinct radionuclide is iodine-129 ; it decays to xenon-129, a stable isotope of xenon which appears in excess relative to other xenon isotopes. It is found in meteorites that condensed from the primordial Solar System dust cloud and trapped primordial iodine-129 (half life 15.7 million years) sometime in a relative short period (probably less than 20 million years) between the iodine-129's creation in a supernova, and the formation of the Solar System by condensation of this dust. The trapped iodine-129 now appears as a relative excess of xenon-129. Iodine-129 was the first extinct radionuclide to be inferred, in 1960. Others are aluminium-26 (also inferred from extra magnesium-26 found in meteorites), and iron-60.
The following table lists some of the most important radiogenic isotope systems used in geology, in order of decreasing half-life of the radioactive parent isotope. The values given for half-life and decay constant are the current consensus values in the Isotope Geology community. [ 1 ]
** indicates ultimate decay product of a series.
Units used in this table Gyr = gigayear = 10 9 years Myr = megayear = 10 6 years kyr = kiloyear = 10 3 years
Radiogenic heating occurs as a result of the release of heat energy from radioactive decay [ 4 ] during the production of radiogenic nuclides. Along with heat from the Primordial Heat (resulting from planetary accretion), radiogenic heating occurring in the mantle and crust make up the two main sources of heat in the Earth's interior . [ 5 ] Most of the radiogenic heating in the Earth results from the decay of the daughter nuclei in the decay chains of uranium-238 and thorium-232 , and potassium-40 . [ 6 ] | https://en.wikipedia.org/wiki/Radiogenic_nuclide |
In British English , a radiogram is a piece of furniture that combined a radio and record player . [ 1 ] The word radiogram is a portmanteau of radio and gramophone . [ 2 ] The corresponding term in American English is console .
Radiograms reached their peak of popularity in the post-war era, supported by a rapidly growing interest in records . Originally they were made of polished wood to blend with the furniture of the 1930s, with many styled by the leading designers of the day. An expensive instrument of entertainment for the house, fitted with a larger loudspeaker than the domestic radio , the radiogram soon began to develop features such as the record autochanger, which would accept six or seven records and play them one after another. Certain recordings could be ordered as a box set which would combine the recorded piece in order, to suit an autochanger set-up. In the 1940s and 1950s, sales of the radiogram, coupled with the then-new F.M. waveband , and the advent of the 45 rpm single and the LP record , meant that many manufacturers considered the radiogram to be more important than the fledgling television set sales. Later models took on the modern lines, piano gloss finish and plastic and gilt trim of the 1960s. Stereogram versions became available to take advantage of stereo records. As tape formats grew in popularity, some later models also incorporated reel-to-reel tape decks, cassette decks , or 8-track tape players, or the ability to connect external tape decks.
As valve radio development ended in the late 1960s and transistors began to take over, radiograms started to become obsolete. By the late 1970s, they had been replaced by more compact equipment, such as the hi-fi and the music centre . [ citation needed ]
Since radiograms were manufactured in such huge numbers they are not as rare or valuable as TV sets or table radios from the same period. An exception to this are models from certain manufacturers which have become collectable such as Hacker Radio Ltd. , Dynatron , Blaupunkt , Braun , and SABA . | https://en.wikipedia.org/wiki/Radiogram_(device) |
A radioimmunoassay ( RIA ) is an immunoassay that uses radiolabeled molecules in a stepwise formation of immune complexes . A RIA is a very sensitive in vitro assay technique used to measure concentrations of substances, usually measuring antigen concentrations (for example, hormone levels in blood ) by use of antibodies .
The RIA technique is extremely sensitive and extremely specific , and although it requires specialized equipment, it remains among the least expensive methods to perform such measurements. It requires special precautions and licensing, since radioactive substances are used. [ citation needed ]
In contrast, an immunoradiometric assay (IRMA) is an immunoassay that uses radiolabeled molecules but in an immediate rather than stepwise way.
A radioallergosorbent test (RAST) is an example of radioimmunoassay. It is used to detect the causative allergen for an allergy .
Classically, to perform a radioimmunoassay, a known quantity of an antigen is made radioactive , frequently by labeling it with gamma-radioactive isotopes of iodine , such as 125-I , or tritium [ 1 ] attached to tyrosine . This radiolabeled antigen is then mixed with a known amount of antibody for that antigen, and as a result, the two specifically bind to one another. Then, a sample of serum from a patient containing an unknown quantity of that same antigen is added. This causes the unlabeled (or "cold") antigen from the serum to compete with the radiolabeled antigen ("hot") for antibody binding sites. As the concentration of "cold" antigen is increased, more of it binds to the antibody, displacing the radiolabeled variant, and reducing the ratio of antibody-bound radiolabeled antigen to free radiolabeled antigen. The bound antigens are then separated and the radioactivity of the free(unbound) antigen remaining in the supernatant is measured using a gamma counter . This value is then compared to a standardised calibration curve to work out the concentration of the unlabelled antigen in the patient serum sample. [ 2 ] RIAs can detect a few picograms of analyte in an experimental tubes if using antibodies of high affinity. [ 1 ]
This method can be used for any biological molecule in principle and is not restricted to serum antigens, nor is it required to use the indirect method of measuring the free antigen instead of directly measuring the captured antigen. For example, if it is undesirable or not possible to radiolabel the antigen or target molecule of interest, a RIA can be done if two different antibodies that recognize the target are available and the target is large enough (e.g., a protein) to present multiple epitopes to the antibodies. One antibody would be radiolabeled as above while the other would remain unmodified. The RIA would begin with the "cold" unlabeled antibody being allowed to interact and bind to the target molecule in solution. Preferably, this unlabeled antibody is immobilized in some way, such as coupled to an agarose bead, coated to a surface, etc. Next, the "hot" radiolabeled antibody is allowed to interact with the first antibody-target molecule complex. After extensive washing, the direct amount of radioactive antibody bound is measured and the amount of target molecule quantified by comparing it to a reference amount assayed at the same time. This method is similar in principle to the non-radioactive sandwich ELISA method. [ 3 ]
This method was developed by Solomon Berson and Rosalyn Sussman Yalow at the Veterans Administration Hospital in the Bronx , New York. [ 4 ] [ 5 ] This revolutionary development earned Dr. Yalow the Nobel Prize for Medicine in 1977, the second woman ever to win it. [ 6 ] In her acceptance speech, Dr. Yalow said, "The world cannot afford the loss of the talents of half its people if we are to solve the many problems which beset us." [ 7 ] Yalow shared the Nobel Prize with Roger Guillemin , and Andrew Schally who earned the prize based on their research into "the peptide hormone production of the brain". [ 6 ]
steps in radioimmunoassay technique | https://en.wikipedia.org/wiki/Radioimmunoassay |
Radioimmunoprecipitation assay buffer (RIPA buffer) is a lysis buffer used to lyse cells and tissue for the radio immunoprecipitation assay (RIPA). [ 1 ] [ 2 ] This buffer is more denaturing than NP-40 or Triton X-100 because it contains the ionic detergents SDS and sodium deoxycholate as active constituents and is particularly useful for disruption of nuclear membranes in the preparation of nuclear extracts. The stronger detergents in RIPA buffer (such as SDS) cause greater protein denaturation and decrease protein-protein interactions.
RIPA buffer recipes vary slightly between authors and may include:
The following ingredients are optional and included as needed:
This biology article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Radioimmunoprecipitation_assay_buffer |
A radioligand is a microscopic particle which consists of a therapeutic radioactive isotope and the cell-targeting compound - the ligand. The ligand is the target binding site, it may be on the surface of the targeted cancer cell for therapeutic purposes. Radioisotopes can occur naturally or be synthesized and produced in a cyclotron/nuclear reactor. The different types of radioisotopes include Y-90, H-3, C-11, Lu-177, Ac-225, Ra-223, In-111, I-131, I-125, etc. Thus, radioligands must be produced in special nuclear reactors for the radioisotope to remain stable. [ 1 ] Radioligands can be used to analyze/characterize receptors, to perform binding assays, to help in diagnostic imaging, and to provide targeted cancer therapy. Radiation is a novel method of treating cancer and is effective in short distances along with being unique/personalizable and causing minimal harm to normal surrounding cells. Furthermore, radioligand binding can provide information about receptor-ligand interactions in vitro and in vivo. Choosing the right radioligand for the desired application is important. The radioligand must be radiochemically pure, stable, and demonstrate a high degree of selectivity, and high affinity for their target. [ 2 ]
Wilhelm Roentgen is credited with the discovery of radioactivity in 1895 with many others such as Antoine Henri Becquerel , Pierre Curie , and Marie Curie following closely behind to further advance the field of radioactivity. [ 3 ] John Lawrence , a physicist at The University of California Berkeley , first used nuclear medicine in humans came in 1936 after extensive use of radioactive phosphorus in mouse models. Often called the father of nuclear medicine, Lawrence treated a leukemia patient with radiophosphorus, which was the first time a radioactive isotope has been used to treat human patients. [ 4 ] Another pioneer in the field, Sam Seidlin, in partnership with Saul Hertz , treated a case of thyroid cancer with radioactive iodine (I-131) 1946. [ 5 ] In the 1950s, nuclear medicine began to gain traction as a medical specialty with the Society of Nuclear Medicine forming in 1954 and later releasing the first copy of the Journal of Nuclear Medicine in 1960. [ 6 ] The use of radioligands and nuclear tagging started to gain popularity in in the early 1960s when Elwood Jensen and Herbert Jacobsen (1962) and later Jack Gorksi, David Toft, G, Shymala, Donald Smith, and Angelo Notides (1968) attempted to identify the estrogen receptor. [ 7 ] The American Medical Association (AMA) officially recognized Nuclear Medicine as a medical specialty in 1970 and the American Board of Nuclear Medicine was established in 1972. Progress came quickly in 1973 when Edward Hoffman, Michael M. Ter-Pogossian, and Michael E. Phelps invented the first PET camera for human use. [ 8 ] The 1980s brought early radioligand studies for neuroendocrine tumors (NETs) which continued into the early 2000s. In 2017 the European Union (EU) approved the use of radioligand therapy for NETs with the U.S. following close behind in 2018. [ 9 ]
Gamma rays
Positron emission
Beta particles
A ligand is a molecule utilized for cell-signaling that binds to a target tissue for cellular communication. There are many different types of ligands including: internal receptors, cell-surface receptors , Ion-channel receptors , G-Protein Coupled Receptors (GPCRs), and enzyme-linked receptors . [ 10 ] Ligands can be divided into two categories, agonists or antagonists. Agonists behave similarly to natural ligands, while antagonists are inhibitors and block the binding of the natural ligand. There are many different subtypes of agonists, including endogenous agonists, super agonist, full agonist, inverse agonist, and irreversible agonist. [ 11 ]
Radioligands are made up of the radioisotope, linker, and ligand. This structure allows the compound to identify and bind to the target tissue while retaining the ability to be tracked and imaged clinically. When a radioligand binds to its target, it alters the microenvironment of the receptor and surrounding tissue, partially due to the structure of the radioligand itself. [ 12 ] Without both the high affinity ligand and the radioisotope, the efficiency of this process is lost.
Radioligands are administered through four main routes: intravenously, subcutaneous injection, intraperitoneally, and orally. While intravenous application is the most used route of injection, the route is dependent on the mechanism of action and overall aim of the binding. [ 13 ] Before application of the ligand, clinicians will perform imaging, generally via Positron Emission Tomography (PET) or Single Photon Emission Computed Tomography (SPECT) for baseline comparison after radioligand administration. Once the radioligand is administered, the radioligand will travel to the target tissue and selectively bind. The structure of the compound allows clinicians to easily identify the path traveled and the destination via repeated imaging and the signal put out by the radiotracer attached to the ligand. [ 14 ]
Direct radiotherapy performed via ionizing radiation can cause tissue damage and hypoxia to tissues other than the target. While this effect is lessened in a target radiotracer therapy utilizing radioligands, there is still an impact on the surrounding tissue described as Radiation Induced Bystander Effect (RIBE). Surrounding cells altered by the radioligand and displaying RIBE can show signs of stress, chromosomal abnormalities, or even experience cell death. However, the type of radiation used, whether 𝜶, β, or both can have a dramatically different effect on both the target binding site and surrounding tissue. [ 15 ] Changes in nearby tissue is not the only possible impact of ligand therapy, there may be immunologic responses from the target tissue that cause changes remotely. This has been deemed, "abscopal effect". [ 16 ] While this mechanism is not well understood, it explains the impact of other tissue, both benign and malignant, after targeted radiotherapy.
Imaging is a useful tool in visualization of the radioligand after injection, with Positron Emission Tomography (PET) and Single Photon Emission Computed Tomography (SPECT) being the most common types of imaging. PET scans are often utilized after radioligand administration because of the ease of use, image accuracy, and non-invasive nature. While PET and SPECT scans function similarly when imaging radioligands, the main difference lies in the type of radiation used, with PET Scans utilizing positrons and SPECT utilizing gamma rays. When comparing the two modalities, PET offers much better image quality and high diagnostic proficiency, however, the high cost limits the overall availability as well as the short half-lives of the positron-emitting isotopes. Alternatively, SPECT imaging is more dynamic because of the lower cost burden and longer half-lives of single-photon emitters. [ 17 ] With advances in technology came hybrid imaging that can combine PET, SPECT, Computed Tomography (CT), and Magnetic Resonance Imaging (MRI). Some hybrid imaging modalities include: SPECT/CT, PET/CT and PET/MRI. [ 18 ] Although combined imaging presents both cost and availability barriers, the technology is an extremely useful diagnostic tool. Often, the patient does not have to be moved for both imaging types to be completed and the clinicians are provided with rich, multi-dimensional imaging. [ 19 ]
Measuring the extent and kinetics of radioligand binding is important in determining information about binding sites of radioligands, and subsequent affinity to potential drugs. Three different binding assays are typically used for radioligand binding; these are saturation, competition, and kinetic binding.
Saturation binding measures the specific binding of a radioligand at varying concentrations while at equilibrium. Through this method, the number of receptors can be determined as well as affinity of the ligand to these receptors. Saturation binding experiments are often called "Scatchard experiments" as they can be graphed as a Scatchard plot . [ 20 ]
Competitive binding experiments aim to determine the binding of a labeled radioligand at one specific concentration while subjected to various concentrations of a competitor, usually an unlabeled ligand. There are many purposes to competitive binding experiments, including being able to validate that the radioligand of interest will bind to the receptor with the expected affinity and potency even in the presence of a competitor. [ 21 ] This experiment would also help determine if the radioligand will be able to recognize and bind to the correct receptor. Competitive binding experiments also serve to study the binding ability of a low-affinity drug, as it can be used as an unlabeled competitor. Finally, receptor number and affinity can also be determined through this experiment. [ 20 ]
Kinetic binding experiments differ from saturation and competition experiments in that they are not done at equilibrium. Instead, they measure the course of binding of the radioligand during the experiment as well as the dissociation to determine calculation of the Kd, and rate constants of binding and dissociation. Kinetic binding experiments are also called dissociation binding experiments and can help evaluate the interaction of the radioligand and the targeted receptor. [ 20 ]
𝜶 and β particles are both used in the treatment of cancers, depending on the size and location of the particular tumor. Alpha particles contain overall higher energy and have a shorter path length, and have greater cytotoxic properties for this reason as compared to β particles. However, due to the shorter path length of these particles, the method of delivery needs to be extremely close to the location of the tumor. Currently, treatments using alpha-emitters exist which consist of alpha emitters attached to carrier molecules. [ 22 ] Some examples of alpha-emitting radioligands include actinium-225, Ra-223-chloride, and Lead-212.36
β particles emit lower energy as compared to α-emitters, but they have the advantage of having longer path length. However, due to their lower energy, more β particles are required to cause damage to tumor cells as compared to α-emitters. [ 22 ] Some examples of β-emitters include Lu-177, Y-90, and I-131. [ 23 ]
Lutathera is a peptide receptor radioligand/radionuclide therapy (approved by the FDA in 2018) specifically for patients with gastroenteropancreatic neuroendocrine tumors (GEP-NETs) that express somatostatin hormone receptors (SSTR). The radioisotope is Lu-177 and the ligand is a SSTR on the surface of tumor cells.
Lu-177 is produced by bombarding the stable isotope Yb-176 (which is found in monazite sand as well as the ores euxenite and xenotime) with neutrons. Yb-176 turns into Yb-177 which is unstable and has a half life of 1.9 hours so it quickly decays into the medical isotope Lu-177. [ 24 ] For mass production, it is better to produce Yb-176 through fission reactors. This is the indirect production method and requires elaborate radiochemical separation, purification, and results in large amounts of radioactive waste. The direct method of producing Lu-177 is by performing neutron irradiation on Lu-176 to Lu-177. This is an inexpensive and effective method to produce Lu-177. [ 25 ] In the United States, the main place that Lu-177 is produced is the University of Missouri Research Reactor.
Once produced, Lu-177 is stable for 72 hours if stored below room temperature. Freeze dried kits of Lutathera do show reduced effectiveness in radiation therapy but they maintain radiochemical purity. [ 25 ] Lu-177 requires radiation shielding for handling. Lu-177 is stored and transported in a vial with lead/plexiglass shielding ready-to-use. Repeated production, timely delivery, and quick administration are important so that the therapy remains effective. [ 26 ]
Once transported to the hospital or cancer treatment / oncology center, the patient is prepped, all necessary tests are done, and the patient requires two separate IV sites for infusion. One site for radioactive Lu-177 infusion and one site for amino acid infusion. Amino acid infusion is needed to reduce radiation toxicity to the organs - specifically the kidneys. The sites are separate to prevent radioactive contamination after therapy. The patient receives therapy by automated syringe, infusion pump, or gravity using long/short needles, tubing, and sodium chloride solution. Antiemetic (anti-nausea) medications or short/long acting octreotide (cancer growth control) can be used post-therapy for symptom management.
The most common side effects include decreased blood cell counts, increased liver enzymes, vomiting, nausea, increased blood glucose, and decreased blood potassium levels. [ 27 ] Lutathera is not given to pregnant or breastfeeding individuals. The therapy shrinks tumors by an average of 30%, reduces disease progression by 72%, and delays the growth of tumors. [ 28 ]
Pluvicto also uses Lu-177 as the radioisotope (which is a beta emitter that decays to Hf-177) but its ligand is a prostate-specific membrane antigen (PSMA) targeted ligand as this radioligand therapy addresses metastatic prostate cancer. [ 29 ] It was FDA approved in 2022. The difference between Lutathera and Pluvicto is shown in the chemical linkages in the images above. The production, transportation, and storage is the same as Lutathera. The therapy is administered intravenously through gravity, syringe, or a Peristaltic Infusion Pump. [ 30 ] The major warnings include renal toxicity, infertility in males, and embryo/fetal harm. General side effects of this radioligand therapy include fatigue, nausea, dry mouth, anemia, decreased appetite, and constipation. Regular blood tests and imaging post-therapy are needed to see if the radioligand therapy is working and its side effects.
The benefits of Pluvicto include delaying tumor growth, extending life by about 20 months, [ 31 ] and destroying tumor cells by damaging the DNA inside those cells.
Xofigo, a radioligand therapy that was FDA approved in 2013, uses Radium-223 dichloride as the radioisotope, but its ligand varies from Pluvicto. Pluvicto only attacks cancer cells expressing PSMA, but Xofigo attacks all bone metastases. Qualified patients are 30% less likely to die when treated by Xofigo than if treated by a placebo. [ 32 ] Ra-223-chloride is an alpha-emitting bone targeting agent.
Bexxar, a radioligand therapy using the radioisotope I-131+Tositumomab (a murine monoclonal antibody) and binding/targeting the ligand CD20 on human B-cells. [ 33 ] CD20 is a membrane spanning protein found on B-cell lymphocytes that is a tumor marker as it is in higher concentration in cancer patients - specifically leukemias or lymphomas (like non-hodgkin's lymphoma). [ 34 ]
I-131 is produced by nuclear fission or through neutron irradiation of Te-130 to convert it to Te-131 which decays to I-131 (produced in the University of Missouri Research Reactor). [ 35 ] I-131 is stored in lead-shielding vials.
24 hours before and 14 days after administration, thyroid protective drugs and KI tablets are administered. I-131 and Tositumomab are administered separately over the course of 14 days intravenously by dosimetric and therapeutic doses. [ 36 ] Side-effects include anemia, fever, rigors or chills, sweating, hypotension, dyspnea, bronchospasm, and nausea. There is a risk of radiation exposure to other individuals (women/children/fetus), anaphylaxis, neutropenia (low neutrophils), and thrombocytopenia (low platelet).
Zevalin , another radioligand therapy that targets non-Hodgkin lymphoma CD20 ligand but using Yttrium-90 as the radioisotope, was FDA approved in 2002.
Each radioligand therapy requires significant patient testing and eligibility requirements before administration. Radioligand therapies for cancer treatment are not the first course of action and generally require the patient to have undergone other previous treatments and many diagnostic imagings (i.e. seeing if specific receptors/antigens exist) to determine the benefit vs. adverse effect of undergoing the radioligand therapy.
For example, the PSMA radioligand therapy (Pluvicto) requires the patient to have end-stage prostate cancer that has metastasized in other organs, the PSMA ligand (confirmed through diagnostic imaging), and gone through hormonal therapies and chemotherapies. [ 37 ] For patient eligibility to get Lutathera radioligand therapy the patient must have disease progression despite receiving somatostatin analog therapy (octreotide or lanreotide), have a locally advanced, inoperable, or metastatic well-differentiated disease, and have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2.
Since the patient group receiving radioligand therapy is narrow, many health care providers are not equipped or eligible to administer radioligand therapy. [ 38 ] PET imaging machines, a lead shielded area, and trained professionals must be available.
With radioligand therapy, there is always the risk of damage to non-cancerous surrounding tissues along with radioisotope toxicity which is always a challenge in determining how to administer and create the radioligand. Furthermore, the radioligand vial is only viable for a limited time and under specific conditions which challenges transport and storage along with feasible application to the patient.
Another limitation is the lack of centers that have trained personnel and equipment for radioligand therapy. Furthermore, individual characteristics affect the exact radiosensitivity to the therapy (thus affecting dosimetry) and are hard to predict without radiobiological models 52 .
In the future, radioligand therapy may expand to include more α-emitter based treatments. Currently, β radioligand therapies are more commonly used in oncology. Clinical trials of α-emitters are underway due to their higher potency and ability to induce double-strand DNA breaks. There are multiple Actinium-225 based PSMA studies that will be launched in 2024. If these prove successful, there is potential for further studies and clinical trials to be done using α-emitters. [ 39 ] Additionally, there is potential for the future use of radioligand therapy in patients with malignant brain tumors. [ 40 ] Finally, there have been recent developments in diagnostic tracers using radioligands, as well as with radioligand-based imaging techniques and in the field of theranostics. [ 41 ] | https://en.wikipedia.org/wiki/Radioligand |
The Radiological Response and Emergency Management System (RREMS) is a system managed by the Department for Energy Security and Net Zero and used by the Government of the United Kingdom [ 1 ] which records and analyses the level of radioactivity across the United Kingdom. A reading is taken from each of the over 200 stations every hour [ 2 ] [ 3 ] and an alert triggered if radiation levels for specific isotopes rise significantly above normal background radiation levels at one or more stations. RREMS replaced the older Radioactive Incident Monitoring Network (RIMNET) system in September 2022. [ 4 ]
Stations are distributed across the UK, but are more concentrated at coastal areas. Many monitoring sites are also located at or nearby airports, including Gatwick , Heathrow , Stansted and Lydd . [ 5 ]
As well as being of use in an emergency, the stations also serve to record historical data on radiation levels.
The precursor to RREMS was the Radioactive Incident Monitoring Network (RIMNET), established in 1988 as a response to the Chernobyl disaster in 1986. [ 4 ] RIMNET was managed by the Met Office and Department for Environment, Food and Rural Affairs .
RIMNET data was collected at a central computer based in a DEFRA building in central London alongside a backup computer at a secret location in the UK.
The modern RREMS system is operated by CGI following a successful contract bid in 2018. The system is run within cloud computing servers. [ 6 ]
The network of monitoring stations includes 93 fixed and an unknown number of mobile stations located strategically across the country. These are operated by Ultra Electronics . [ 7 ]
This radioactivity –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Radiological_Response_and_Emergency_Management_System |
A radiological information system ( RIS ) [ 1 ] is the core system for the electronic management of medical imaging departments. The major functions of the RIS can include patient scheduling, resource management , examination performance tracking, reporting, results distribution, and procedure billing. [ 2 ] RIS complements HIS (hospital information systems) and PACS (picture archiving and communication system) , and is critical to efficient workflow to radiology practices. [ 3 ]
Radiological information systems commonly support the following features: [ 1 ]
In addition, a RIS often supports the following: [ 2 ] | https://en.wikipedia.org/wiki/Radiological_information_system |
Radiological warfare is any form of warfare involving deliberate radiation poisoning or contamination of an area with radioisotopes .
Nuclear warfare , both via fission and fusion weapons , creates radioisotopes in the form of fission products and neutron-activated surface material. This fallout is incorporated into military planning. Neutron bombs are designed to maximize the lethal radiation area and minimize the blast. These uses are generally not considered direct radiological warfare, but salted bombs , which produce maximize radioisotope production in a nuclear blast, are.
Radiological weapons are normally classified as weapons of mass destruction (WMDs), [ 1 ] with delivery methods explored including aerial dispersal and missile warheads. They can also be targeted at individuals, such as the assassination of Alexander Litvinenko by the Russian FSB , using radioactive polonium-210 . [ 2 ]
Numerous countries have expressed an interest in radiological weapons programs, several have actively pursued them. Radiological weapons have been tested in the United States , Soviet Union , Ba'athist Iraq , [ 3 ] Israel , [ 4 ] and China . [ 5 ]
The United States and Soviet Union during the 1980s jointly attempted to promulgate a comprehensive prohibition treaty on radiological weapons via the Committee on Disarmament , but negotiations stalled over the prohibition of attacks on nuclear facilities, in the wake of the 1981 Israeli bombing of an Iraqi nuclear reactor .
The first high-activity radioactive material suitable for radiological warfare was produced in the reactor spent fuel of the Hanford Site , during the Manhattan Project . Over two months prior to the Trinity test , a calibration test was carried out using an assembly similar to a dirty bomb . On May 7, 1945, 108 tons of explosives dispersed a single slug irradiated at the Hanford Site to over 1,400 curies.
Prior to the Normandy landings , members of the Manhattan Project anticipated a risk that the German nuclear program had operational reactors and would use plutonium isotopes or fission products from the spent fuel as a radiological weapon. The Supreme Headquarters Allied Expeditionary Force authorized Operation Peppermint , to develop and distribute Geiger counters , film packets, and other radiation survey meters to detect radiological warfare.
The United States pursued research into an offensive radiological weapons program in the post-war period. Supporters included Ernest Lawrence and Edward Teller . Zirconium and niobium radioisotope fission products were originally considered, but tantalum-182 was concluded to be most effective. Inherently, a radiological weapons stockpile requires constant operation of production reactors , to replenish the rapidly decaying weapon material. This came into conflict with the infrastructure requirements of the emerging nuclear industrial complex, which was demanding all US production reactor capacity for plutonium, but especially the short half-life polonium-210, at the time crucial for neutron initiators . [ 3 ]
A salted bomb is a nuclear weapon that is equipped with a large quantity of radiologically inert salting material. The radiological warfare agents are produced through neutron capture by the salting materials of the neutron radiation emitted by the nuclear weapon. This avoids the problems of having to stockpile the highly radioactive material, as it is produced when the bomb explodes. [ 6 ] The result is a more intense fallout than from regular nuclear weapons and can render an area uninhabitable for a long period.
The cobalt bomb is an example of a radiological warfare weapon, where cobalt-59 is converted to cobalt-60 by neutron capture. Initially, gamma radiation of the nuclear fission products from an equivalent sized "clean" fission-fusion-fission bomb (assuming the amount of radioactive dust particles generated are equal) are much more intense than cobalt-60: 15,000 times more intense at 1 hour; 35 times more intense at 1 week; 5 times more intense at 1 month; and about equal at 6 months. Thereafter fission drops off rapidly so that cobalt-60 fallout is 8 times more intense than fission at 1 year and 150 times more intense at 5 years. The very long-lived isotopes produced by fission would overtake the cobalt-60 again after about 75 years. [ 7 ]
Other salted bomb variants that do not use cobalt have also been theorized. [ 8 ] [ 9 ] For example, salting with sodium -23, that transmutes to sodium-24 , which because of its 15-hour half-life results in intense radiation. [ 10 ] [ 11 ]
An air burst is preferred if the effects of thermal radiation and blast wave is to be maximized for an area (i.e. area covered by direct line of sight and sufficient luminosity to cause burning, and formation of mach stem respectively). Both fission and fusion weapons will irradiate the detonation site with neutron radiation, causing neutron activation of the material there. Fission and fusion weapons (which derive most of their energy from fission reactions) release fission product fallout. Air will not form isotopes useful for radiological warfare when neutron-activated. By detonating them at or near the surface instead, the ground will be vaporized, become radioactive, and when it cools down and condenses into particles cause significant fallout . [ 12 ]
A far lower-tech radiological weapon than those discussed above is a " dirty bomb " or radiological dispersal device , whose purpose is to disperse radioactive dust over an area. The release of radioactive material may involve no special "weapon" or side forces like a blast explosion and include no direct killing of people from its radiation source, but rather could make whole areas or structures unusable or unfavorable for the support of human life. The radioactive material may be dispersed slowly over a large area, and it can be difficult for the victims to initially know that such a radiological attack is being carried out, especially if detectors for radioactivity are not installed beforehand. [ 13 ]
Radiological warfare with dirty bombs could be used for nuclear terrorism , spreading or intensifying fear. In relation to these weapons, nation states can also spread rumor, disinformation and fear. [ 14 ] [ 15 ] [ 16 ]
In 1981, the Israeli Air Force bombed the unfinished Osiraq Nuclear Reactor in Iraq.
In 2007, the Israeli Air Force bombed an unfinished Syrian nuclear reactor at the Al Kibar site .
In July 2023, during Russia’s invasion of Ukraine, Russia was accused of preparing to bomb the Zaporizhzhia nuclear power plant in Ukraine, in order to use the nuclear reactors as dirty bombs. [ 17 ] [ 18 ] | https://en.wikipedia.org/wiki/Radiological_warfare |
Radioluminescence is the phenomenon by which light is produced in a material by bombardment with ionizing radiation such as alpha particles , beta particles , or gamma rays . Radioluminescence is used as a low level light source for night illumination of instruments or signage. Radioluminescent paint is occasionally used for clock hands and instrument dials, enabling them to be read in the dark. Radioluminescence is also sometimes seen around high-power radiation sources, such as nuclear reactors and radioisotopes .
Radioluminescence occurs when an incoming particle of ionizing radiation collides with an atom or molecule, exciting an orbital electron to a higher energy level. The particle usually comes from the radioactive decay of an atom of a radioisotope , an isotope of an element which is radioactive. The electron then returns to its ground energy level by emitting the extra energy as a photon of light. A chemical that releases light of a particular color when struck by ionizing radiation is called a phosphor . Radioluminescent light sources usually consist of a radioactive substance mixed with, or in proximity to, a phosphor.
Since radioactivity was discovered around the beginning of the 20th century, the main application of radioluminescence has been in radioluminescent paint , used on watch and compass dials, gunsights , aircraft flight instrument faces, and other instruments, allowing them to be seen in darkness. Radioluminescent paint consists of a mixture of a chemical containing a radioisotope with a radioluminescent chemical ( phosphor ). The continuous radioactive decay of the isotope's atoms releases radiation particles which strike the molecules of the phosphor, causing them to emit light. The constant bombardment by radioactive particles causes the chemical breakdown of many types of phosphor, so radioluminescent paints lose some of their luminosity during their working life.
Radioluminescent materials may also be used in the construction of an optoelectric nuclear battery , a type of radioisotope generator in which nuclear energy is converted into light. The radioluminescence of nitrogen in air can be used to detect alpha radiation in nuclear contamination sites. [ 1 ]
The first use of radioluminescence was in luminous paint containing radium , a natural radioisotope . Beginning in 1908, luminous paint containing a mixture of radium and copper - doped zinc sulfide was used to paint watch faces and instrument dials, giving a greenish glow. Phosphors containing copper -doped zinc sulfide (ZnS:Cu) yield blue-green light; copper and manganese -doped zinc sulfide ( ZnS:Cu,Mn ), yielding yellow-orange light are also used. Radium-based luminescent paint is no longer used due to the radiation hazard posed to persons manufacturing the dials. These phosphors are not suitable for use in layers thicker than 25 mg/cm 2 , as the self-absorption of the light then becomes a problem. Zinc sulfide undergoes degradation of its crystal lattice structure, leading to gradual loss of brightness significantly faster than the depletion of radium.
ZnS:Ag coated spinthariscope screens were used by Ernest Rutherford in his experiments discovering the atomic nucleus .
Radium was used in luminous paint until the 1960s, when it was replaced with the other radioisotopes mentioned above due to health concerns. [ 2 ] In addition to alpha and beta particles , radium emits penetrating gamma rays , which can pass through the metal and glass of a watch dial, and skin. A typical older radium wristwatch dial has a radioactivity of 3–10 kBq and could expose its wearer to an annual dose of 24 millisieverts if worn continuously. [ 2 ] Another health hazard is its decay product, the radioactive gas radon , which constitutes a significant risk even at extremely low concentrations when inhaled. Radium's long half-life of 1600 years means that surfaces coated with radium paint, such as watch faces and hands, remain a health hazard long after their useful life is over. There are still millions of luminous radium clock, watch, and compass faces and aircraft instrument dials owned by the public. The case of the " Radium Girls ", workers in watch factories in the early 1920s who painted watch faces with radium paint and later contracted fatal cancer through ingesting radium when they pointed their brushes with their lips, increased public awareness of the hazards of radioluminescent materials, and radioactivity in general.
In the second half of the 20th century, radium was progressively replaced with paint containing promethium -147. Promethium is a low-energy beta-emitter , which, unlike alpha emitters like radium, does not degrade the phosphor lattice, so the luminosity of the material will not degrade so quickly. It also does not emit the penetrating gamma rays which radium does. The half-life of 147 Pm is only 2.62 years, so in a decade the radioactivity of a promethium dial will decline to only 1/16 of its original value, making it safer to dispose of, compared to radium with its half life of 1600 years. This short half-life meant that the luminosity of promethium dials also dropped by half every 2.62 years, giving them a short useful life, which led to promethium's replacement by tritium.
Promethium-based paint was used to illuminate Apollo Lunar Module electrical switch tips and painted on control panels of the Lunar Roving Vehicle . [ 3 ]
The latest generation of radioluminescent materials is based on tritium , a radioactive isotope of hydrogen with half-life of 12.32 years that emits very low-energy beta radiation. It is used on wristwatch faces, gun sights , and emergency exit signs . The tritium gas is contained in a small glass tube, coated with a phosphor on the inside. Beta particles emitted by the tritium strike the phosphor coating and cause it to fluoresce , emitting light, usually yellow-green.
Tritium is used because it is believed to pose a negligible threat to human health, in contrast to the previous radioluminescent source, radium, which proved to be a significant radiological hazard. The low-energy 5.7 keV beta particles emitted by tritium cannot pass through the enclosing glass tube. Even if they could, they are not able to penetrate human skin. Tritium is only a health threat if ingested or inhaled. Since tritium is a gas, if a tritium tube breaks, the gas dissipates in the air and is diluted to safe concentrations.
Tritium has a half-life of 12.32 years, so the brightness of a tritium light source will decline to half its initial value in that time.
Infrared radiofluorescence (sometimes spelt radio-fluorescence) is a dating technique involving the infrared (~ 880 nm) luminescence signal of orthoclase from exposure to ionizing radiation . [ 4 ] It can reveal the last time of daylight exposure of sediments, e.g., a layer of sand exposed to light before deposition. [ 5 ] [ 6 ] | https://en.wikipedia.org/wiki/Radioluminescence |
Radiolysis is the dissociation of molecules by ionizing radiation . It is the cleavage of one or several chemical bonds resulting from exposure to high- energy flux . The radiation in this context is associated with ionizing radiation ; radiolysis is therefore distinguished from, for example, photolysis of the Cl 2 molecule into two Cl- radicals , where ( ultraviolet or visible spectrum ) light is used.
The chemistry of concentrated solutions under ionizing radiation is extremely complex. Radiolysis can locally modify redox conditions, and therefore the speciation and the solubility of the compounds.
Of all the radiation-based chemical reactions that have been studied, the most important is the decomposition of water. [ 1 ] When exposed to radiation, water undergoes a breakdown sequence into hydrogen peroxide , hydrogen radicals , and assorted oxygen compounds, such as ozone , which when converted back into oxygen releases great amounts of energy. Some of these are explosive. This decomposition is produced mainly by alpha particles , which can be entirely absorbed by very thin layers of water.
Summarizing, the radiolysis of water can be written as: [ 2 ]
It is believed that the enhanced concentration of hydroxyl present in irradiated water in the inner coolant loops of a light-water reactor must be taken into account when designing nuclear power plants, to prevent coolant loss resulting from corrosion .
The current interest in nontraditional methods for the generation of hydrogen has prompted a revisit of radiolytic splitting of water, where the interaction of various types of ionizing radiation (α, β, and γ) with water produces molecular hydrogen. This reevaluation was further prompted by the current availability of large amounts of radiation sources contained in the fuel discharged from nuclear reactors . This spent fuel is usually stored in water pools, awaiting permanent disposal or reprocessing . The yield of hydrogen resulting from the irradiation of water with β and γ radiation is low (G-values = <1 molecule per 100 electronvolts of absorbed energy) but this is largely due to the rapid reassociation of the species arising during the initial radiolysis. If impurities are present or if physical conditions are created that prevent the establishment of a chemical equilibrium, the net production of hydrogen can be greatly enhanced. [ 3 ]
Another approach uses radioactive waste as an energy source for regeneration of spent fuel by converting sodium borate into sodium borohydride . By applying the proper combination of controls, stable borohydride compounds may be produced and used as hydrogen fuel storage medium.
A study conducted in 1976 found an order-of-magnitude estimate can be made of the average hydrogen production rate that could be obtained by utilizing the energy liberated via radioactive decay. Based on the primary molecular hydrogen yield of 0.45 molecules/100 eV, it would be possible to obtain 10 tons per day. Hydrogen production rates in this range are not insignificant, but are small compared with the average daily usage (1972) of hydrogen in the U.S. of about 2 x 10^4 tons. Addition of a hydrogen-atom donor could increase this about a factor of six. It was shown that the addition of a hydrogen-atom donor such as formic acid enhances the G value for hydrogen to about 2.4 molecules per 100 eV absorbed. The same study concluded that designing such a facility would likely be too unsafe to be feasible. [ 4 ]
Gas generation by radiolytic decomposition of hydrogen-containing materials has been an area of concern for the transport and storage of radioactive materials and waste for a number of years. Potentially combustible and corrosive gases can be generated while at the same time, chemical reactions can remove hydrogen, and these reactions can be enhanced by the presence of radiation. The balance between these competing reactions is not well known at this time.
When radiation enters the body, it will interact with the atoms and molecules of the cells (mainly made of water) to produce free radicals and molecules that are able to diffuse far enough to reach the critical target in the cell, the DNA , and damage it indirectly through some chemical reaction. This is the main damage mechanism for photons as they are used for example in external beam radiation therapy .
Typically, the radiolytic events that lead to the damage of the (tumor)-cell DNA are subdivided into different stages that take place on different time scales: [ 5 ]
A suggestion has been made [ 6 ] that in the early stages of the Earth's development when its radioactivity was almost two orders of magnitude higher than at present, radiolysis could have been the principal source of atmospheric oxygen, which ensured the conditions for the origin and development of life . Molecular hydrogen and oxidants produced by the radiolysis of water may also provide a continuous source of energy to subsurface microbial communities (Pedersen, 1999). Such speculation is supported by a discovery in the Mponeng Gold Mine in South Africa , where the researchers found a community dominated by a new phylotype of Desulfotomaculum , feeding on primarily radiolytically produced H 2 . [ 7 ] [ 8 ]
Pulse radiolysis is a recent method of initiating fast reactions to study reactions occurring on a timescale faster than approximately one hundred microseconds , when simple mixing of reagents is too slow and other methods of initiating reactions have to be used.
The technique involves exposing a sample of material to a beam of highly accelerated electrons , where the beam is generated by a linac . It has many applications. It was developed in the late 1950s and early 1960s by John Keene in Manchester and Jack W. Boag in London.
Flash photolysis is an alternative to pulse radiolysis that uses high-power light pulses (e.g. from an excimer laser ) rather than beams of electrons to initiate chemical reactions. Typically ultraviolet light is used which requires less radiation shielding than required for the X-rays emitted in pulse radiolysis. | https://en.wikipedia.org/wiki/Radiolysis |
Radiometry is a set of techniques for measuring electromagnetic radiation , including visible light . Radiometric techniques in optics characterize the distribution of the radiation's power in space, as opposed to photometric techniques, which characterize the light's interaction with the human eye. The fundamental difference between radiometry and photometry is that radiometry gives the entire optical radiation spectrum, while photometry is limited to the visible spectrum. Radiometry is distinct from quantum techniques such as photon counting.
The use of radiometers to determine the temperature of objects and gasses by measuring radiation flux is called pyrometry . Handheld pyrometer devices are often marketed as infrared thermometers .
Radiometry is important in astronomy , especially radio astronomy , and plays a significant role in Earth remote sensing . The measurement techniques categorized as radiometry in optics are called photometry in some astronomical applications, contrary to the optics usage of the term.
Spectroradiometry is the measurement of absolute radiometric quantities in narrow bands of wavelength. [ 1 ]
Integral quantities (like radiant flux ) describe the total effect of radiation of all wavelengths or frequencies , while spectral quantities (like spectral power ) describe the effect of radiation of a single wavelength λ or frequency ν . To each integral quantity there are corresponding spectral quantities , defined as the quotient of the integrated quantity by the range of frequency or wavelength considered. [ 2 ] For example, the radiant flux Φ e corresponds to the spectral power Φ e, λ and Φ e, ν .
Getting an integral quantity's spectral counterpart requires a limit transition . This comes from the idea that the precisely requested wavelength photon existence probability is zero. Let us show the relation between them using the radiant flux as an example:
Integral flux, whose unit is W : Φ e . {\displaystyle \Phi _{\mathrm {e} }.} Spectral flux by wavelength, whose unit is W/ m : Φ e , λ = d Φ e d λ , {\displaystyle \Phi _{\mathrm {e} ,\lambda }={d\Phi _{\mathrm {e} } \over d\lambda },} where d Φ e {\displaystyle d\Phi _{\mathrm {e} }} is the radiant flux of the radiation in a small wavelength interval [ λ − d λ 2 , λ + d λ 2 ] {\displaystyle [\lambda -{d\lambda \over 2},\lambda +{d\lambda \over 2}]} .
The area under a plot with wavelength horizontal axis equals to the total radiant flux.
Spectral flux by frequency, whose unit is W/ Hz : Φ e , ν = d Φ e d ν , {\displaystyle \Phi _{\mathrm {e} ,\nu }={d\Phi _{\mathrm {e} } \over d\nu },} where d Φ e {\displaystyle d\Phi _{\mathrm {e} }} is the radiant flux of the radiation in a small frequency interval [ ν − d ν 2 , ν + d ν 2 ] {\displaystyle [\nu -{d\nu \over 2},\nu +{d\nu \over 2}]} .
The area under a plot with frequency horizontal axis equals to the total radiant flux.
The spectral quantities by wavelength λ and frequency ν are related to each other, since the product of the two variables is the speed of light ( λ ⋅ ν = c {\displaystyle \lambda \cdot \nu =c} ):
The integral quantity can be obtained by the spectral quantity's integration:
Φ e = ∫ 0 ∞ Φ e , λ d λ = ∫ 0 ∞ Φ e , ν d ν = ∫ 0 ∞ λ Φ e , λ d ln λ = ∫ 0 ∞ ν Φ e , ν d ln ν . {\displaystyle \Phi _{\mathrm {e} }=\int _{0}^{\infty }\Phi _{\mathrm {e} ,\lambda }\,d\lambda =\int _{0}^{\infty }\Phi _{\mathrm {e} ,\nu }\,d\nu =\int _{0}^{\infty }\lambda \Phi _{\mathrm {e} ,\lambda }\,d\ln \lambda =\int _{0}^{\infty }\nu \Phi _{\mathrm {e} ,\nu }\,d\ln \nu .} | https://en.wikipedia.org/wiki/Radiometry |
A radionuclide ( radioactive nuclide , radioisotope or radioactive isotope ) is a nuclide that has excess numbers of either neutrons or protons , giving it excess nuclear energy, and making it unstable. This excess energy can be used in one of three ways: emitted from the nucleus as gamma radiation ; transferred to one of its electrons to release it as a conversion electron ; or used to create and emit a new particle ( alpha particle or beta particle ) from the nucleus. During those processes, the radionuclide is said to undergo radioactive decay . [ 1 ] These emissions are considered ionizing radiation because they are energetic enough to liberate an electron from another atom. The radioactive decay can produce a stable nuclide or will sometimes produce a new unstable radionuclide which may undergo further decay. Radioactive decay is a random process at the level of single atoms: it is impossible to predict when one particular atom will decay. [ 2 ] [ 3 ] [ 4 ] [ 5 ] However, for a collection of atoms of a single nuclide the decay rate, and thus the half-life ( t 1/2 ) for that collection, can be calculated from their measured decay constants . The range of the half-lives of radioactive atoms has no known limits and spans a time range of over 55 orders of magnitude.
Radionuclides occur naturally or are artificially produced in nuclear reactors , cyclotrons , particle accelerators or radionuclide generators . There are about 730 radionuclides with half-lives longer than 60 minutes (see list of nuclides ). Thirty-two of those are primordial radionuclides that were created before the Earth was formed. At least another 60 radionuclides are detectable in nature, either as daughters of primordial radionuclides or as radionuclides produced through natural production on Earth by cosmic radiation. More than 2400 radionuclides have half-lives less than 60 minutes. Most of those are only produced artificially, and have very short half-lives. For comparison, there are 251 stable nuclides .
All chemical elements can exist as radionuclides. Even the lightest element, hydrogen , has a well-known radionuclide, tritium . Elements heavier than lead , and the elements technetium and promethium , exist only as radionuclides.
Unplanned exposure to radionuclides generally has a harmful effect on living organisms including humans, although low levels of exposure occur naturally without harm. The degree of harm will depend on the nature and extent of the radiation produced, the amount and nature of exposure (close contact, inhalation or ingestion), and the biochemical properties of the element; with increased risk of cancer the most usual consequence. However, radionuclides with suitable properties are used in nuclear medicine for both diagnosis and treatment. An imaging tracer made with radionuclides is called a radioactive tracer . A pharmaceutical drug made with radionuclides is called a radiopharmaceutical .
On Earth, naturally occurring radionuclides fall into three categories: primordial radionuclides, secondary radionuclides, and cosmogenic radionuclides.
Many of these radionuclides exist only in trace amounts in nature, including all cosmogenic nuclides. Secondary radionuclides will occur in proportion to their half-lives, so short-lived ones will be very rare. For example, polonium can be found in uranium ores at about 0.1 mg per metric ton (1 part in 10 10 ). [ 7 ] [ 8 ] Further radionuclides may occur in nature in virtually undetectable amounts as a result of rare events such as spontaneous fission or uncommon cosmic ray interactions.
Radionuclides are produced as an unavoidable result of nuclear fission and thermonuclear explosions . The process of nuclear fission creates a wide range of fission products , most of which are radionuclides. Further radionuclides can be created from irradiation of the nuclear fuel (creating a range of actinides ) and of the surrounding structures, yielding activation products . This complex mixture of radionuclides with different chemistries and radioactivity makes handling nuclear waste and dealing with nuclear fallout particularly problematic. [ citation needed ]
Synthetic radionuclides are deliberately synthesised using nuclear reactors , particle accelerators or radionuclide generators: [ 9 ]
Radionuclides are used in two major ways: either for their radiation alone ( irradiation , nuclear batteries ) or for the combination of chemical properties and their radiation (tracers, biopharmaceuticals).
The following table lists properties of selected radionuclides illustrating the range of properties and uses.
Key: Z = atomic number ; N = neutron number ; DM = decay mode; DE = decay energy; EC = electron capture
Radionuclides are present in many homes as they are used inside the most common household smoke detectors . The radionuclide used is americium-241 , which is created by bombarding plutonium with neutrons in a nuclear reactor. It decays by emitting alpha particles and gamma radiation to become neptunium-237 . Smoke detectors use a very small quantity of 241 Am (about 0.29 micrograms per smoke detector) in the form of americium dioxide . 241 Am is used as it emits alpha particles which ionize the air in the detector's ionization chamber . A small electric voltage is applied to the ionized air which gives rise to a small electric current. In the presence of smoke, some of the ions are neutralized, thereby decreasing the current, which activates the detector's alarm. [ 14 ] [ 15 ]
Radionuclides that find their way into the environment may cause harmful effects as radioactive contamination . They can also cause damage if they are excessively used during treatment or in other ways exposed to living beings, by radiation poisoning . Potential health damage from exposure to radionuclides depends on a number of factors, and "can damage the functions of healthy tissue/organs. Radiation exposure can produce effects ranging from skin redness and hair loss, to radiation burns and acute radiation syndrome . Prolonged exposure can lead to cells being damaged and in turn lead to cancer. Signs of cancerous cells might not show up until years, or even decades, after exposure." [ 16 ]
Following is a summary table for the list of 989 nuclides with half-lives greater than one hour. A total of 251 nuclides have never been observed to decay, and are classically considered stable. Of these, 90 are believed to be absolutely stable except to proton decay (which has never been observed), while the rest are " observationally stable " and theoretically can undergo radioactive decay with extremely long half-lives.
The remaining tabulated radionuclides have half-lives longer than 1 hour, and are well-characterized (see list of nuclides for a complete tabulation). They include 30 nuclides with measured half-lives longer than the estimated age of the universe (13.8 billion years [ 17 ] ), and another four nuclides with half-lives long enough (> 100 million years) that they are radioactive primordial nuclides , and may be detected on Earth, having survived from their presence in interstellar dust since before the formation of the Solar System , about 4.6 billion years ago. Another 60+ short-lived nuclides can be detected naturally as daughters of longer-lived nuclides or cosmic-ray products. The remaining known nuclides are known solely from artificial nuclear transmutation .
Numbers are not exact, and may change slightly in the future, as "stable nuclides" are observed to be radioactive with very long half-lives.
This is a summary table [ 18 ] for the 989 nuclides with half-lives longer than one hour (including those that are stable), given in list of nuclides .
This list covers common isotopes, most of which are available in very small quantities to the general public in most countries. Others that are not publicly accessible are traded commercially in industrial, medical, and scientific fields and are subject to government regulation. | https://en.wikipedia.org/wiki/Radionuclide |
Radiopharmaceuticals , or medicinal radiocompounds , are a group of pharmaceutical drugs containing radioactive isotopes . Radiopharmaceuticals can be used as diagnostic and therapeutic agents. Radiopharmaceuticals emit radiation themselves, which is different from contrast media which absorb or alter external electromagnetism or ultrasound. Radiopharmacology is the branch of pharmacology that specializes in these agents.
The main group of these compounds are the radiotracers used to diagnose dysfunction in body tissues . While not all medical isotopes are radioactive, radiopharmaceuticals are the oldest and remain the most common of such drugs.
As with other pharmaceutical drugs, there is standardization of the drug nomenclature for radiopharmaceuticals, although various standards coexist. The International Nonproprietary Names (INNs), United States Pharmacopeia (USP) names, and IUPAC names for these agents are usually similar other than trivial style differences. [ 1 ] The details are explained at Radiopharmacology § Drug nomenclature for radiopharmaceuticals .
A list of nuclear medicine radiopharmaceuticals follows. Some radioisotopes are used in ionic or inert form without attachment to a pharmaceutical; these are also included. There is a section for each radioisotope with a table of radiopharmaceuticals using that radioisotope. The sections are ordered alphabetically by the English name of the radioisotope. Sections for the same element are then ordered by atomic mass number .
47 Ca is a beta and gamma emitter.
11 C is a positron emitter.
Parathyroid imaging
14 C is a beta emitter.
51 Cr is a gamma emitter.
57 Co is a gamma emitter.
58 Co is a gamma emitter.
169 Er is a beta emitter.
18 F is a positron emitter with a half-life of 109 minutes. It is produced in medical cyclotrons, usually from oxygen-18, and then chemically attached to a pharmaceutical formulation.
Myocardial imaging
67 Ga is a gamma emitter.
68 Ga is a positron emitter, with a 68-minute half-life , produced by elution from germanium-68 in a gallium-68 generator or by proton irradiation of zinc-68.
3 H or tritium is a beta emitter.
111 In is a gamma emitter.
Iodine-123 (I-123) is a gamma emitter. It is used only diagnostically, as its radiation is penetrating and short-lived.
Thyroid metastases imaging
125 I is a gamma emitter with a long half-life of 59.4 days (the longest of all radioiodines used in medicine). Iodine-123 is preferred for imaging, so I-125 is used diagnostically only when the test requires a longer period to prepare the radiopharmaceutical and trace it, such as a fibrinogen scan to diagnose clotting. I-125's gamma radiation is of medium penetration, making it more useful as a therapeutic isotope for brachytherapy implant of radioisotope capsules for local treatment of cancers.
131 I is a beta and gamma emitter. It is used both to destroy thyroid and thyroid cancer tissues (via beta radiation, which is short-range), and also other neuroendocrine tissues when used in MIBG. It can also be seen by a gamma camera , and can serve as a diagnostic imaging tracer, when treatment is also being attempted at the same time. However iodine-123 is usually preferred when only imaging is desired.
59 Fe is a beta and gamma emitter.
81 Kr m is a gamma emitter.
177 Lu is a beta emitter.
13 N is a positron emitter.
15 O is a positron emitter.
Myocardial blood flow imaging
32 P is a beta emitter.
223 Ra is an alpha emitter.
82 Rb is a positron and gamma emitter.
153 Sm is a beta and gamma emitter.
75 Se is a gamma emitter.
22 Na is a positron and gamma emitter.
24 Na is a beta and gamma emitter.
89 Sr is a beta emitter.
Technetium-99m is a gamma emitter. It is obtained on-site at the imaging center as the soluble pertechnetate which is eluted from a technetium-99m generator , and then either used directly as this soluble salt, or else used to synthesize a number of technetium-99m-based radiopharmaceuticals.
Stomach and salivary gland imaging Meckel's diverticulum imaging Brain imaging Micturating cystogram First pass blood flow imaging First pass peripheral vascular imaging
GI Bleeding
Gastric emptying imaging
Spleen imaging
Cardiac blood pool imaging Peripheral vascular imaging
First pass blood flow imaging
Non-specific tumor imaging Thyroid tumor imaging Breast imaging Myocardial imaging
Myocardial imaging
201 Tl is a gamma emitter.
Thyroid tumor imaging Myocardial imaging Parathyroid imaging
133 Xe is a gamma emitter.
90 Y is a beta emitter. | https://en.wikipedia.org/wiki/Radiopharmaceutical |
Radiopharmacology is radiochemistry applied to medicine and thus the pharmacology of radiopharmaceuticals ( medicinal radiocompounds , that is, pharmaceutical drugs that are radioactive ). Radiopharmaceuticals are used in the field of nuclear medicine as radioactive tracers in medical imaging and in therapy for many diseases (for example, brachytherapy ). Many radiopharmaceuticals use technetium-99m (Tc-99m) which has many useful properties as a gamma-emitting tracer nuclide . In the book Technetium a total of 31 different radiopharmaceuticals based on Tc-99m are listed for imaging and functional studies of the brain , myocardium , thyroid , lungs , liver , gallbladder , kidneys , skeleton , blood and tumors . [ 1 ]
The term radioisotope , which in its general sense refers to any radioactive isotope ( radionuclide ), has historically been used to refer to all radiopharmaceuticals, and this usage remains common. Technically, however, many radiopharmaceuticals incorporate a radioactive tracer atom into a larger pharmaceutically-active molecule, which is localized in the body, after which the radionuclide tracer atom allows it to be easily detected with a gamma camera or similar gamma imaging device. An example is fludeoxyglucose in which fluorine-18 is incorporated into deoxyglucose . Some radioisotopes (for example gallium-67 , gallium-68 , and radioiodine ) are used directly as soluble ionic salts, without further modification. This use relies on the chemical and biological properties of the radioisotope itself, to localize it within the body.
See nuclear medicine .
Production of a radiopharmaceutical involves two processes:
Radionuclides used in radiopharmaceuticals are mostly radioactive isotopes of elements with atomic numbers less than that of bismuth , that is, they are radioactive isotopes of elements that also have one or more stable isotopes. These may be roughly divided into two classes:
Because radiopharmeuticals require special licenses and handling techniques, they are often kept in local centers for medical radioisotope storage, often known as radiopharmacies . A radiopharmacist may dispense them from there, to local centers where they are handled at the practical medicine facility.
As with other pharmaceutical drugs, there is standardization of the drug nomenclature for radiopharmaceuticals, although various standards coexist. The International Nonproprietary Name (INN) gives the base drug name, followed by the radioisotope (as mass number, no space, element symbol) in parentheses with no superscript, followed by the ligand (if any). It is common to see square brackets and superscript superimposed onto the INN name, because chemical nomenclature (such as IUPAC nomenclature) uses those. The United States Pharmacopeia (USP) name gives the base drug name, followed by the radioisotope (as element symbol, space, mass number) with no parentheses, no hyphen, and no superscript, followed by the ligand (if any). The USP style is not the INN style, despite their being described as one and the same in some publications (e.g., AMA , [ 4 ] whose style for radiopharmaceuticals matches the USP style). The United States Pharmacopeial Convention is a sponsor organization of the USAN Council , and the USAN for a given drug is often the same as the USP name. | https://en.wikipedia.org/wiki/Radiopharmacology |
Radioresistance is the level of ionizing radiation that organisms are able to withstand.
Ionizing-radiation-resistant organisms (IRRO) were defined as organisms for which the dose of acute ionizing radiation (IR) required to achieve 90% reduction (D10) is greater than 1,000 gray (Gy) [ 1 ]
Radioresistance is surprisingly high in many organisms, in contrast to previously held views. For example, the study of environment, animals and plants around the Chernobyl disaster area has revealed an unexpected survival of many species, despite the high radiation levels. A Brazilian study in a hill in the state of Minas Gerais which has high natural radiation levels from uranium deposits, has also shown many radioresistant insects , worms and plants. [ 2 ] [ 3 ] Certain extremophiles , such as the bacteria Deinococcus radiodurans and the tardigrades , can withstand large doses of ionizing radiation on the order of 5,000 Gy . [ 4 ] [ 5 ] [ 6 ]
In the graph on left, a dose/survival curve for a hypothetical group of cells has been drawn with and without a rest time for the cells to recover. Other than the recovery time partway through the irradiation, the cells would have been treated identically.
Radioresistance may be induced by exposure to small doses of ionizing radiation. Several studies have documented this effect in yeast , bacteria , protozoa , algae , plants, insects, as well as in in vitro mammalian and human cells and in animal models . Several cellular radioprotection mechanisms may be involved, such as alterations in the levels of some cytoplasmic and nuclear proteins and increased gene expression , DNA repair and other processes. Also biophysical models presented general basics for this phenomenon. [ 7 ]
Many organisms have been found to possess a self-repair mechanism that can be activated by exposure to radiation in some cases. Two examples of this self-repair process in humans are described below.
Devair Alves Ferreira received a large dose (7.0 Gy ) during the Goiânia accident , and lived, whereas his wife, who got a dose of 5.7 Gy, died. The most likely explanation [ citation needed ] is that his dose was fractionated into many smaller doses which were absorbed over a length of time while his wife stayed in the house more and was subjected to continuous irradiation without a break so giving the self repair mechanisms in her body less time to repair some of the damage done by the radiation. This resulted in her death. He also eventually died in 1994. In the same way some of the persons who worked in the basement of the wrecked Chernobyl have built up doses of 10 Gy, these workers received these doses in small fractions so the acute effects were avoided.
It has been found in radiation biology experiments that if a group of cells are irradiated then as the dose increases the number of cells which survive decrease. It has also been found that if a population of cells are given a dose before being set aside (without being irradiated) for a length of time before being irradiated again then the radiation has less of an ability to cause cell death . The human body contains many types of cells and a human can be killed by the loss of a single tissue in a vital organ [ citation needed ] . For many short term radiation deaths (3 days to 30 days) the loss of cells forming blood cells ( bone marrow ) and the cells in the digestive system (wall of the intestines ) cause death.
There is strong evidence that radioresistance can be genetically determined and inherited, at least in some organisms. Heinrich Nöthel, a geneticist from the Freie Universität Berlin carried out the most extensive study about radioresistance mutations using the common fruit fly , Drosophila melanogaster , in a series of 14 publications.
From the perspective of evolutionary history and causation, radioresistance does not appear to be an adaptive trait because there is no documented naturally occurring selection pressure that could have bestowed a fitness advantage to the ability for organisms to withstand doses of ionizing radiation in the range that several extremophile species have been observed to be capable of surviving. [ 8 ] This is primarily because the Earth's magnetic field shields all its inhabitants from solar cosmic radiation and galactic cosmic rays, [ 9 ] which are the two primary sources of ionizing radiation across the Solar System , [ 10 ] and even including all documented terrestrial sources of ionizing radiation such as radon gas and primordial radionuclides at geographical locations considered to be natural high-level radiation sites, the yearly dose of natural background radiation [ 11 ] remains tens of thousands of times smaller than the levels of ionizing radiation that many highly radioresistant organisms can withstand.
One possible explanation for the existence of radioresistance is that it is an example of co-opted adaptation or exaptation, where radioresistance could be an indirect consequence of the evolution of a different, linked adaptation that has been positively selected for by evolution. For example, the desiccation-adaptation hypothesis proposes that the extreme temperatures present in the habitats of hyperthermophiles like Deinococcus radiodurans cause cellular damage that is virtually identical to damage typically caused by ionizing radiation, and that the cellular repair mechanisms that have evolved to repair this heat or desiccation damage are generalizable to radiation damage as well, allowing D. radiodurans to survive extreme doses of ionizing radiation. [ 12 ] Exposure to gamma radiation leads to cellular DNA damage including alterations in nitrogenous base-pairing, sugar-phosphate backbone damage, and double-stranded DNA lesions. [ 13 ] The extraordinarily efficient cellular repair mechanisms that Deinococcus species like D. radiodurans have evolved to repair heat-damage are likely also capable of reversing the effects of DNA damage wrought by ionizing radiation, such as by piecing back together any components of their genome that have been fragmented by the radiation. [ 14 ] [ 15 ] [ 16 ]
Bacillus sp. producing unusually radiation (and peroxide) resistant spores, have been isolated from spacecraft assembly facilities, and are thought of as candidates that could ride piggyback on spacecraft through interplanetary transfer. [ 17 ] [ 18 ] [ 19 ] [ 20 ] [ 21 ] Genome analysis of some of these radiation resistant spore producers have thrown some light on the genetic traits that could be responsible for the resistances observed. [ 22 ] [ 23 ] [ 24 ] [ 25 ]
In general, radioresistance in prokaryotes is achieved by two cellular mechanisms. [ 26 ] The first is protection of the proteome and DNA from ionizing radiation induced damage. The second is recruitment of highly sophisticated DNA repair mechanisms that enable the reconstruction of a fully functional genome . These DNA repair mechanisms include homologous recombinational repair, and extended synthesis-dependent strand annealing . [ 26 ]
Radioresistance is also a term sometimes used in medicine ( oncology ) for cancer cells which are difficult to treat with radiotherapy . Radioresistance of cancer cells may be intrinsic or induced by the radiation therapy itself.
The comparison in the table below is only meant to give approximate indications of radioresistance for different species and should be taken with great caution. There are generally big differences in radioresistance for one species among experiments, due to the way radiation affects living tissues and to different experimental conditions. We should for example consider that because radiation impedes cell division, immature organisms are less resistant to radiations than adults, and adults are sterilized at doses much lower than that necessary to kill them. For example, for the insect parasitoid Habrobracon hebetor , the LD 50 for haploid embryo during cleavage (1–3 hours of age) is 200 R , but about 4 hours later it is of 7,000 R (for X-ray intensity of 110 R/minute), and haploid (= male) embryos are more resistant than diploid (= female) embryos. [ 27 ] The mortality of adults H. hebetor exposed to a dose of 180,250 R is the same to this of a non-irradiated control group (food was not provided to either groups) (for 6,000 R/minute). [ 28 ] [ 29 ] However, a lower dose of 102,000 R (for 6,000 R/minute) is sufficient to induce a state of lethargy in H. hebetor that is manifested by a complete cessation of activity, including cessation of feeding, and these individuals eventually let themselves starve to death. [ 29 ] And an even lower dose of 4,858 R (for 2,650 R/minute) is sufficient to sterilize adult female H. hebetor (sterility arises 3 days post-exposure). [ 30 ] Other important factors that influence the level of radioresistance include: The length of time during which a dose of radiation is delivered—with doses delivered during longer periods, or at time intervals, being associated with greatly reduced negative effects; [ 30 ] [ 31 ] The feeding state of individuals—with pre-fed and post-fed individuals being more resistant to radiations compared to starved individuals; [ 30 ] [ 31 ] The type of radiation used (e.g., tardigrades Milnesium tardigradum irradiated with heavy ions have a higher survival than when irradiated with gamma rays, for a same irradiation dose); [ 32 ] The physiological state of individuals (e.g., the tardigrade species Richtersius coronifer and Milnesium tardigradum are more resistant to gamma-ray radiation when in the hydrated state, and Macrobiotus areolatus is more resistant to X-ray radiation when in the anhydrobiotic state). [ 32 ] The way lethality is measured is also source of variation for the estimated radioresistance of a species. Irradiated specimens are not instantly killed, unless exposed to a very high dose (acute dose). [ 33 ] Therefore, irradiated specimens die over a certain period of time and lower irradiation doses correspond to longer survival. This means that the radiation dose LD 50 fluctuates with the time at which it is measured. For example, the β radiation dose that causes 50% mortality in the American cockroach at 25 days post-exposure is 5,700 R, but to reach 50% mortality at 3 days post-exposure, 45,610 R are needed. [ 31 ] 25 days can represent a long survival period for short lived species, such as insects, but would represent a very short survival time for long lived species, such as mammals, so comparing survival of different species after the same amount of time post-exposure also poses some challenges of interpretation. These examples illustrate the many issues associated with comparison of radioresistance among species and the need for caution when doing so.
∗ While an LD 50 has been reported for wild type C. elegans individuals, an upper lethal limit has not been established, rather "nearly all animals were alive with no indication of excess lethality up to 800 Gy, the highest dose... measured." [ 40 ] | https://en.wikipedia.org/wiki/Radioresistance |
Radiosensitivity is the relative susceptibility of cells, tissues, organs or organisms to the harmful effect of ionizing radiation .
Cells are least sensitive when in the S phase , then the G 1 phase , then the G 2 phase , and most sensitive in the M phase of the cell cycle . This is described by the 'law of Bergonié and Tribondeau', formulated in 1906: X-rays are more effective on cells which have a greater reproductive activity. [ 1 ] [ 2 ]
From their observations, they concluded that quickly dividing tumor cells are generally more sensitive than the majority of body cells. This is not always true. Tumor cells can be hypoxic and therefore less sensitive to X-rays because most of their effects are mediated by the free radicals produced by ionizing oxygen.
It has meanwhile been shown that the most sensitive cells are those that are undifferentiated , well nourished, dividing quickly and highly active metabolically . Amongst the body cells, the most sensitive are spermatogonia and erythroblasts , epidermal stem cells , gastrointestinal stem cells. [ 3 ] The least sensitive are nerve cells and muscle fibers .
Very sensitive cells are also oocytes and lymphocytes , although they are resting cells and do not meet the criteria described above. The reasons for their sensitivity are not clear.
There also appears to be a genetic basis for the varied vulnerability of cells to ionizing radiation. [ 4 ] This has been demonstrated across several cancer types and in normal tissues. [ 5 ] [ 6 ]
The damage to the cell can be lethal (the cell dies) or sublethal (the cell can repair itself). Cell damage can ultimately lead to health effects which can be classified as either Tissue Reactions or Stochastic Effects according to the International Commission on Radiological Protection .
Tissue reactions have a threshold of irradiation under which they do not appear and above which they typically appear. Fractionation of dose, dose rate, the application of antioxidants and other factors may affect the precise threshold at which a tissue reaction occurs. Tissue reactions include skin reactions (epilation, erythema, moist desquamation), cataracts, circulatory disease, and other conditions. Seven proteins were discovered in a systematic review, which correlated with radiosensitivity in normal tissues: γH2AX, TP53BP1, VEGFA, CASP3, CDKN2A, IL6, and IL1B. [ 7 ] [ 8 ]
Stochastic effects do not have a threshold of irradiation, are coincidental, and cannot be avoided. They can be divided into somatic and genetic effects. Among the somatic effects, secondary cancer is the most important. It develops because radiation causes DNA mutations directly and indirectly. Direct effects are those caused by ionizing particles and rays themselves, while the indirect effects are those that are caused by free radicals, generated especially in water radiolysis and oxygen radiolysis. The genetic effects confer the predisposition of radiosensitivity to the offspring. [ 9 ] The process is not well understood yet.
For decades, the main cellular target for radiation induced damage was thought to be the DNA molecule. [ 10 ] This view has been challenged by data indicating that in order to increase survival, the cells must protect their proteins, which in turn repair the damage in the DNA. [ 11 ] An important part of protection of proteins (but not DNA) against the detrimental effects of reactive oxygen species (ROS), which are the main mechanism of radiation toxicity, is played by non-enzymatic complexes of manganese ions and small organic metabolites. [ 11 ] These complexes were shown to protect the proteins from oxidation in vitro [ 12 ] and also increased radiation survival in mice. [ 13 ] An application of the synthetically reconstituted protective mixture with manganese was shown to preserve the immunogenicity of viral and bacterial epitopes at radiation doses far above those necessary to kill the microorganisms, thus opening a possibility for a quick whole-organism vaccine production. [ 14 ] The intracellular manganese content and the nature of complexes it forms (both measurable by electron paramagnetic resonance ) were shown to correlate with radiosensitivity in bacteria, archaea, fungi and human cells. [ 15 ] An association was also found between total cellular manganese contents and their variation, and clinically inferred radioresponsiveness in different tumor cells, a finding that may be useful for more precise radiodosages and improved treatment of cancer patients. [ 16 ] | https://en.wikipedia.org/wiki/Radiosensitivity |
In radiometry , radiosity is the radiant flux leaving (emitted, reflected and transmitted by) a surface per unit area, and spectral radiosity is the radiosity of a surface per unit frequency or wavelength , depending on whether the spectrum is taken as a function of frequency or of wavelength. [ 1 ] The SI unit of radiosity is the watt per square metre ( W/m 2 ), while that of spectral radiosity in frequency is the watt per square metre per hertz (W·m −2 ·Hz −1 ) and that of spectral radiosity in wavelength is the watt per square metre per metre (W·m −3 )—commonly the watt per square metre per nanometre ( W·m −2 ·nm −1 ). The CGS unit erg per square centimeter per second ( erg·cm −2 ·s −1 ) is often used in astronomy . Radiosity is often called intensity [ 2 ] in branches of physics other than radiometry, but in radiometry this usage leads to confusion with radiant intensity .
Radiosity of a surface , denoted J e ("e" for "energetic", to avoid confusion with photometric quantities), is defined as [ 3 ]
where
For an opaque surface, the transmitted component of radiosity J e,tr vanishes and only two components remain:
In heat transfer , combining these two factors into one radiosity term helps in determining the net energy exchange between multiple surfaces.
Spectral radiosity in frequency of a surface , denoted J e,ν , is defined as [ 3 ]
where ν is the frequency.
Spectral radiosity in wavelength of a surface , denoted J e,λ , is defined as [ 3 ]
where λ is the wavelength.
The radiosity of an opaque , gray and diffuse surface is given by
where
Normally, E e is the unknown variable and will depend on the surrounding surfaces. So, if some surface i is being hit by radiation from some other surface j , then the radiation energy incident on surface i is E e, ji A i = F ji A j J e, j where F ji is the view factor or shape factor , from surface j to surface i . So, the irradiance of surface i is the sum of radiation energy from all other surfaces per unit surface of area A i :
Now, employing the reciprocity relation for view factors F ji A j = F ij A i ,
and substituting the irradiance into the equation for radiosity, produces
For an N surface enclosure, this summation for each surface will generate N linear equations with N unknown radiosities, [ 4 ] and N unknown temperatures. For an enclosure with only a few surfaces, this can be done by hand. But, for a room with many surfaces, linear algebra and a computer are necessary.
Once the radiosities have been calculated, the net heat transfer Q ˙ i {\displaystyle {\dot {Q}}_{i}} at a surface can be determined by finding the difference between the incoming and outgoing energy:
Using the equation for radiosity J e, i = ε i σ T i 4 + (1 − ε i ) E e, i , the irradiance can be eliminated from the above to obtain
where M e, i ° is the radiant exitance of a black body .
For an enclosure consisting of only a few surfaces, it is often easier to represent the system with an analogous circuit rather than solve the set of linear radiosity equations. To do this, the heat transfer at each surface is expressed as
where R i = (1 − ε i )/( A i ε i ) is the resistance of the surface.
Likewise, M e, i ° − J e, i is the blackbody exitance minus the radiosity and serves as the 'potential difference'. These quantities are formulated to resemble those from an electrical circuit V = IR .
Now performing a similar analysis for the heat transfer from surface i to surface j ,
where R ij = 1/( A i F ij ).
Because the above is between surfaces, R ij is the resistance of the space between the surfaces and J e, i − J e, j serves as the potential difference.
Combining the surface elements and space elements, a circuit is formed. The heat transfer is found by using the appropriate potential difference and equivalent resistances , similar to the process used in analyzing electrical circuits .
In the radiosity method and circuit analogy, several assumptions were made to simplify the model. The most significant is that the surface is a diffuse emitter. In such a case, the radiosity does not depend on the angle of incidence of reflecting radiation and this information is lost on a diffuse surface. In reality, however, the radiosity will have a specular component from the reflected radiation . So, the heat transfer between two surfaces relies on both the view factor and the angle of reflected radiation.
It was also assumed that the surface is a gray body, that is to say its emissivity is independent of radiation frequency or wavelength. However, if the range of radiation spectrum is large, this will not be the case. In such an application, the radiosity must be calculated spectrally and then integrated over the range of radiation spectrum.
Yet another assumption is that the surface is isothermal . If it is not, then the radiosity will vary as a function of position along the surface. However, this problem is solved by simply subdividing the surface into smaller elements until the desired accuracy is obtained. [ 4 ] | https://en.wikipedia.org/wiki/Radiosity_(radiometry) |
A radiosonde is a battery-powered telemetry instrument carried into the atmosphere usually by a weather balloon that measures various atmospheric parameters and transmits them by radio to a ground receiver. Modern radiosondes measure or calculate the following variables: altitude , pressure , temperature , relative humidity , wind (both wind speed and wind direction ), cosmic ray readings at high altitude and geographical position ( latitude / longitude ). Radiosondes measuring ozone concentration are known as ozonesondes. [ 1 ]
Radiosondes may operate at a radio frequency of 403 MHz or 1680 MHz. A radiosonde whose position is tracked as it ascends to give wind speed and direction information is called a rawinsonde ("radar wind -sonde"). [ 2 ] [ 3 ] Most radiosondes have radar reflectors and are technically rawinsondes. A radiosonde that is dropped from an airplane and falls, rather than being carried by a balloon is called a dropsonde . Radiosondes are an essential source of meteorological data, and hundreds are launched all over the world daily.
The first flights of aerological instruments were done in the second half of the 19th century with kites and meteographs , a recording device measuring pressure and temperature that would be recovered after the experiment. This proved difficult because the kites were linked to the ground and were very difficult to manoeuvre in gusty conditions. Furthermore, the sounding was limited to low altitudes because of the link to the ground.
Gustave Hermite and Georges Besançon , from France, were the first in 1892 to use a balloon to fly the meteograph. In 1898, Léon Teisserenc de Bort organized at the Observatoire de Météorologie Dynamique de Trappes the first regular daily use of these balloons. Data from these launches showed that the temperature lowered with height up to a certain altitude, which varied with the season, and then stabilized above this altitude. De Bort's discovery of the tropopause and stratosphere was announced in 1902 at the French Academy of Sciences. [ 4 ] Other researchers, like Richard Aßmann and William Henry Dines , were working at the same times with similar instruments.
In 1924, Colonel William Blaire in the U.S. Signal Corps did the first primitive experiments with weather measurements from balloon, making use of the temperature dependence of radio circuits. The first true radiosonde that sent precise encoded telemetry from weather sensors was invented in France by Robert Bureau [ fr ] . Bureau coined the name "radiosonde" and flew the first instrument on January 7, 1929. [ 4 ] [ 5 ] Developed independently a year later, Pavel Molchanov flew a radiosonde on January 30, 1930. Molchanov's design became a popular standard because of its simplicity and because it converted sensor readings to Morse code , making it easy to use without special equipment or training. [ 6 ]
Working with a modified Molchanov sonde, Sergey Vernov was the first to use radiosondes to perform cosmic ray readings at high altitude. On April 1, 1935, he took measurements up to 13.6 km (8.5 mi) using a pair of Geiger counters in an anti-coincidence circuit to avoid counting secondary ray showers. [ 6 ] [ 7 ] This became an important technique in the field, and Vernov flew his radiosondes on land and sea over the next few years, measuring the radiation's latitude dependence caused by the Earth's magnetic field .
In 1936, the U.S. Navy assigned the U.S. Bureau of Standards (NBS) to develop an official radiosonde for the Navy to use. [ 8 ] The NBS gave the project to Harry Diamond , who had previously worked on radio navigation and invented a blind landing system for airplanes. [ 9 ] The organization led by Diamond eventually (in 1992) became a part of the U.S. Army Research Laboratory . In 1937, Diamond, along with his associates Francis Dunmore and Wilbur Hinmann, Jr., created a radiosonde that employed audio-frequency subcarrier modulation with the help of a resistance-capacity relaxation oscillator. In addition, this NBS radiosonde was capable of measuring temperature and humidity at higher altitudes than conventional radiosondes at the time due to the use of electric sensors. [ 8 ] [ 10 ]
In 1938, Diamond developed the first ground receiver for the radiosonde, which prompted the first service use of the NBS radiosondes in the Navy. Then in 1939, Diamond and his colleagues developed a ground-based radiosonde called the “remote weather station,” which allowed them to automatically collect weather data in remote and inhospitable locations. [ 11 ] By 1940, the NBS radiosonde system included a pressure drive, which measured temperature and humidity as functions of pressure. [ 8 ] It also gathered data on cloud thickness and light intensity in the atmosphere. [ 12 ] Due to this and other improvements in cost (about $25), weight (> 1 kilogram), and accuracy, hundreds of thousands of NBS-style radiosondes were produced nationwide for research purposes, and the apparatus was officially adopted by the U.S. Weather Bureau. [ 8 ] [ 10 ]
Diamond was given the Washington Academy of Sciences Engineering Award in 1940 and the IRE Fellow Award (which was later renamed the Harry Diamond Memorial Award) in 1943 for his contributions to radio-meteorology. [ 11 ] [ 13 ]
The expansion of economically important government weather forecasting services during the 1930s and their increasing need for data motivated many nations to begin regular radiosonde observation programs
In 1985, as part of the Soviet Union 's Vega program , the two Venus probes, Vega 1 and Vega 2 , each dropped a radiosonde into the atmosphere of Venus . The sondes were tracked for two days.
Although modern remote sensing by satellites, aircraft and ground sensors is an increasing source of atmospheric data, none of these systems can match the vertical resolution (30 m (98 ft) or less) and altitude coverage (30 km (19 mi)) of radiosonde observations, so they remain essential to modern meteorology. [ 2 ]
Although hundreds of radiosondes are launched worldwide each day year-round, fatalities attributed to radiosondes are rare. The first known example was the electrocution of a lineman in the United States who was attempting to free a radiosonde from high-tension power lines in 1943. [ 14 ] [ 15 ] In 1970, an Antonov 24 operating Aeroflot Flight 1661 suffered a loss of control after striking a radiosonde in flight resulting in the death of all 45 people on board.
A rubber or latex balloon filled with either helium or hydrogen lifts the device up through the atmosphere . The maximum altitude to which the balloon ascends is determined by the diameter and thickness of the balloon. Balloon sizes can range from 100 to 3,000 g (3.5 to 105.8 oz). As the balloon ascends through the atmosphere, the pressure decreases, causing the balloon to expand. Eventually, the balloon will expand to the extent that its skin will break, terminating the ascent. An 800 g (28 oz) balloon will burst at about 21 km (13 mi). [ 16 ] After bursting, a small parachute on the radiosonde's support line may slow its descent to Earth, while some rely on the aerodynamic drag of the shredded remains of the balloon, and the very light weight of the package itself. A typical radiosonde flight lasts 60 to 90 minutes. One radiosonde from Clark Air Base , Philippines, reached an altitude of 155,092 ft (47,272 m).
The modern radiosonde communicates via radio with a computer that stores all the variables in real time. The first radiosondes were observed from the ground with a theodolite , and gave only a wind estimation by the position. With the advent of radar by the Signal Corps it was possible to track a radar target carried by the balloons with the SCR-658 radar . Modern radiosondes can use a variety of mechanisms for determining wind speed and direction, such as a radio direction finder or GPS . The weight of a radiosonde is typically 250 g (8.8 oz).
Sometimes radiosondes are deployed by being dropped from an aircraft instead of being carried aloft by a balloon. Radiosondes deployed in this way are called dropsondes .
Radiosondes weather balloons have conventionally been used as means of measuring atmospheric profiles of humidity, temperature, pressure, wind speed and direction. [ 17 ] High-quality, spatially and temporally “continuous” data from upper-air monitoring along with surface observations are critical bases for understanding weather conditions and climate trends and providing weather and climate information for the welfare of societies. Reliable and timely information underpin society’s preparedness to extreme weather conditions and to changing climate patterns. [ 17 ]
Worldwide, there are about 1,300 radiosonde launch sites. [ 18 ] Most countries share data with the rest of the world through international agreements. Nearly all routine radiosonde launches occur one hour before the official observation times of 0000 UTC and 1200 UTC to center the observation times during the roughly two-hour ascent. [ 19 ] [ 20 ] Radiosonde observations are important for weather forecasting , severe weather watches and warnings , and atmospheric research.
The United States National Weather Service launches radiosondes twice daily from 92 stations, 69 in the conterminous United States, 13 in Alaska, nine in the Pacific, and one in Puerto Rico. It also supports the operation of 10 radiosonde sites in the Caribbean . [ 20 ] A list of U.S. operated land based launch sites can be found in Appendix C, U.S. Land-based Rawinsonde Stations [ 21 ] of the Federal Meteorological Handbook #3, [ 22 ] titled Rawinsonde and Pibal Observations, dated May 1997.
The UK launches Vaisala RS41 radiosondes [ 23 ] four times daily (an hour before 00, 06, 12, and 18 UTC) from 6 launch sites (south to north): Camborne , (lat,lon)=(50.218, -5.327), SW tip of England; Herstmonceux (50.89, 0.318), near SE coast; Watnall , (53.005, -1.25), central England; Castor Bay, (54.50, -6.34), near the SE corner of Lough Neagh in Northern Ireland; Albemarle , (55.02, -1.88), NE England; and Lerwick , (60.139, -1.183), Shetland , Scotland . [ 24 ] [ 25 ]
Raw upper air data is routinely processed by supercomputers running numerical models. Forecasters often view the data in a graphical format, plotted on thermodynamic diagrams such as Skew-T log-P diagrams , Tephigrams , and or Stüve diagrams , all useful for the interpretation of the atmosphere's vertical thermodynamics profile of temperature and moisture as well as kinematics of vertical wind profile. [ 17 ]
Radiosonde data is a crucially important component of numerical weather prediction. Because a sonde may drift several hundred kilometers during the 90- to 120-minute flight, there may be concern that this could introduce problems into the model initialization. [ 17 ] However, this appears not to be so except perhaps locally in jet stream regions in the stratosphere. [ 26 ] This issue may in future be solved by weather drones , which have precise control over their location and can compensate for drift. [ 27 ]
Lamentably, in less developed parts of the globe such as Africa, which has high vulnerability to impacts of extreme weather events and climate change, there is paucity of surface- and upper-air observations. The alarming state of the issue was highlighted in 2020 by the World Meteorological Organisation [ 28 ] which stated that "the situation in Africa shows a dramatic decrease of almost 50% from 2015 to 2020 in the number of radiosonde flights, the most important type of surface-based observations. Reporting now has poorer geographical coverage". Over the last two decades, some 82% of the countries in Africa have experienced severe (57%) and moderate (25%) radiosonde data gap. [ 17 ] This dire situation has prompted call for urgent need to fill the data gap in Africa and globally. The vast data gap in such a large part the global landmass, home to some of the most vulnerable societies, the aforementioned call has galvanised a global effort [ 29 ] to “plug the data gap” in the decade ahead and halt a further deterioration in the observation networks.
According to the International Telecommunication Union , a meteorological aids service (also: meteorological aids radiocommunication service ) is – according to Article 1.50 of the ITU Radio Regulations (RR) [ 30 ] – defined as "A radiocommunication service used for meteorological, including hydrological, observations and exploration. Furthermore, according to article 1.109 of the ITU RR: [ 31 ]
A radiosonde is an automatic radio transmitter in the meteorological aids service usually carried on an aircraft , free balloon , kite or parachute, and which transmits meteorological data. Each radio transmitter shall be classified by the radiocommunication service in which it operates permanently or temporarily.
The allocation of radio frequencies is provided according to Article 5 of the ITU Radio Regulations (edition 2012). [ 32 ]
In order to improve harmonisation in spectrum utilisation, the majority of service-allocations stipulated in this document were incorporated in national Tables of Frequency Allocations and Utilisations which is with-in the responsibility of the appropriate national administration. The allocation might be primary, secondary, exclusive, and shared.
However, military usage, in bands where there is civil usage, will be in accordance with the ITU Radio Regulations. | https://en.wikipedia.org/wiki/Radiosonde |
Radiosurgery is surgery using radiation , [ 1 ] that is, the destruction of precisely selected areas of tissue using ionizing radiation rather than excision with a blade. Like other forms of radiation therapy (also called radiotherapy), it is usually used to treat cancer . Radiosurgery was originally defined by the Swedish neurosurgeon Lars Leksell as "a single high dose fraction of radiation, stereotactically directed to an intracranial region of interest". [ 2 ]
In stereotactic radiosurgery ( SRS ), the word " stereotactic " refers to a three-dimensional coordinate system that enables accurate correlation of a virtual target seen in the patient's diagnostic images with the actual target position in the patient. Stereotactic radiosurgery may also be called stereotactic body radiation therapy (SBRT) or stereotactic ablative radiotherapy (SABR) when used outside the central nervous system (CNS). [ 3 ]
Stereotactic radiosurgery was first developed in 1949 by the Swedish neurosurgeon Lars Leksell to treat small targets in the brain that were not amenable to conventional surgery. The initial stereotactic instrument he conceived used probes and electrodes. [ 4 ] The first attempt to supplant the electrodes with radiation was made in the early fifties, with x-rays . [ 5 ] The principle of this instrument was to hit the intra-cranial target with narrow beams of radiation from multiple directions. The beam paths converge in the target volume, delivering a lethal cumulative dose of radiation there, while limiting the dose to the adjacent healthy tissue. Ten years later significant progress had been made, due in considerable measure to the contribution of the physicists Kurt Liden and Börje Larsson. [ 6 ] At this time, stereotactic proton beams had replaced the x-rays. [ 7 ] The heavy particle beam presented as an excellent replacement for the surgical knife, but the synchrocyclotron was too clumsy. Leksell proceeded to develop a practical, compact, precise and simple tool which could be handled by the surgeon himself. In 1968 this resulted in the Gamma Knife, which was installed at the Karolinska Institute and consisted of several cobalt-60 radioactive sources placed in a kind of helmet with central channels for irradiation with gamma rays. [ 8 ] This prototype was designed to produce slit-like radiation lesions for functional neurosurgical procedures to treat pain, movement disorders, or behavioral disorders that did not respond to conventional treatment. The success of this first unit led to the construction of a second device, containing 179 cobalt-60 sources. This second Gamma Knife unit was designed to produce spherical lesions to treat brain tumors and intracranial arteriovenous malformations (AVMs). [ 9 ] Additional units were installed in the 1980s all with 201 cobalt-60 sources. [ 10 ]
In parallel to these developments, a similar approach was designed for a linear particle accelerator or Linac. Installation of the first 4 MeV clinical linear accelerator began in June 1952 in the Medical Research Council (MRC) Radiotherapeutic Research Unit at the Hammersmith Hospital , London. [ 11 ] The system was handed over for physics and other testing in February 1953 and began to treat patients on 7 September that year. Meanwhile, work at the Stanford Microwave Laboratory led to the development of a 6 MeV accelerator, which was installed at Stanford University Hospital, California, in 1956. [ 12 ] Linac units quickly became favored devices for conventional fractionated radiotherapy but it lasted until the 1980s before dedicated Linac radiosurgery became a reality. In 1982, the Spanish neurosurgeon J. Barcia-Salorio began to evaluate the role of cobalt-generated and then Linac-based photon radiosurgery for the treatment of AVMs and epilepsy . [ 13 ] In 1984, Betti and Derechinsky described a Linac-based radiosurgical system. [ 14 ] Winston and Lutz further advanced Linac-based radiosurgical prototype technologies by incorporating an improved stereotactic positioning device and a method to measure the accuracy of various components. [ 15 ] Using a modified Linac, the first patient in the United States was treated in Boston Brigham and Women's Hospital in February 1986. [ citation needed ]
Technological improvements in medical imaging and computing have led to increased clinical adoption of stereotactic radiosurgery and have broadened its scope in the 21st century. [ 16 ] [ 17 ] The localization accuracy and precision that are implicit in the word "stereotactic" remain of utmost importance for radiosurgical interventions and are significantly improved via image-guidance technologies such as the N-localizer [ 18 ] and Sturm-Pastyr localizer [ 19 ] that were originally developed for stereotactic surgery .
In the 21st century the original concept of radiosurgery expanded to include treatments comprising up to five fractions , and stereotactic radiosurgery has been redefined as a distinct neurosurgical discipline that utilizes externally generated ionizing radiation to inactivate or eradicate defined targets, typically in the head or spine, without the need for a surgical incision. [ 20 ] Irrespective of the similarities between the concepts of stereotactic radiosurgery and fractionated radiotherapy the mechanism to achieve treatment is subtly different, although both treatment modalities are reported to have identical outcomes for certain indications. [ 21 ] Stereotactic radiosurgery has a greater emphasis on delivering precise, high doses to small areas, to destroy target tissue while preserving adjacent normal tissue. The same principle is followed in conventional radiotherapy although lower dose rates spread over larger areas are more likely to be used (for example as in VMAT treatments). Fractionated radiotherapy relies more heavily on the different radiosensitivity of the target and the surrounding normal tissue to the total accumulated radiation dose . [ 20 ] Historically, the field of fractionated radiotherapy evolved from the original concept of stereotactic radiosurgery following discovery of the principles of radiobiology : repair, reassortment, repopulation, and reoxygenation. [ 22 ] Today, both treatment techniques are complementary, as tumors that may be resistant to fractionated radiotherapy may respond well to radiosurgery, and tumors that are too large or too close to critical organs for safe radiosurgery may be suitable candidates for fractionated radiotherapy. [ 21 ]
Today, both Gamma Knife and Linac radiosurgery programs are commercially available worldwide. While the Gamma Knife is dedicated to radiosurgery, many Linacs are built for conventional fractionated radiotherapy and require additional technology and expertise to become dedicated radiosurgery tools. There is not a clear difference in efficacy between these different approaches. [ 23 ] [ 24 ] The major manufacturers, Varian and Elekta offer dedicated radiosurgery Linacs as well as machines designed for conventional treatment with radiosurgery capabilities. Systems designed to complement conventional Linacs with beam-shaping technology, treatment planning, and image-guidance tools to provide. [ 25 ] An example of a dedicated radiosurgery Linac is the CyberKnife , a compact Linac mounted onto a robotic arm that moves around the patient and irradiates the tumor from a large set of fixed positions, thereby mimicking the Gamma Knife concept.
The fundamental principle of radiosurgery is that of selective ionization of tissue, by means of high-energy beams of radiation. Ionization is the production of ions and free radicals which are damaging to the cells . These ions and radicals, which may be formed from the water in the cell or biological materials, can produce irreparable damage to DNA, proteins, and lipids, resulting in the cell's death. Thus, biological inactivation is carried out in a volume of tissue to be treated, with a precise destructive effect. The radiation dose is usually measured in grays (one gray (Gy) is the absorption of one joule of energy per kilogram of mass). A unit that attempts to take into account both the different organs that are irradiated and the type of radiation is the sievert , a unit that describes both the amount of energy deposited and the biological effectiveness. [ citation needed ]
When used outside the CNS it may be called stereotactic body radiation therapy (SBRT) or stereotactic ablative radiotherapy (SABR). [ 3 ]
Radiosurgery is performed by a multidisciplinary team of neurosurgeons , radiation oncologists and medical physicists to operate and maintain highly sophisticated, highly precise and complex instruments, including medical linear accelerators, the Gamma Knife unit and the Cyberknife unit. The highly precise irradiation of targets within the brain and spine is planned using information from medical images that are obtained via computed tomography , magnetic resonance imaging , and angiography . [ citation needed ]
Radiosurgery is indicated primarily for the therapy of tumors, vascular lesions and functional disorders. Significant clinical judgment must be used with this technique and considerations must include lesion type, pathology if available, size, location and age and general health of the patient. General contraindications to radiosurgery include excessively large size of the target lesion, or lesions too numerous for practical treatment. Patients can be treated within one to five days as outpatients . By comparison, the average hospital stay for a craniotomy (conventional neurosurgery, requiring the opening of the skull) is about 15 days. The radiosurgery outcome may not be evident until months after the treatment. Since radiosurgery does not remove the tumor but inactivates it biologically, lack of growth of the lesion is normally considered to be treatment success. General indications for radiosurgery include many kinds of brain tumors, such as acoustic neuromas , germinomas , meningiomas , metastases , trigeminal neuralgia , arteriovenous malformations, and skull base tumors, among others.
Stereotatic radiosurgery of the spinal metastasis is efficient in controlling pain in up to 90% of the cases and ensures stability of the tumours on imaging evaluation in 95% of the cases, and is more efficient for spinal metastasis involving one or two segments. Meanwhile, conventional external beam radiotherapy is more suitable for multiple spinal involvement. [ 26 ]
SRS may be administered alone or in combination with other therapies. For brain metastases, these treatment options include whole brain radiation therapy (WBRT), surgery, and systemic therapies. However, a recent systematic review found no difference in the affects on overall survival or deaths due to brain metastases when comparing SRS treatment alone to SRS plus WBRT treatment or WBRT alone. [ 27 ] [ 28 ]
Expansion of stereotactic radiotherapy to other lesions is increasing, and includes liver cancer, lung cancer, pancreatic cancer, etc. [ citation needed ]
The New York Times reported in December 2010 that radiation overdoses had occurred with the linear accelerator method of radiosurgery, due in large part to inadequate safeguards in equipment retrofitted for stereotactic radiosurgery. [ 29 ] In the U.S. the Food and Drug Administration (FDA) regulates these devices, whereas the Gamma Knife is regulated by the Nuclear Regulatory Commission .
This is evidence that immunotherapy may be useful for treatment of radiation necrosis following stereotactic radiotherapy. [ 30 ]
The selection of the proper kind of radiation and device depends on many factors including lesion type, size, and location in relation to critical structures. Data suggest that similar clinical outcomes are possible with all of the various techniques. More important than the device used are issues regarding indications for treatment, total dose delivered, fractionation schedule and conformity of the treatment plan. [ citation needed ]
A Gamma Knife (also known as the Leksell Gamma Knife) is used to treat brain tumors by administering high-intensity gamma radiation therapy in a manner that concentrates the radiation over a small volume. The device was invented in 1967 at the Karolinska Institute in Stockholm , Sweden, by Lars Leksell , Romanian-born neurosurgeon Ladislau Steiner, and radiobiologist Börje Larsson from Uppsala University , Sweden.
A Gamma Knife typically contains 201 cobalt-60 sources of approximately 30 curies each (1.1 TBq ), placed in a hemispheric array in a heavily shielded assembly. The device aims gamma radiation through a target point in the patient's brain. The patient wears a specialized helmet that is surgically fixed to the skull, so that the brain tumor remains stationary at the target point of the gamma rays. An ablative dose of radiation is thereby sent through the tumor in one treatment session, while surrounding brain tissues are relatively spared.
Gamma Knife therapy, like all radiosurgery, uses doses of radiation to kill cancer cells and shrink tumors, delivered precisely to avoid damaging healthy brain tissue. Gamma Knife radiosurgery is able to accurately focus many beams of gamma radiation on one or more tumors. Each individual beam is of relatively low intensity, so the radiation has little effect on intervening brain tissue and is concentrated only at the tumor itself.
Gamma Knife radiosurgery has proven effective for patients with benign or malignant brain tumors up to 4 cm (1.6 in) in size, vascular malformations such as an arteriovenous malformation (AVM), pain, and other functional problems. [ 31 ] [ 32 ] [ 33 ] [ 34 ] For treatment of trigeminal neuralgia the procedure may be used repeatedly on patients.
Acute complications following Gamma Knife radiosurgery are rare, [ 35 ] and complications are related to the condition being treated. [ 36 ] [ 37 ]
A linear accelerator (linac) produces x-rays from the impact of accelerated electrons striking a high z target, usually tungsten. The process is also referred to as "x-ray therapy" or "photon therapy." The emission head, or " gantry ", is mechanically rotated around the patient in a full or partial circle. The table where the patient is lying, the "couch", can also be moved in small linear or angular steps. The combination of the movements of the gantry and of the couch allow the computerized planning of the volume of tissue that is going to be irradiated. Devices with a high energy of 6 MeV are commonly used for the treatment of the brain, due to the depth of the target. The diameter of the energy beam leaving the emission head can be adjusted to the size of the lesion by means of collimators . They may be interchangeable orifices with different diameters, typically varying from 5 to 40 mm in 5 mm steps, or multileaf collimators, which consist of a number of metal leaflets that can be moved dynamically during treatment in order to shape the radiation beam to conform to the mass to be ablated. As of 2017 [update] Linacs were capable of achieving extremely narrow beam geometries, such as 0.15 to 0.3 mm. Therefore, they can be used for several kinds of surgeries which hitherto had been carried out by open or endoscopic surgery, such as for trigeminal neuralgia. Long-term follow-up data has shown it to be as effective as radiofrequency ablation, but inferior to surgery in preventing the recurrence of pain. [ citation needed ]
The first such systems were developed by John R. Adler , a Stanford University professor of neurosurgery and radiation oncology, and Russell and Peter Schonberg at Schonberg Research, and commercialized under the brand name CyberKnife.
Protons may also be used in radiosurgery in a procedure called Proton Beam Therapy (PBT) or proton therapy . Protons are extracted from proton donor materials by a medical synchrotron or cyclotron , and accelerated in successive transits through a circular, evacuated conduit or cavity, using powerful magnets to shape their path, until they reach the energy required to just traverse a human body, usually about 200 MeV. They are then released toward the region to be treated in the patient's body, the irradiation target. In some machines, which deliver protons of only a specific energy, a custom mask made of plastic is interposed between the beam source and the patient to adjust the beam energy to provide the appropriate degree of penetration. The phenomenon of the Bragg peak of ejected protons gives proton therapy advantages over other forms of radiation, since most of the proton's energy is deposited within a limited distance, so tissue beyond this range (and to some extent also tissue inside this range) is spared from the effects of radiation. This property of protons, which has been called the " depth charge effect" by analogy to the explosive weapons used in anti-submarine warfare, allows for conformal dose distributions to be created around even very irregularly shaped targets, and for higher doses to targets surrounded or backstopped by radiation-sensitive structures such as the optic chiasm or brainstem. The development of "intensity modulated" techniques allowed similar conformities to be attained using linear accelerator radiosurgery. [ citation needed ]
As of 2013 [update] there was no evidence that proton beam therapy is better than any other types of treatment in most cases, except for a "handful of rare pediatric cancers". Critics, responding to the increasing number of very expensive PBT installations, spoke of a "medical arms race " and "crazy medicine and unsustainable public policy". [ 38 ] | https://en.wikipedia.org/wiki/Radiosurgery |
Radiosynthesis is a fully automated synthesis method in which radioactive compounds are produced. [ 1 ] Radiosynthesis is generally carried out by several nuclear interface modules , which are protected by the lead shielding and controlled by a computer semi-automatically. The set-ups of modules are different depending on the type of product and synthesis process . Consequently, the modules should be adapted with the synthesis stages. In some cases, such stages of synthesis are carried out manually in order to optimize the radiochemical yield or due to the incompatibility or lack of module. [ 2 ]
Radiosynthesis modules consist of following constant components:
There are also some components which are added based on the synthesis set-up such as stirrers, sterile filters, Sep-Paks™, vials, bottles, detectors etc..
Before every synthesis, the modules should be washed. It should also be mentioned that according to Half-life of radionuclides, a relaxation time is needed between the syntheses in each module. Fig.1 shows the schematic of a sample module.
Radiosynthesis modules are often combined with a cyclotron or other radio nuclide generator .
This chemical reaction article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Radiosynthesis |
Radiosynthesis is the theorized capture and metabolism , by living organisms, of energy from ionizing radiation , analogously to photosynthesis . Metabolism of ionizing radiation was theorized as early as 1956 by the Russian microbiologist S. I. Kuznetsov . [ 1 ]
Beginning in the 1990s, researchers at the Chernobyl Nuclear Power Plant uncovered some 200 species of apparently radiotrophic fungi containing the pigment melanin on the walls of the reactor room and in the surrounding soil. [ 2 ] [ 3 ] Such "melanized" fungi have also been discovered in nutrient-poor, high-altitude areas which are exposed to high levels of ultraviolet radiation. [ 4 ]
Following the Ukrainian results, an American team at the Albert Einstein College of Medicine of Yeshiva University in New York began experimenting with radiation exposure of melanin and melanized fungi. They found that ionizing radiation increased the ability of melanin to support an important metabolic reaction, and that Cryptococcus neoformans fungi grew three times faster than normal. [ 5 ] [ 4 ] Microbiologist Ekaterina Dadachova suggested such fungi could serve as a food supply and source of radiation protection for interplanetary astronauts , who would be exposed to cosmic rays . [ 4 ]
In 2014, the American research group was awarded a patent for a method of enhancing the growth of microorganisms through increasing melanin content. The inventors of this process claimed their fungi were employing radiosynthesis, and hypothesized that radiosynthesis may have played a role in early life on Earth, by allowing melanized fungi to act as autotrophs . [ 6 ]
From October 2018 through March 2019, NASA conducted an experiment aboard the International Space Station to study radiotrophic fungi as a potential radiation barrier to the harmful radiation in space. Radiotrophic fungi have many possible applications on Earth as well, potentially including a disposal method for nuclear waste or use as high-altitude biofuel or a nutrition source. [ 7 ] | https://en.wikipedia.org/wiki/Radiosynthesis_(metabolism) |
Radiotrophic fungi are fungi that can perform the hypothetical biological process called radiosynthesis , which means using ionizing radiation as an energy source to drive metabolism. It has been claimed that radiotrophic fungi have been found in extreme environments such as in the Chernobyl Nuclear Power Plant .
Most radiotrophic fungi use melanin in some capacity to survive. [ 1 ] The process of using radiation and melanin for energy has been termed radiosynthesis , and is thought to be analogous to anaerobic respiration . [ 2 ] However, it is not known if multi-step processes such as photosynthesis or chemosynthesis are used in radiosynthesis or even if radiosynthesis exists in living organisms.
Many fungi have been isolated from the area around the destroyed Chernobyl Nuclear Power Plant , some of which have been observed directing their growth of hyphae toward radioactive graphite from the disaster, a phenomenon called “radiotropism”. [ 3 ] [ 4 ] Study has ruled out the presence of carbon as the resource attracting the fungal colonies, and in fact concluded that some fungi will preferentially grow in the direction of the source of beta and gamma ionizing radiation, but were not able to identify the biological mechanism behind this effect. [ 4 ] It has also been observed that other melanin -rich fungi were discovered in the cooling water from some other working nuclear reactors. The light-absorbing compound in the fungus cell membranes had the effect of turning the water black. [ 5 ] While there are many cases of extremophiles (organisms that can live in severe conditions such as that of the radioactive power plant), a hypothetical radiotrophic fungus would grow because of the radiation, rather than in spite of it. [ 6 ]
Further research conducted at the Albert Einstein College of Medicine showed that three melanin-containing fungi— Cladosporium sphaerospermum , Wangiella dermatitidis , and Cryptococcus neoformans —increased in biomass and accumulated acetate faster in an environment in which the radiation level was 500 times higher than in the normal environment. C. sphaerospermum in particular was chosen due to this species being found in the reactor at Chernobyl. Exposure of C. neoformans cells to these radiation levels rapidly (within 20–40 minutes of exposure) altered the chemical properties of its melanin , and increased melanin-mediated rates of electron transfer (measured as reduction of ferricyanide by NADH ) three- to four-fold compared with unexposed cells. However, each culture was performed with at least limited nutrients provided to each fungus. The increase in biomass and other effects could be caused either by the cells directly deriving energy from ionizing radiation, or by the radiation allowing the cells to utilize traditional nutrients either more efficiently or more rapidly. [ 6 ]
Outside of the fungal studies, similar effects on melanin electron-transport capability were observed by the authors after exposure to non-ionizing radiation. The authors did not conclude whether light or heat radiation would have a similar effect on living fungal cells. [ 6 ]
Melanins are a family of dark-colored, naturally occurring pigments with radiation-shielding properties. These pigments can absorb electromagnetic radiation due to their molecular structure, which results in their dark color; this quality suggests that melanin could help protect radiotropic fungi from ionizing radiation. It has been suggested that melanin's radiation-shielding properties are due to its ability to trap free radicals formed during radiolysis of water. [ 7 ] Melanin production is also advantageous to the fungus in that it can aid survival in many extreme environments. Examples of these environments include the Chernobyl Nuclear Power Plant , the International Space Station , and the Transantarctic Mountains . Melanin may also be able to help the fungus metabolize radiation , but more evidence and research is still needed. [ 1 ]
Melanization may come at some metabolic cost to the fungal cells. In the absence of radiation, some non-melanized fungi (that had been mutated in the melanin pathway) grew faster than their melanized counterparts. Limited uptake of nutrients due to the melanin molecules in the fungal cell wall or toxic intermediates formed in melanin biosynthesis have been suggested to contribute to this phenomenon. [ 6 ] It is consistent with the observation that despite being capable of producing melanin, many fungi do not synthesize melanin constitutively (i.e., all the time), but often only in response to external stimuli or at different stages of their development. [ 8 ] The exact biochemical processes in the suggested melanin-based synthesis of organic compounds or other metabolites for fungal growth, including the chemical intermediates (such as native electron donor and acceptor molecules) in the fungal cell and the location and chemical products of this process, are unknown.
It is hypothesized that radiotrophic fungi could potentially be used as a shield to protect against radiation , [ 2 ] specifically in affiliation to the use of astronauts in space or other atmospheres. An experiment taking place at the International Space Station in December 2018 through January 2019 was conducted in order to test whether radiotrophic fungi could provide protection from ionizing radiation in space, as part of research efforts preceding a possible trip to Mars . This experiment used the radiotrophic strain of the fungus Cladosporium sphaerospermum . [ 2 ] The growth of this fungus and its ability to deflect the effects of ionizing radiation were studied for 30 days aboard the International Space Station . This experimental trial yielded very promising results.
The amount of radiation deflected was found to directly correlate with the amount of fungus. There was no difference in the reduction of ionizing radiation between the experimental and control group within the first 24 hour period; however, once the fungus had reached an adequate maturation, and with a 180° protection radius, amounts of ionizing radiation were significantly reduced as compared to the control group. With a 1.7 mm thick shield of melanized radiotrophic Cladosporium sphaerospermum , measurements of radiation nearing the end of the experimental trial were found to be 2.42% lower, demonstrating radiation deflecting capabilities five times that of the control group. Under circumstances in which the fungi would fully encompass an entity, radiation levels would be reduced by an estimated 4.34±0.7%. [ 2 ] Estimations indicate that approximately a 21 cm thick layer could significantly deflect the annual amount of radiation received on Mars’ surface. Limitations to the use of a radiotrophic fungi based shield include increased mass on missions. However as a viable substitute to reduce overall mass on potential Mars missions, a mixture with equal mole concentration of Martian soil , melanin , and a layer of fungi roughly 9 cm thick, could be used. [ 2 ]
[1] "This black fungus might be healing chernobyl by "drinking radiation" a biologist explains. | https://en.wikipedia.org/wiki/Radiotrophic_fungus |
The Radium Dial Company was one of a few now defunct United States companies, along with the United States Radium Corporation , involved in the painting of clocks, watches and other instrument dials using radioluminescent paint containing radium . The resulting dials are now collectively known as radium dials . The luminous paint used on the dials contained a mixture of zinc sulfide activated with silver, and powdered radium, a product that the Radium Dial Company named Luma . However, unlike the US Radium Corporation, Radium Dial Company was specifically set up to only paint dials, and no other radium processing took place at the premises.
The company is notable for being involved in the radium poisoning of the Radium Girls . The workers in the factories were told that the radium paint was harmless. Radium's negative health effects were well-known at the time, however it was thought that small amounts of radium were not dangerous and even a cure for lack of energy. [ 1 ] The workers in the factories consumed deadly amounts of radium due to being told by management to "point" their brushes on their lips for a fine tip. [ 2 ] The young workers also used the radium paints to adorn their fingernails, lips and teeth to make them glow. This led to significant health problems and deaths among the company's workforce. The workers eventually sued Radium Dial Company and received financial compensation for their health problems, though the Radium Dial Company continuously appealed so this process took years and many workers had already died of their injuries. [ 3 ] This litigation led to significant reforms in workplace safety and eventually led to the establishment of OSHA decades later.
The Radium Dial Company was started in 1917 and was in full production of painted dials by 1918. The company was a division of the Standard Chemical Company based in the Marshall Field Annex building in Chicago . In 1920 the company relocated to Peru, Illinois to closer proximity to the clock manufacturer and major customer, Westclox .
By 1922 the company had moved to a former high school building at 1022 Columbus Street in Ottawa, Illinois [ 4 ] where it remained until the mid-1930s. At the highest point in production (around 1925), the Radium Dial Company employed around 1,000 young women who turned out around 4,300 dials each day [ citation needed ] .
The company was headed by Joseph A. Kelly Sr. at the time of its dissolution during the trial. Kelly opened up a new corporation called Luminous Processes Inc. a few blocks away from the Radium Dial Company in Ottawa, Illinois shortly after closing down the Radium Dial Company. [ 5 ] [ 6 ] Luminous Processes Inc. continued producing fluorescent watch dials powered by radium radioactivity until 1978. [ 7 ] [ 8 ] | https://en.wikipedia.org/wiki/Radium_Dial_Company |
Radium and radon are important contributors to environmental radioactivity . Radon occurs naturally as a result of decay of radioactive elements in soil and it can accumulate in houses built on areas where such decay occurs. Radon is a major cause of cancer; it is estimated to contribute to ~2% of all cancer related deaths in Europe. [ 1 ]
Radium, like radon, is radioactive and is found in small quantities in nature and is hazardous to life if radiation exceeds 20-50 mSv /year. Radium is a decay product of uranium and thorium . [ 2 ] Radium may also be released into the environment by human activity: for example, in improperly discarded products painted with radioluminescent paint.
Residues from the oil and gas industry often contain radium and its daughters. The sulfate scale from an oil well can be very radium rich. The water inside an oil field is often very rich in strontium , barium and radium , while seawater is very rich in sulfate : so if water from an oil well is discharged into the sea or mixed with seawater, the radium is likely to be brought out of solution by the barium/strontium sulfate which acts as a carrier precipitate. [ 3 ]
It is not unknown for local contamination to arise from improper disposal of radium-based radioluminescent paints. [ 4 ]
Eben Byers was a wealthy American socialite whose death in 1932 from using a radioactive quackery product called Radithor is a prominent example of a death caused by radium. Radithor contained ~1 μCi (40 kBq) of 226 Ra and 1 μCi of 228 Ra per bottle. Radithor was taken by mouth and radium, being a calcium mimic, has a very long biological halflife in bone . [ 5 ]
Most of the dose is due to the decay of the polonium ( 218 Po) and lead ( 214 Pb) daughters of 222 Rn. By controlling exposure to the daughters the radioactive dose to the skin and lungs can be reduced by at least 90%. This can be done by wearing a dust mask, and wearing a suit to cover the entire body. Note that exposure to smoke at the same time as radon and radon daughters will increase the harmful effect of the radon. In uranium miners radon has been found to be more carcinogenic in smokers than in non-smokers. [ 3 ]
Radon concentration in open air varies between 1 and 100 Bq m −3 . [ 6 ] Radon can be found in some spring waters and hot springs . [ 7 ] The towns of Misasa , Japan , and Bad Kreuznach , Germany boast radium-rich springs which emit radon, as does Radium Springs, New Mexico .
Radon exhausts naturally from the ground, particularly in certain regions, especially but not only regions with granitic soils. However, not all granitic regions are prone to high emissions of radon. For instance, while the rock which Aberdeen is on is very radium rich, the rock lacks the cracks required for the radon to migrate. In other nearby areas of Scotland (to the north of Aberdeen) and in Cornwall / Devon the radon is very much able to leave the rock.
Radon is a decay product of radium which in turn is a decay product of uranium. Maps of average radon levels in houses are available, to assist in planning mitigation measures. [ 8 ]
While high uranium in the soil / rock under a house does not always lead to a high radon level in air, a positive correlation between the uranium content of the soil and the radon level in air can be seen.
Radon harms indoor air quality in many homes. (See "In houses" below.)
Radon ( 222 Rn) released into the air decays to 210 Pb and other radioisotopes and the levels of 210 Pb can be measured. It is important to note that the rate of deposition of this radioisotope is very dependent on the season. Here is a graph of the deposition rate observed in Japan . [ 9 ]
Well water can be very rich in radon; the use of this water inside a house is another route allowing radon to enter the house. The radon can enter the air and then be a source of exposure to the humans, or the water can be consumed by humans which is a different exposure route. [ 10 ]
Rainwater can be highly radioactive due to high levels of radon and its decay progenies 214 Bi and 214 Pb; the concentrations of these radioisotopes can be high enough to seriously disrupt radiation monitoring at nuclear power plants. [ 11 ] The highest levels of radon in rainwater occur during thunderstorms, and it is hypothesized that radon is concentrated in thunderstorms because it forms some positive ions during thunderstorms. [ 12 ] Estimates of the age of raindrops have been obtained from measuring the isotopic abundance of radon's short-lived decay progeny in rainwater. [ 13 ]
Water, oil and gas from a well often contain radon . The radon decays to form solid radioisotopes which form coatings on the inside of pipework. In an oil processing plant the area of the plant where propane is processed is often one of the more contaminated areas of the plant as radon has a similar boiling point to propane. [ 14 ]
Because uranium minerals emit radon gas, and their harmful and highly radioactive decay products , uranium mining is considerably more dangerous than other (already dangerous) hard rock mining , requiring adequate ventilation systems if the mines are not open pit . In the 1950s, a significant number of American uranium miners were Navajo , as many uranium deposits were discovered on Navajo reservations . A statistically significant proportion of these miners later developed small-cell lung cancer , a type of cancer usually not associated with smoking, after exposure to uranium ore and radon-222 , a natural decay product of uranium. [ 15 ] The cancer causing agent has been shown to be the radon which is produced by the uranium, and not the uranium itself. [ 16 ] Some survivors and their descendants received compensation under the Radiation Exposure Compensation Act in 1990.
The level of radon in the air of mines is now normally controlled by law. In a working mine, the radon level can be controlled by ventilation , sealing off old workings and controlling the water in the mine. The level in a mine can go up when a mine is abandoned; it can reach a level which can cause the skin to become red (a mild radiation burn ). The radon levels in some of the mines can reach 400 to 700 kBq m −3 . [ 17 ]
A common unit of exposure of lung tissue to alpha emitters is the working level month ( WLM ), this is where the human lungs have been exposed for 170 hours (a typical month worth of work for a miner) to air which has 3.7 kBq of 222 Rn (in equilibrium with its decay products). This is air which has the alpha dose rate of 1 working level ( WL ). It is estimated that the average person ( general public ) is subject to 0.2 WLM per year, which works out at about 15 to 20 WLM in a lifetime. According to the NRC, 1 WLM is a 5 to 10 mSv lung dose (0.5 to 1.0 rem ), while the Organisation for Economic Co-operation and Development (OECD) consider that 1 WLM is equal to a lung dose of 5.5 mSv, and the International Commission on Radiological Protection (ICRP) consider 1 WLM to be a 5 mSv lung dose for professional workers (and a 4 mSv lung dose for the general public). Lastly the United Nations Scientific Committee on the Effects of Atomic Radiation (UNSCEAR) consider that the exposure of the lungs to 1 Bq of 222 Rn (in equilibrium with its decay products) for one year will cause a dose of 61 μSv. [ 18 ]
In humans a relationship between lung cancer and radon has been shown to exist (beyond all reasonable doubt) for exposures of 100 WLM and above. By using the data from several studies it has been possible to show that an increased risk can be caused by a dose as low as 15 to 20 WLM. Sadly these studies have been difficult as the random errors in the data are very large. It is likely that the miners are also subject to other effects which can harm their lungs while at work (for example dust and diesel fumes). [ citation needed ]
It has been known since at least the 1950s that radon is present in indoor air, and research into its effects on human health started in the early 1970s. [ 19 ] The danger of radon exposure in dwellings received more widespread public awareness after 1984, as a result of the case of Stanley Watras , an employee at the Limerick nuclear power plant in Pennsylvania . [ 20 ] Mr. Watras set off the radiation alarms (see Geiger counter ) on his way into work for two weeks straight while authorities searched for the source of the contamination . They were shocked to find that the source was astonishingly high levels of radon in his basement and it was not related to the nuclear plant. The risks associated with living in his house were estimated to be equivalent to smoking 135 packs of cigarettes every day. [ 21 ]
Depending how houses are built and ventilated, radon may accumulate in basements and dwellings. The European Union recommends that mitigation should be taken starting from concentrations of 400 Bq /m 3 for old houses, and 200 Bq/m 3 for new ones. [ 22 ]
The National Council on Radiation Protection and Measurements (NCRP) recommends action for any house with a concentration higher than 8 pCi /L (300 Bq/m 3 ).
The United States Environmental Protection Agency recommends action for any house with a concentration higher than 148 Bq/m 3 (given as 4 pCi /L). Nearly one in 15 homes in the U.S. has a high level of indoor radon according to their statistics. The U.S. Surgeon General and EPA recommend all homes be tested for radon. Since 1985, millions of homes have been tested for radon in the U.S. [ 22 ]
By adding a crawl space under the ground floor, which is subject to forced ventilation, the radon level in the house can be lowered. [ 23 ] | https://en.wikipedia.org/wiki/Radium_and_radon_in_the_environment |
Radium bromide is the bromide salt of radium , with the formula RaBr 2 . It is produced during the process of separating radium from uranium ore . This inorganic compound was discovered by Pierre and Marie Curie in 1898, and the discovery sparked a huge interest in radiochemistry and radiotherapy . Since elemental radium oxidizes readily in air and water, radium salts are the preferred chemical form of radium to work with. [ 3 ] Even though it is more stable than elemental radium, radium bromide is still extremely toxic, and can explode under certain conditions. [ 4 ]
After the Curies discovered radium (in the form of radium chloride ) in 1898, scientists began to isolate radium on an industrial scale, with the intent of using it for radiotherapy treatments. Radium salts, including radium bromide, were most often used by placing the chemical in a tube that was then passed over or inserted into diseased tissue in the body. Many of the first scientists to try to determine radium's uses were affected by their exposure to the radioactive material. Pierre Curie went so far as to self-inflict a severe chemical skin reaction by applying a radium source directly to his forearm, which ultimately created a skin lesion. [ 5 ] All types of therapeutic tests were performed for different skin diseases including eczema , lichen and psoriasis . Later, it was hypothesized that radium could be used to treat cancerous diseases.
However, during this time frame, radium also gained popularity among pseudoscientific "health remedy" industries, which promoted radium as an essential element that could "heal" and "reinvigorate" cells in the human body and remove poisonous substances. As a result, radium gained popularity as a "health trend" in the 1920s and radium salts were added to food, drinks, clothing, toys, and even toothpaste. [ 6 ] Furthermore, many respectable journals and newspapers in the early 1900s published statements claiming that radium posed no health hazard.
The main problem with the growth of interest in radium was the lack of radium on earth itself. In 1913, it was reported that the Radium Institute had four grams of radium total, which at the time was more than half the world supply. [ 6 ] Numerous countries and institutions across the world set out to extract as much radium as possible, a time-consuming and expensive task. It was reported in Science magazine in 1919 that the United States had produced approximately 55 grams of radium since 1913, which was also more than half the radium produced in the world at the time. [ 7 ] A principal source for radium is pitchblende , which holds a total of 257 mg of radium per ton of U 3 O 8 . [ 3 ] With so little product recovered from such a large amount of material, it was difficult to extract a large quantity of radium. This was the reason radium bromide became one of the most expensive materials on earth. In 1921, it was stated in Time magazine that one ton of radium cost 17,000,000,000 Euros, whereas one ton of gold cost 208,000 Euros and one ton of diamond cost 400,000,000 Euros. [ 6 ]
Radium bromide was also found to induce phosphorescence at normal temperatures. [ 8 ] This led to the US army manufacturing and supplying luminous watches and gun sights to soldiers. It also allowed for the invention of the spinthariscope , which soon became a popular household item. [ 9 ]
Radium bromide is a luminous salt that causes the air surrounding it, even when encased in a tube, to glow a brilliant green and demonstrate all bands of the nitrogen spectrum. It is possible that the effect of the alpha radiation on the nitrogen in the air causes this luminescence . Radium bromide is highly reactive and crystals can sometimes explode, especially if heated. Helium gas evolved from alpha particles can accumulate within the crystals, which can cause them to weaken and rupture.
Radium bromide will crystallize when separated from aqueous solution. It forms a dihydrate , very similar to barium bromide . [ 4 ]
Radium is obtained from uranium or pitchblende ores by the "Curie method", which involves two major stages. In the first stage the ore is treated with sulfuric acid dissolves many components. The residue contains, barium, radium, and lead sulfates. The mixture will then be treated with sodium chloride and sodium carbonate to remove the lead. The second stage involves separation of the barium from the radium. [ 3 ] [ 4 ]
Radium bromide can be obtained from radium chloride by reaction with a stream of hydrogen bromide . [ 4 ]
Radium bromide, like all radium compounds, is highly radioactive and very toxic. Due to its chemical similarity to calcium , radium tends to accumulate in the bones, where it irradiates the bone marrow and can cause anemia , leukemia , sarcoma , bone cancer , genetic defects, infertility , ulcers, and necrosis . Symptoms of poisoning can take years to develop, by which time it is usually too late for any effective medical treatment. Radium bromide also poses a severe environmental hazard , amplified due to its high solubility in water, and it can bioaccumulate and cause long-lasting damage to organisms. [ citation needed ]
Radium bromide is highly reactive, and crystals can explode if violently shocked or heated. This is, in part, due to self-damage of the crystals by alpha radiation, which weakens the lattice structure. [ dubious – discuss ]
Radium and radium salts were commonly used for treating cancer ; however, these treatments have been mostly phased out in favor of less toxic chemicals such as technetium or strontium-89 . [ 6 ] Radium bromide was also used in luminous paint on watches, but its use was ultimately phased out in the 1960-1970s in favor of less dangerous chemicals like promethium and tritium . | https://en.wikipedia.org/wiki/Radium_bromide |
Radium chlorate is an inorganic compound with formula Ra(ClO 3 ) 2 . [ 1 ]
While pure radium chlorate has never been prepared, [ 1 ] it is known to form coprecipitates using barium chlorate as a carrier. [ 2 ] These react with excess ammoniacal ammonium carbonate to form a mixed precipitate of radium carbonate with barium carbonate . [ 2 ]
Predicted values of its thermodynamic properties are available from Lowson (1985). [ 3 ]
Solutions containing radium chlorate may be obtained by dissolving soluble radium salts in a solution of barium chlorate: [ 2 ]
It is claimed to have application in the production of self luminous watch components. [ 4 ] | https://en.wikipedia.org/wiki/Radium_chlorate |
Radium dials are watch , clock and other instrument dials painted with luminous paint containing radium-226 to produce radioluminescence . Radium dials were produced throughout most of the 20th century before being replaced by safer tritium -based luminous material in the 1970s and finally by non-toxic, non-radioactive strontium aluminate –based photoluminescent material from the middle 1990s.
Radium was discovered by Marie and Pierre Curie in 1898 [ 1 ] and was soon combined with paint to make luminescent paint , which was applied to clocks, airplane instruments, and the like, to be able to read them in the dark. [ 2 ]
In 1914, Dr. Sabin Arnold von Sochocky and Dr. George S. Willis founded the Radium Luminous Material Corporation. The company made luminescent paint. The company later changed its name to the United States Radium Corporation . [ 3 ] The use of radium to provide luminescence for hands and indices on watches soon followed.
The Ingersoll Watch division of the Waterbury Clock Company , a nationally-known maker of low-cost pocket and wristwatches, was a leading popularizer of the use of radium for watch hands and indices through the introduction of their "Radiolite" watches in 1916. [ 4 ] The Radiolite series, made in various sizes and models, became a signature of the Connecticut-based company.
Radium dials were typically painted by young women, who used to 'point' their brushes by licking and shaping the bristles prior to painting the fine lines and numbers on the dials. This practice resulted in the ingestion of radium, which caused serious jaw-bone degeneration and malignancy and other dental diseases. The disease, radium-induced osteonecrosis , was recognized as an occupational disease in 1925 after a group of radium painters, known as the Radium Girls , from the United States Radium Corporation sued. By 1930, all dial painters stopped pointing their brushes by mouth. Stopping this practice drastically reduced the amount of radium ingested and therefore, the incidence of malignancy.
Luminous Processes employees interviewed by a journalist in 1978 stated they had been left ignorant of radium's dangers. They were told that eliminating lip-pointing had ended earlier problems. They worked in unvented rooms, they wore smocks that they laundered at home. Geiger counters could pick up readings from pants returned from a dry cleaner and from clothes stored away in a cedar chest." [ 5 ]
According to the United States Environmental Protection Agency, "radioactive antiques [including watches] are usually not a health risk as long as they are intact and in good condition." [ 6 ] However, radium is highly radioactive, emitting alpha , beta , and gamma radiation — the effects of which are particularly deleterious if inhaled or ingested since there is no shielding within the body. [ 6 ] Indeed, the body treats radium as it does calcium , storing it in bone where it may cause bone degeneration and cancer. [ 6 ]
Therefore, it is of the utmost importance that watches with radium dials should not be taken apart [ 6 ] without proper training, technique, and facilities. Radium paint can be ingested by inhaling flaking paint particles. The alpha particles emitted by the radium, which is taken up in bone, will kill off surrounding bone tissue, resulting in a condition loosely referred to as radium jaw . Inhaled or ingested particles may deposit a high local dose with a risk of radiation-caused lung or gastrointestinal cancer. Penetrating gamma radiation produced by some dials also represents a significant health risk.
Although old radium dials generally no longer produce light, this is due to the breakdown of the crystal structure of the luminous zinc sulfide rather than the radioactive decay of the radium. The radium isotope ( 226 Ra ) used has a half-life of about 1,600 years, [ 7 ] so radium dials remain essentially just as radioactive as when originally painted 50 or 100 years ago, whether or not they remain luminous.
Radium dials held near the face have been shown to produce radiation doses in excess of 10 μSv / hour. [ citation needed ] After about 20 minutes this delivers the equivalent of one whole day's worth of normal background radiation . [ citation needed ] This rate probably only represents the dose rate from gamma emission, as the alpha emission will be stopped by the lacquer, or crystal, or case; hence, the dose rate following ingestion or inhalation of the dust could be much higher.
Chronic exposure to high levels of radium can result in an increased incidence of bone , liver , or breast cancer . [ 7 ] Decaying radium also produces the gas radon , recognized as the second leading cause of lung cancer in the United States [ 7 ] and the United Kingdom. [ 8 ] A 2018 study by researchers from the University of Northampton found that a collection of 30 vintage military watches with radium dials kept in a small, unventilated room produced a radon concentration 134 times greater than the UK's recommended "safe" level. [ 8 ]
Ingestion of radium has been linked to anemia , cataracts , broken teeth, and reduced bone growth. [ 9 ]
In the United States there does not seem to have ever been prohibitory legislation passed banning the use of radium in clocks and watches. It was only with the passage of the Energy Policy Act of 2005 that the United States Nuclear Regulatory Commission (NRC) was given oversight of the use of radium. [ 10 ] Prior to that date, "the federal government had a limited role, if any, in ensuring the safe use of radium," according to the NRC. [ 10 ] The element was phased out of use by industry acting under its own volition as superior and safer luminous materials entered the marketplace. | https://en.wikipedia.org/wiki/Radium_dial |
In differential geometry , the radius of curvature , R , is the reciprocal of the curvature . For a curve , it equals the radius of the circular arc which best approximates the curve at that point. For surfaces , the radius of curvature is the radius of a circle that best fits a normal section or combinations thereof. [ 1 ] [ 2 ] [ 3 ]
In the case of a space curve , the radius of curvature is the length of the curvature vector .
In the case of a plane curve , then R is the absolute value of [ 3 ]
where s is the arc length from a fixed point on the curve, φ is the tangential angle and κ is the curvature .
If the curve is given in Cartesian coordinates as y ( x ) , i.e., as the graph of a function , then the radius of curvature is (assuming the curve is differentiable up to order 2)
R = | ( 1 + y ′ 2 ) 3 2 y ″ | , {\displaystyle R=\left|{\frac {\left(1+y'^{\,2}\right)^{\frac {3}{2}}}{y''}}\right|\,,}
where y ′ = d y d x , {\textstyle y'={\frac {dy}{dx}}\,,} y ″ = d 2 y d x 2 , {\textstyle y''={\frac {d^{2}y}{dx^{2}}},} and | z | denotes the absolute value of z .
If the curve is given parametrically by functions x ( t ) and y ( t ) , then the radius of curvature is
R = | d s d φ | = | ( x ˙ 2 + y ˙ 2 ) 3 2 x ˙ y ¨ − y ˙ x ¨ | {\displaystyle R=\left|{\frac {ds}{d\varphi }}\right|=\left|{\frac {\left({{\dot {x}}^{2}+{\dot {y}}^{2}}\right)^{\frac {3}{2}}}{{\dot {x}}{\ddot {y}}-{\dot {y}}{\ddot {x}}}}\right|}
where x ˙ = d x d t , {\textstyle {\dot {x}}={\frac {dx}{dt}},} x ¨ = d 2 x d t 2 , {\textstyle {\ddot {x}}={\frac {d^{2}x}{dt^{2}}},} y ˙ = d y d t , {\textstyle {\dot {y}}={\frac {dy}{dt}},} and y ¨ = d 2 y d t 2 . {\textstyle {\ddot {y}}={\frac {d^{2}y}{dt^{2}}}.}
Heuristically, this result can be interpreted as [ 2 ]
R = | v | 3 | v × v ˙ | , {\displaystyle R={\frac {\left|\mathbf {v} \right|^{3}}{\left|\mathbf {v} \times \mathbf {\dot {v}} \right|}}\,,}
where
| v | = | ( x ˙ , y ˙ ) | = R d φ d t . {\displaystyle \left|\mathbf {v} \right|={\big |}({\dot {x}},{\dot {y}}){\big |}=R{\frac {d\varphi }{dt}}\,.}
If γ : ℝ → ℝ n is a parametrized curve in ℝ n then the radius of curvature at each point of the curve, ρ : ℝ → ℝ , is given by [ 3 ]
ρ = | γ ′ | 3 | γ ′ | 2 | γ ″ | 2 − ( γ ′ ⋅ γ ″ ) 2 . {\displaystyle \rho ={\frac {\left|{\boldsymbol {\gamma }}'\right|^{3}}{\sqrt {\left|{\boldsymbol {\gamma }}'\right|^{2}\,\left|{\boldsymbol {\gamma }}''\right|^{2}-\left({\boldsymbol {\gamma }}'\cdot {\boldsymbol {\gamma }}''\right)^{2}}}}\,.}
As a special case, if f ( t ) is a function from ℝ to ℝ , then the radius of curvature of its graph , γ ( t ) = ( t , f ( t )) , is
ρ ( t ) = | 1 + f ′ 2 ( t ) | 3 2 | f ″ ( t ) | . {\displaystyle \rho (t)={\frac {\left|1+f'^{\,2}(t)\right|^{\frac {3}{2}}}{\left|f''(t)\right|}}.}
Let γ be as above, and fix t . We want to find the radius ρ of a parametrized circle which matches γ in its zeroth, first, and second derivatives at t . Clearly the radius will not depend on the position γ ( t ) , only on the velocity γ ′( t ) and acceleration γ ″( t ) . There are only three independent scalars that can be obtained from two vectors v and w , namely v · v , v · w , and w · w . Thus the radius of curvature must be a function of the three scalars | γ ′( t ) | 2 , | γ ″( t ) | 2 and γ ′( t ) · γ ″( t ) . [ 3 ]
The general equation for a parametrized circle in ℝ n is
g ( u ) = a cos ( h ( u ) ) + b sin ( h ( u ) ) + c {\displaystyle \mathbf {g} (u)=\mathbf {a} \cos(h(u))+\mathbf {b} \sin(h(u))+\mathbf {c} }
where c ∈ ℝ n is the center of the circle (irrelevant since it disappears in the derivatives), a , b ∈ ℝ n are perpendicular vectors of length ρ (that is, a · a = b · b = ρ 2 and a · b = 0 ), and h : ℝ → ℝ is an arbitrary function which is twice differentiable at t .
The relevant derivatives of g work out to be
| g ′ | 2 = ρ 2 ( h ′ ) 2 g ′ ⋅ g ″ = ρ 2 h ′ h ″ | g ″ | 2 = ρ 2 ( ( h ′ ) 4 + ( h ″ ) 2 ) {\displaystyle {\begin{aligned}|\mathbf {g} '|^{2}&=\rho ^{2}(h')^{2}\\\mathbf {g} '\cdot \mathbf {g} ''&=\rho ^{2}h'h''\\|\mathbf {g} ''|^{2}&=\rho ^{2}\left((h')^{4}+(h'')^{2}\right)\end{aligned}}}
If we now equate these derivatives of g to the corresponding derivatives of γ at t we obtain
| γ ′ ( t ) | 2 = ρ 2 h ′ 2 ( t ) γ ′ ( t ) ⋅ γ ″ ( t ) = ρ 2 h ′ ( t ) h ″ ( t ) | γ ″ ( t ) | 2 = ρ 2 ( h ′ 4 ( t ) + h ″ 2 ( t ) ) {\displaystyle {\begin{aligned}|{\boldsymbol {\gamma }}'(t)|^{2}&=\rho ^{2}h'^{\,2}(t)\\{\boldsymbol {\gamma }}'(t)\cdot {\boldsymbol {\gamma }}''(t)&=\rho ^{2}h'(t)h''(t)\\|{\boldsymbol {\gamma }}''(t)|^{2}&=\rho ^{2}\left(h'^{\,4}(t)+h''^{\,2}(t)\right)\end{aligned}}}
These three equations in three unknowns ( ρ , h ′( t ) and h ″( t ) ) can be solved for ρ , giving the formula for the radius of curvature:
ρ ( t ) = | γ ′ ( t ) | 3 | γ ′ ( t ) | 2 | γ ″ ( t ) | 2 − ( γ ′ ( t ) ⋅ γ ″ ( t ) ) 2 , {\displaystyle \rho (t)={\frac {\left|{\boldsymbol {\gamma }}'(t)\right|^{3}}{\sqrt {\left|{\boldsymbol {\gamma }}'(t)\right|^{2}\,\left|{\boldsymbol {\gamma }}''(t)\right|^{2}-{\big (}{\boldsymbol {\gamma }}'(t)\cdot {\boldsymbol {\gamma }}''(t){\big )}^{2}}}}\,,}
or, omitting the parameter t for readability,
ρ = | γ ′ | 3 | γ ′ | 2 | γ ″ | 2 − ( γ ′ ⋅ γ ″ ) 2 . {\displaystyle \rho ={\frac {\left|{\boldsymbol {\gamma }}'\right|^{3}}{\sqrt {\left|{\boldsymbol {\gamma }}'\right|^{2}\;\left|{\boldsymbol {\gamma }}''\right|^{2}-\left({\boldsymbol {\gamma }}'\cdot {\boldsymbol {\gamma }}''\right)^{2}}}}\,.}
For a semi-circle of radius a in the upper half-plane with R = | − a | = a , {\textstyle R=|-a|=a\,,}
y = a 2 − x 2 y ′ = − x a 2 − x 2 y ″ = − a 2 ( a 2 − x 2 ) 3 2 . {\displaystyle {\begin{aligned}y&={\sqrt {a^{2}-x^{2}}}\\y'&={\frac {-x}{\sqrt {a^{2}-x^{2}}}}\\y''&={\frac {-a^{2}}{\left(a^{2}-x^{2}\right)^{\frac {3}{2}}}}\,.\end{aligned}}}
For a semi-circle of radius a in the lower half-plane y = − a 2 − x 2 . {\displaystyle y=-{\sqrt {a^{2}-x^{2}}}\,.}
The circle of radius a has a radius of curvature equal to a .
In an ellipse with major axis 2 a and minor axis 2 b , the vertices on the major axis have the smallest radius of curvature of any points, R = b 2 a {\textstyle R={b^{2} \over a}} ; and the vertices on the minor axis have the largest radius of curvature of any points, R = a 2 / b .
The radius of curvature of an ellipse as a function of the geocentric coordinate t {\displaystyle t} with tan t = y x {\displaystyle \tan t={\frac {y}{x}}} is R ( t ) = ( b 2 cos 2 t + a 2 sin 2 t ) 3 / 2 a b . {\displaystyle R(t)={\frac {(b^{2}\cos ^{2}t+a^{2}\sin ^{2}t)^{3/2}}{ab}}.} It has its minima at t = 0 {\displaystyle t=0} and t = 180 ∘ {\displaystyle t=180^{\circ }} and its maxima at t = ± 90 ∘ {\displaystyle t=\pm 90^{\circ }} .
Stress in the semiconductor structure involving evaporated thin films usually results from the thermal expansion (thermal stress) during the manufacturing process. Thermal stress occurs because film depositions are usually made above room temperature. Upon cooling from the deposition temperature to room temperature, the difference in the thermal expansion coefficients of the substrate and the film cause thermal stress. [ 4 ]
Intrinsic stress results from the microstructure created in the film as atoms are deposited on the substrate. Tensile stress results from microvoids (small holes, considered to be defects) in the thin film, because of the attractive interaction of atoms across the voids.
The stress in thin film semiconductor structures results in the buckling of the wafers. The radius of the curvature of the stressed structure is related to stress tensor in the structure, and can be described by modified Stoney formula . [ 5 ] The topography of the stressed structure including radii of curvature can be measured using optical scanner methods. The modern scanner tools have capability to measure full topography of the substrate and to measure both principal radii of curvature, while providing the accuracy of the order of 0.1% for radii of curvature of 90 meters and more. [ 6 ] | https://en.wikipedia.org/wiki/Radius_of_curvature |
The radius of gyration or gyradius of a body about the axis of rotation is defined as the radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass, if the total mass of the body were concentrated there. The radius of gyration has dimensions of distance [L] or [M 0 LT 0 ] and the SI unit is the metre (m).
Mathematically the radius of gyration is the root mean square distance of the object's parts from either its center of mass or a given axis, depending on the relevant application. It is actually the perpendicular distance from point mass to the axis of rotation. One can represent a trajectory of a moving point as a body. Then radius of gyration can be used to characterize the typical distance travelled by this point.
Suppose a body consists of n {\displaystyle n} particles each of mass m {\displaystyle m} . Let r 1 , r 2 , r 3 , … , r n {\displaystyle r_{1},r_{2},r_{3},\dots ,r_{n}} be their perpendicular distances from the axis of rotation. Then, the moment of inertia I {\displaystyle I} of the body about the axis of rotation is
If all the masses are the same ( m {\displaystyle m} ), then the moment of inertia is I = m ( r 1 2 + r 2 2 + ⋯ + r n 2 ) {\displaystyle I=m(r_{1}^{2}+r_{2}^{2}+\cdots +r_{n}^{2})} .
Since m = M / n {\displaystyle m=M/n} ( M {\displaystyle M} being the total mass of the body),
From the above equations, we have
Radius of gyration is the root mean square distance of particles from axis formula
Therefore, the radius of gyration of a body about a given axis may also be defined as the root mean square distance of the various particles of the body from the axis of rotation. It is also known as a measure of the way in which the mass of a rotating rigid body is distributed about its axis of rotation.
Radius of gyration (in polymer science)( s {\displaystyle s} , unit: nm or SI unit: m): For a macromolecule composed of n {\displaystyle n} mass elements, of masses m i {\displaystyle m_{i}} , i {\displaystyle i} =1,2,…, n {\displaystyle n} , located at fixed distances s i {\displaystyle s_{i}} from the centre of mass, the radius of gyration is the square-root of the mass average of s i 2 {\displaystyle s_{i}^{2}} over all mass elements, i.e.,
Note: The mass elements are usually taken as the masses of the skeletal groups constituting the macromolecule, e.g., –CH 2 – in poly(methylene). [ 1 ]
In structural engineering , the two-dimensional radius of gyration is used to describe the distribution of cross sectional area in a column around its centroidal axis with the mass of the body. The radius of gyration is given by the following formula:
Where I {\displaystyle I} is the second moment of area and A {\displaystyle A} is the total cross-sectional area.
The gyration radius is useful in estimating the stiffness of a column. If the principal moments of the two-dimensional gyration tensor are not equal, the column will tend to buckle around the axis with the smaller principal moment. For example, a column with an elliptical cross-section will tend to buckle in the direction of the smaller semiaxis.
In engineering , where continuous bodies of matter are generally the objects of study, the radius of gyration is usually calculated as an integral.
The radius of gyration about a given axis ( r g axis {\displaystyle r_{\mathrm {g} {\text{ axis}}}} ) can be calculated in terms of the mass moment of inertia I axis {\displaystyle I_{\text{axis}}} around that axis, and the total mass m ;
I axis {\displaystyle I_{\text{axis}}} is a scalar , and is not the moment of inertia tensor . [ 2 ]
In polymer physics , the radius of gyration is used to describe the dimensions of a polymer chain . The radius of gyration of an individual homopolymer with degree of polymerization N at a given time is defined as: [ 3 ]
where r m e a n {\displaystyle \mathbf {r} _{\mathrm {mean} }} is the mean position of the monomers.
As detailed below, the radius of gyration is also proportional to the root mean square distance between the monomers:
As a third method, the radius of gyration can also be computed by summing the principal moments of the gyration tensor .
Since the chain conformations of a polymer sample are quasi infinite in number and constantly change over time, the "radius of gyration" discussed in polymer physics must usually be understood as a mean over all polymer molecules of the sample and over time. That is, the radius of gyration which is measured as an average over time or ensemble :
where the angular brackets ⟨ … ⟩ {\displaystyle \langle \ldots \rangle } denote the ensemble average .
An entropically governed polymer chain (i.e. in so called theta conditions) follows a random walk in three dimensions. The radius of gyration for this case is given by
Note that although a N {\displaystyle aN} represents the contour length of the polymer, a {\displaystyle a} is strongly dependent of polymer stiffness and can vary over orders of magnitude. N {\displaystyle N} is reduced accordingly.
One reason that the radius of gyration is an interesting property is that it can be determined experimentally with static light scattering as well as with small angle neutron- and x-ray scattering . This allows theoretical polymer physicists to check their models against reality.
The hydrodynamic radius is numerically similar, and can be measured with Dynamic Light Scattering (DLS).
To show that the two definitions of R g 2 {\displaystyle R_{\mathrm {g} }^{2}} are identical,
we first multiply out the summand in the first definition:
Carrying out the summation over the last two terms and using the definition of r m e a n {\displaystyle \mathbf {r} _{\mathrm {mean} }} gives the formula
On the other hand, the second definition can be calculated in the same way as follows.
Thus, the two definitions are the same.
The last transformation uses the relationship
In data analysis, the radius of gyration is used to calculate many different statistics including the spread of geographical locations. These locations have recently been collected from social media users to investigate the typical mentions of a user. This can be useful for understanding how a certain group of users on social media use the platform. | https://en.wikipedia.org/wiki/Radius_of_gyration |
A decimal separator is a symbol that separates the integer part from the fractional part of a number written in decimal form. Different countries officially designate different symbols for use as the separator. The choice of symbol can also affect the choice of symbol for the thousands separator used in digit grouping.
Any such symbol can be called a decimal mark , decimal marker , or decimal sign . Symbol-specific names are also used; decimal point and decimal comma refer to a dot (either baseline or middle ) and comma respectively, when it is used as a decimal separator; these are the usual terms used in English, [ 1 ] [ 2 ] [ 3 ] with the aforementioned generic terms reserved for abstract usage. [ 4 ] [ 5 ]
In many contexts, when a number is spoken, the function of the separator is assumed by the spoken name of the symbol: comma or point in most cases. [ 6 ] [ 2 ] [ 7 ] In some specialized contexts, the word decimal is instead used for this purpose (such as in International Civil Aviation Organization -regulated air traffic control communications). In mathematics, the decimal separator is a type of radix point , a term that also applies to number systems with bases other than ten.
In the Middle Ages , before printing, a bar ( ¯ ) over the units digit was used to separate the integral part of a number from its fractional part , as in 9 9 95 (meaning 99.95 in decimal point format). A similar notation remains in common use as an underbar to superscript digits, especially for monetary values without a decimal separator, as in 99 95 . Later, a "separatrix" (i.e., a short, roughly vertical ink stroke) between the units and tenths position became the norm among Arab mathematicians (e.g. 99 ˌ 95), while an L-shaped or vertical bar (|) served as the separatrix in England. [ 8 ] When this character was typeset , it was convenient to use the existing comma (99 , 95) or full stop (99 . 95) instead.
Positional decimal fractions appear for the first time in a book by the Arab mathematician Abu'l-Hasan al-Uqlidisi written in the 10th century. [ 9 ] The practice is ultimately derived from the decimal Hindu–Arabic numeral system used in Indian mathematics , [ 10 ] and popularized by the Persian mathematician Al-Khwarizmi , [ 11 ] when Latin translation of his work on the Indian numerals introduced the decimal positional number system to the Western world. His Compendious Book on Calculation by Completion and Balancing presented the first systematic solution of linear and quadratic equations in Arabic.
Gerbert of Aurillac marked triples of columns with an arc (called a "Pythagorean arc"), when using his Hindu–Arabic numeral-based abacus in the 10th century. Fibonacci followed this convention when writing numbers, such as in his influential work Liber Abaci in the 13th century. [ 12 ]
The earliest known record of using the decimal point is in the astronomical tables compiled by the Italian merchant and mathematician Giovanni Bianchini in the 1440s. [ 13 ] [ contradictory ]
Tables of logarithms prepared by John Napier in 1614 and 1619 used the period (full stop) as the decimal separator, which was then adopted by Henry Briggs in his influential 17th century work.
In France , the full stop was already in use in printing to make Roman numerals more readable, so the comma was chosen. [ 14 ]
Many other countries, such as Italy, also chose to use the comma to mark the decimal units position. [ 14 ] It has been made standard by the ISO for international blueprints. [ 15 ] However, English-speaking countries took the comma to separate sequences of three digits. In some countries, a raised dot or dash ( upper comma ) may be used for grouping or decimal separator; this is particularly common in handwriting.
In the United States , the full stop or period (.) is used as the standard decimal separator.
In the nations of the British Empire (and, later, the Commonwealth of Nations ), the full stop could be used in typewritten material and its use was not banned, although the interpunct (a.k.a. decimal point, point or mid dot) was preferred as a decimal separator, in printing technologies that could accommodate it, e.g. 99·95 . [ 17 ] However, as the mid dot was already in common use in the mathematics world to indicate multiplication, the SI rejected its use as the decimal separator.
During the beginning of British metrication in the late 1960s and with impending currency decimalisation , there was some debate in the United Kingdom as to whether the decimal comma or decimal point should be preferred: the British Standards Institution and some sectors of industry advocated the comma and the Decimal Currency Board advocated for the point. In the event, the point was chosen by the Ministry of Technology in 1968. [ 18 ]
When South Africa adopted the metric system , it adopted the comma as its decimal separator, [ 19 ] although a number of house styles, including some English-language newspapers such as The Sunday Times , continue to use the full stop. [ citation needed ]
Previously, signs along California roads expressed distances in decimal numbers with the decimal part in superscript, as in 3 7 , meaning 3.7. [ 20 ] Though California has since transitioned to mixed numbers with common fractions , the older style remains on postmile markers and bridge inventory markers.
The three most spoken international auxiliary languages , Ido , Esperanto , and Interlingua , all use the comma as the decimal separator.
Interlingua has used the comma as its decimal separator since the publication of the Interlingua Grammar in 1951. [ 21 ]
Esperanto also uses the comma as its official decimal separator, whilst thousands are usually separated by non-breaking spaces (e.g. 12 345 678,9 ). It is possible to separate thousands by a full stop (e.g. 12.345.678,9 ), though this is not as common. [ 22 ]
Ido's Kompleta Gramatiko Detaloza di la Linguo Internaciona Ido (Complete Detailed Grammar of the International Language Ido) officially states that commas are used for the decimal separator whilst full stops are used to separate thousands, millions, etc. So the number 12,345,678.90123 (in American notation), for instance, would be written 12.345.678,90123 in Ido.
The 1931 grammar of Volapük uses the comma as its decimal separator but, somewhat unusually, the middle dot as its thousands separator (12·345·678,90123). [ 23 ]
In 1958, disputes between European and American delegates over the correct representation of the decimal separator nearly stalled the development of the ALGOL computer programming language. [ 24 ] ALGOL ended up allowing different decimal separators, but most computer languages and standard data formats (e.g., C , Java , Fortran , Cascading Style Sheets (CSS) ) specify a dot. C++ and a couple of others permit a quote (') as thousands separator, and many others like Python and Julia, (only) allow '_' as such a separator (it's usually ignored, i.e. also allows 1_00_00_000 aligning with the Indian number style of 1,00,00,000 that would be 10,000,000 in the US).
In mathematics and computing , a radix point or radix character is a symbol used in the display of numbers to separate the integer part of the value from its fractional part . In English and many other languages (including many that are written right-to-left), the integer part is at the left of the radix point, and the fraction part at the right of it. [ 25 ]
A radix point is most often used in decimal (base 10) notation, when it is more commonly called the decimal point (the prefix deci- implying base 10 ). In English-speaking countries , the decimal point is usually a small dot (.) placed either on the baseline, or halfway between the baseline and the top of the digits ( · ) [ 26 ] [ a ] In many other countries, the radix point is a comma (,) placed on the baseline. [ 26 ] [ a ]
These conventions are generally used both in machine displays ( printing , computer monitors ) and in handwriting . It is important to know which notation is being used when working in different software programs. The respective ISO standard defines both the comma and the small dot as decimal markers, but does not explicitly define universal radix marks for bases other than 10.
Fractional numbers are rarely displayed in other number bases , but, when they are, a radix character may be used for the same purpose. When used with the binary ( base 2 ) representation, it may be called "binary point".
The 22nd General Conference on Weights and Measures [ 27 ] declared in 2003, "The symbol for the decimal marker shall be either the point on the line or the comma on the line." It further reaffirmed, [ 27 ]
Numbers may be divided in groups of three in order to facilitate reading; neither dots nor commas are ever inserted in the spaces between groups
That is, " 1 000 000 000 " is preferred over "1,000,000,000" or "1.000.000.000". This use has therefore been recommended by technical organizations, such as the United States's National Institute of Standards and Technology . [ 28 ]
Past versions of ISO 8601 , but not the 2019 revision, also stipulated normative notation based on SI conventions, adding that the comma is preferred over the full stop. [ 29 ]
ISO 80000-1 stipulates, "The decimal sign is either a comma or a point on the line." The standard does not stipulate any preference, observing that usage will depend on customary usage in the language concerned, but adds a note that as per ISO/IEC directives, all ISO standards should use the comma as the decimal marker.
For ease of reading, numbers with many digits (e.g. numbers over 999) may be divided into groups using a delimiter , [ 30 ] such as comma ( , ), dot ( . ), half-space or thin space ( " " ), space ( " " ), underscore ( _ ; as in maritime "21_450"), [ citation needed ] or apostrophe ( ' ). In some countries, these "digit group separators" are only employed to the left of the decimal separator; in others, they are also used to separate numbers with a long fractional part . An important reason for grouping is that it allows rapid judgement of the number of digits, via telling at a glance (" subitizing ") rather than counting (contrast, for example, 100 000 000 with 100000000 for one hundred million).
The use of thin spaces as separators [ 31 ] : 133 instead of dots or commas (for example: 20 000 and 1 000 000 for "twenty thousand" and "one million"), has been official policy of the International Bureau of Weights and Measures (BIPM) since 1948 (and reaffirmed in 2003), [ 27 ] as well as of the International Union of Pure and Applied Chemistry (IUPAC), [ 32 ] [ 33 ] the American Medical Association 's widely followed AMA Manual of Style , and the UK Metrication Board , among others.
The groups created by the delimiters tend to follow the usages of local languages, which vary. In European languages, large numbers are read in groups of thousands, and the delimiter (occuring every three digits when used) may be called a "thousands separator". In East Asian cultures , particularly China , Japan , and Korea , large numbers are read in groups of myriads ( 10 000s ), but the delimiter often separates the digits into groups of three. [ citation needed ]
The Indian numbering system is more complex: it groups the rightmost three digits together (until the hundreds place) and then groups digits in sets of two. For example, one trillion would be written "10,00,00,00,00,000" or " 10 kharab ". [ 34 ]
The convention for digit group separators historically varied among countries, but usually sought to distinguish the delimiter from the decimal separator. Traditionally, English-speaking countries (except South Africa) [ 35 ] employed commas as the delimiter – 10,000 – and other European countries employed periods or spaces: 10.000 or 10 000 . Because of the confusion that could result in international documents, in recent years, the use of spaces as separators has been advocated by the superseded SI/ISO 31-0 standard , [ 36 ] as well as by the BIPM and IUPAC. These groups have also begun advocating the use of a "thin space" in "groups of three". [ 32 ] [ 33 ]
Within the United States, the American Medical Association's widely followed AMA Manual of Style also calls for a thin space. [ 30 ] In programming languages and online encoding environments (for example, ASCII -only languages and environments) a thin space is not practical or available. Often, either underscores [ 37 ] and regular word spaces, or no delimiters at all are used instead.
Digit group separators can occur either as part of the data or as a mask through which the data is displayed. This is an example of the separation of presentation and content , making it possible to display numbers in spaced groups while not inserting any whitespace characters into the string of digits that make up those numbers. In many computing contexts, it is preferred to omit the digit group separators from the data and instead overlay them as a mask (an input mask or an output mask).
Common examples include spreadsheets and databases , in which currency values are entered without such marks but are displayed with them inserted. Similarly, phone numbers can have hyphens, spaces or parentheses as a mask rather than as data. In web content , digit grouping can be done with CSS . This is useful because the number can be copied and pasted elsewhere (such as into a calculator) and parsed by the computer as-is (i.e., without the user manually purging the extraneous characters). For example:
In some programming languages , it is possible to group the digits in the program's source code to make it easier to read (see: Integer literal § Digit separators ) . Examples include: Ada , C# (since version 7.0 ), [ 38 ] D , Go (since version 1.13 ), Haskell (from GHC version 8.6.1 ), Java , JavaScript (since ES2021 ), Kotlin , [ 39 ] OCaml , Perl , Python (since version 3.6 ), PHP (since version 7.4 ), [ 40 ] Ruby , Rust and Zig .
Java, JavaScript, Swift , Julia and free-form Fortran 90 use the underscore ( _ ) character for this purpose. As such, these languages would allow the number seven hundred million to be entered as "700_000_000". On the other hand, fixed-form Fortran ignores whitespace in all contexts, so " 700 000 000 " would be allowed. In C++14 , Rebol and Red , the use of an apostrophe for digit grouping is allowed. Thus, "700'000'000" would be allowed in those languages.
The code shown below, written in Kotlin, illustrates the use of separators to increase readability:
The International Bureau of Weights and Measures states that "when there are only four digits before or after the decimal marker, it is customary not to use a space to isolate a single digit." [ 32 ] Likewise, some manuals of style state that thousands separators should not be used in normal text for numbers from 1000 to 9999 where no decimal fractional part is shown (or, in other words, for four-digit whole numbers), whereas others use thousands separators and others use both. For example, APA style stipulates a thousands separator for "most figures of 1000 or more" except for page numbers, binary digits, temperatures, etc.
There are always "common-sense" country-specific exceptions to digit grouping, such as year numbers, postal codes , and ID numbers of predefined nongrouped format, which style guides usually point out.
In binary (base-2), a full space can be used between groups of four digits, corresponding to a nibble , or equivalently to a hexadecimal digit. For integer numbers, dots are used as well to separate groups of four bits. [ b ] Alternatively, binary digits may be grouped by threes, corresponding to an octal digit. Similarly, in hexadecimal (base-16), full spaces are usually used to group digits into twos, making each group correspond to a byte . [ c ] Additionally, groups of eight bytes are often separated by a hyphen. [ c ]
In countries with a decimal comma, the decimal point is also common as the "international" notation [ citation needed ] because of the influence of devices, such as electronic calculators , which use the decimal point. Most computer operating systems allow selection of the decimal separator; programs that have been carefully internationalized will follow this, but some programs ignore it and a few may even fail to operate if the setting has been changed.
Computer interfaces may be set to the Unicode international "Common locale" using LC_NUMERIC=C as defined at "Unicode CLDR project" . Unicode Consortium . Details of the current (2020) definitions may be found at "01102-POSIX15897" . Unicode Consortium .
Countries where a comma ( , ) is used as a decimal separator include:
Countries where a dot ( . ) is used as a decimal separator include:
Notes
Unicode defines a decimal separator key symbol (⎖ in hex U+2396, decimal 9110) which looks similar to the apostrophe . This symbol is from ISO/IEC 9995 and is intended for use on a keyboard to indicate a key that performs decimal separation.
In the Arab world , where Eastern Arabic numerals are used for writing numbers, a different character is used to separate the integer and fractional parts of numbers. It is referred to as an Arabic decimal separator (U+066B, rendered: ٫ ) in Unicode . An Arabic thousands separator (U+066C, rendered: ٬ ) also exists. Example: ۹٬۹۹۹٫۹۹ (9,999.99)
In Persian , the decimal separator is called momayyez . The Unicode Consortium's investigation concluded that "computer programs should render U+066B as a shortened, lowered, and possibly more slanted slash ( ٫ ); this should be distinguishable from the slash at the first sight." To separate sequences of three digits, an Arabic thousands separator (rendered as: ٬ ), a Latin comma, or a blank space may be used; however this is not a standard. [ 49 ] [ 50 ] [ 51 ] Example: ۹٬۹۹۹٫۹۹ (9,999.99)
In English Braille , the decimal point, ⠨ , is distinct from both the comma, ⠂ , and the full stop, ⠲ .
The following examples show the decimal separator and the thousands separator in various countries that use the Arabic numeral system.
Used with Western Arabic numerals (0123456789):
Used with Eastern Arabic numerals (٠١٢٣٤٥٦٧٨٩):
Used with keyboards: | https://en.wikipedia.org/wiki/Radix_point |
Rado's theorem is a theorem from the branch of mathematics known as Ramsey theory . It is named for the German mathematician Richard Rado . It was proved in his thesis, Studien zur Kombinatorik .
Let A x = 0 {\displaystyle A\mathbf {x} =\mathbf {0} } be a system of linear equations, where A {\displaystyle A} is a matrix with integer entries. This system is said to be r {\displaystyle r} -regular if, for every r {\displaystyle r} -coloring of the natural numbers 1, 2, 3, ..., the system has a monochromatic solution. A system is regular if it is r-regular for all r ≥ 1.
Rado's theorem states that a system A x = 0 {\displaystyle A\mathbf {x} =\mathbf {0} } is regular if and only if the matrix A satisfies the columns condition . Let c i denote the i -th column of A . The matrix A satisfies the columns condition provided that there exists a partition C 1 , C 2 , ..., C n of the column indices such that if s i = Σ j ∈ C i c j {\displaystyle s_{i}=\Sigma _{j\in C_{i}}c_{j}} , then
Folkman's theorem , the statement that there exist arbitrarily large sets of integers all of whose nonempty sums are monochromatic, may be seen as a special case of Rado's theorem concerning the regularity of the system of equations
where T ranges over each nonempty subset of the set {1, 2, ..., x }. [ 2 ]
Other special cases of Rado's theorem are Schur's theorem and Van der Waerden's theorem . For proving the former apply Rado's theorem to the matrix ( 1 1 − 1 ) {\displaystyle (1\ 1\ {-1})} . For Van der Waerden's theorem with m chosen to be length of the monochromatic arithmetic progression, one can for example consider the following matrix:
( 1 1 − 1 0 ⋯ 0 0 1 2 0 − 1 ⋯ 0 0 ⋮ ⋮ ⋮ ⋮ ⋱ ⋮ ⋮ 1 m − 1 0 0 ⋯ − 1 0 1 m 0 0 ⋯ 0 − 1 ) {\displaystyle \left({\begin{matrix}1&1&-1&0&\cdots &0&0\\1&2&0&-1&\cdots &0&0\\\vdots &\vdots &\vdots &\vdots &\ddots &\vdots &\vdots \\1&m-1&0&0&\cdots &-1&0\\1&m&0&0&\cdots &0&-1\end{matrix}}\right)}
Given a system of linear equations it is a priori unclear how to check computationally that it is regular. Fortunately, Rado's theorem provides a criterion which is testable in finite time. Instead of considering colourings (of infinitely many natural numbers), it must be checked that the given matrix satisfies the columns condition. Since the matrix consists only of finitely many columns, this property can be verified in finite time.
However, the subset sum problem can be reduced to the problem of computing the required partition C 1 , C 2 , ..., C n of columns: Given an input set S for the subset sum problem we can write the elements of S in a matrix of shape 1 × | S |. Then the elements of S corresponding to vectors in the partition C 1 sum to zero. The subset sum problem is NP-complete . Hence, verifying that a system of linear equations is regular is also an NP-complete problem. | https://en.wikipedia.org/wiki/Rado's_theorem_(Ramsey_theory) |
Radon is a chemical element ; it has symbol Rn and atomic number 86. It is a radioactive noble gas and is colorless and odorless. Of the three naturally occurring radon isotopes , only 222 Rn has a sufficiently long half-life (3.825 days) for it to be released from the soil and rock where it is generated. Radon isotopes are the immediate decay products of radium isotopes. The instability of 222 Rn, its most stable isotope, makes radon one of the rarest elements. Radon will be present on Earth for several billion more years despite its short half-life, because it is constantly being produced as a step in the decay chains of 238 U and 232 Th , both of which are abundant radioactive nuclides with half-lives of at least several billion years. The decay of radon produces many other short-lived nuclides , known as "radon daughters", ending at stable isotopes of lead . [ 3 ] 222 Rn occurs in significant quantities as a step in the normal radioactive decay chain of 238 U, also known as the uranium series , which slowly decays into a variety of radioactive nuclides and eventually decays into stable 206 Pb . 220 Rn occurs in minute quantities as an intermediate step in the decay chain of 232 Th, also known as the thorium series , which eventually decays into stable 208 Pb .
Radon was discovered in 1899 by Ernest Rutherford and Robert B. Owens at McGill University in Montreal , and was the fifth radioactive element to be discovered. First known as "emanation", the radioactive gas was identified during experiments with radium, thorium oxide, and actinium by Friedrich Ernst Dorn , Rutherford and Owens, and André-Louis Debierne , respectively, and each element's emanation was considered to be a separate substance: radon, thoron, and actinon. Sir William Ramsay and Robert Whytlaw-Gray considered that the radioactive emanations may contain a new element of the noble gas family, and isolated "radium emanation" in 1909 to determine its properties. In 1911, the element Ramsay and Whytlaw-Gray isolated was accepted by the International Commission for Atomic Weights , and in 1923, the International Committee for Chemical Elements and the International Union of Pure and Applied Chemistry (IUPAC) chose radon as the accepted name for the element's most stable isotope, 222 Rn; thoron and actinon were also recognized by IUPAC as distinct isotopes of the element. [ 4 ]
Under standard conditions, radon is gaseous and can be easily inhaled, posing a health hazard. However, the primary danger comes not from radon itself, but from its decay products, known as radon daughters. These decay products, often existing as single atoms or ions, can attach themselves to airborne dust particles. Although radon is a noble gas and does not adhere to lung tissue (meaning it is often exhaled before decaying), the radon daughters attached to dust are more likely to stick to the lungs. This increases the risk of harm, as the radon daughters can cause damage to lung tissue. [ 5 ] Radon and its daughters are, taken together, often the single largest contributor to an individual's background radiation dose, but due to local differences in geology, [ 6 ] the level of exposure to radon gas differs by location. A common source of environmental radon is uranium-containing minerals in the ground; it therefore accumulates in subterranean areas such as basements. Radon can also occur in ground water, such as spring waters and hot springs. [ 7 ] Radon trapped in permafrost may be released by climate-change -induced thawing of permafrosts , [ 8 ] and radon may also be released into groundwater and the atmosphere following seismic events leading to earthquakes , which has led to its investigation in the field of earthquake prediction . [ 9 ] It is possible to test for radon in buildings, and to use techniques such as sub-slab depressurization for mitigation . [ 10 ] [ 11 ]
Epidemiological studies have shown a clear association between breathing high concentrations of radon and incidence of lung cancer . [ 12 ] Radon is a contaminant that affects indoor air quality worldwide. According to the United States Environmental Protection Agency (EPA), radon is the second most frequent cause of lung cancer, after cigarette smoking, causing 21,000 lung cancer deaths per year in the United States. About 2,900 of these deaths occur among people who have never smoked. While radon is the second most frequent cause of lung cancer, it is the number one cause among non-smokers, according to EPA policy-oriented estimates. [ 13 ] Significant uncertainties exist for the health effects of low-dose exposures. [ 14 ]
Radon is a colorless, odorless, and tasteless [ 15 ] gas and therefore is not detectable by human senses alone. At standard temperature and pressure , it forms a monatomic gas with a density of 9.73 kg/m 3 , about 8 times the density of the Earth's atmosphere at sea level, 1.217 kg/m 3 . [ 16 ] It is one of the densest gases at room temperature (a few are denser, e.g. CF 3 (CF 2 ) 2 CF 3 and WF 6 ) and is the densest of the noble gases. Although colorless at standard temperature and pressure, when cooled below its freezing point of 202 K (−71 °C; −96 °F), it emits a brilliant radioluminescence that turns from yellow to orange-red as the temperature lowers. [ 17 ] Upon condensation , it glows because of the intense radiation it produces. [ 18 ] It is sparingly soluble in water, but more soluble than lighter noble gases. It is appreciably more soluble in organic liquids than in water. Its solubility equation is as follows: [ 19 ]
where χ {\displaystyle \chi } is the molar fraction of radon, T {\displaystyle T} is the absolute temperature, and A {\displaystyle A} and B {\displaystyle B} are solvent constants.
Radon is a member of the zero- valence elements that are called noble gases, and is chemically not very reactive . The inert pair effect stabilizes the 6s shell, making it unavailable for bonding—a consequence only understood within relativistic quantum chemistry . [ 20 ] : 66 The 3.8-day half-life of 222 Rn makes it useful in physical sciences as a natural tracer . Because radon is a gas at standard conditions, unlike its decay-chain parents, it can readily be extracted from them for research. [ 21 ]
It is inert to most common chemical reactions, such as combustion , because the outer valence shell contains eight electrons . This produces a stable, minimum energy configuration in which the outer electrons are tightly bound. [ 22 ] Its first ionization energy —the minimum energy required to extract one electron from it—is 1037 kJ/mol. [ 23 ] In accordance with periodic trends , radon has a lower electronegativity than the element one period before it, xenon , and is therefore more reactive. Early studies concluded that the stability of radon hydrate should be of the same order as that of the hydrates of chlorine ( Cl 2 ) or sulfur dioxide ( SO 2 ), and significantly higher than the stability of the hydrate of hydrogen sulfide ( H 2 S ). [ 24 ]
Because of its cost and radioactivity, experimental chemical research is seldom performed with radon, and as a result there are very few reported compounds of radon, all either fluorides or oxides . Radon can be oxidized by powerful oxidizing agents such as fluorine , thus forming radon difluoride ( RnF 2 ). [ 25 ] It decomposes back to its elements at a temperature of above 523 K (250 °C; 482 °F), and is reduced by water to radon gas and hydrogen fluoride: it may also be reduced back to its elements by hydrogen gas. [ 26 ] It has a low volatility and was thought to be RnF 2 . Because of the short half-life of radon and the radioactivity of its compounds, it has not been possible to study the compound in any detail. Theoretical studies on this molecule predict that it should have a Rn–F bond distance of 2.08 ångströms (Å), and that the compound is thermodynamically more stable and less volatile than its lighter counterpart xenon difluoride ( XeF 2 ). [ 27 ] The octahedral molecule RnF 6 was predicted to have an even lower enthalpy of formation than the difluoride. [ 28 ] The [RnF] + ion is believed to form by the following reaction: [ 29 ]
For this reason, antimony pentafluoride together with chlorine trifluoride and N 2 F 2 Sb 2 F 11 have been considered for radon gas removal in uranium mines due to the formation of radon–fluorine compounds. [ 21 ] Radon compounds can be formed by the decay of radium in radium halides, a reaction that has been used to reduce the amount of radon that escapes from targets during irradiation . [ 26 ] Additionally, salts of the [RnF] + cation with the anions SbF − 6 , TaF − 6 , and BiF − 6 are known. [ 26 ] Radon is also oxidised by dioxygen difluoride to RnF 2 at 173 K (−100 °C; −148 °F). [ 26 ]
Radon oxides are among the few other reported compounds of radon ; [ 30 ] only the trioxide ( RnO 3 ) has been confirmed. [ 31 ] > The higher fluorides RnF 4 and RnF 6 have been claimed, are calculated to be stable, but have not been confirmed. [ 20 ] They may have been observed in experiments where unknown radon-containing products distilled together with xenon hexafluoride : these may have been RnF 4 , RnF 6 , or both. [ 26 ] Trace-scale heating of radon with xenon, fluorine, bromine pentafluoride , and either sodium fluoride or nickel fluoride was claimed to produce a higher fluoride as well which hydrolysed to form RnO 3 . While it has been suggested that these claims were really due to radon precipitating out as the solid complex [RnF] + 2 [NiF 6 ] 2− , the fact that radon coprecipitates from aqueous solution with CsXeO 3 F has been taken as confirmation that RnO 3 was formed, which has been supported by further studies of the hydrolysed solution. That [RnO 3 F] − did not form in other experiments may have been due to the high concentration of fluoride used. Electromigration studies also suggest the presence of cationic [HRnO 3 ] + and anionic [HRnO 4 ] − forms of radon in weakly acidic aqueous solution (pH > 5), the procedure having previously been validated by examination of the homologous xenon trioxide. [ 31 ]
The decay technique has also been used. Avrorin et al. reported in 1982 that 212 Fr compounds cocrystallised with their caesium analogues appeared to retain chemically bound radon after electron capture; analogies with xenon suggested the formation of RnO 3 , but this could not be confirmed. [ 32 ]
It is likely that the difficulty in identifying higher fluorides of radon stems from radon being kinetically hindered from being oxidised beyond the divalent state because of the strong ionicity of radon difluoride ( RnF 2 ) and the high positive charge on radon in RnF + ; spatial separation of RnF 2 molecules may be necessary to clearly identify higher fluorides of radon, of which RnF 4 is expected to be more stable than RnF 6 due to spin–orbit splitting of the 6p shell of radon (Rn IV would have a closed-shell 6s 2 6p 2 1/2 configuration). Therefore, while RnF 4 should have a similar stability to xenon tetrafluoride ( XeF 4 ), RnF 6 would likely be much less stable than xenon hexafluoride ( XeF 6 ): radon hexafluoride would also probably be a regular octahedral molecule, unlike the distorted octahedral structure of XeF 6 , because of the inert pair effect . [ 33 ] [ 34 ] Because radon is quite electropositive for a noble gas, it is possible that radon fluorides actually take on highly fluorine-bridged structures and are not volatile. [ 34 ] Extrapolation down the noble gas group would suggest also the possible existence of RnO, RnO 2 , and RnOF 4 , as well as the first chemically stable noble gas chlorides RnCl 2 and RnCl 4 , but none of these have yet been found. [ 26 ]
Radon carbonyl (RnCO) has been predicted to be stable and to have a linear molecular geometry . [ 35 ] The molecules Rn 2 and RnXe were found to be significantly stabilized by spin-orbit coupling . [ 36 ] Radon caged inside a fullerene has been proposed as a drug for tumors . [ 37 ] Despite the existence of Xe(VIII), no Rn(VIII) compounds have been claimed to exist; RnF 8 should be highly unstable chemically [ 20 ] (XeF 8 is thermodynamically unstable).
Radon reacts with the liquid halogen fluorides ClF, ClF 3 , ClF 5 , BrF 3 , BrF 5 , and IF 7 to form RnF 2 . In halogen fluoride solution, radon is nonvolatile and exists as the RnF + and Rn 2+ cations; addition of fluoride anions results in the formation of the complexes RnF − 3 and RnF 2− 4 , paralleling the chemistry of beryllium (II) and aluminium (III). [ 26 ] The standard electrode potential of the Rn 2+ /Rn couple has been estimated as +2.0 V, [ 38 ] although there is no evidence for the formation of stable radon ions or compounds in aqueous solution. [ 26 ]
Radon has no stable isotopes . Thirty-nine radioactive isotopes have been characterized, with mass numbers ranging from 193 to 231. [ 39 ] [ 40 ] Six of them, from 217 to 222 inclusive, occur naturally. The most stable isotope is 222 Rn (half-life 3.82 days), which is a decay product of 226 Ra , the latter being itself a decay product of 238 U . [ 41 ] A trace amount of the (highly unstable) isotope 218 Rn (half-life about 35 milliseconds ) is also among the daughters of 222 Rn. The isotope 216 Rn would be produced by the double beta decay of natural 216 Po; while energetically possible, this process has however never been seen. [ 42 ]
Three other radon isotopes have a half-life of over an hour: 211 Rn (about 15 hours), 210 Rn (2.4 hours) and 224 Rn (about 1.8 hours). However, none of these three occur naturally. 220 Rn, also called thoron, is a natural decay product of the most stable thorium isotope ( 232 Th). It has a half-life of 55.6 seconds and also emits alpha radiation . Similarly, 219 Rn is derived from the most stable isotope of actinium ( 227 Ac)—named "actinon"—and is an alpha emitter with a half-life of 3.96 seconds. [ 39 ]
222 Rn belongs to the radium and uranium-238 decay chain, and has a half-life of 3.8235 days. Its first four products (excluding marginal decay schemes ) are very short-lived, meaning that the corresponding disintegrations are indicative of the initial radon distribution. Its decay goes through the following sequence: [ 39 ]
The radon equilibrium factor [ 43 ] is the ratio between the activity of all short-period radon progenies (which are responsible for most of radon's biological effects), and the activity that would be at equilibrium with the radon parent.
If a closed volume is constantly supplied with radon, the concentration of short-lived isotopes will increase until an equilibrium is reached where the overall decay rate of the decay products equals that of the radon itself. The equilibrium factor is 1 when both activities are equal, meaning that the decay products have stayed close to the radon parent long enough for the equilibrium to be reached, within a couple of hours. Under these conditions, each additional pCi/L of radon will increase exposure by 0.01 working level (WL, a measure of radioactivity commonly used in mining). These conditions are not always met; in many homes, the equilibrium factor is typically 40%; that is, there will be 0.004 WL of daughters for each pCi/L of radon in the air. [ 44 ] 210 Pb takes much longer to come in equilibrium with radon, dependent on environmental factors, [ 45 ] but if the environment permits accumulation of dust over extended periods of time, 210 Pb and its decay products may contribute to overall radiation levels as well. Several studies on the radioactive equilibrium of elements in the environment find it more useful to use the ratio of other 222 Rn decay products with 210 Pb, such as 210 Po, in measuring overall radiation levels. [ 46 ]
Because of their electrostatic charge , radon progenies adhere to surfaces or dust particles, whereas gaseous radon does not. Attachment removes them from the air, usually causing the equilibrium factor in the atmosphere to be less than 1. The equilibrium factor is also lowered by air circulation or air filtration devices, and is increased by airborne dust particles, including cigarette smoke. The equilibrium factor found in epidemiological studies is 0.4. [ 47 ]
Radon was discovered in 1899 by Ernest Rutherford and Robert B. Owens at McGill University in Montreal . [ 48 ] It was the fifth radioactive element to be discovered, after uranium, thorium, radium, and polonium. [ 49 ] [ 50 ] [ 51 ] In 1899, Pierre and Marie Curie observed that the gas emitted by radium remained radioactive for a month. [ 52 ] Later that year, Rutherford and Owens noticed variations when trying to measure radiation from thorium oxide. [ 48 ] Rutherford noticed that the compounds of thorium continuously emit a radioactive gas that remains radioactive for several minutes, and called this gas "emanation" (from Latin : emanare , to flow out, and emanatio , expiration), [ 53 ] and later "thorium emanation" ("Th Em"). In 1900, Friedrich Ernst Dorn reported some experiments in which he noticed that radium compounds emanate a radioactive gas he named "radium emanation" ("Ra Em"). [ 54 ] In 1901, Rutherford and Harriet Brooks demonstrated that the emanations are radioactive, but credited the Curies for the discovery of the element. [ 55 ] In 1903, similar emanations were observed from actinium by André-Louis Debierne , and were called "actinium emanation" ("Ac Em"). [ 56 ]
Several shortened names were soon suggested for the three emanations: exradio , exthorio , and exactinio in 1904; [ 57 ] radon (Ro), thoron (To), and akton or acton (Ao) in 1918; [ 58 ] radeon , thoreon , and actineon in 1919, [ 59 ] and eventually radon , thoron , and actinon in 1920. [ 60 ] (The name radon is not related to that of the Austrian mathematician Johann Radon .) The likeness of the spectra of these three gases with those of argon, krypton, and xenon, and their observed chemical inertia led Sir William Ramsay to suggest in 1904 that the "emanations" might contain a new element of the noble-gas family. [ 57 ]
In 1909, Ramsay and Robert Whytlaw-Gray isolated radon and determined its melting temperature and critical point . [ 61 ] Because it does not conform to expected periodic trends, their obtained melting point (the only experimental value) was questioned in 1925 by Friedrich Paneth and E. Rabinowitsch, but ab initio Monte Carlo simulations from 2018 agree almost exactly with Ramsay and Gray's result. [ 62 ] In 1910, they determined its density (that showed it was the heaviest known gas) and its position in the periodic table. [ 61 ] They wrote that " L'expression l'émanation du radium est fort incommode " ("the expression 'radium emanation' is very awkward") and suggested the new name niton (Nt) (from Latin : nitens , shining) to emphasize the radioluminescence property, [ 63 ] and in 1912 it was accepted by the International Commission for Atomic Weights . In 1923, the International Committee for Chemical Elements and International Union of Pure and Applied Chemistry (IUPAC) chose the name of the most stable isotope, radon, as the name of the element. The isotopes thoron and actinon were later renamed 220 Rn and 219 Rn. This has caused some confusion in the literature regarding the element's discovery as while Dorn had discovered radon the isotope, he was not the first to discover radon the element. [ 4 ]
As late as the 1960s, the element was also referred to simply as emanation . [ 64 ] The first synthesized compound of radon, radon fluoride, was obtained in 1962. [ 65 ] Even today, the word radon may refer to either the element or its isotope 222 Rn, with thoron remaining in use as a short name for 220 Rn to stem this ambiguity. The name actinon for 219 Rn is rarely encountered today, probably due to the short half-life of that isotope. [ 4 ]
The danger of high exposure to radon in mines, where exposures can reach 1,000,000 Bq /m 3 , has long been known. In 1530, Paracelsus described a wasting disease of miners, the mala metallorum , and Georg Agricola recommended ventilation in mines to avoid this mountain sickness ( Bergsucht ). [ 66 ] In 1879, this condition was identified as lung cancer by Harting and Hesse in their investigation of miners from Schneeberg, Germany. [ 67 ] The first major studies with radon and health occurred in the context of uranium mining in the Joachimsthal region of Bohemia . [ 68 ] In the US, studies and mitigation only followed decades of health effects on uranium miners of the Southwestern US employed during the early Cold War ; standards were not implemented until 1971. [ 69 ]
In the early 20th century in the US, gold contaminated with the radon daughter 210 Pb entered the jewelry industry. This was from gold brachytherapy seeds that had held 222 Rn, which were melted down after the radon had decayed. [ 70 ]
The presence of radon in indoor air was documented as early as 1950. Beginning in the 1970s, research was initiated to address sources of indoor radon, determinants of concentration, health effects, and mitigation approaches. In the US, the problem of indoor radon received widespread publicity and intensified investigation after a widely publicized incident in 1984. During routine monitoring at a Pennsylvania nuclear power plant, a worker was found to be contaminated with radioactivity. A high concentration of radon in his home was subsequently identified as responsible. [ 71 ] [ 67 ]
Discussions of radon concentrations in the environment refer to 222 Rn, the decay product of uranium and radium. While the average rate of production of 220 Rn (from the thorium decay series) is about the same as that of 222 Rn, the amount of 220 Rn in the environment is much less than that of 222 Rn because of the short half-life of 220 Rn (55 seconds, versus 3.8 days respectively). [ 3 ]
Radon concentration in the atmosphere is usually measured in becquerel per cubic meter (Bq/m 3 ), the SI derived unit . Another unit of measurement common in the US is picocuries per liter (pCi/L); 1 pCi/L = 37 Bq/m 3 . [ 44 ] Typical domestic exposures average about 48 Bq/m 3 indoors, though this varies widely, and 15 Bq/m 3 outdoors. [ 73 ]
In the mining industry, the exposure is traditionally measured in working level (WL), and the cumulative exposure in working level month (WLM); 1 WL equals any combination of short-lived 222 Rn daughters ( 218 Po, 214 Pb, 214 Bi, and 214 Po) in 1 liter of air that releases 1.3 × 10 5 MeV of potential alpha energy; [ 44 ] 1 WL is equivalent to 2.08 × 10 −5 joules per cubic meter of air (J/m 3 ). [ 3 ] The SI unit of cumulative exposure is expressed in joule-hours per cubic meter (J·h/m 3 ). One WLM is equivalent to 3.6 × 10 −3 J·h/m 3 . An exposure to 1 WL for 1 working-month (170 hours) equals 1 WLM cumulative exposure. The International Commission on Radiological Protection recommends an annual limit of 4.8WLM for miners. [ 74 ] : R5 Assuming 2000 hours of work per year, this corresponds to a concentration of 1500 Bq/m 3 .
222 Rn decays to 210 Pb and other radioisotopes. The levels of 210 Pb can be measured. The rate of deposition of this radioisotope is weather-dependent. [ 75 ]
Radon concentrations found in natural environments are much too low to be detected by chemical means. A 1,000 Bq/m 3 (relatively high) concentration corresponds to 0.17 picogram per cubic meter (pg/m 3 ). The average concentration of radon in the atmosphere is about 6 × 10 −18 molar percent , or about 150 atoms in each milliliter of air. [ 76 ] The radon activity of the entire Earth's atmosphere originates from only a few tens of grams of radon, consistently replaced by decay of larger amounts of radium, thorium, and uranium. [ 77 ]
Radon is produced by the radioactive decay of radium-226, which is found in uranium ores, phosphate rock, shales, igneous and metamorphic rocks such as granite, gneiss, and schist, and to a lesser degree, in common rocks such as limestone. [ 6 ] [ 78 ] Every square mile of surface soil, to a depth of 6 inches (2.6 km 2 to a depth of 15 cm), contains about 1 gram of radium, which releases radon in small amounts to the atmosphere. [ 3 ] It is estimated that 2.4 billion curies (90 EBq) of radon are released from soil annually worldwide. [ 79 ] This is equivalent to some 15.3 kilograms (34 lb).
Radon concentration can differ widely from place to place. In the open air, it ranges from 1 to 100 Bq/m 3 , even less (0.1 Bq/m 3 ) above the ocean. In caves or ventilated mines, or poorly ventilated houses, its concentration climbs to 20–2,000 Bq/m 3 . [ 80 ]
Radon concentration can be much higher in mining contexts. Ventilation regulations instruct to maintain radon concentration in uranium mines under the "working level", with 95th percentile levels ranging up to nearly 3 WL (546 pCi 222 Rn per liter of air; 20.2 kBq/m 3 , measured from 1976 to 1985). [ 3 ] The concentration in the air at the (unventilated) Gastein Healing Gallery averages 43 kBq/m 3 (1.2 nCi/L) with maximal value of 160 kBq/m 3 (4.3 nCi/L). [ 81 ]
Radon mostly appears with the radium/ uranium series (decay chain) ( 222 Rn), and marginally with the thorium series ( 220 Rn). The element emanates naturally from the ground, and some building materials, all over the world, wherever traces of uranium or thorium are found, and particularly in regions with soils containing granite or shale , which have a higher concentration of uranium. Not all granitic regions are prone to high emissions of radon. Being a rare gas, it usually migrates freely through faults and fragmented soils, and may accumulate in caves or water. Owing to its very short half-life (four days for 222 Rn), radon concentration decreases very quickly when the distance from the production area increases. Radon concentration varies greatly with season and atmospheric conditions. For instance, it has been shown to accumulate in the air if there is a meteorological inversion and little wind. [ 82 ]
High concentrations of radon can be found in some spring waters and hot springs. [ 83 ] The towns of Boulder, Montana ; Misasa ; Bad Kreuznach , Germany; and the country of Japan have radium-rich springs that emit radon. To be classified as a radon mineral water, radon concentration must be above 2 nCi/L (74 kBq/m 3 ). [ 84 ] The activity of radon mineral water reaches 2 MBq/m 3 in Merano and 4 MBq/m 3 in Lurisia (Italy). [ 81 ]
Natural radon concentrations in the Earth's atmosphere are so low that radon-rich water in contact with the atmosphere will continually lose radon by volatilization . Hence, ground water has a higher concentration of 222 Rn than surface water , because radon is continuously produced by radioactive decay of 226 Ra present in rocks. Likewise, the saturated zone of a soil frequently has a higher radon content than the unsaturated zone because of diffusional losses to the atmosphere. [ 85 ]
In 1971, Apollo 15 passed 110 km (68 mi) above the Aristarchus plateau on the Moon , and detected a significant rise in alpha particles thought to be caused by the decay of 222 Rn. The presence of 222 Rn has been inferred later from data obtained from the Lunar Prospector alpha particle spectrometer. [ 86 ]
Radon is found in some petroleum . Because radon has a similar pressure and temperature curve to propane , and oil refineries separate petrochemicals based on their boiling points, the piping carrying freshly separated propane in oil refineries can become contaminated because of decaying radon and its products. [ 87 ]
Residues from the petroleum and natural gas industry often contain radium and its daughters. The sulfate scale from an oil well can be radium rich, while the water, oil, and gas from a well often contains radon. Radon decays to form solid radioisotopes that form coatings on the inside of pipework. [ 87 ]
Measurement of radon levels in the first decades of its discovery was mainly done to determine the presence of radium and uranium in geological surveys. In 1956, most likely the first indoor survey of radon decay products was performed in Sweden, [ 88 ] with the intent of estimating the public exposure to radon and its decay products. From 1975 up until 1984, small studies in Sweden, Austria, the United States and Norway aimed to measure radon indoors and in metropolitan areas. [ 67 ]
High concentrations of radon in homes were discovered by chance in 1984 after the stringent radiation testing conducted at the new Limerick Generating Station nuclear power plant in Montgomery County, Pennsylvania, United States revealed that Stanley Watras , a construction engineer at the plant, was contaminated by radioactive substances even though the reactor had never been fueled and Watras had been decontaminated each evening. It was determined that radon levels in his home's basement were in excess of 100,000 Bq/m 3 (2.7 nCi/L); he was told that living in the home was the equivalent of smoking 135 packs of cigarettes a day, and he and his family had increased their risk of developing lung cancer by 13 or 14 percent. [ 89 ] The incident dramatized the fact that radon levels in particular dwellings can occasionally be orders of magnitude higher than typical. [ 90 ] Since the incident in Pennsylvania, millions of short-term radon measurements have been taken in homes in the United States. Outside the United States, radon measurements are typically performed over the long term. [ 67 ]
In the United States, typical domestic exposures are of approximately 100 Bq/m 3 (2.7 pCi/L) indoors. Some level of radon will be found in all buildings. Radon mostly enters a building directly from the soil through the lowest level in the building that is in contact with the ground. High levels of radon in the water supply can also increase indoor radon air levels. Typical entry points of radon into buildings are cracks in solid foundations and walls, construction joints, gaps in suspended floors and around service pipes, cavities inside walls, and the water supply. [ 15 ] Radon concentrations in the same place may differ by double/half over one hour, and the concentration in one room of a building may be significantly different from the concentration in an adjoining room. [ 3 ]
The distribution of radon concentrations will generally differ from room to room, and the readings are averaged according to regulatory protocols. Indoor radon concentration is usually assumed to follow a log-normal distribution on a given territory. [ 91 ] Thus, the geometric mean is generally used for estimating the "average" radon concentration in an area. [ 92 ] The mean concentration ranges from less than 10 Bq/m 3 to over 100 Bq/m 3 in some European countries. [ 93 ]
Some of the highest radon hazard in the US is found in Iowa and in the Appalachian Mountain areas in southeastern Pennsylvania. [ 94 ] Iowa has the highest average radon concentrations in the US due to significant glaciation that ground the granitic rocks from the Canadian Shield and deposited it as soils making up the rich Iowa farmland. [ 95 ] Many cities within the state, such as Iowa City , have passed requirements for radon-resistant construction in new homes. The second highest readings in Ireland were found in office buildings in the Irish town of Mallow, County Cork , prompting local fears regarding lung cancer. [ 96 ]
Since radon is a colorless, odorless gas, the only way to know how much is present in the air or water is to perform tests. In the US, radon test kits are available to the public at retail stores, such as hardware stores, for home use, and testing is available through licensed professionals, who are often home inspectors . Efforts to reduce indoor radon levels are called radon mitigation . In the US, the EPA recommends all houses be tested for radon. In the UK, under the Housing Health & Safety Rating System, property owners have an obligation to evaluate potential risks and hazards to health and safety in a residential property. [ 97 ] Alpha-radiation monitoring over the long term is a method of testing for radon that is more common in countries outside the United States. [ 67 ]
Radon is obtained as a by-product of uraniferous ores processing after transferring into 1% solutions of hydrochloric or hydrobromic acids . The gas mixture extracted from the solutions contains H 2 , O 2 , He, Rn, CO 2 , H 2 O and hydrocarbons . The mixture is purified by passing it over copper at 993 K (720 °C; 1,328 °F) to remove the H 2 and the O 2 , and then KOH and P 2 O 5 are used to remove the acids and moisture by sorption . Radon is condensed by liquid nitrogen and purified from residue gases by sublimation . [ 98 ]
Radon commercialization is regulated, [ citation needed ] but it is available in small quantities for the calibration of 222 Rn measurement systems. In 2008 it was priced at almost US$6,000 (equivalent to $8,763 in 2024) per milliliter of radium solution (which only contains about 15 picograms of actual radon at any given moment). [ 99 ] Radon is produced commercially by a solution of radium-226 (half-life of 1,600 years). Radium-226 decays by alpha-particle emission, producing radon that collects over samples of radium-226 at a rate of about 1 mm 3 /day per gram of radium; equilibrium is quickly achieved and radon is produced in a steady flow, with an activity equal to that of the radium (50 Bq). Gaseous 222 Rn (half-life of about four days) escapes from the capsule through diffusion . [ 100 ] Radon sources have also been produced for scientific purposes through the implantation of radium-226 into solid stainless steel . [ 101 ]
Radon trace concentration above oceans or in Antarctica can be lower than 0.1 Bq/m 3 , [ 102 ] with changes in radon levels being used to track foreign pollutants. [ 103 ]
An EPA survey [ 104 ] of 11,000 homes across the USA found an average of 46 Bq/m 3 .
An early-20th-century form of quackery was the treatment of maladies in a radiotorium . [ 108 ] It was a small, sealed room for patients to be exposed to radon for its "medicinal effects". The carcinogenic nature of radon due to its ionizing radiation became apparent later. Radon's molecule-damaging radioactivity has been used to kill cancerous cells, [ 109 ] but it does not increase the health of healthy cells. [ citation needed ] The ionizing radiation causes the formation of free radicals , which results in cell damage , causing increased rates of illness, including cancer .
Exposure to radon has been suggested to mitigate autoimmune diseases such as arthritis in a process known as radiation hormesis . [ 110 ] [ 111 ] As a result, in the late 20th century and early 21st century, "health mines" established in Basin, Montana , attracted people seeking relief from health problems such as arthritis through limited exposure to radioactive mine water and radon. The practice is discouraged because of the well-documented ill effects of high doses of radiation on the body. [ 112 ]
Radioactive water baths have been applied since 1906 in Jáchymov , Czech Republic, but even before radon discovery they were used in Bad Gastein , Austria. Radium-rich springs are also used in traditional Japanese onsen in Misasa , Tottori Prefecture . Drinking therapy is applied in Bad Brambach , Germany, and during the early 20th century, water from springs with radon in them was bottled and sold (this water had little to no radon in it by the time it got to consumers due to radon's short half-life). [ 113 ] Inhalation therapy is carried out in Gasteiner-Heilstollen , Austria; Świeradów-Zdrój , Czerniawa-Zdrój , Kowary , Lądek-Zdrój , Poland; Harghita Băi , Romania; and Boulder, Montana . In the US and Europe, there are several "radon spas", where people sit for minutes or hours in a high-radon atmosphere, such as at Bad Schmiedeberg , Germany. [ 111 ] [ 114 ]
Radon has been produced commercially for use in radiation therapy, but for the most part has been replaced by radionuclides made in particle accelerators and nuclear reactors . Radon has been used in implantable seeds, made of gold or glass, primarily used to treat cancers, known as brachytherapy . The gold seeds were produced by filling a long tube with radon pumped from a radium source, the tube being then divided into short sections by crimping and cutting. The gold layer keeps the radon within, and filters out the alpha and beta radiations, while allowing the gamma rays to escape (which kill the diseased tissue). The activities might range from 0.05 to 5 millicuries per seed (2 to 200 MBq). [ 109 ] The gamma rays are produced by radon and the first short-lived elements of its decay chain ( 218 Po, 214 Pb, 214 Bi, 214 Po).
After 11 half-lives (42 days), radon radioactivity is at 1/2,048 of its original level. At this stage, the predominant residual activity of the seed originates from the radon decay product 210 Pb, whose half-life (22.3 years) is 2,000 times that of radon and its descendants 210 Bi and 210 Po. [ citation needed ]
211 Rn can be used to generate 211 At, which has uses in targeted alpha therapy . [ 115 ]
Radon emanation from the soil varies with soil type and with surface uranium content, so outdoor radon concentrations can be used to track air masses to a limited degree. [ 116 ] [ a ] Because of radon's rapid loss to air and comparatively rapid decay, radon is used in hydrologic research that studies the interaction between groundwater and streams . Any significant concentration of radon in a river may be an indicator that there are local inputs of groundwater. [ 117 ]
Radon soil concentration has been used to map buried close-subsurface geological faults because concentrations are generally higher over the faults. [ 118 ] Similarly, it has found some limited use in prospecting for geothermal gradients . [ 119 ]
Some researchers have investigated changes in groundwater radon concentrations for earthquake prediction . [ 120 ] [ 121 ] Increases in radon were noted before the 1966 Tashkent [ 122 ] and 1994 Mindoro [ 121 ] earthquakes. Radon has a half-life of approximately 3.8 days, which means that it can be found only shortly after it has been produced in the radioactive decay chain. For this reason, it has been hypothesized that increases in radon concentration is due to the generation of new cracks underground, which would allow increased groundwater circulation, flushing out radon. The generation of new cracks might not unreasonably be assumed to precede major earthquakes. In the 1970s and 1980s, scientific measurements of radon emissions near faults found that earthquakes often occurred with no radon signal, and radon was often detected with no earthquake to follow. It was then dismissed by many as an unreliable indicator. [ 123 ] As of 2009, it was under investigation as a possible earthquake precursor by NASA ; [ 9 ] further research into the subject has suggested that abnormalities in atmospheric radon concentrations can be an indicator of seismic movement. [ 124 ]
Radon is a known pollutant emitted from geothermal power stations because it is present in the material pumped from deep underground. It disperses rapidly, and no radiological hazard has been demonstrated in various investigations. In addition, typical systems re-inject the material deep underground rather than releasing it at the surface, so its environmental impact is minimal. [ 125 ] In 1989, a survey of the collective dose received due to radon in geothermal fluids was measured at 2 man- sieverts per gigawatt-year of electricity produced, in comparison to the 2.5 man-sieverts per gigawatt-year produced from 14 C emissions in nuclear power plants . [ 126 ]
In the 1940s and 1950s, radon produced from a radium source was used for industrial radiography . [ 127 ] Other X-ray sources such as 60 Co and 192 Ir became available after World War II and quickly replaced radium and thus radon for this purpose, being of lower cost and hazard. [ 128 ]
222 Rn decay products have been classified by the International Agency for Research on Cancer as being carcinogenic to humans, [ 129 ] and as a gas that can be inhaled, lung cancer is a particular concern for people exposed to elevated levels of radon for sustained periods. During the 1940s and 1950s, when safety standards requiring expensive ventilation in mines were not widely implemented, [ 130 ] radon exposure was linked to lung cancer among non-smoking miners of uranium and other hard rock materials in what is now the Czech Republic, and later among miners from the Southwestern US [ 131 ] and South Australia . [ 132 ] Despite these hazards being known in the early 1950s, [ 133 ] this occupational hazard remained poorly managed in many mines until the 1970s. During this period, several entrepreneurs opened former uranium mines in the US to the general public and advertised alleged health benefits from breathing radon gas underground. Health benefits claimed included relief from pain, sinus problems, asthma, and arthritis, [ 134 ] but the government banned such advertisements in 1975, [ 135 ] and subsequent works have debated the truth of such claimed health effects, citing the documented ill effects of radiation on the body. [ 136 ]
Since that time, ventilation and other measures have been used to reduce radon levels in most affected mines that continue to operate. In recent years, the average annual exposure of uranium miners has fallen to levels similar to the concentrations inhaled in some homes. This has reduced the risk of occupationally-induced cancer from radon, although health issues may persist for those who are currently employed in affected mines and for those who have been employed in them in the past. [ 137 ] As the relative risk for miners has decreased, so has the ability to detect excess risks among that population. [ 138 ]
Residues from processing of uranium ore can also be a source of radon. Radon resulting from the high radium content in uncovered dumps and tailing ponds [ 3 ] can be easily released into the atmosphere and affect people living in the vicinity. [ 140 ] The release of radon may be mitigated by covering tailings with soil or clay, though other decay products may leach into groundwater supplies. [ 139 ]
Non-uranium mines may pose higher risks of radon exposure, as workers are not continuously monitored for radiation, and regulations specific to uranium mines do not apply. A review of radon level measurements across non-uranium mines found the highest concentrations of radon in non-metal mines, such as phosphorus and salt mines . [ 141 ] However, older or abandoned uranium mines without ventilation may still have extremely high radon levels. [ 142 ]
In addition to lung cancer, researchers have theorized a possible increased risk of leukemia due to radon exposure. Empirical support from studies of the general population is inconsistent; a study of uranium miners found a correlation between radon exposure and chronic lymphocytic leukemia , [ 143 ] and current research supports a link between indoor radon exposure and poor health outcomes (i.e., an increased risk of lung cancer or childhood leukemia ). [ 144 ] Legal actions taken by those involved in nuclear industries, including miners, millers, transporters, nuclear site workers, and their respective unions have resulted in compensation for those affected by radon and radiation exposure under programs such as the compensation scheme for radiation-linked diseases (in the United Kingdom) [ 145 ] and the Radiation Exposure Compensation Act (in the United States). [ 146 ]
Radon has been considered the second leading cause of lung cancer in the United States and leading environmental cause of cancer mortality by the EPA, [ 147 ] with the first one being smoking . [ 148 ] Others have reached similar conclusions for the United Kingdom [ 137 ] and France. [ 149 ] Radon exposure in buildings may arise from subsurface rock formations and certain building materials (e.g., some granites). [ 150 ] The greatest risk of radon exposure arises in buildings that are airtight, insufficiently ventilated, and have foundation leaks that allow air from the soil into basements and dwelling rooms. [ 151 ] In some regions, such as Niška Banja , Serbia and Ullensvang , Norway, outdoor radon concentrations may be exceptionally high, though compared to indoors, where people spend more time and air is not dispersed and exchanged as often, outdoor exposure to radon is not considered a significant health risk. [ 152 ]
Radon exposure (mostly radon daughters) has been linked to lung cancer in case-control studies performed in the US, Europe and China. There are approximately 21,000 deaths per year in the US (0.0063% of a population of 333 million) due to radon-induced lung cancers. [ 13 ] [ 153 ] In Europe, 2% of all cancers have been attributed to radon; [ 154 ] in Slovenia in particular, a country with a high concentration of radon, about 120 people (0.0057% of a population of 2.11 million) die yearly because of radon. [ 155 ] One of the most comprehensive radon studies performed in the US by epidemiologist R. William Field and colleagues found a 50% increased lung cancer risk even at the protracted exposures at the EPA's action level of 4 pCi/L. North American and European pooled analyses further support these findings. [ 151 ] However, the conclusion that exposure to low levels of radon leads to elevated risk of lung cancer has been disputed, [ 156 ] and analyses of the literature point towards elevated risk only when radon accumulates indoors [ 144 ] and at levels above 100 Bq/m 3 . [ 154 ]
Thoron ( 220 Rn) is less studied than 222 Rn in regards to domestic exposure due to its shorter half-life. However, it has been measured at comparatively high concentrations in buildings with earthen architecture, such as traditional half-timbered houses and modern houses with clay wall finishes, [ 157 ] and in regions with thorium- and monazite -rich soil and sand. [ 158 ] Thoron is a minor contributor to the overall radiation dose received due to indoor radon exposure, [ 159 ] and can interfere with 222 Rn measurements when not taken into account. [ 158 ]
WHO presented in 2009 a recommended reference level (the national reference level), 100 Bq/m 3 , for radon in dwellings. The recommendation also says that where this is not possible, 300 Bq/m 3 should be selected as the highest level. A national reference level should not be a limit, but should represent the maximum acceptable annual average radon concentration in a dwelling. [ 160 ]
The actionable concentration of radon in a home varies depending on the organization doing the recommendation, for example, the EPA encourages that action be taken at concentrations as low as 74 Bq/m 3 (2 pCi/L), [ 73 ] and the European Union recommends action be taken when concentrations reach 400 Bq/m 3 (11 pCi/L) for old houses and 200 Bq/m 3 (5 pCi/L) for new ones. [ 161 ] On 8 July 2010, the UK's Health Protection Agency issued new advice setting a "Target Level" of 100 Bq/m 3 whilst retaining an "Action Level" of 200 Bq/m 3 . [ 162 ] Similar levels (as in the UK) are published by Norwegian Radiation and Nuclear Safety Authority (DSA) [ 163 ] with the maximum limit for schools, kindergartens, and new dwellings set at 200 Bq/m 3 , where 100 Bq/m 3 is set as the action level. [ 164 ]
Results from epidemiological studies indicate that the risk of lung cancer increases with exposure to residential radon. A well known example of source of error is smoking, the main risk factor for lung cancer. In the US, cigarette smoking is estimated to cause 80% to 90% of all lung cancers. [ 165 ]
According to the EPA, the risk of lung cancer for smokers is significant due to synergistic effects of radon and smoking. For this population about 62 people in a total of 1,000 will die of lung cancer compared to 7 people in a total of 1,000 for people who have never smoked. [ 13 ] It cannot be excluded that the risk of non-smokers should be primarily explained by an effect of radon.
Radon, like other known or suspected external risk factors for lung cancer, is a threat for smokers and former smokers. This was demonstrated by the European pooling study. [ 166 ] A commentary [ 166 ] to the pooling study stated: "it is not appropriate to talk simply of a risk from radon in homes. The risk is from smoking, compounded by a synergistic effect of radon for smokers. Without smoking, the effect seems to be so small as to be insignificant."
According to the European pooling study, there is a difference in risk for the histological subtypes of lung cancer and radon exposure. Small-cell lung carcinoma , which has a high correlation with smoking, has a higher risk after radon exposure. For other histological subtypes such as adenocarcinoma , the type that primarily affects non-smokers, the risk from radon appears to be lower. [ 166 ] [ 167 ]
A study of radiation from post- mastectomy radiotherapy shows that the simple models previously used to assess the combined and separate risks from radiation and smoking need to be developed. [ 168 ] This is also supported by new discussion about the calculation method, the linear no-threshold model , which routinely has been used. [ 169 ]
A study from 2001, which included 436 non-smokers with lung cancer and a control group of 1649 non-smokers without lung cancer, showed that exposure to radon increased the risk of lung cancer in non-smokers. The group that had been exposed to tobacco smoke in the home appeared to have a much higher risk, while those who were not exposed to passive smoking did not show any increased risk with increasing radon exposure. [ 170 ]
The effects of radon if ingested are unknown, although studies have found that its biological half-life ranges from 30 to 70 minutes, with 90% removal at 100 minutes. In 1999, the US National Research Council investigated the issue of radon in drinking water. The risk associated with ingestion was considered almost negligible; [ 171 ] Water from underground sources may contain significant amounts of radon depending on the surrounding rock and soil conditions, whereas surface sources generally do not. [ 172 ] Radon is also released from water when temperature is increased, pressure is decreased and when water is aerated. Optimum conditions for radon release and exposure in domestic living from water occurred during showering. Water with a radon concentration of 10 4 pCi/L can increase the indoor airborne radon concentration by 1 pCi/L under normal conditions. [ 78 ] However, the concentration of radon released from contaminated groundwater to the air has been measured at 5 orders of magnitude less than the original concentration in water. [ 173 ]
Ocean surface concentrations of radon exchange within the atmosphere, causing 222 Rn to increase through the air-sea interface. [ 174 ] Although areas tested were very shallow, additional measurements in a wide variety of coastal regimes should help define the nature of 222 Rn observed.
There are relatively simple tests for radon gas. In some countries these tests are methodically done in areas of known systematic hazards. Radon detection devices are commercially available. Digital radon detectors provide ongoing measurements giving both daily, weekly, short-term and long-term average readouts via a digital display. Short-term radon test devices used for initial screening purposes are inexpensive, in some cases free. There are important protocols for taking short-term radon tests and it is imperative that they be strictly followed. The kit includes a collector that the user hangs in the lowest habitable floor of the house for two to seven days. The user then sends the collector to a laboratory for analysis. Long term kits, taking collections for up to one year or more, are also available. An open-land test kit can test radon emissions from the land before construction begins. [ 13 ] Radon concentrations can vary daily, and accurate radon exposure estimates require long-term average radon measurements in the spaces where an individual spends a significant amount of time. [ 175 ]
Radon levels fluctuate naturally, due to factors like transient weather conditions, so an initial test might not be an accurate assessment of a home's average radon level. Radon levels are at a maximum during the coolest part of the day when pressure differentials are greatest. [ 78 ] Therefore, a high result (over 4 pCi/L) justifies repeating the test before undertaking more expensive abatement projects. Measurements between 4 and 10 pCi/L warrant a long-term radon test. Measurements over 10 pCi/L warrant only another short-term test so that abatement measures are not unduly delayed. The EPA has advised purchasers of real estate to delay or decline a purchase if the seller has not successfully abated radon to 4 pCi/L or less. [ 13 ]
Because the half-life of radon is only 3.8 days, removing or isolating the source will greatly reduce the hazard within a few weeks. Another method of reducing radon levels is to modify the building's ventilation. Generally, the indoor radon concentrations increase as ventilation rates decrease. [ 3 ] In a well-ventilated place, the radon concentration tends to align with outdoor values (typically 10 Bq/m 3 , ranging from 1 to 100 Bq/m 3 ). [ 13 ]
The four principal ways of reducing the amount of radon accumulating in a house are: [ 13 ] [ 176 ]
According to the EPA, the method to reduce radon "...primarily used is a vent pipe system and fan, which pulls radon from beneath the house and vents it to the outside", which is also called sub-slab depressurization, active soil depressurization, or soil suction. [ 13 ] Generally indoor radon can be mitigated by sub-slab depressurization and exhausting such radon-laden air to the outdoors, away from windows and other building openings. "[The] EPA generally recommends methods which prevent the entry of radon. Soil suction, for example, prevents radon from entering your home by drawing the radon from below the home and venting it through a pipe, or pipes, to the air above the home where it is quickly diluted" and the "EPA does not recommend the use of sealing alone to reduce radon because, by itself, sealing has not been shown to lower radon levels significantly or consistently". [ 177 ]
Positive-pressure ventilation systems can be combined with a heat exchanger to recover energy in the process of exchanging air with the outside, and simply exhausting basement air to the outside is not necessarily a viable solution as this can actually draw radon gas into a dwelling. Homes built on a crawl space may benefit from a radon collector installed under a "radon barrier" (a sheet of plastic that covers the crawl space). [ 13 ] [ 178 ] For crawl spaces, the EPA states that "[a]n effective method to reduce radon levels in crawl space homes involves covering the earth floor with a high-density plastic sheet. A vent pipe and fan are used to draw the radon from under the sheet and vent it to the outdoors. This form of soil suction is called submembrane suction, and when properly applied is the most effective way to reduce radon levels in crawl space homes." [ 177 ] | https://en.wikipedia.org/wiki/Radon |
Radon hexafluoride is a binary chemical compound of radon and fluorine with the chemical formula RnF 6 . [ 1 ] [ 2 ] [ 3 ] This is still a hypothetical compound that has not been synthesized so far.
The compound is calculated to be less stable than radon difluoride . Radon hexafluoride is expected to have an octahedral molecular geometry , unlike the C 3v of xenon hexafluoride . [ 4 ] [ 5 ]
The Rn-F bonds in radon hexafluoride is predicted to be shorter and more stable compared to Xe-F bonds in xenon hexafluoride. [ 5 ]
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Radon_hexafluoride |
Radon mitigation is any process used to reduce radon gas concentrations in the breathing zones of occupied buildings, or radon from water supplies. Radon is a significant contributor to environmental radioactivity and indoor air pollution . Exposure to radon can cause serious health problems such as lung cancer . [ 1 ]
Mitigation of radon in the air by active soil depressurization is most effective. Concrete slabs, sub-floors, and/or crawlspaces are sealed, an air pathway is then created to exhaust radon above the roof-line, and a radon mitigation fan is installed to run permanently. In particularly troublesome dwellings, air exchangers can be used to reduce indoor radon concentrations. Treatment systems using aeration or activated charcoal are available to remove radon from domestic water supplies. There is no proven link between radon in water and gastrointestinal cancers; however, extremely high radon concentrations in water can be aerosolized by faucets and shower heads and contribute to high indoor radon levels in the air.
The first step in mitigation is testing. No level of radiation is considered completely safe, but as it cannot be eliminated, governments around the world have set various action levels to provide guidance on when radon concentrations should be reduced. The World Health Organization's International Radon Project has recommended an action level of 100 Bq/m 3 (2.7 pCi /L) for radon in the air. [ 2 ] Radon in the air is considered to be a larger health threat than radon in domestic water. The US Environmental Protection Agency recommendation is to not test for radon in water unless a radon in air test shows concentrations above the action level. However, in some U.S. states such as Maine where radon levels are higher than the national average, it is recommend that all well water should be tested for radon. The U.S. government has not set an action level for radon in water.
Air-radon levels fluctuate naturally on a daily and seasonal basis. A short term test (90 days or less) might not be an accurate assessment of a home's average radon level, but is recommended for initial testing to quickly determine unhealthy conditions. Transient weather such as wind and changes in barometric pressure can affect short-term concentrations as well as ventilation, such as open windows and the operation of exhaust fans.
Testing for radon in the air is accomplished using passive or active devices placed in the building. Some devices are promptly sent to a laboratory for analysis, others calculate the results on-site including digital Radon detectors. Radon-in-water testing requires a water sample being sent to a laboratory.
Retesting is recommended in several situations, for example, before spending money on the installation of a mitigation system. Test results which exceed accuracy tolerances also require re-testing. When a mitigation system installation is warranted, a retest after the system is functional is advised to be sure the system is effectively reducing the radon concentration below the action level, and after any mitigation system repairs such as replacing a fan unit. The US EPA recommends retesting homes with radon problems every two years to ensure proper system function. Due to the vast fluctuation in indoor radon levels, the EPA recommends all homes be tested at least once every five years. [ 3 ]
ASTM E-2121 is a US standard for reducing airborne radon in homes as far as practicable below the action level of 4 picocuries per liter (pCi/L) (148 Bq /m 3 ). [ 4 ] [ 5 ] Some states recommend achieving 2.0 pCi/L or less.
Radon test kits are commercially available [ 6 ] and can be used by homeowners and tenants and in limited cases by landlords, except when a property is for sale.
Commercially available test kits include a passive collector that the user places in the lowest livable floor of the house for 2 to 7 days. The user then sends the collector to a laboratory for analysis. Long-term kits, taking collections from 91 days to one year, are also available. Open land test kits can test radon emissions from the land before construction begins, but are not recommended by the EPA because they do not accurately predict the final indoor radon level. The EPA and the National Environmental Health Association have identified 15 types of radon test devices. [ 7 ] A Lucas cell is one type of device.
Retesting is specifically recommended in several situations. Measurements between 4 and 10 pCi/L (148 and 370 Bq/m 3 ) warrant a follow-up short-term or long-term radon test before mitigation. Measurements over 10 pCi/L (370 Bq/m 3 ) warrant only another short-term test (not a long-term test) so that abatement measures are not unduly delayed.
Progress has been made regarding radon in the home. A total of 37 states have now [ when? ] passed legislation requiring home-sellers to disclose known radon levels before completing the transaction (although only a handful have introduced criminal penalties for misrepresentation). [ 8 ] And over half the legislatures have written radon into their state's building code. [ 9 ] Purchasers of real estate may delay or decline a purchase if the seller has not successfully abated radon to less than 4 pCi/L.
The accuracy of the residential radon test depends upon whether closed house conditions are maintained. Thus the occupants will be instructed not to open windows, etc., for ventilation during the pendency of test, usually two days or more. However, the occupants, if the present owners, will be motivated to pass the test and insure the sale, so they might be tempted to open a window to get a lower radon score. Moreover, there may be children or immature teens or young adults in the house who will open a window for ventilation notwithstanding instructions not to do so, particularly in uncomfortably hot weather. Accordingly, whether the potential purchaser should trust the result of such a test is problematic.
Management of radon service provider certification has evolved since being introduced by the EPA in 1986. In the 1990s this service was "privatized" and the National Environmental Health Association (NEHA) helped transition the voluntary National Radon Proficiency Program (NRPP) to be administered by private firms. As of 2012 [update] , the NRPP is administered by the American Association of Radon Scientists and Technologists (AARST). [ 10 ]
Some states, such as Maine, require landlords to test their rental properties and turn the results in to the state. In limited cases the landlord or tenants may do the testing themselves. The rules in each state vary. In many cases there are private contractors that will inspect hired by the city.
Health Canada recommends regular annual testing, either by hiring a qualified tester or by using a home-testing kit that should be checked quarterly. [ 11 ]
Canadian Government, in conjunction with the territories and provinces, developed the guideline [ 12 ] to indicate when remedial action should be taken was originally set at 800 Bq/m 3 ( becquerels per cubic meter) and since reduced to 200 Bq/m 3 . This new guideline was approved by the Federal Provincial Territorial Radiation Protection Committee in October 2006. [ 13 ]
Radon testing in the UK is managed by UKradon and the UKHSA . [ 14 ]
The Norwegian Radiation and Nuclear Safety Authority (DSA) developed the protocol [ 15 ] for radon measurements in residential dwellings [ 16 ] with respect to rental accommodation, which is governed by The Radiation Protection Regulations. [ 17 ]
Because high levels of radon have been found in every state of the United States, [ 18 ] testing for radon and installing radon mitigation systems has become a specialized industry since the 1980s. Many states have implemented programs that affect home buying and awareness in the real estate community; however, radon testing and mitigation systems are not generally mandatory unless specified by the local jurisdiction. [ 19 ]
Anticipated high radon levels can be mitigated during building design and construction by a combination of ensuring a perfectly sealed foundation, allowing sufficient passive dispersal of under-slab gas around rather than through the building, and proper building ventilation. In many instances, such approaches may achieve a sufficient reduction of radon levels compared to other buildings where such approaches were not taken. However, quality of implementation is crucial and testing after construction is necessary. For instance, even a small gap in the sealing of the slab may be sufficient for excessive quantities of radon to enter, given pressure differentials.
Where such approaches were not taken during construction or have proven insufficiently effective, remediation is needed. According to the EPA's "A Citizen's Guide to Radon", [ 20 ] the method to reduce radon "primarily used is a vent pipe system and fan, which pulls radon from beneath the house and vents it to the outside", which is also called sub-slab depressurization, soil suction, or active soil depressurization (ASD). Generally indoor radon can be mitigated by sub-slab depressurization and exhausting such radon-laden air to the outdoors, away from windows and other building openings. [ 21 ] "EPA generally recommends methods which prevent the entry of radon. Soil suction, for example, prevents radon from entering your home by drawing the radon from below the home and venting it through a pipe, or pipes, to the air above the home where it is quickly diluted" and "EPA does not recommend the use of sealing alone to reduce radon because, by itself, sealing has not been shown to lower radon levels significantly or consistently" according to the EPA's "Consumer's Guide to Radon Reduction: How to Fix Your Home". [ 22 ] Ventilation systems can utilize a heat exchanger or energy recovery ventilator to recover part of the energy otherwise lost in the process of exchanging air with the outside. For crawlspaces, the EPA states, [ 22 ] "An effective method to reduce radon levels in crawlspace homes involves covering the earth floor with a high-density plastic sheet. A vent pipe and fan are used to draw the radon from under the sheet and vent it to the outdoors. This form of soil suction is called submembrane suction, and when properly applied is the most effective way to reduce radon levels in crawlspace homes."
In South Florida, most radon mitigation is performed by use of fixed rate mechanical ventilation. Radon mitigation training in Florida does not include problems associated with mechanical ventilation systems, such as high indoor humidity, mold, moldy odors, property damage or health consequences of human occupation in high humidity of moldy environments [ citation needed ] . As a result, most Florida radon mitigators are unaware of and do not incorporate existing building science moisture management technology into mechanical ventilation radon installations. Home inspectors may not necessarily be aware of the mold risks associated with radon mitigation by mechanical ventilation.
The average cost for an ASD radon mitigation system in Minnesota is $1500. [ 23 ] These costs are very dependent on the type of home and age of construction. [ 24 ]
Radon removal from water supplies may be at a treatment plant, point of entry, or point of use. Public water supplies in the United States were required to treat for radionuclides beginning in 2003 but private wells are not regulated by the federal government as of 2014 [update] . The radon can be captured by granular activated charcoal (GAR) or released into the air through aeration of the water. Radon will naturally dissipate from water over a period of days, but the quantity of storage needed to treat the water in this manner makes home systems of this type impracticably large. [ 25 ]
Activated carbon systems capture radon from the water. The amount of radiation accumulates over time and the filter material may reach the level of requiring disposal as a radioactive waste . However, in the United States there are no regulations concerning radiation levels and disposal of radon treatment waste as of 2014 [update] .
Aeration systems move the radon from the water to the air. Radon gas discharged into the air is the release of a pollutant, and may become regulated in the United States. | https://en.wikipedia.org/wiki/Radon_mitigation |
In mathematics , the Radon–Nikodym theorem is a result in measure theory that expresses the relationship between two measures defined on the same measurable space . A measure is a set function that assigns a consistent magnitude to the measurable subsets of a measurable space. Examples of a measure include area and volume, where the subsets are sets of points; or the probability of an event, which is a subset of possible outcomes within a wider probability space .
One way to derive a new measure from one already given is to assign a density to each point of the space, then integrate over the measurable subset of interest. This can be expressed as
where ν is the new measure being defined for any measurable subset A and the function f is the density at a given point. The integral is with respect to an existing measure μ , which may often be the canonical Lebesgue measure on the real line R or the n -dimensional Euclidean space R n (corresponding to our standard notions of length, area and volume). For example, if f represented mass density and μ was the Lebesgue measure in three-dimensional space R 3 , then ν ( A ) would equal the total mass in a spatial region A .
The Radon–Nikodym theorem essentially states that, under certain conditions, any measure ν can be expressed in this way with respect to another measure μ on the same space. The function f is then called the Radon–Nikodym derivative and is denoted by d ν d μ {\displaystyle {\tfrac {d\nu }{d\mu }}} . [ 1 ] An important application is in probability theory , leading to the probability density function of a random variable .
The theorem is named after Johann Radon , who proved the theorem for the special case where the underlying space is R n in 1913, and for Otto Nikodym who proved the general case in 1930. [ 2 ] In 1936 Hans Freudenthal generalized the Radon–Nikodym theorem by proving the Freudenthal spectral theorem , a result in Riesz space theory; this contains the Radon–Nikodym theorem as a special case. [ 3 ]
A Banach space Y is said to have the Radon–Nikodym property if the generalization of the Radon–Nikodym theorem also holds, mutatis mutandis , for functions with values in Y . All Hilbert spaces have the Radon–Nikodym property.
The Radon–Nikodym theorem involves a measurable space ( X , Σ ) {\displaystyle (X,\Sigma )} on which two σ-finite measures are defined, μ {\displaystyle \mu } and ν . {\displaystyle \nu .} It states that, if ν ≪ μ {\displaystyle \nu \ll \mu } (that is, if ν {\displaystyle \nu } is absolutely continuous with respect to μ {\displaystyle \mu } ), then there exists a Σ {\displaystyle \Sigma } - measurable function f : X → [ 0 , ∞ ) , {\displaystyle f:X\to [0,\infty ),} such that for any measurable set A ∈ Σ , {\displaystyle A\in \Sigma ,} ν ( A ) = ∫ A f d μ . {\displaystyle \nu (A)=\int _{A}f\,d\mu .}
The function f {\displaystyle f} satisfying the above equality is uniquely defined up to a μ {\displaystyle \mu } - null set , that is, if g {\displaystyle g} is another function which satisfies the same property, then f = g {\displaystyle f=g} μ {\displaystyle \mu } - almost everywhere . The function f {\displaystyle f} is commonly written d ν d μ {\frac {d\nu }{d\mu }} and is called the Radon–Nikodym derivative . The choice of notation and the name of the function reflects the fact that the function is analogous to a derivative in calculus in the sense that it describes the rate of change of density of one measure with respect to another (the way the Jacobian determinant is used in multivariable integration).
A similar theorem can be proven for signed and complex measures : namely, that if μ {\displaystyle \mu } is a nonnegative σ-finite measure, and ν {\displaystyle \nu } is a finite-valued signed or complex measure such that ν ≪ μ , {\displaystyle \nu \ll \mu ,} that is, ν {\displaystyle \nu } is absolutely continuous with respect to μ , {\displaystyle \mu ,} then there is a μ {\displaystyle \mu } -integrable real- or complex-valued function g {\displaystyle g} on X {\displaystyle X} such that for every measurable set A , {\displaystyle A,} ν ( A ) = ∫ A g d μ . {\displaystyle \nu (A)=\int _{A}g\,d\mu .}
In the following examples, the set X is the real interval [0,1], and Σ {\displaystyle \Sigma } is the Borel sigma-algebra on X .
The theorem is very important in extending the ideas of probability theory from probability masses and probability densities defined over real numbers to probability measures defined over arbitrary sets. It tells if and how it is possible to change from one probability measure to another. Specifically, the probability density function of a random variable is the Radon–Nikodym derivative of the induced measure with respect to some base measure (usually the Lebesgue measure for continuous random variables ).
For example, it can be used to prove the existence of conditional expectation for probability measures. The latter itself is a key concept in probability theory , as conditional probability is just a special case of it.
Amongst other fields, financial mathematics uses the theorem extensively, in particular via the Girsanov theorem . Such changes of probability measure are the cornerstone of the rational pricing of derivatives and are used for converting actual probabilities into those of the risk neutral probabilities .
If μ and ν are measures over X , and μ ≪ ν
The Radon–Nikodym theorem above makes the assumption that the measure μ with respect to which one computes the rate of change of ν is σ-finite .
Here is an example when μ is not σ-finite and the Radon–Nikodym theorem fails to hold.
Consider the Borel σ-algebra on the real line . Let the counting measure , μ , of a Borel set A be defined as the number of elements of A if A is finite, and ∞ otherwise. One can check that μ is indeed a measure. It is not σ -finite, as not every Borel set is at most a countable union of finite sets. Let ν be the usual Lebesgue measure on this Borel algebra. Then, ν is absolutely continuous with respect to μ , since for a set A one has μ ( A ) = 0 only if A is the empty set , and then ν ( A ) is also zero.
Assume that the Radon–Nikodym theorem holds, that is, for some measurable function f one has
for all Borel sets. Taking A to be a singleton set , A = { a } , and using the above equality, one finds
for all real numbers a . This implies that the function f , and therefore the Lebesgue measure ν , is zero, which is a contradiction.
Assuming ν ≪ μ , {\displaystyle \nu \ll \mu ,} the Radon–Nikodym theorem also holds if μ {\displaystyle \mu } is localizable and ν {\displaystyle \nu } is accessible with respect to μ {\displaystyle \mu } , [ 5 ] : p. 189, Exercise 9O i.e., ν ( A ) = sup { ν ( B ) : B ∈ P ( A ) ∩ μ pre ( R ≥ 0 ) } {\displaystyle \nu (A)=\sup\{\nu (B):B\in {\cal {P}}(A)\cap \mu ^{\operatorname {pre} }(\mathbb {R} _{\geq 0})\}} for all A ∈ Σ . {\displaystyle A\in \Sigma .} [ 6 ] : Theorem 1.111 (Radon–Nikodym, II) [ 5 ] : p. 190, Exercise 9T(ii)
This section gives a measure-theoretic proof of the theorem. There is also a functional-analytic proof, using Hilbert space methods, that was first given by von Neumann .
For finite measures μ and ν , the idea is to consider functions f with f dμ ≤ dν . The supremum of all such functions, along with the monotone convergence theorem , then furnishes the Radon–Nikodym derivative. The fact that the remaining part of μ is singular with respect to ν follows from a technical fact about finite measures. Once the result is established for finite measures, extending to σ -finite, signed, and complex measures can be done naturally. The details are given below.
Constructing an extended-valued candidate First, suppose μ and ν are both finite-valued nonnegative measures. Let F be the set of those extended-value measurable functions f : X → [0, ∞] such that:
F ≠ ∅ , since it contains at least the zero function. Now let f 1 , f 2 ∈ F , and suppose A is an arbitrary measurable set, and define:
Then one has
and therefore, max{ f 1 , f 2 } ∈ F .
Now, let { f n } be a sequence of functions in F such that
By replacing f n with the maximum of the first n functions, one can assume that the sequence { f n } is increasing. Let g be an extended-valued function defined as
By Lebesgue's monotone convergence theorem , one has
for each A ∈ Σ , and hence, g ∈ F . Also, by the construction of g ,
Proving equality Now, since g ∈ F ,
defines a nonnegative measure on Σ . To prove equality, we show that ν 0 = 0 .
Suppose ν 0 ≠ 0 ; then, since μ is finite, there is an ε > 0 such that ν 0 ( X ) > ε μ ( X ) . To derive a contradiction from ν 0 ≠ 0 , we look for a positive set P ∈ Σ for the signed measure ν 0 − ε μ (i.e. a measurable set P , all of whose measurable subsets have non-negative ν 0 − εμ measure), where also P has positive μ -measure. Conceptually, we're looking for a set P , where ν 0 ≥ ε μ in every part of P . A convenient approach is to use the Hahn decomposition ( P , N ) for the signed measure ν 0 − ε μ .
Note then that for every A ∈ Σ one has ν 0 ( A ∩ P ) ≥ ε μ ( A ∩ P ) , and hence,
where 1 P is the indicator function of P . Also, note that μ ( P ) > 0 as desired; for if μ ( P ) = 0 , then (since ν is absolutely continuous in relation to μ ) ν 0 ( P ) ≤ ν ( P ) = 0 , so ν 0 ( P ) = 0 and
contradicting the fact that ν 0 ( X ) > εμ ( X ) .
Then, since also
g + ε 1 P ∈ F and satisfies
This is impossible because it violates the definition of a supremum ; therefore, the initial assumption that ν 0 ≠ 0 must be false. Hence, ν 0 = 0 , as desired.
Restricting to finite values Now, since g is μ -integrable, the set { x ∈ X : g ( x ) = ∞} is μ - null . Therefore, if a f is defined as
then f has the desired properties.
Uniqueness As for the uniqueness, let f , g : X → [0, ∞) be measurable functions satisfying
for every measurable set A . Then, g − f is μ -integrable, and
In particular, for A = { x ∈ X : f ( x ) > g ( x )}, or { x ∈ X : f ( x ) < g ( x )} . It follows that
and so, that ( g − f ) + = 0 μ -almost everywhere; the same is true for ( g − f ) − , and thus, f = g μ -almost everywhere, as desired.
If μ and ν are σ -finite, then X can be written as the union of a sequence { B n } n of disjoint sets in Σ , each of which has finite measure under both μ and ν . For each n , by the finite case, there is a Σ -measurable function f n : B n → [0, ∞) such that
for each Σ -measurable subset A of B n . The sum ( ∑ n f n 1 B n ) := f {\textstyle \left(\sum _{n}f_{n}1_{B_{n}}\right):=f} of those functions is then the required function such that ν ( A ) = ∫ A f d μ {\textstyle \nu (A)=\int _{A}f\,d\mu } .
As for the uniqueness, since each of the f n is μ -almost everywhere unique, so is f .
If ν is a σ -finite signed measure, then it can be Hahn–Jordan decomposed as ν = ν + − ν − where one of the measures is finite. Applying the previous result to those two measures, one obtains two functions, g , h : X → [0, ∞) , satisfying the Radon–Nikodym theorem for ν + and ν − respectively, at least one of which is μ -integrable (i.e., its integral with respect to μ is finite). It is clear then that f = g − h satisfies the required properties, including uniqueness, since both g and h are unique up to μ -almost everywhere equality.
If ν is a complex measure , it can be decomposed as ν = ν 1 + iν 2 , where both ν 1 and ν 2 are finite-valued signed measures. Applying the above argument, one obtains two functions, g , h : X → [0, ∞) , satisfying the required properties for ν 1 and ν 2 , respectively. Clearly, f = g + ih is the required function.
Lebesgue's decomposition theorem shows that the assumptions of the Radon–Nikodym theorem can be found even in a situation which is seemingly more general. Consider a σ-finite positive measure μ {\displaystyle \mu } on the measure space ( X , Σ ) {\displaystyle (X,\Sigma )} and a σ-finite signed measure ν {\displaystyle \nu } on Σ {\displaystyle \Sigma } , without assuming any absolute continuity. Then there exist unique signed measures ν a {\displaystyle \nu _{a}} and ν s {\displaystyle \nu _{s}} on Σ {\displaystyle \Sigma } such that ν = ν a + ν s {\displaystyle \nu =\nu _{a}+\nu _{s}} , ν a ≪ μ {\displaystyle \nu _{a}\ll \mu } , and ν s ⊥ μ {\displaystyle \nu _{s}\perp \mu } . The Radon–Nikodym theorem can then be applied to the pair ν a , μ {\displaystyle \nu _{a},\mu } .
This article incorporates material from Radon–Nikodym theorem on PlanetMath , which is licensed under the Creative Commons Attribution/Share-Alike License . | https://en.wikipedia.org/wiki/Radon–Nikodym_theorem |
Retinoic acid early inducible 1 (RAE-1) family of murine cell surface glycoproteins is composed of at least five members (RAE-1α-ε). [ 1 ] Genes encoding these proteins are located on mouse chromosome 10. [ 1 ] RAE-1 proteins are related to MHC class I , they are made up of external α1α2 domain which is linked to the cell membrane by the GPI anchor. [ 1 ] They function as stress-induced ligands for NKG2D receptor and their expression is low or absent on normal cells. [ 1 ] However, they are constitutively expressed on some tumour cells and they can be upregulated by retinoic acid . [ 1 ]
This protein -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Rae-1_family |
The Raether limit is the physical limiting value of the multiplication factor ( M ) or gas gain in an ionization avalanche process ( Townsend avalanche ).
Even though, theoretically, it seems as if M can increase without limit (exponentially), physically, it is limited to about M < 10 8 or α x < 20 (where α is the first Townsend coefficient and x is the length of the path of ionization, starting from the point of the primary ionization).
Heinz Raether postulated that this was due to the effect of the space charge on the electric field. [ 1 ]
The multiplication factor or gas gain is of fundamental importance for the operation of the proportional counter and Geiger counter ionizing radiation detectors. | https://en.wikipedia.org/wiki/Raether_limit |
Rafael Artzy ( Hebrew : רפאל ארצי ; 23 July 1912 – 22 August 2006) was an Israeli mathematician specializing in geometry .
Artzy was born July 23, 1912, in Königsberg , Germany . His father was Edward I. Deutschlander and his mother Ida Freudenheim. Rafael studied at Königsberg University from 1930 to 1933. He transferred to Hebrew University and obtained a master's degree in 1934. He married Elly Iwiansky on October 12, 1934. Rafael continued his studies at Hebrew University under Theodore Motzkin , obtaining a Ph.D. in 1945. Elly and Rafael raised three children: Ehud, Michal, and Barak. Ehud and Barak died before their father. Michal Artzy is emeritus professor in Marine Civilization [ 1 ] at the University of Haifa .
Rafael served as both teacher and principal of Israel High School from 1934 to 1951. He was an instructor and assistant professor at the Israel Institute of Technology from 1951 to 1956.
Rafael Artzy took up a position as research associate and lecturer at University of Wisconsin, Madison in 1956. That year he also made his first of many contributions to Mathematical Reviews . Artzy became associate professor at University of North Carolina, Chapel Hill in 1960. The following year Rutgers University made him a full professor. In 1964 he was a visitor at the Institute for Advanced Study . [ 2 ] He wrote Linear Geometry (1965) which was favorably reviewed by H. S. M. Coxeter [ 3 ] In 1965 Artzy was at State University of New York in Buffalo . In 1967 he joined Temple University where he was for five years.
In 1972 Rafael Artzy returned to Israel and participated in mathematics at Technion in Haifa. He helped organize a quadrennial conference on geometry at Haifa. For instance, in March 1979 such a conference was held and the proceedings Geometry and Differential Geometry was edited by Artzy and I. Vaisman and published as Lecture Notes in Mathematics #792. In 1992 he published Geometry. An Algebraic Approach [ 4 ] Artzy had made 224 contributions to Mathematical Reviews by his last submission in 1995. | https://en.wikipedia.org/wiki/Rafael_Artzy |
Rafael Bombelli ( baptised on 20 January 1526; died 1572) [ a ] [ 1 ] [ 2 ] was an Italian mathematician . Born in Bologna , he is the author of a treatise on algebra and is a central figure in the understanding of imaginary numbers .
He was the one who finally managed to address the problem with imaginary numbers. In his 1572 book, L'Algebra , Bombelli solved equations using the method of del Ferro / Tartaglia . He introduced the rhetoric that preceded the representative symbols + i and - i and described how they both worked.
Rafael Bombelli was baptised on 20 January 1526 [ 3 ] in Bologna, Papal States . He was born to Antonio Mazzoli, a wool merchant, and Diamante Scudieri, a tailor's daughter. The Mazzoli family was once quite powerful in Bologna. When Pope Julius II came to power, in 1506, he exiled the ruling family, the Bentivoglios . The Bentivoglio family attempted to retake Bologna in 1508, but failed. Rafael's grandfather participated in the coup attempt, and was captured and executed. Later, Antonio was able to return to Bologna, having changed his surname to Bombelli to escape the reputation of the Mazzoli family. Rafael was the oldest of six children. Rafael received no college education, but was instead taught by an engineer-architect by the name of Pier Francesco Clementi .
Bombelli felt that none of the works on algebra by the leading mathematicians of his day provided a careful and thorough exposition of the subject. Instead of another convoluted treatise that only mathematicians could comprehend, Rafael decided to write a book on algebra that could be understood by anyone. His text would be self-contained and easily read by those without higher education.
Bombelli died in 1572 in Rome.
In the book that was published in 1572, entitled Algebra , Bombelli gave a comprehensive account of the algebra known at the time. He was the first European to write down the way of performing computations with negative numbers. The following is an excerpt from the text:
"Plus times plus makes plus Minus times minus makes plus Plus times minus makes minus Minus times plus makes minus Plus 8 times plus 8 makes plus 64 Minus 5 times minus 6 makes plus 30 Minus 4 times plus 5 makes minus 20 Plus 5 times minus 4 makes minus 20"
As was intended, Bombelli used simple language as can be seen above so that anybody could understand it. But at the same time, he was thorough.
Bombelli introduced, for the first time in a printed text (in Book II of his Algebra), a form of index notation in which the equation x 3 = 6 x + 40 {\displaystyle x^{3}=6x+40} appeared as 1U3 a. 6U1 p. 40. [ 4 ] in which he wrote the U3 as a raised bowl-shape (like the curved part of the capital letter U) with the number 3 above it. Full symbolic notation was developed shortly thereafter by the French mathematician François Viète .
Perhaps more importantly than his work with algebra, however, the book also includes Bombelli's monumental contributions to complex number theory. Before he writes about complex numbers, he points out that they occur in solutions of equations of the form x 3 = a x + b , {\displaystyle x^{3}=ax+b,} given that ( a / 3 ) 3 > ( b / 2 ) 2 , {\displaystyle (a/3)^{3}>(b/2)^{2},} which is another way of stating that the discriminant of the cubic is negative. The solution of this kind of equation requires taking the cube root of the sum of one number and the square root of some negative number.
Before Bombelli delves into using imaginary numbers practically, he goes into a detailed explanation of the properties of complex numbers. Right away, he makes it clear that the rules of arithmetic for imaginary numbers are not the same as for real numbers. This was a big accomplishment, as even numerous subsequent mathematicians were extremely confused on the topic.
Bombelli avoided confusion by giving a special name to square roots of negative numbers, instead of just trying to deal with them as regular radicals like other mathematicians did. This made it clear that these numbers were neither positive nor negative. This kind of system avoids the confusion that Euler encountered. Bombelli called the imaginary number i "plus of minus" and used "minus of minus" for - i .
Bombelli had the foresight to see that imaginary numbers were crucial and necessary to solving quartic and cubic equations . At the time, people cared about complex numbers only as tools to solve practical equations. As such, Bombelli was able to get solutions using Scipione del Ferro's rule , even in casus irreducibilis , where other mathematicians such as Cardano had given up.
In his book, Bombelli explains complex arithmetic as follows:
"Plus by plus of minus, makes plus of minus. Minus by plus of minus, makes minus of minus. Plus by minus of minus, makes minus of minus. Minus by minus of minus, makes plus of minus. Plus of minus by plus of minus, makes minus. Plus of minus by minus of minus, makes plus. Minus of minus by plus of minus, makes plus. Minus of minus by minus of minus makes minus."
After dealing with the multiplication of real and imaginary numbers, Bombelli goes on to talk about the rules of addition and subtraction. He is careful to point out that real parts add to real parts, and imaginary parts add to imaginary parts.
Bombelli is generally regarded as the inventor of complex numbers, as no one before him had made rules for dealing with such numbers, and no one believed that working with imaginary numbers would have useful results. Upon reading Bombelli's Algebra , Leibniz praised Bombelli as an ". . . outstanding master of the analytical art." Crossley writes in his book, "Thus we have an engineer, Bombelli, making practical use of complex numbers perhaps because they gave him useful results, while Cardan found the square roots of negative numbers useless. Bombelli is the first to give a treatment of any complex numbers. . . It is remarkable how thorough he is in his presentation of the laws of calculation of complex numbers. . ." [ 5 ]
In honor of his accomplishments, a Moon crater was named Bombelli .
Bombelli used a method related to simple continued fractions to calculate square roots . He did not yet have the concept of a continued fraction, and below is the algorithm of a later version given by Pietro Cataldi (1613). [ 6 ]
The method for finding n {\displaystyle {\sqrt {n}}} begins with n = ( a ± r ) 2 = a 2 ± 2 a r + r 2 {\displaystyle n=(a\pm r)^{2}=a^{2}\pm 2ar+r^{2}\ } with 0 < r < 1 {\displaystyle 0<r<1\ } , from which it can be shown that r = | n − a 2 | 2 a ± r {\displaystyle r={\frac {|n-a^{2}|}{2a\pm r}}} . Repeated substitution of the expression on the right hand side for r {\displaystyle r} into itself yields a continued fraction
for the root but Bombelli is more concerned with better approximations for r {\displaystyle r} . The value chosen for a {\displaystyle a} is either of the whole numbers whose squares n {\displaystyle n} lies between. The method gives the following convergents for 13 {\displaystyle {\sqrt {13}}\ } while the actual value is 3.605551275... :
The last convergent equals 3.605550883... . Bombelli's method should be compared with formulas and results used by Heros and Archimedes . The result 265 153 < 3 < 1351 780 {\displaystyle {\frac {265}{153}}<{\sqrt {3}}<{\frac {1351}{780}}} used by Archimedes in his determination of the value of π {\displaystyle \pi } can be found by using 1 and 0 for the initial values of r {\displaystyle r} .
https://www.people.iup.edu/gsstoudt/history/bombelli/bombelli.pdf | https://en.wikipedia.org/wiki/Rafael_Bombelli |
Rafael Moure-Eraso (born May 2, 1946) is a former chairman and chief executive of the U.S. Chemical Safety and Hazard Investigation Board (CSB).
Moure-Eraso was born in Cali , Colombia , in 1946. He grew up in Bogotá where he was educated by Augustinian friars and at the University of Los Andes . [ 2 ]
He received his B.Sc. in chemical engineering from the University of Pittsburgh in 1967 and M.Sc. in chemical engineering from Bucknell University in 1970. He received his M.Sc. and Ph.D. from the University of Cincinnati in Environmental Health-Industrial Hygiene in 1974 and 1982. [ 3 ]
For over 30 years, Moure-Eraso has been involved in workplace safety issues. [ 4 ] Prior to joining the CSB Moure-Eraso served as a member of the National Advisory Committee on Occupational Health (NACOSH) for the Occupational Safety and Health Administration (OSHA) and as a member of the Scientific Advisory Committee of the National Institute for Occupational Safety and Health (NIOSH). [ 5 ] Moure-Eraso has also worked as a chemical engineer for Rohm and Haas and the Dow Chemical Company . [ 6 ] He was a faculty member at the University of Massachusetts Lowell for 22 years and chairman of the university's Department of Work Environment for 5 years. [ 7 ] He has also served as an industrial hygienist engineer with the national offices of the United Automobile Workers union and the Oil, Chemical and Atomic Workers International Union . [ 8 ]
Moure-Eraso was nominated by President Barack Obama to the U.S. Chemical Safety Board in March 2010 and confirmed by the Senate in June 2010. [ 4 ]
In March 2015, he was called to testify in front of the House Oversight Committee regarding the management of the Chemical Safety Board. Following that testimony fourteen members of the committee issued a letter to the White House calling on the president to use his statutory authority to remove Moure-Eraso from his position as chairman of the CSB. The letter cited a pattern of retaliation against whistleblowers, disenfranchisement of fellow board members, low morale in the organization, and possible violations of the Federal Records Act by using personal email accounts for official business. [ 9 ]
Moure-Eraso told the Los Angeles Times : "A lot of it is political. The mission of the organization is to produce good reports that make a difference for safety. We are doing that. I can show that we are producing the best reports ever produced in the agency. I stand by that. All of this other talk is peripheral... There have been a lot of accusations, but none of those have ever ended in any findings. The Office of Special Counsel has made no recommendations. Anybody can claim actions against whistleblowers, but there’s no evidence of this. To just say it is not enough. What I would like to be judged for is the quality of the product and the fulfillment of our mission. There will always be people complaining. But they are all rumors." [ 10 ] He resigned his post on March 26, 2015. [ 11 ] | https://en.wikipedia.org/wiki/Rafael_Moure-Eraso |
In chemical separation terminology, the raffinate (from French raffiner , to refine) is a product which has had a component or components removed. The product having the removed materials is referred to as the extract . For example, in solvent extraction , the raffinate is the liquid stream which remains after solutes from the original liquid are removed through contact with an immiscible liquid. In metallurgy, raffinating refers to a process in which impurities are removed from liquid material. [ 1 ]
In pressure swing adsorption the raffinate refers to the gas which is not adsorbed during the high pressure stage. The species which is desorbed from the adsorbent at low pressure may be called the "extract" product. [ 2 ]
In naphtha cracking process, C4R1 refers to C4 residual obtained after separation of 1,3-butadiene from C4 raffinate stream and which, mainly consists of isobutylene 40~50 wt% and cis - or trans - 2-butene 30~35 wt%. Normally C4R1 is a side product in 1,3-butadiene plant and feed to tert -butyl alcohol plant.
In naphtha cracking process, C4R2 refers to C4 residual obtained after separation of 1,3-butadiene and isobutylene from C4 raffinate stream and which mainly consists of cis - or trans -2-butene 50~60 wt%, 1-butene 10~15 wt%, and n - butane ~20 wt%. Normally C4R2 is a side product in tert -butyl alcohol plant if C4R1 is used for feed.
In naphtha cracking process, C4R3 refers to C4 residual obtained after separation of 1,3-butadiene, isobutylene, and 1-butene from C4 raffinate stream which mainly consists of cis - or trans -2-butene, n -butane, and unseparated 1-butene. Normally C4R3 is being process through a selective hydrogenation unit (SHU) and CDHydro deisobutenizer unit to produce isobutylene as a feed to tert -butyl alcohol plant.
In naphtha cracking process, C4R4 refers to C4 residual obtained after separation of 1,3-butadiene, isobutylene, 1-butene, and cis - or trans -2-butene from C4 raffinate stream which mainly consists of n -butane. Normally C4R4 is a side product in tert -butyl alcohol plant if C4R3 is used for feed. | https://en.wikipedia.org/wiki/Raffinate |
A rafter is one of a series of sloped structural members such as steel beams that extend from the ridge or hip to the wall plate , downslope perimeter or eave , and that are designed to support the roof shingles , roof deck, roof covering and its associated loads. [ 2 ] A pair of rafters is called a couple . In home construction, rafters are normally made of wood . Exposed rafters are a feature of some traditional roof styles.
In recent buildings there is a preference for trussed rafters on the grounds of cost, economy of materials, off-site manufacture, and ease of construction, as well as design considerations including span limitations and roof loads (weight from above). [ citation needed ]
There are many names for rafters depending on their location, shape, or size (see below).
The earliest surviving roofs in Europe are of common rafters on a tie beam ; this assembly is known as a "closed couple". Later, principal rafters and common rafters were mixed, which is called a major/minor or primary/secondary roof system.
Historically many rafters, including hip rafters, often tapered in height 1/5 to 1/6 of their width, with the larger end at the foot. Architect George Woodward discusses the purpose of this in 1860: "The same amount of strength can be had with a less amount of lumber. There is an additional labor in sawing such rafters, as well as a different calculation to be made in using up a log to the best advantage. It is necessary always to order this special bill of rafters direct from the mill, and the result will be that the extra cost will, nine times out of ten, overbalance the amount saved." [ 3 ] John Muller also discussed a one-sixth taper for rafters. [ 4 ]
A piece added at the foot to create an overhang or change the roof pitch is called a sprocket, or coyau in French. The projecting piece on the gable of a building forming an overhang is called a lookout .
A rafter can be reinforced with a strut , principal purlin , collar beam , or, rarely, an auxiliary rafter (see below).
Rafter types include:
Rafters are usually made of pine or cedar. For longer span rafters, building materials manufacturers have created laminated veneer lumber (LVL) rafters that can be 2–5 times longer than typical wood rafter. In the US, most wood rafters have maximum length of 20 feet (6.1 m). [ 5 ] If a longer rafter is needed, LVL is an alternative. | https://en.wikipedia.org/wiki/Rafter |
The Ragulator-Rag complex is a regulator of lysosomal signalling and trafficking in eukaryotic cells, which plays an important role in regulating cell metabolism and growth in response to nutrient availability in the cell. [ 1 ] The Ragulator-Rag Complex is composed of five LAMTOR subunits, which work to regulate MAPK and mTOR complex 1 . [ 2 ] The LAMTOR subunits form a complex with Rag GTPase and v-ATPase, which sits on the cell’s lysosomes and detects the availability of amino acids. [ 1 ] If the Ragulator complex receives signals for low amino acid count, it will start the process of catabolizing the cell. If there is an abundance of amino acids available to the cell, the Ragulator complex will signal that the cell can continue to grow. [ 1 ] Ragulator proteins come in two different forms: Rag A/Rag B and Rag C/Rag D. These interact to form heterodimers with one another.
mTORC1 is a complex within the lysosome membrane that initiates growth when promoted by a stimulus, such as growth factors. A GTPase is a key component in cell signaling, and there were, in 2010, four RAG complexes discovered within the lysosomes of cells. In 2008, it was thought that these RAG complexes would slow down autophagy and activate cell growth by interacting with mTORC1. [ 3 ] However, in 2010, the Ragulator was discovered. Researchers determined that the function of this Ragulator was to interact with the RAG A, B, C, and D complexes to promote cell growth. This discovery also led to the first use of the term “Rag-Ragulator” complex, because of the interaction between these two. [ 4 ]
The amino acid level, cell growth, and other important factors are influenced by the mTOR Complex 1 pathway. On the lysosomal surface, the amino acids signal the activation of the four Rag proteins (RagA, RagB, RagC, and RagD) to translocate mTORC1 to the site of activation. [ 5 ]
A 2014 study noted that AMPK (AMP-activated protein kinase) and mTOR play important roles in managing different metabolic programs. It was also found that the protein complex v-ATPase-Ragulator was essential for activation of mTOR and AMPK. The v-ATPase-Ragulator complex is also used as an initiating sensor for energy stress, and serves as an endosomal docking site for LKB1-mediated AMPK activation by forming the v-ATPase-Ragulator-AXIN/LKB1-AMPK complex. This allows a switch between catabolism and anabolism . [ 6 ]
In 2016, it was established that RagA and Lamtor4 were key to microglia functioning and biogenesis regulation within the lysosome. Further studies also indicate that the Ragulator-Rag complex interacts with proteins other than mTORC1, including an interaction with v-ATPase, which facilitates functions within microglia of the lysosome. [ 7 ]
In 2017, the Ragulator was thought to regulate the position of the lysosome, and interact with BORC, a multi subunit complex located on the surface of the lysosomal membrane. [ 8 ] Both BORC and mTORC1 work together in activating the GTPases to change the position of the lysosome. It was concluded that BORC and GTPases compete for a binding site in the LAMTOR 2 protein to reposition the lysosome. [ 9 ]
While the intricate functions of the Ragulator-Rag Complex are not fully understood, it is known that the Ragulator-Rag Complex associates with the lysosome and plays a key role in mTOR (mammalian target of rapamycin) signaling regulation. [ 10 ] mTOR signaling is sensitive to amino acid concentrations in the cytoplasm of the cell, and the Ragulator complex works to detect amino acid concentration and transmit signals that activate, or inhibit, mTORC1 . [ 11 ]
The Ragulator, along with the Rag GTPases and v-ATPases , are part of an amino acid identifying pathway, and are necessary for the localization of the mTORC1 to the lysosome surface. The Ragulator and v-ATPases reside on the lysosomal surface. The Rag GTPases cannot be directly bound to the lysosome because they lack the proteins necessary to bind to its lipid bilayer, so Rag GTPases must instead be anchored to the Ragulator. [ 12 ] The Ragulator is bound to the surface via the V-ATPase. [ 13 ] The Ragulator is a crystalized structure composed of five different subunits; LAMTOR 1, LAMTOR 2, LAMTOR 3, LAMTOR 4, LAMTOR 5. There are two sets of obligate heterodimers in the complex, LAMTOR 2/3, which sits right above LAMTOR 4/5. [ 12 ] The LAMTOR 1 dimer does not have the same structure as the other subunits. LAMTOR 1 surrounds most of the two heterodimers , providing structural support and keeping the heterodimers in place. When amino acids are present, the subunits are folded and positioned in such a way that allows for the Rag-GTPases to be anchored to its primary docking site of LAMTOR 2/3 on the Ragulator. [ 12 ] The Rag-GTPases consist of two sets of heterodimers; RAGs A/B and RAGs C/D. Before Rag-GTPases can bind to the Ragulator, Rag A/B must be GTP loaded via guanine nucleotide exchange factors (GEFs), and RAG C/D must be GDP loaded. [ 14 ] Once Rag-GTPases are bound to the regulator complex, the mTORC1 can be translocated to the surface of the lysosome. At the lysosomal surface, the mTORC1 will then bind to Rheb , but only if Rheb was first loaded to a GTP via GEFs. [ 13 ] If the amount of nutrients and the concentration of amino acids are sufficient, mTORC1 will be activated.
The lysosomal membrane is the main area in which mTORC1 is activated. However, some activation can occur in the Golgi apparatus and the peroxisome. [ 15 ] In mammalian cells, GTPase RagA and RagB are heterodimers with RagC and RagD, respectively. When enough amino acids are present, RagA/B GTPase becomes activated, which leads to the translocation of mTORC1 from the cytoplasm to the lysosome surface, via the Raptor. This process brings mTORC1 in close enough proximity to Rheb for Rheb to either (1) cause a conformational change to mTORC1, leading to and increase in substrate turnover, or (2) induce kinase activity of mTORC1. Rags do not contain membrane-targeting sequences, and as a result, depend on the entire Ragulator-Rag Complex to bind to the lysosome, activating mTORC1. [ 16 ]
While most amino acids indirectly activate mTORC1 in mammals, Leucine has the ability to directly activate mTORC1 in cells that are depleted of amino acids. Yeast contain LRS (leucyltRNA synthetase), which is a molecule that can interact with Rags, directly activating the molecule. [ 16 ]
The complex consists of five subunits, [ 2 ] named LAMTOR 1-5 ( Late endosomal/lysosomal adaptor, mapk and mtor activator 1 ), however several have alternative names. | https://en.wikipedia.org/wiki/Ragulator-Rag_complex |
Raikov’s theorem, named for Russian mathematician Dmitrii Abramovich Raikov , is a result in probability theory . It is well known that if each of two independent random variables ξ 1 and ξ 2 has a Poisson distribution , then their sum ξ=ξ 1 +ξ 2 has a Poisson distribution as well. It turns out that the converse is also valid. [ 1 ] [ 2 ] [ 3 ]
Suppose that a random variable ξ has Poisson's distribution and admits a decomposition as a sum ξ=ξ 1 +ξ 2 of two independent random variables. Then the distribution of each summand is a shifted Poisson's distribution.
Raikov's theorem is similar to Cramér’s decomposition theorem . The latter result claims that if a sum of two independent random variables has normal distribution , then each summand is normally distributed as well. It was also proved by Yu.V.Linnik that a convolution of normal distribution and Poisson's distribution possesses a similar property ( Linnik's theorem [ ru ] ).
Let X {\displaystyle X} be a locally compact Abelian group . Denote by M 1 ( X ) {\displaystyle M^{1}(X)} the convolution semigroup of probability distributions on X {\displaystyle X} , and by E x {\displaystyle E_{x}} the degenerate distribution concentrated at x ∈ X {\displaystyle x\in X} . Let x 0 ∈ X , λ > 0 {\displaystyle x_{0}\in X,\lambda >0} .
The Poisson distribution generated by the measure λ E x 0 {\displaystyle \lambda E_{x_{0}}} is defined as a shifted distribution of the form
μ = e ( λ E x 0 ) = e − λ ( E 0 + λ E x 0 + λ 2 E 2 x 0 / 2 ! + … + λ n E n x 0 / n ! + … ) . {\displaystyle \mu =e(\lambda E_{x_{0}})=e^{-\lambda }(E_{0}+\lambda E_{x_{0}}+\lambda ^{2}E_{2x_{0}}/2!+\ldots +\lambda ^{n}E_{nx_{0}}/n!+\ldots ).}
One has the following
Let μ {\displaystyle \mu } be the Poisson distribution generated by the measure λ E x 0 {\displaystyle \lambda E_{x_{0}}} . Suppose that μ = μ 1 ∗ μ 2 {\displaystyle \mu =\mu _{1}*\mu _{2}} , with μ j ∈ M 1 ( X ) {\displaystyle \mu _{j}\in M^{1}(X)} . If x 0 {\displaystyle x_{0}} is either an infinite order element, or has order 2, then μ j {\displaystyle \mu _{j}} is also a Poisson's distribution. In the case of x 0 {\displaystyle x_{0}} being an element of finite order n ≠ 2 {\displaystyle n\neq 2} , μ j {\displaystyle \mu _{j}} can fail to be a Poisson's distribution. | https://en.wikipedia.org/wiki/Raikov's_theorem |
Railveyor is a remote controlled, electrically powered light-rail haulage solution for surface and underground applications in the mining and aggregate industries. Railveyor Technologies Global Inc. is a private Sudbury, Canada -based industrial bulk material handling and material haulage company that manufactures and installs Railveyor systems.
Railveyor's light-rail system was first demonstrated by its inventor, Mike Dibble, in conjunction with the Florida Institute of Phosphate Research from 1999-2001. Since then it has been installed commercially by Harmony Gold at its Phakisa Gold Mine in Free State, South Africa. [ 1 ] Canadian entrepreneur Risto Laamanen incorporated the business, secured the global distribution rights, and set up a second demonstration and test site with Vale S.A. at their Frood Stobie mine in Sudbury, Ontario, Canada in 2008. [ 2 ] [ 3 ] [ 4 ] Following successful testing of the system at the Frood Stobie test site, a Railveyor system was installed at Vale's Copper Cliff Mine 114 Ore Body Mine and became operational in 2012, [ 5 ] with the intention of using the Railveyor system as an enabling technology for rapid mine development and high speed production. [ 6 ]
Risto Laamanen died on July 7, 2009, [ 7 ] but the Laamanen family continue to be large investors in the private company, Railveyor Technologies Global Inc., along with investors from Canada and the United States of America.
The Railveyor system incorporates a remotely operated electrically powered series of two wheeled railcars driven by power stations located along on a light-rail track. [ 8 ] Because the cars are remotely operated and compact in size, they can be used as an enabling technology for rapid development and high speed production at the working face. The Railveyor system can reduce capital costs and infrastructure, travelling below shafts and in spaces as small as 10 by 12 feet or 3.05 m by 3.66 m. [ 9 ] Using multiple train systems in tandem optimizes continuous material haulage. [ 10 ] The railcars can travel at variable speeds up to 18 mph, or 8 metres/second, and climb grades of 20%. [ 11 ] The company claims that the system combines the best features of conveyors, rail, and truck haulage, including travelling on 20% inclines, increased capacity and availability, reduced installation time, a small profile, and a short turning radius of 95 feet or 30 m. [ 12 ] The system is used for underground and surface applications in the mining and aggregate industries. | https://en.wikipedia.org/wiki/Rail-Veyor |
RITES Ltd , formerly known as Rail India Technical and Economic Service Limited , is an Indian public sector undertaking and engineering consultancy corporation, specializing in the field of transport infrastructure . Established in 1974 by the Indian Railways , the company's initial charter was to provide consultancy services in rail transport management to operators in India and abroad. RITES has since diversified into planning and consulting services for other infrastructure, including airports, ports, highways and urban planning. [ 2 ]
As of 2011, it has executed projects in over 62 countries. [ 3 ] The company got listed on both NSE and BSE in July 2018. [ 4 ] [ 5 ]
Major railway companies and projects that have had projects with RITES as a consultant include: | https://en.wikipedia.org/wiki/Rail_India_Technical_and_Economic_Service |
Rail directions are used to describe train directions on rail systems. The terms used may be derived from such sources as compass directions, altitude directions, or other directions. These directions are often specific to system, country, or region.
Many rail systems use the concept of a centre (usually a major city) to define rail directions.
In British practice, railway directions are usually described as "up" and "down", with "up" being towards a major location. This convention is applied not only to the trains and the tracks, but also to items of lineside equipment and to areas near a track. Since British trains run on the left , the "up" side of a line is usually on the left when proceeding in the "up" direction.
On most of the network, "up" is the direction towards London . In most of Scotland , with the exception of the West and East Coast Main Lines , and the Borders Railway , "up" is towards Edinburgh . The Valley Lines network around Cardiff has its own peculiar usage, relating to the literal meaning of travelling "up" and "down" the valley. On the former Midland Railway "up" was towards Derby . On the Northern Ireland Railways network, "up" generally means toward Belfast (the specific zero milepost varying from line to line); except for cross-border services to Dublin , where Belfast is "down". Mileposts normally increase in the "down" direction, but there are exceptions, such as the Trowbridge line between Bathampton Junction and Hawkeridge Junction, where mileage increases in the "up" direction. [ 1 ]
Individual tracks will have their own names, such as Up Main or Down Loop . Trains running towards London are normally referred to as "up" trains, and those away from London as "down". Hence the down Night Riviera runs to Penzance and the up Flying Scotsman to London King's Cross . [ citation needed ] This distinction is less meaningful for trains not travelling towards or away from London; for instance a CrossCountry train from Manchester to Bournemouth uses "up" lines as far as Reading and "down" lines thereafter.
In China, railway directions with terminus in Beijing are described as "up" ( 上行 , shàngxíng ) and "down" ( 下行 , xiàxíng ), with "up" towards Beijing ; while trains leaving Beijing are "down". Trains run through Beijing may have two or more numbers, for example, the train from Harbin to Shanghai K58/55 uses two different numbers: on the Harbin–Tianjin section, the train runs toward Beijing, the train is known as K58, but on the Tianjin–Shanghai section, the train is known as K55; the opposite train from Shanghai to Harbin is known as K56/57, while K56 is used from Shanghai to Tianjin and K57 is used from Tianjin to Harbin. [ 2 ] Generally even numbers denote trains heading towards Beijing while odd numbers are those heading away from the capital.
In Japan, railway directions are referred to as "up" ( 上り , Nobori ) and "down" ( 下り , Kudari ) , and these terms are widely employed in timetables, [ 3 ] as well as station announcements and signage. For JR Group trains, trains heading towards Tokyo Station are considered "up" trains, while those heading away are "down" trains, with a notable exceptions for the Yamanote and Osaka Loop lines which are both loop lines operated by JR Group companies. There is also an exception for the Keihin Tohoku line and other similar trains that runs past Tokyo Station, as officially the line is part of Tohoku Line north of Tokyo Station and Tokaido Line south, so the trains are referred as Northbound/Southbound. For other, private railway operators, the designation of "up" or "down" (if at all) usually relies on where the company is headquartered as "up".
In Hong Kong, most lines have their "down" direction towards the terminal closer to Central , with the exception of Disneyland Resort line , where the down line is towards Disneyland to be consistent with Tung Chung line where it branches from. On Tuen Ma line , the "down" end is Wu Kai Sha . The up/down direction was switched in the former Ma On Shan line such that it could be connected with the former West Rail line . [ 4 ] The direction is signposted along the track, with the mileage increasing in the up direction, and also on the platform ends.
The railway systems of the Australian states have generally followed the practices of railways in the United Kingdom. Railway directions are usually described as "up" and "down", with "up" being towards the major location in most states, which is usually the capital city of the state. In New South Wales , trains running away from Sydney are "down" trains, while in Victoria , trains running away from Melbourne are "down" trains. An interstate train travelling from Sydney to Melbourne is a "down" train until it crosses the state border at Albury, where it changes its classification to an "up" train. Even in states that follow this practice, exceptions exist for individual lines. In the state of Queensland , "up" and "down" directions are individually defined for each line. Therefore, a train heading towards the main railway station in Brisbane ( Roma Street station ) would be classified as an "up" train on some lines but as a "down" train on other lines. [ 5 ] In South Australia ,
there are two (2) up/down origins: Port Augusta and Adelaide .
In Taiwan, trains travelling north towards Keelung on the Western Trunk Line and towards Badu on the Yilan Line are considered "up" trains. However, on other parts of the network, the terminology "clockwise" and "counter-clockwise" is used instead.
In Sweden, where trains run on the left ( unlike roads which switched to running on the right in 1967 ), "up" ( uppspår ) refers to trains heading northbound, while "down" ( nedspår ) refers to trains heading southbound. Even numbers are always used for "up" trains while odd numbers are always used for "down" trains.
In many commuter rail and rapid transit services in the United States, the rail directions are related to the location of the city centre. The term inbound is used for the direction leading in toward the city centre and outbound is used for the opposite direction leading out of the city centre. [ 6 ] [ 7 ]
Some British rail directions commonly used are London and Country . The London end of a station platform or train is the end nearer to London. First class accommodation, where provided, is usually at this end. The country end is the opposite end. This usage is problematic where more than one route to London exists (e.g. at Exeter St Davids via Salisbury or Bristol, or Edinburgh Waverley ).
In France, railway directions are usually described as Pair and Impair (meaning Even and Odd ), corresponding to Up and Down in the British system. Pair means heading toward Paris, and Impair means heading away from Paris. This convention is applied not only to the trains and the tracks, but also to items of lineside equipment. Pair is also quasi-homophonic with Paris , so direction P is equivalent either with direction Pair or with direction Paris .
A similar system is in use in Italy, where directions can be Pari or Dispari ( Even and Odd respectively). Pari ( Even ) trains conventionally travel north- and west-bound. The city of Paris is referenced in colloquial use ( Parigi in Italian), with Pari trains virtually leading towards it (Paris being in a north-western direction from any point in Italy).
Polish railways also use parzysty and nieparzysty ( even and odd ) to designate line directions, with odd directions usually heading away from major cities (with historical exceptions in place) and thus functionally the equivalent of the British "down" direction. The odd direction is the direction of increasing mileage. With rail traffic in Poland operating on the right-hand side, down/odd tracks are usually on the right on double-track lines, and signalling equipment numbering follows this. Train numbers adhere to this directional principle to the extreme: trains entering a line in opposite direction of their previous line will change numbers accordingly (with numbering pairs: 0/1, 2/3, 4/5, 6/7, 8/9), and to give an example, 1300 and 1301 are the exact same train in Poland, with the even and odd numbers applying over different sections of its journey.
In Russia (and ex-USSR countries), the "even direction" is usually north- and eastbound, while the "odd direction" is south- and westbound. Trains travelling "even" and "odd" usually receive even and odd numbers as well as track and signal numbers, respectively.
In double track loop lines – such as those encircling a city – the tracks, trains and trackside equipment can be identified by their relative distance from the centre of the loop. Inner refers to the track and its trains that are closer to the topological centre. Outer refers to the track and its trains that are furthermost from the topological centre. One example is the City Circle line in the Sydney Trains system.
For circle routes , the directions may indicate clockwise or counterclockwise (anti-clockwise) bound trains. For example, on the Circle line of London Underground or the loop of the Central line , the directions are often referred to as "inner rail" (anti-clockwise) or "outer rail" (clockwise).
The same practice is used for circle routes in Japan, such as the Yamanote Line in Tokyo and the Osaka Loop Line , where directions are usually referred to as "outer" ( 外回り , soto-mawari ) and "inner" ( 内回り , uchi-mawari ) , in a system where trains go clockwise on the outer track and counter-clockwise on the inner track.
Most railroads in the United States use nominal cardinal directions for the directions of their lines, which often differ from actual compass directions . These directions are often referred to as "railroad" north, south, east, or west, to avoid confusion with the compass directions.
Typically an entire railroad system (the lines of a railroad or a related group of railroads) will describe all of its lines by only two directions, either east and west , or north and south . This greatly reduces the possibility of misunderstanding the direction in which a train is travelling as it traverses lines which may twist and turn or even reverse direction for a distance. These directions also have significance in resolving conflicts between trains running in opposite directions. For example, many railroads specify that trains of equal class running to the east are superior to those running west. This means that, if two trains are approaching a passing siding on a single-track line , the inferior westbound train must "take the siding" and wait there for the superior eastbound train to pass.
In the United States, most railroads use "east and west", and it is unusual for a railroad to designate "north and south" (the New York City Subway , the Chicago "L" , and the Washington Metro are rare examples). Even-numbered trains (superior) travel east (or north). Odd-numbered trains (inferior) travel west (or south).
On the London Underground , geographic direction naming generally prevails (e.g. eastbound, westbound) except for the Circle line where it is Outer Rail and Inner Rail.
In New York City , the terms uptown and downtown are used in the subway to refer to northbound and southbound respectively. [ 8 ] The nominal railroad direction is determined by how the line will travel when it enters Manhattan .
For railways in China that are not connected with Beijing, north and west are used as "up", and east and south as "down". Odd numbered train codes are used for "down" trains, while even numbers are used for "up"; for example, train T27 from Beijing West to Lhasa is "down" (going away from Beijing) since 27 is odd.
In Germany, the tracks outside of station limits are called "Regelgleis" (usual track) and "Gegengleis" (opposite track). As trains in Germany usually drive on the right side, the Regelgleis is typically the right-side track, with some exceptions. When the direction of travel changes, the tracks' names also change, so the names of the adjacent stations are added. For example, the usual track from A-town to B-ville would also be the opposite track from B-ville to A-town. If two or more lines run parallel (German railway lines can only have one or two tracks outside station limits by definition), the name of the railway line is also added (usually something like goods line, S-Bahn, long-distance tracks, regional tracks, etc.).
Before being called Regel- and Gegengleis, the tracks were referred to as "right" (as in correct) and "false" track, with the right track being on the right side. As the use of the word "false" implied that it was wrong to drive on it, Deutsche Bahn considered changing the names to "Right" and "Left" track. However, this would have led to some cases where the "Right" track would be on the left side of the line and vice versa. | https://en.wikipedia.org/wiki/Rail_directions |
The Railway Preservation Society of Ireland (RPSI) is a railway preservation group founded in 1964 and operating throughout Ireland. Mainline steam train railtours are operated from Dublin , while short train rides are operated up and down the platform at Whitehead, County Antrim , and as of 2023, the group sometimes operates mainline trains in Northern Ireland using hired-in NIR diesel trains from Belfast . The RPSI has bases in Dublin and Whitehead, with the latter having a museum. [ 1 ] The society owns heritage wagons, carriages, steam engines, diesel locomotives and metal-bodied carriages suitable for mainline use.
The society has developed several bases over time, with Whitehead joined by Sallins, then Mullingar, and also Inchicore and Connolly in Dublin. As of 2019, three locations are in operation: Whitehead, Inchicore and Connolly.
Whitehead, near Belfast, has a long history as an excursion station, and the RPSI developed a working steam and engineering depot there. This was added to by the development of a museum. [ 2 ]
The Whitehead Railway Museum opened without ceremony in early 2017, [ 2 ] after a 5-year project to expand the site from a depot to include a rebuilt Whitehouse Excursion station and the museum. The total cost was £3.1m from various funding sources. [ 2 ] The museum received 10,000 visitors in 2017, its first year, and 15,000 in 2018. [ 3 ] The museum contains five galleries and it is possible for visitors to see various heritage steam and diesel locomotives and observe work on railway carriage restoration. Guides from the society are present. [ 3 ]
The RPSI has arrangements for storage of stock at Inchicore Works , with maintenance also being carried out there. [ 2 ]
In 2015 the RPSI secured an arrangement with Iarnród Éireann to lease the locomotive shed just to the north of Connolly for the maintenance and storage of mainline diesel locomotives. [ 2 ]
The RPSI moved into the loco shed at Mullingar in 1974 [ 4 ] and based steam locos 184 and 186 there. Carriages were also restored there. The base later become derelict, with funding instead being channeled to Whitehead, including a board decision not to spend money on the green carriages based at Mullingar. [ 5 ] Generating Van 3173 was the last vehicle to be overhauled. [ 6 ] The site was eventually handed back to the local council and Irish Rail, in preparation for new housing development, with remaining carriages moved to other locations, including one to the new Maam Cross railway project. [ citation needed ]
Prior to Mullingar, Sallins Goods Shed was used as a base. [ 7 ]
The Society used to operate mainline steam trains from Whitehead and Belfast. Since 2023, these have ceased, as the late Noel Playfair (NIR driver) passed away. Which means the society has had to work with NIR to come up with new operating agreements and hopefully getting operations restarted. Whithead still operates within the yard on train rides while maintenance.is still carried out on the mainline cariages and locos based here, ready for the future. [ citation needed ]
The Society possesses 9 steam locomotives (plus one more operated by them but owned by the Ulster Folk and Transport Museum ), typically only a small number will be operational at any time: [ 8 ] [ a ]
The RPSI has three Great Northern Railway of Ireland 4-4-0 's within its fleet. [ 8 ] No. 131, a Q class , was built in 1901. [ 12 ] The others are S class no. 171 Slieve Gullion and V class No. 85 Merlin , [ 8 ] although the latter is owned by the Ulster Folk & Transport Museum and is on loan. These locomotives are suitable for longer distance main line work, but are speed restricted if they need to run tender-first in the event they cannot be turned. [ citation needed ]
The RPSI's Northern Counties Committee (NCC) 2-6-4 T , WT class No. 4 holds significant records. It worked the last steam passenger train on Northern Ireland Railways , and with No. 53 operated the last stone goods train on 22 October 1970. Acquired by the RPSI in June 1971 it then went on to work over most of the remaining Irish railway network. [ 13 ] [ a ] They also own a SLNCR Lough class .
The Society possesses three goods tender locomotives all of which are suitable for slower speed passenger workings. Two of these are from the 101 (J15) class , of which over 100 were built between 1866 and 1903 and which lasted until the end of the steam era on CIÉ in 1963. [ 14 ] The RPSI possesses two examples of these simple, reliable and robust engines, No. 184 with a saturated boiler and round-shaped firebox, and No. 186 with a superheated boiler and squarer Belpaire firebox . [ 14 ] No. 461, a 2-6-0 DSER 15 and 16 Class heavy goods locomotive, is the only Dublin and South Eastern Railway example that has been preserved. [ 15 ]
Shunting locomotives are useful and economical for shunting and short passenger work within Whitehead yard. These include the 0-6-0 ST .3 'R.H. Smyth' , affectionally known as Harvey , which has also been used to pull ballast hoppers for NIR . [ 16 ] There is also No3BG "Guinness", a Hudswell Clarke engine presented by Guinness to the Society in 1965. [ 17 ]
The RPSI has indicated it has a strategy to create a mainline heritage diesel fleet. [ 18 ] It has acquired four c. 65t 1,000 horsepower (750 kW) General Motors Bo-Bos ; CIÉ 121 Class number 134 and CIÉ 141 Class numbers 141, 142 and 175. [ 8 ] [ 19 ]
The RPSI used to own two NIR 101 Class Hunslet diesels Numbered 101 and 102. [ 20 ] They scrapped 101 and 102 was transferred to the Ulster Folk & Transport Museum. [ citation needed ]
The RPSI also has some small diesel shunters, including a Ruston from Carlow sugar factory, a planet diesel from Irish Shell and a unilok diesel from the UTA. [ 21 ]
In the 2000s, with more rail stringent regulations, the RPSI was forced to acquire rakes of metal bodied carriages for mainline railtours. [ 22 ]
Whitehead has a collection of historic wagons, including a GNR brakevan named Ivan, restored by their award-winning Youth team, a Guinness van and NCC handcrane and a GSWR ballast hopper and an oil tanker from Irish Shell.
The main work of the society is in securing and maintaining steam rolling stock, with a view to running rail tours and Mulligan, in "One Hundred and Fifty Years of Irish Railways" noted that the RPSI did "sterling work" in the area of organising of such rail tours around the island, following the end of steam as a regular means of service provision on UTA and CIÉ lines. [ 23 ]
The RPSI has been able to assist in the provision of suitable rolling stock for train-related scenes in films made on the island of Ireland. [ 23 ] The shooting of The First Great Train Robbery in 1978 was an early significant involvement in film making by the RPSI. [ 24 ]
Five Foot Three is the RPSI's membership magazine. It is published annually [ 25 ]
On 7 November 2014, an RPSI train chartered by Web Summit blocked a level crossing in Midleton for over 25 minutes. The operation was referred to the Commission for Railway Regulation. The resulting investigation found that the Society had knowingly run a train that was too long for the station's platform and that it would block a level crossing, yet senior IR management overrode their internal safety department by allowing the train to run. [ 26 ] [ 27 ] [ 28 ]
On 7 July 2019, a serious incident occurred at Gorey when No.85 ran out of water and the fusible plug melted in the firebox. The Civil Defense had to cool down the boiler with hoses while the crew were evacuated from the cab and a rescue diesel summoned from Dublin. [ 29 ] [ 30 ]
Media related to Railway Preservation Society of Ireland at Wikimedia Commons | https://en.wikipedia.org/wiki/Railway_Preservation_Society_of_Ireland |
Railway Technical Research Institute ( 鉄道総合技術研究所 , Tetsudō Sōgō Gijutsu Kenkyūsho ) , or RTRI ( 鉄道総研 , Tetsudō Sōken ) , is the technical research company under the Japan Railways group of companies.
RTRI was established in its current form in 1986 just before Japanese National Railways (JNR) was privatised and split into separate JR group companies. It conducts research on everything related to trains, railways and their operation. It is funded by the government and private rail companies. It works both on developing new railway technology, such as magnetic levitation , and on improving the safety and economy of current technology.
Its research areas include earthquake detection and alarm systems, obstacle detection on level crossings, improving adhesion between train wheels and tracks, reducing energy usage, noise barriers and preventing vibrations.
RTRI is the main developer in the Japanese SCMaglev program.
The RTRI is developing a variable gauge system, called the " Gauge Change Train ", to allow 1,435 mm ( 4 ft 8 + 1 ⁄ 2 in ) Shinkansen trains to access 1,067 mm ( 3 ft 6 in ) lines of the original rail network. [ 2 ] | https://en.wikipedia.org/wiki/Railway_Technical_Research_Institute |
A train accident or train wreck is a type of disaster involving one or more trains . Train wrecks often occur as a result of miscommunication , as when a moving train meets another train on the same track, when the wheels of train come off the track or when a boiler explosion occurs. Train accidents have often been widely covered in popular media and in folklore . A head-on collision between two trains is colloquially called a " cornfield meet " in the United States. [ 1 ]
Classification of railway accidents , both in terms of cause and effect, is a valuable aid in studying rail (and other) accidents to help to prevent similar ones occurring in the future. Systematic investigation for over 150 years has led to the railways' excellent safety record (compared, for example, with road transport ). Ludwig von Stockert (1913) proposed a classification of accidents by their effects (consequences); e.g. head-on-collisions , rear-end collisions , derailments . Schneider and Mase (1968) proposed an additional classification by causes; e.g. driver 's errors, signalmen 's errors, mechanical faults. Similar categorisations had been made by implication in previous books e.g. Rolt (1956), but Stockert's and Schneider/Mase's are more systematic and complete. With minor changes, they represent best knowledge.
Other | https://en.wikipedia.org/wiki/Railway_accident |
Railway costing is the calculation of the variable and fixed costs of rail movements. Variable costs are those that increase or decrease with changes in the traffic volumes or service levels and include fuel, maintenance and train crew costs, for example. Fixed costs are normally associated with items such as head office, interest charges and other overhead. Unit costs can then be calculated based on the expenses of the railway divided into standard categories.
In order to assist in its deliberations regarding rate and service complaints, the Canadian Transportation Agency has identified various types of costs. These costs include:
The methodology used in railway costing breaks down the costs of rail traffic to their unit value and from there determines their relationship to traffic handled and service provided. Therefore, as traffic and services change, the effect of these changes can be estimated from the unit values previously determined. The costing model methodology allows for variable costs to increase as traffic increases, whereas the fixed costs will remain constant, regardless of the overall level of traffic.
Railway costing is typically performed using mathematical models . Using unit costs from current operating data and current accounting and operating information, it is possible to develop costing information for the railway. This costing information may be used to estimate the operating cost of a new line and to determine whether it is economically viable. Alternatively, the model could be used to estimate the cost effects of changing speed limits along a route. The savings that can be achieved with a railway costing model are endless. For example, by knowing the costs of doing business, a railway can appropriately determine the tariffs to be charged.
In addition, railway costing models typically handle passenger and freight traffic, making them applicable in more situations, including mixed traffic situations.
some commercial variations of railway costing models have been implemented, including the OSCAR railway costing model developed by CPCS Transcom Limited . CPCS is an international infrastructure development firm and has successfully used this model in dozens of its projects worldwide.
The Cartage railway costing model was developed by Vectorail, a global supplier of railway costing solutions with more than forty years of experience in the field. | https://en.wikipedia.org/wiki/Railway_costing |
Railway engineering is a multi-faceted engineering discipline dealing with the design, construction and operation of all types of rail transport systems. It encompasses a wide range of engineering disciplines, including civil engineering , computer engineering , electrical engineering , mechanical engineering , industrial engineering and production engineering . A great many other engineering sub-disciplines are also called upon.
With the advent of the railways in the early nineteenth century, a need arose for a specialized group of engineers capable of dealing with the unique problems associated with railway engineering. As the railways expanded and became a major economic force, a great many engineers became involved in the field, probably the most notable in Britain being Richard Trevithick , George Stephenson and Isambard Kingdom Brunel . Today, railway systems engineering continues to be a vibrant field of engineering.
This rail-transport related article is a stub . You can help Wikipedia by expanding it .
This engineering-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Railway_engineering |
Railway spine was a nineteenth-century diagnosis for the post-traumatic symptoms of passengers involved in railroad accidents .
The first full-length medical study of the condition was John Eric Erichsen 's classic book, On Railway and Other Injuries of the Nervous System . [ 1 ] For this reason, railway spine is often known as Erichsen's disease .
Railway collisions were a frequent occurrence in the early 19th century. Exacerbating the problem was that railway cars were flimsy, wooden structures with no protection for the occupants.
Soon a group of people started coming forward who claimed that they had been injured in train crashes, but had no obvious evidence of injury. The railroads rejected these claims as fake, sometimes belittling people's pain as litigation neurosis , implying that the only real problem was the injured person making a legal claim. [ 2 ]
The nature of symptoms caused by "railway spine" was hotly debated in the late 19th century, notably at the meetings of the (Austrian) Imperial Society of Physicians in Vienna, 1886. Germany's leading neurologist, Hermann Oppenheim , claimed that all railway spine symptoms were due to physical damage to the spine or brain, whereas French and British scholars, notably Jean-Martin Charcot and Herbert Page, insisted that some symptoms could be caused by hysteria (now known as conversion disorder ). [ 3 ] [ 4 ] [ 5 ]
Erichsen observed that those most likely to be injured in a railway crash were those sitting with their backs to the acceleration. This is the same injury mechanism found in whiplash . As with automobile accidents, railway and airplane accidents are now known to cause posttraumatic stress disorder (PTSD) and other psychosomatic symptoms in addition to physical trauma. [ 6 ] | https://en.wikipedia.org/wiki/Railway_spine |
Railway troops are soldiers who are also railway engineers . They build, repair, operate or destroy militarily relevant railway lines and their associated infrastructure.
The establishment of railway troops by the great powers followed the emergence, rapid growth and rising importance of the railway network, when the advantages of the railway for the transport of troops, heavy weapons and supplies became recognised. Originally these were known (at least in the German-speaking areas of Europe) as field railways . In many countries, however, there were little or no military units of this type.
In the American Civil War , unlimited authority over all railway lines in the North was given to General McClellan . To begin with, McClellan formed a construction corps from ordinary soldiers, but he soon recognised that the lack of training of these troops for technical work meant that a specially organised corps was needed within the Union Army for technically trained civil engineers and workers. During the war this branch of the army grew to about 25,000 men. They were divided into railway operating units as well as construction units with sub-units for line and bridge building.
The construction units had the task of building new lines, repairing destroyed railway facilities or even destroying them themselves. The operating units managed the provision and proper use of operational materiel and services. For large construction projects, civilian workers were also contracted, for example, up to 1,400 carpenters were employed to build the Etowah and Chattahoochee Bridge.
The large and often decisive influence that these railway troops had on the course of the American Civil war, resulted in the European states establishing similar formations.
In 1866, Prussia formed three railway units during mobilisation for the Austro-Prussian War . These units comprised twelve railway engineers and a detachment of about 50 men provided by the Ministry of Trade .
The 2nd Railway Regiment ( II. Eisenbahnregiment ) was linked to the Royal Prussian Military Railway at Berlin. This railway, which was part of the army budget was managed by the Royal Military Railway Division ( Königliche Direction der Militäreisenbahn ).
The activity of the railway regiment was similar to that of the American construction units, whilst operating commissions ( Betriebskommissionen ), specially raised by the Ministry of Trade, ran operations on the occupied railways.
Until the First World War , there was a Royal Bavarian Railway Battalion in Bavaria . A monument in the Bundeswehr Headquarters on Munich 's Dachauer Straße (on the corner of Hedwig-Dransfeld-Allee) commemorates the Bavarian railway troops and is open to the public.
Experience from the Austro-Prussia War led to plans for a permanent military organisation for field railways which, even during peacetime, would maintain a cadre of personnel trained in railway engineering. Because this could not be achieved by the outbreak of the Franco-Prussian War in 1870, field railway units were again raised: five Prussian units and one Bavarian unit. They were, however, considerably better equipped than those of 1866: each had 20 civilian engineers, 4 officers and about 200 foremen and soldiers. In addition, for larger construction tasks, additional civilian workers were engaged. The operation of railway in the occupied territories was again taken over by operating commissions. The railway units were frequently deployed during the Franco-Prussian War, for example in repairing bridges that had been destroyed and in constructing the railway to circumnavigate the fortress at Metz .
In Prussia, on 1 October 1871, a railway battalion was formed, the basis for the subsequent railway regiment and for the Railway Brigade, established on 1 April 1890, which had 3 regiments each of two battalions of four companies . The Railway Brigade was given a depot management and an operating unit for the operation of the Royal Prussian Military Railway , whose officers and men were provided in turn by various the units within the Brigade.
From 1 October 1899, the railway troops became part of the Corps of Transport ( Verkehrstruppen ) and were thus placed under the Inspector of Transport. Its men were trained in railway construction and railway operations and were intended to replace the old field railway units with railway companies and the operation commissions with railway operating companies and military railway divisions. In war, the railway troops were reinforced by reserves and Landwehr soldiers .
To train the railway troops, responsibility for managing the railway line from Berlin via Zossen to Jüterbog ( Royal Prussian Military Railway ) had been transferred to the army. [ 1 ]
In addition to these facilities for the construction and operation of standard gauge railway, the railway troops managed materiel in order to be able to build and operate field railways . These were utilised on a large scale during the First World War behind the front line for the transport of troops and supplies. The field railways were subordinated to the Master of Field Railways ( Chef des Feldeisenbahnwesens or FECH). Railways troops were also deployed to protect the Deutsche Reichsbahn during the Second World War .
Shortly after its foundation, the Bundeswehr established a railway engineering training and trials company which, in 1961, was renamed (Sp)PiLVsuKp 872 and became part of 870 Special Engineer Training and Trials Battalion ( Spezialpionierlehr- und Versuchsbataillon 870 ) in the German Territorial Army . The company was disbanded in 1974 and its tasks taken on by other engineer units.
In the NVA there continued to be railway engineer units. As a result, the history of railway troops in Germany ended with the disbandment of the NVA in 1990.
The Spanish Army maintained a railway engineering unit until 2008, this being the Railway Regiment No. 13 ( Regimiento de Ferrocarriles Nº 13 ). It originated with the railway companies created in 1872, in each of the two then existing engineer regiments. In 1884, a Railway Battalion was created. This was increased to a regiment in 1912, further being increased to two regiments in 1936. During the Spanish Civil War , two railway groups were created, these being the Railway Mobilization and Practice Battalions Group and the Railway Sappers Battalions Group. In 1963, these were transformed into regiments. In 1994, the two regiments were merged into the single Railway Regiment No 13, which was disbanded in 2008. [ 2 ]
Until 2003, the Swiss Army had a branch of service for military railway operations and for a few years beyond that continued to have the so-called Eisenbahnsappeurkompanien ("railway engineer companies"). [ 3 ] [ 4 ] It operated the ten-storey underground K85 command bunker in Zürich, which was accessible via the Hirschengraben Tunnel and is not open to the public today. [ 5 ] | https://en.wikipedia.org/wiki/Railway_troops |
The railway network of Sardinia includes lines that develop for a total of about 1,038 km in length, of which 430 km [ 1 ] with an ordinary gauge and about 608 km [ 2 ] narrow gauge (950 mm ), with an average density of 43 m of rail per km 2 , a figure that drops to 25 m/km 2 considering only public transport lines.
Railway operations on the island are managed by two companies. The first, the Ferrovie dello Stato Italiane group, manages the 4 ordinary gauge railway lines that make up the main network of the island through the subsidiaries RFI and Trenitalia. The remaining 4 sections active in public transport, all narrow gauge, constitute the secondary network, extended by 169 km [ 3 ] and entirely managed by ARST Sp A., a transport company wholly owned by the Autonomous Region of Sardinia. [ 4 ] This company also controls 438 km [ 3 ] of tourist lines, always narrow gauge, active especially in summer and at the request of groups of tourists.
The Sardinian railway network is present in all provinces, even if there are areas without railways. There are also several railways (all narrow gauge) which over the decades have been closed and dismantled.
Sardinia, immediately after the Unification of Italy, found itself to be the only territory in the Kingdom without a railway network for public transport: the only lines present were in fact private railways for industrial use. The first railway to enter into operation on the island was the one between the mine of San Leone and the pier of La Maddalena near Capoterra, [ 5 ] a line open to traffic in 1862 . The lack of a public railway network led island politicians several times to request government intervention to grant this service also to Sardinia.
After various doubts and objections from national politicians, in 1862 an Italian-English consortium, headed by cavalier Gaetano Semenza, obtained the concession for the construction of the network that would link Cagliari to Iglesias, Porto Torres and Terranova Pausania (in Olbia). The consortium formed the Royal Company of the Sardinian Railways in London, which between studies of the routes, problems of conventions with the State and of various kinds, opened the first stretch of railway (Cagliari- Villasor) in April 1871.
The construction of the planned lines, based on a project by the Welsh engineer Benjamin Piercy, ended in 1881, but in the meantime, for the traffic of passengers to the continent, it was decided to use the new maritime docking of Golfo Aranci instead of that of Terranova. The fact made it necessary to build an extension of the railway, which joined the two Gallura ports in 1883.
Sardinia finally had its own railways and, as of December 31, 1899, 30 steam locomotives, 106 carriages, 23 baggage and 436 wagons for freight service were operating on the Royal Railways.
However, the layout of the Royal Railways network excluded various areas of the island from the possibility of using trains. In fact, many centers complained that they had been cut off from this very important progress in island transport [ 6 ] because of the distance from the railway tracks. It was thus decided in 1885, with Law 3011 of March 22 of that year, to grant the possibility of building a secondary network that connected the more isolated centers with the main cities and with the network of the Royal Railways. Given the specific request for an economy construction, it was decided to use a 950 mm track gauge, which would also have helped the engineers in planning the routes in the inaccessible internal areas of Sardinia/
The following year the works were entrusted to the " Italian Society for the Secondary Railways of Sardinia " (SFSS), which, building at a fast pace, inaugurated its first lines after only 17 months. In fact, already on February 15, 1888 the SFSS opened the Cagliari-Isili and the line from Tempio Pausania to the SFSS station in Monti, which borders the homonymous port of the Royal Railways . By the end of the decade they were also inaugurated the dorsal Bosa - Macomer - Nuoro and Sassari-Alghero, while from Isili the railway was extended to arise .
Before the end of the century, the Mandas-Arbatax and its Gairo-Jerzu branch were also inaugurated, in addition another link connecting the main and secondary networks was opened to traffic, connecting the Tirso station of Macomer-Nuoro to the strategic Chilivani slipway . In all 590 km of railway track were built, and in many cases the works were completed well in advance, also thanks to the workers who came to build on average 300 meters of line per day. This figure is even more significant if we consider the morphology of the territories where the lines were made and the physical effort that the excavations and drilling in the rock required to the teams of workers.
However, the project was not without criticism from many users, who contested the excessive distance of most of the stations from their respective villages, [ 7 ] which was linked to the exploitation of the internal forests of the island, whose valuable timber was transported by the new railway. [ 8 ] Furthermore, the average speeds maintained by the SFSS trains, certainly not very high, created some discontent among the passengers. [ 7 ] [ 8 ]
In 1898, meanwhile, the extension of the ordinary gauge network grew by 6 km, those of the new portion of the railway track open between Iglesias and its hamlet Monteponi, strategically important for the transport of minerals that were extracted in this location and in the surrounding area.
Despite the complaints, both networks fully achieved the purpose for which they were born, that is to encourage the transport of people and goods between the various areas of Sardinia, until then only linked to animal traction vehicles. The importance of the railway for the island can be seen from the length of the trips, which were no longer measured in days, but in hours.
In any case, the areas isolated from the railway were still several, and in the years immediately preceding the First World War the regional authorities asked the various mayors for proposals and advice for new railway lines. Among the recommended railways, many were rejected due to lack of funds or uneconomicness. Other lines were planned, such as those of the Sulcis (whose connections at that time were ensured by car transport [ 9 ] ), but the war forced a postponement of the works, while some proposals for relations in the Sassari area were taken into consideration in the subsequent years.
In those years the only railways to see the light were Isili-Villacidro and its Villamar-Ales branch. The project for the construction of these lines was approved in 1912, and construction was entrusted to the " Society for the Complementary Railways of Sardinia " (FCS). The project also included the use of 5 km of the Isili-Sorgono line, in the stretch between Isili and the Sarcidano station (where the new railway actually started), which led to the common management of this portion of the line with the SFSS. The inauguration of the two lines dates back to June 21, 1915, and the first passengers on the trains were the soldiers leaving for the battlefields of the First World War.
Over the years, the Sardinian railway network has remained largely unchanged as a route: not considering the closure of some sections, the only changes to the routes concerned mainly small / medium-sized variants and rectification works to speed up journeys. In any case, the total lack of electrification of the network and the tortuosity of the lines in certain areas mean that the average train speeds are rather low compared to the rest of Italy, [ 10 ] which in some cases has compromised the competitiveness of the railway towards bus lines. [ 10 ]
Commonly, the Sardinian network is divided into the main ordinary gauge network (that of the FS, managed through the subsidiary Rete Ferroviaria Italiana ) and the secondary narrow gauge network (of the ARST).
Various lines closed after the Second World War and were subsequently dismantled, in almost all cases due to the choice of converting services to road transport, which was considered cheaper.
The grounds and infrastructure works (bridges, tunnels) are however still present, and in more than one case the proposal has been made to recover these routes as cycle paths. [ 11 ] | https://en.wikipedia.org/wiki/Railways_in_Sardinia |
Railworthiness [ 1 ] [ 2 ] is the property or ability of a locomotive , passenger car , freight car , train or any kind of railway vehicle to be in proper operating condition or to meet acceptable safety standards of project , manufacturing , maintenance and railway use for transportation of persons, luggage or cargo .
Railworthiness is the condition of the rail system and its suitability for rail operations in that it has been designed, constructed, maintained and operated to approved standards and limitations by competent and authorised individuals, who are acting as members of an approved organisation and whose work is both certified as correct and accepted on behalf of the rail system owner.
This rail-transport related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Railworthiness |
Rain Without Thunder: The Ideology of the Animal Rights Movement is a 1996 book by American legal scholar Gary L. Francione . The basic premise of the book is that there is a fundamental difference between those that call for animal welfare reform and those that call for the complete abolition of animal use (called ' welfarism ' and ' abolitionism '), and that animals have a fundamental right to not be exploited.
Francione argues that the animal rights movement only emerged in the late 1970s and 1980s. Until that time, concern for animals was limited to ensuring that animals were well cared for during their exploitation. [ 1 ] The animal rights position calls for the total abolition of animal use and exploitation, as "animals, like humans, have inherent value that must be respected". [ 2 ]
Francione also describes a third category, which is that of the 'new welfarist'. New welfarists are those that argue the best path to animal rights or abolition is through welfare reform and believe that welfare reform will make humans more receptive to inherently valuing animals. Francione argues that new welfarism does not work, and actually prolongs animal exploitation . Francione describes the welfarist or new welfarist movement as simply advocating for "longer chains for the slaves".
Francione describes the differing philosophies of Peter Singer and Tom Regan toward animal use. He criticises heavily the utilitarian position of Singer, [ 3 ] who believes that animal use is acceptable so long as their interests are given equal consideration to humans, and praises Regan's deontological position of giving all animals rights.
Francione argues that most animal rights groups are too passive in their approach, and have diluted their messages in the hopes of gaining cultural acceptance. [ 3 ] The only group which has not done this, according to Francione, is Animal Liberation Front , which performs rescues for animals, often of a dangerous or illegal nature.
One of the key criticisms that Francione makes of welfarists and new welfarists is that welfarism reform simply does not work, and in fact is harmful to the cause as welfare reform is argued to make people more comfortable with animal exploitation, and therefore less likely to stop using animals. Welfare reform is also claimed to make the animal exploitation industry more efficient. [ 4 ] Carcass damage occurs when food animals are improperly slaughtered and bruise themselves in their deathroes. Welfare reform to slaughter animals more humanely reduces the likelihood of this occurring, improving profits and public image for animal slaughterers.
Francione argues that advocating for welfare reform does nothing to challenge the 'research establishment', and in fact that the livestock industry already advocates welfare reform. [ 3 ] The Animal Welfare Act , passed in 1966 and amended in 1985, is heralded as a victory by welfare advocates, but is useless according to Francione, and is indistinguishable from the status quo.
Francione claims that the methodology of new welfarists in pursuing welfare reform cannot result in the abolition of their legal property status, which he argues is what matters most. [ 5 ] [ 6 ] Further, he argues that the short and long term goals of new welfarism are in direct conflict. He also argues that it is wrong to surrender the rights of animals today in the hopes of achieving rights for animals sometime in the future.
Rain Without Thunder and the views depicted within have been criticised by those within the animal movement. One criticism is that Francione depicts a purist ideal and does not care for incremental approaches to animal welfare, but wants the end of animal use now and is not interested in discussing the practicality or methodology to make this happen. [ 7 ]
Francione heavily criticises utilitarianism, particularly through its main modern proponent, Peter Singer. The book has been criticised, however, for not stepping into the active debate between consequentialism and deontology , instead taking it for granted that deontology and a rights approach are correct. [ 3 ] In praising Tom Regan, he ignores the fact that Regan himself is an advocate of a hierarchy that allows the killing of some forms of life but not mammals. [ 3 ]
The style of the book itself has been criticised as being long-winded and repetitive, with excessive detail that would be of interest only to an insider of the movement. [ 3 ] | https://en.wikipedia.org/wiki/Rain_Without_Thunder_(book) |
Rain gardens , also called bioretention facilities , are one of a variety of practices designed to increase rain runoff reabsorption by the soil. They can also be used to treat polluted stormwater runoff . Rain gardens are designed landscape sites that reduce the flow rate, total quantity, and pollutant load of runoff from impervious urban areas like roofs, driveways, walkways, parking lots, and compacted lawn areas. [ 1 ] Rain gardens rely on plants and natural or engineered soil medium to retain stormwater and increase the lag time of infiltration , while remediating and filtering pollutants carried by urban runoff. Rain gardens provide a method to reuse and optimize any rain that falls, reducing or avoiding the need for additional irrigation . A benefit of planting rain gardens is the consequential decrease in ambient air and water temperature, a mitigation that is especially effective in urban areas containing an abundance of impervious surfaces that absorb heat in a phenomenon known as the heat-island effect . [ 2 ]
Rain garden plantings commonly include wetland edge vegetation, such as wildflowers , sedges , rushes , ferns , shrubs and small trees . These plants take up nutrients and water that flow into the rain garden, and they release water vapor back to the atmosphere through the process of transpiration . [ 3 ] Deep plant roots also create additional channels for stormwater to filter into the ground. Root systems enhance infiltration , maintain or even augment soil permeability, provide moisture redistribution, and sustain diverse microbial populations involved in biofiltration . [ 4 ] Microbes help to break down organic compounds (including some pollutants) and remove nitrogen.
Rain gardens are beneficial for many reasons; they improve water quality by filtering runoff, provide localized flood control , create aesthetic landscaping sites, and provide diverse planting opportunities. They also encourage wildlife and biodiversity , tie together buildings and their surrounding environments in integrated and environmentally advantageous ways. Rain gardens can improve water quality in nearby bodies of water and recharge depleted groundwater supply. Rain gardens also reduce the amount of polluted runoff that enters the storm sewer system, which discharges directly to surface waters and causes erosion , water pollution and flooding . [ 5 ] Rain gardens also reduce energy consumption by decreasing the load on conventional stormwater infrastructure.
The first rain gardens were created to mimic the natural water retention areas that developed before urbanization occurred. The rain gardens for residential use were developed in 1990 in Prince George's County, Maryland , when Dick Brinker, a developer building a new housing subdivision had the idea to replace the traditional best management practices (BMP) pond with a bioretention area. He approached Larry Coffman, an environmental engineer and the county's Associate Director for Programs and Planning in the Department of Environmental Resources, with the idea. [ 6 ] The result was the extensive use of rain gardens in Somerset, a residential subdivision which has a 300–400 sq ft (28–37 m 2 ) rain garden on each house's property. [ 7 ] This system proved to be highly cost-effective. Instead of a system of curbs , sidewalks , and gutters , which would have cost nearly $400,000, the planted drainage swales cost $100,000 to install. [ 6 ] This was also much more cost effective than building BMP ponds that could handle 2-, 10-, and 100-year storm events. [ 6 ] Flow monitoring done in later years showed that the rain gardens have resulted in a 75–80% reduction in stormwater runoff during a regular rainfall event. [ 7 ]
Some de facto rain gardens predate their recognition by professionals as a significant LID ( Low Impact Development ) tool. Any shallow garden depression implemented to capture and filter rain water within the garden so as to avoid draining water offsite is at conception a rain garden—particularly if vegetation is planted and maintained with recognition of its role in this function. Vegetated roadside swales , now promoted as “ bioswales ”, remain the conventional runoff drainage system in many parts of the world from long before extensive networks of concrete sewers became the conventional engineering practice in the industrialized world. What is new about such technology is the emerging rigor of increasingly quantitative understanding of how such tools may make sustainable development possible. This is as true for developed communities retrofitting bioretention into existing stormwater management infrastructure as it is for developing communities seeking a faster and more sustainable development path. [ citation needed ]
In developed urban areas, naturally occurring depressions where storm water would pool are typically covered by impermeable surfaces, such as asphalt , pavement, or concrete, and are leveled for automobile use. Stormwater is directed into storm drains which may cause overflows of combined sewer systems or pollution, erosion , or flooding of waterways receiving the storm water runoff. [ 8 ] [ 9 ] [ 10 ] Redirected stormwater is often warmer than the groundwater normally feeding a stream, and has been linked to upset in some aquatic ecosystems primarily through the reduction of dissolved oxygen (DO). Stormwater runoff is also a source of a wide variety of pollutants washed off hard or compacted surfaces during rain events. These pollutants may include volatile organic compounds , pesticides , herbicides , hydrocarbons and trace metals . [ 11 ]
Stormwater management occurs on a watershed scale to prevent downstream impacts on urban water quality. [ 12 ] A watershed is maintained through the cyclical accumulation, storage, and flow of groundwater . [ 2 ] Naturally occurring watersheds are damaged when they are sealed by an impervious surface, which diverts pollutant-carrying stormwater runoff into streams. Urban watersheds are affected by greater quantities of pollutants due to the consequences of anthropogenic activities within urban environments. [ 13 ] Rainfall on impermeable surfaces accumulates surface runoff containing oil, bacteria, and sediment that eventually makes its way to streams and groundwater. [ 2 ] Stormwater control strategies such as infiltration gardens treat contaminated surface runoff and return processed water to the underlying soil, helping to restore the watershed system. The effectiveness of stormwater control systems is measured by the reduction of the amount of rainfall that becomes runoff ( retention ), and the lag time (rate of depletion) of the runoff. [ 14 ] Even rain gardens with small capacities for daily infiltration can create a positive cumulative impact on mitigating urban runoff. Increasing the number of permeable surfaces by designing rain gardens reduces the amount of polluted stormwater that reaches natural bodies of water and recharges groundwater at a higher rate. [ 15 ] Additionally, adding a rain garden to a site that experiences excessive rainwater runoff mitigates the water quantity load on public stormwater systems. [ citation needed ]
The bioretention approach to water treatment, and specifically rain gardens in this context, is two-fold: to utilize the natural processes within landscapes and soils to transport, store, and filter stormwater before it becomes runoff, and to reduce the overall amount of impervious surface covering the ground that allow for contaminated urban runoff. [ 16 ] Rain gardens perform most effectively when they interact with the greater system of stormwater control. This integrated approach to water treatment is called the "stormwater chain", which consists of all associated techniques to prevent surface run-off, retain run-off for infiltration or evaporation, detain run-off and release it at a predetermined rate, and convey rainfall from where it lands to detention or retention facilities. [ 16 ] Rain gardens have many reverberating effects on the greater hydrological system. In a bioretention system such as a rain garden, water filters through layers of soil and vegetation media, which treat the water before it enters the groundwater system or an underdrain. Any remaining runoff from a rain garden will have a lower temperature than runoff from an impervious surface, which reduces the thermal shock on receiving bodies of water. Additionally, increasing the amount of permeable surfaces by designing urban rain gardens reduces the amount of polluted stormwater that reaches natural bodies of water and recharges groundwater at a higher rate. [ 17 ]
The concept of LID (low-impact design) for stormwater management is based on bioretention : a landscape and water design practice that utilizes the chemical, biological, and physical properties of soils, microorganisms, and plants to control the quality and quantity of water flow within a site. [ 16 ] Bioretention facilities are primarily designed for water management, and can treat urban runoff, stormwater, groundwater, and in special cases, wastewater . Carefully designed constructed wetlands are necessary for the bioretention of sewage water or grey water , which have greater effects on human health than the implications of treating urban runoff and rainfall. Environmental benefits of bioretention sites include increased wildlife diversity and habitat production and minimized energy use and pollution. Prioritizing water management through natural bioretention sites eliminates the possibility of covering the land with impermeable surfaces. [ 18 ]
Bioretention controls the stormwater quantity through interception, infiltration, evaporation, and transpiration. [ 16 ] First, rainfall is captured by plant tissue (leaves and stems) and in the soil micropores . Then, water performs infiltration - the downward movement of water through soil - and is stored in the soil until the substrate reaches its moisture capacity, when it begins to pool at the top of the bioretention feature. The pooled water and water from plant and soil surfaces is then evaporated into the atmosphere. Optimal design of bioretention sites aim for shallow pooled water to reach a higher rate of evaporation. Water also evaporates through the leaves of the plants in the feature and back to the atmosphere, which is a process known as evapotranspiration . [ 19 ]
Stormwater quality can be controlled by bioretention through settling, filtration, assimilation, adsorption , degradation, and decomposition. [ 16 ] When water pools on top of a bioretention feature, suspended solids and large particles will settle out. Dust particles, soil particles, and other small debris are filtered out of the water as it moves downward through the soil and interspersed plant roots. Plants take up some of the nutrients for use in their growth processes, or for mineral storage. Dissolved chemical substances from the water also bind to the surfaces of plant roots, soil particles, and other organic matter in the substrate and are rendered ineffective. Soil microorganisms break down remaining chemicals and small organic matter and effectively decompose the pollutants into a saturated soil matter. [ 20 ]
Even though natural water purification is based on the design of planted areas, the key components of bioremediation are the soil quality and microorganism activity. These features are supported by plants, which create secondary pore space to increase soil permeability, prevent soil compaction through complex root structure growth, provide habitats for the microorganisms on the surfaces of their roots, and transport oxygen to the soil. [ 20 ]
Stormwater garden design encompasses a wide range of features based on the principles of bioretention. These facilities are then organized into a sequence and incorporated into the landscape in the order that rainfall moves from buildings and permeable surfaces to gardens, and eventually, to bodies of water. A rain garden requires an area where water can collect and infiltrate , and plants can maintain infiltration rates, diverse microorganism communities, and water storage capacity. Because infiltration systems manage storm water quantity by reducing storm water runoff volumes and peak flows, rain garden design must begin with a site analysis and assessment of the rainfall loads on the proposed bioretention system. [ 13 ] This will lead to different knowledge about each site, which will affect the choice of plantings and substrate systems. At a minimum, rain gardens should be designed for the peak runoff rate during the most severe expected storm. The load applied on the system will then determine the optimal design flow rate. [ 15 ]
Existing gardens can be adapted to perform like rain gardens by adjusting the landscape so that downspouts and paved surfaces drain into existing planting areas. Even though existing gardens have loose soil and well-established plants, they may need to be augmented in size and/or with additional, diverse plantings to support a higher infiltration capacity. Also, many plants do not tolerate saturated roots for long and will not be able to handle the increased flow of water. Rain garden plant species should be selected to match the site conditions after the required location and storage capacity of the bioretention area are determined. In addition to mitigating urban runoff, the rain garden may contribute to urban habitats for native butterflies , birds , and beneficial insects . [ 21 ]
Rain gardens are at times confused with bioswales . Swales slope to a destination, while rain gardens are level; however, a bioswale may end with a rain garden as a part of a larger stormwater management system. Drainage ditches may be handled like bioswales and even include rain gardens in series, saving time and money on maintenance. Part of a garden that nearly always has standing water is a water garden , wetland , or pond, and not a rain garden. Rain gardens also differ from retention basins , where the water will infiltrate the ground at a much slower rate, within a day or two. [ 22 ]
Collected water is filtered through the strata of soil or engineering growing soil, called substrate. After the soil reaches its saturation limit, excess water pools on the surface of the soil and eventually infiltrates the natural soil below. The bioretention soil mixture should typically contain 60% sand , 20% compost , and 20% topsoil . Soils with higher concentrations of compost have shown improved effects on filtering groundwater and rainwater. [ 23 ] Non-permeable soil needs to be removed and replaced periodically to generate maximum performance and efficiency if used in the bioretention system. The sandy soil (bioretention mixture) cannot be combined with a surrounding soil that has a lower sand content because the clay particles will settle in between the sand particles and form a concrete-like substance that is not conducive to infiltration, according to a 1983 study. [ 24 ] Compact lawn soil cannot harbor groundwater nearly as well as sandy soils, because the micropores within the soil are not sufficient for retaining substantial runoff levels. [ 16 ]
When an area's soils are not permeable enough to allow water to drain and filter at an appropriate rate, the soil should be replaced and an underdrain installed. Sometimes a drywell with a series of gravel layers near the lowest spot in the rain garden will help facilitate percolation and avoid clogging at the sedimentation basin. [ 13 ] However, a drywell placed at the lowest spot can become clogged with silt prematurely, turning the garden into an infiltration basin and defeating its purpose as a bioretention system. The more polluted the runoff water, the longer it must be retained in the soil for purification. Capacity for a longer purification period is often achieved by installing several smaller rain garden basins with soil deeper than the seasonal high water table . In some cases lined bioretention cells with subsurface drainage are used to retain smaller amounts of water and filter larger amounts without letting water percolate as quickly. A five-year study by the U.S. Geological Survey indicates that rain gardens in urban clay soils can be effective without the use of underdrains or replacement of native soils with the bioretention mix. Yet it also indicates that pre-installation infiltration rates should be at least .25 in/hour. Type D soils will require an underdrain paired with the sandy soil mix in order to drain properly. [ 25 ]
Rain gardens are often located near a building's roof drainpipe (with or without rainwater tanks ). Most rain gardens are designed to be an endpoint of a building's or urban site's drainage system with a capacity to percolate all incoming water through a series of soil or gravel layers beneath the surface plantings. A French drain may be used to direct a portion of the rainwater to an overflow location for heavier rain events. If the bioretention site has additional runoff directed from downspouts leading from the roof of a building, or if the existing soil has a filtration rate faster than 5 inches per hour, the substrate of the rain garden should include a layer of gravel or sand beneath the topsoil to meet that increased infiltration load. [ 2 ] If not originally designed to include a rain garden onsite, downpipes from the roof can be disconnected and diverted to a rain garden for retrofit stormwater management. This reduces the amount of water load on the conventional drainage system, and instead directs water for infiltration and treatment through bioretention features. By reducing peak stormwater discharge, rain gardens extend hydraulic lag time and somewhat mimic the natural water cycle displaced by urban development and allow for groundwater recharge. While rain gardens always allow for restored groundwater recharge, and reduced stormwater volumes, they may not improve pollution unless remediation materials are included in the design of the filtration layers. [ 26 ]
Typical rain garden plants are herbaceous perennials and grasses, which are chosen for their porous root structure and high growth rate. [ 16 ] Trees and shrubs can also be planted to cover larger areas on the bioretention site. Although specific plants are selected and designed for respective soils and climates, [ 27 ] plants that can tolerate both saturated and dry soil are typically used for the rain garden. They need to be maintained for maximum efficiency, and be compatible with adjacent land uses. Native and adapted plants are commonly selected for rain gardens because they are more tolerant of the local climate, soil, and water conditions; have deep and variable root systems for enhanced water infiltration and drought tolerance; increase habitat value, diversity for local ecological communities, and overall sustainability once established. Vegetation with dense and uniform root structure depth helps to maintain consistent infiltration throughout the bioretention system. [ 28 ] There can be trade-offs associated with using native plants, including lack of availability for some species, late spring emergence, short blooming season, and relatively slow establishment.
It is important to plant a wide variety of species so the rain garden is functional during all climatic conditions. It is likely that the garden will experience a gradient of moisture levels across its functional lifespan, so some drought tolerant plantings are desirable. There are four categories of a vegetative species’ moisture tolerance that can be considered when choosing plants for a rain garden. Wet soil is constantly full of water with long periods of pooling surface water; this category includes swamp and marsh sites. Moist soil is always slightly damp, and plants that thrive in this category can tolerate longer periods of flooding. Mesic soil is neither very wet nor very dry; plants that prefer this category can tolerate brief periods of flooding. [ 16 ] Dry soil is ideal for plants that can withstand long dry periods. Plantings chosen for rain gardens must be able to thrive during both extreme wet and dry spells, since rain gardens periodically swing between these two states. A rain garden in temperate climates will unlikely dry out completely, but gardens in dry climates will need to sustain low soil moisture levels during periods of drought. On the other hand, rain gardens are unlikely to suffer from intense waterlogging, since the function of a rain garden is that excess water is drained from the site. Plants typically found in rain gardens are able to soak up large amounts of rainfall during the year as an intermediate strategy during the dry season. [ 16 ] Transpiration by growing plants accelerates soil drying between storms. Rain gardens perform best using plants that grow in regularly moist soils, because these plants can typically survive in drier soils that are relatively fertile (contain many nutrients).
Chosen vegetation needs to respect site constraints and limitations, and especially should not impede the primary function of bioretention. Trees under power lines, or that up-heave sidewalks when soils become moist, or whose roots seek out and clog drainage tiles can cause expensive damage. Trees generally contribute to bioretention sites the most when they are located close enough to tap moisture in the rain garden depression, yet do not excessively shade the garden and allow for evaporation. That said, shading open surface waters can reduce excessive heating of vegetative habitats. Plants tolerate inundation by warm water for less time than they tolerate cold water because heat drives out dissolved oxygen , thus a plant tolerant of early spring flooding may not survive summer inundation. [ 16 ]
Rain gardens are designed to capture the initial flow of stormwater and reduce the accumulation of toxins flowing directly into natural waterways through ground filtration. Natural remediation of contaminated stormwater is an effective, cost-free treatment process. Directing water to flow through soil and vegetation achieves particle pollutant capture, while atmospheric pollutants are captured in plant membranes and then trapped in soil, where most of them begin to break down. These approaches help to diffuse runoff, which allows contaminants to be distributed across the site instead of concentrated. [ 29 ] The National Science Foundation , the United States Environmental Protection Agency , and a number of research institutions are presently studying the impact of augmenting rain gardens with materials capable of capture or chemical reduction of the pollutants to benign compounds.
The primary challenge of rain garden design is predicting the types of pollutants and the acceptable loads of pollutants the rain garden's filtration system can process during high impact storm events. Contaminants may include organic material, such as animal waste and oil spills, as well as inorganic material, such as heavy metals and fertilizer nutrients . These pollutants are known to cause harmful over-promotion of plant and algal growth if they seep into streams and rivers. The challenge of predicting pollutant loads is specifically acute when a rain event occurs after a longer dry period. The initial storm water is often highly contaminated with the accumulated pollutants from dry periods. Rain garden designers have previously focused on finding robust native plants and encouraging adequate biofiltration, but recently have begun augmenting filtration layers with media specifically suited to chemically reduce redox of incoming pollutant streams. Certain plant species are very effective at storing mineral nutrients, which are only released once the plant dies and decays. Other species can absorb heavy metal contaminants. Cutting back and entirely removing these plants at the end of the growth cycle completely removes these contaminants. This process of cleaning up polluted soils and stormwater is called phytoremediation . [ 16 ] | https://en.wikipedia.org/wiki/Rain_garden |
A rain shadow is an area of significantly reduced rainfall behind a mountainous region, on the side facing away from prevailing winds , known as its leeward side.
Evaporated moisture from bodies of water (such as oceans and large lakes ) is carried by the prevailing onshore breezes towards the drier and hotter inland areas. When encountering elevated landforms , the moist air is driven upslope towards the peak , where it expands, cools, and its moisture condenses and starts to precipitate . If the landforms are tall and wide enough, most of the humidity will be lost to precipitation over the windward side (also known as the rainward side) before ever making it past the top. As the air descends the leeward side of the landforms, it is compressed and heated, producing Foehn winds that absorb moisture downslope and cast a broad "shadow" of dry climate region behind the mountain crests . This climate typically takes the form of shrub–steppe , xeric shrublands , or deserts .
The condition exists because warm moist air rises by orographic lifting to the top of a mountain range. As atmospheric pressure decreases with increasing altitude, the air has expanded and adiabatically cooled to the point that the air reaches its adiabatic dew point (which is not the same as its constant pressure dew point commonly reported in weather forecasts). At the adiabatic dew point, moisture condenses onto the mountain and it precipitates on the top and windward sides of the mountain. The air descends on the leeward side, but due to the precipitation it has lost much of its moisture. Typically, descending air also gets warmer because of adiabatic compression (as with foehn winds) down the leeward side of the mountain, which increases the amount of moisture that it can absorb and creates an arid region. [ 1 ]
There are regular patterns of prevailing winds found in bands round Earth's equatorial region. The zone designated the trade winds is the zone between about 30° N and 30° S, blowing predominantly from the northeast in the Northern Hemisphere and from the southeast in the Southern Hemisphere . [ 2 ] The westerlies are the prevailing winds in the middle latitudes between 30 and 60 degrees latitude , blowing predominantly from the southwest in the Northern Hemisphere and from the northwest in the Southern Hemisphere. [ 3 ] Some of the strongest westerly winds in the middle latitudes can come in the Roaring Forties of the Southern Hemisphere, between 30 and 50 degrees latitude. [ 4 ]
Examples of notable rain shadowing include:
On the largest scale, the entirety of the North American Interior Plains are shielded from the prevailing Westerlies carrying moist Pacific weather by the North American Cordillera . More pronounced effects are observed, however, in particular valley regions within the Cordillera, in the direct lee of specific mountain ranges. [ 11 ] This includes much of the Basin and Range Province in the United States and Mexico .
The Pacific Coast Ranges create rain shadows near the West Coast:
Most rain shadows in the western United States are due to the Sierra Nevada mountains in California and Cascade Mountains , mostly in Oregon and Washington . [ 11 ]
The Colorado Front Range is limited to precipitation that crosses over the Continental Divide . While many locations west of the Divide may receive as much as 1,000 millimetres (40 in) of precipitation per year, some places on the eastern side, notably the cities of Denver and Pueblo, Colorado , typically receive only about 12 to 19 inches. Thus, the Continental Divide acts as a barrier for precipitation. This effect applies only to storms traveling west-to-east. When low pressure systems skirt the Rocky Mountains and approach from the south, they can generate high precipitation on the eastern side and little or none on the western slope.
Further east: | https://en.wikipedia.org/wiki/Rain_shadow |
Rainbow Loom is a plastic tool used to weave colourful rubber and plastic bands (called loom bands ) into decorative items such as bracelets and charms. It was invented in 2010 by Cheong Choon Ng in Novi, Michigan . [ 1 ]
The Rainbow Loom is a plastic pegboard measuring 2 inches (51 mm) by 8 inches (200 mm). [ 2 ] It has push pin -type pegs over which small, coloured rubber bands are looped and pulled by a rainbow loom crochet hook. The resulting looped knots, known as Brunnian links , can be assembled on the loom into bracelets and other shapes. [ 3 ] The Rainbow Loom kit includes the loom (the pegboard), a rainbow loom hook, 25 special C-shaped clips to connect both ends of the bracelet, [ 3 ] and 600+ small rubber bands in assorted colours.
Rainbow Loom was created by Cheong Choon Ng, a Malaysian immigrant of Chinese descent who came to the United States in 1991 to attend Wichita State University , where he earned a graduate degree in mechanical engineering . [ 1 ] [ 4 ] He was employed as a crash-test engineer for Nissan Motor Company in 2010. He conceived the idea of a toy loom for rubber-band crafting after seeing his young daughters make rubber-band bracelets. He tried to show them how they could link the rubber bands together but was unsuccessful because of the large size of his fingers, so he stuck a scrap board with multiple rows of pegs on which the bands could be linked more easily. [ 5 ]
The bracelets became popular with the neighborhood children, and his daughter suggested that he sell them. He spent six months developing the loom kit and designed 28 versions. [ 5 ] His prototype, which he called Twistz Bandz, [ 6 ] used a wooden board, pegs, and dental hooks. [ 3 ] He invested $10,000 and found a factory in China to manufacture the parts, which he and his wife assembled in their home in June 2011. [ 7 ] Ng decided to rename his product after discovering that an elastic hair band on the market was named Twist Band , and his brother and niece came up with the name Rainbow Loom. [ 4 ]
Efforts to sell the loom online and in toy stores, however, were unsuccessful because customers did not understand how to use the product. [ 1 ] [ 7 ] Ng started a website and filmed instructional videos featuring his daughters and niece. [ 7 ] In summer 2012, Ng received his first store orders from franchises of Learning Express Toys , a specialty crafts chain, and sales picked up. [ 1 ] In June 2013 arts and crafts retail chain Michaels test-marketed the product in 32 stores; by August the chain was carrying Rainbow Loom in its 1,100 U.S. locations. [ 7 ] Rainbow Loom is also sold at Mastermind Toys in Canada and specialty stores. [ 4 ] As of August 2013, 600 retailers were selling Rainbow Loom at a retail price of $15 to $17. [ 1 ] The kits are manufactured in China, and Ng supervises distribution out of a 7,500 square feet (700 m 2 ) warehouse near his home. [ 1 ]
In 2013, Ng worked with The Beadery and Toner Plastics to produce the Wonder Loom , a redesigned version of the Rainbow Loom that is made in the United States. The Wonder Loom is sold by Walmart . [ 8 ] In April 2014, Ng released a travel-sized version of the Rainbow Loom called the Monster Tail, which allows simple bracelets to be made on only eight pegs, arranged in a rectangle. [ 9 ] [ 10 ]
In mid-May 2015, Rainbow Loom released two new products:
The Alpha Loom, another travel-sized loom that can be used to make vibrantly coloured name bracelets with special types of new bands, which are twice as thick but half the size of regular bands. It has seven pegs on either side, and it comes with a special hook that has seven hooks on so users can hook over seven bands at once, instead of one. It also comes with an instruction manual with pixelated grids for users to photocopy, cut out, measure around the wrist, and design the patterns themselves, with pictures and letters to spell words.
The Hair Loom Studio, also released in May 2015, is used to make designs on the Rainbow Loom, Finger Loom, or Monster Tail, which can then be transferred onto the user's hair by pushing the design off a "guide tube" onto a long strand of hair. The bands for this are made of silicone and can be removed without pulling at the hair. There are two versions of the Hair Loom Studio, a large "double" and a small "single" loom.
Targeted at children aged 8 to 14, [ 11 ] Rainbow Loom became a popular pastime in summer camps and summer clubs in 2013, according to The New York Times and Today . [ 1 ] [ 6 ] Grade school-age children make and swap their rubber-band bracelets in the same way as friendship bracelets , and children have posted thousands of their own instructional videos online. [ 1 ] [ 2 ] [ 6 ] As of October 2013, Rainbow Loom's YouTube channel featured 66 how-to videos and had received nearly 4 million views. [ 2 ] In November 2013 third-graders at St. John the Worker school in Orefield, Pennsylvania participated in a "Rainbow Loom-a-thon", weaving rubber-band bracelets for cancer patients. [ 12 ]
Rainbow Loom was named one of the three most popular toys of 2013 by Cyber Monday Awards [ 13 ] and was the most-searched toy on Google that same year. [ 14 ] It was described in a 2014 BBC News article as "one of the most popular toys in the world". [ 15 ]
Among the celebrities seen wearing Rainbow Loom bracelets given to them by fans are Prince William, Duke of Cambridge , Catherine, Duchess of Cambridge , David Beckham , Harry Styles , Miley Cyrus , and Pope Francis . [ 16 ]
In October 2013 two New York City schools banned Rainbow Loom bracelets, stating they were distracting students in the classroom and breeding animosity in the playground. [ 17 ] Two Orlando, Florida schools have also enforced strict rules on wearing and trading Rainbow Loom bracelets. [ 18 ] A Wallingford, Connecticut school had also banned the creation and exchange of Rainbow loom band bracelets, due to the rise of arguments that arose from band exchanges. [ 19 ]
Choon Ng applied to the United States Patent and Trademark Office in 2010 for a patent on Rainbow Loom. He then received US Patent No. 8,485,565 for "Brunnian link making device and kit" on July 16, 2013. [ 20 ] Ng received a second US Patent, No. 8,684,420 on April 1, 2014. [ 21 ]
In August 2013 Ng filed suit against Zenacon LLC, makers of FunLoom; LaRose Industries LLC, makers of Cra-Z-Loom; and Toys "R" Us , distributors of Cra-Z-Loom, alleging that the rival products copied the design of the C-shaped fasteners used in rubber-band jewelry-making on the Rainbow Loom. LaRose Industries immediately lodged a countersuit against Ng's company, Choon's Design LLC. [ 3 ] In August 2014, LaRose challenged Choon's patent and filed the first-ever post-grant review proceeding brought under the America Invents Act . The review ended in January 2015 after a settlement. [ 22 ]
In some of the knock-off versions, high levels of the carcinogenic substance phthalate have been found, in some cases well above the allowed limit in children's toys in Europe. British investigators found phthalate levels over 400 times the legal limit, and several toy stores have removed these products. [ 23 ]
The Norwegian Environment Agency also found higher than legal levels of DEHP , and several products have been banned from the market. However, it has been confirmed that it was only some non-Rainbow Loom-brand charms, and not bands. [ 24 ] [ 25 ] | https://en.wikipedia.org/wiki/Rainbow_Loom |
Rainer Marutzky ( Halle , 1947) [ 1 ] [ 2 ] [ 3 ] is a German wood scientist , who is emeritus professor of wood chemistry at the Technical University of Braunschweig and former director of the Fraunhofer Institute for Wood Research, Wilhelm Klauditz Institute (WKI) in Braunschweig , Germany .
He was born on 11 August 1947 in Halle , Germany .
In 1968, following his military service, he pursued studies in chemistry at the Technical University of Braunschweig from 1968 to 1973. Under the mentorship of Professor Karl Wagner, he earned his doctoral degree and subsequently served as a post-doctoral fellow at the Society for Biotechnology in Braunschweig-Stöckheim, specializing in enzyme chemistry. In 1976, he became a memmer of the Fraunhofer Institute for Wood Research as a research associate.
He successfully completed his habilitation at the Institute of Natural Sciences at the Technische Universität Braunschweig in 1991. He was appointed as university professor in 1996. His pioneering research work was predominantly related to the deleterious emissions from the wood-based products and the industrial environment. [ 4 ] [ 5 ] He was also actively engaged in European standardization initiatives. [ 6 ] [ 7 ] Marutzky held the position of director of the Fraunhofer WKI from 1989 until December 2009, [ 8 ] when he was officially retired.
His yearlong efforts are evidenced by many publications in both German and international scientific journals, [ 9 ] along with his participation as a keynote speaker and expert at various international scientific symposia. [ 10 ] [ 11 ] [ 12 ]
In 1988, Marutzky along with Edmone Roffael and Lutz Mehlhorn were awarded by the International Association iVTH for their research work on the topic "Investigations on the formaldehyde emissions from wood-based materials and other materials, and the development of methods to reduce formaldehyde emission potential." [ 13 ] He has also received several other awards in the field of wood science and technology. [ 14 ] [ 15 ]
Presently, he is a technical advisor to the International Association for Technical Wood Matters (iVTH). [ 16 ] | https://en.wikipedia.org/wiki/Rainer_Marutzky |
Rainer Waser (born 16 September 1955, in Frankfurt ) [ 1 ] is a German professor of Electrical Engineering [ 2 ] at RWTH Aachen University . He is also director of the section Electronic Materials at the Peter Grünberg Institute which is located on the campus of Jülich Research Center ( Forschungszentrum Jülich ). His research and teaching is on solid-state chemistry and defect chemistry to electronic properties and modelling, the technology of new materials and the physical properties of construction components.
Important findings include insights in the functioning of the so-called memristors . [ 3 ]
Waser grew up in Heusenstamm near Frankfurt. [ 4 ] He studied Physical Chemistry at Darmstadt University of Technology where he received a diploma degree in 1979. Then he went to the University of Southampton to conduct research at the Institute of Electrochemistry. After that he turned to Darmstadt and worked as scientific assistant until he completed his PhD.
Waser joined the Philips research laboratories (research group Electronic Ceramics ) at Aachen. In 1992, Waser accepted a Chair for Electronic Materials in the Faculty of Electrical Science and Information Technology at RWTH Aachen University. In 2012, Waser was elected to the post of Speaker of the Department of Electrical Engineering and Information Technology at Aachen university. Waser was awarded the renowned Gottfried Wilhelm Leibniz Prize in 2014. [ 5 ]
A comprehensive list can be found in the cv on the institute's website. [ 6 ] | https://en.wikipedia.org/wiki/Rainer_Waser |
The rainflow-counting algorithm is used in calculating the fatigue life of a component in order to convert a loading sequence of varying stress into a set of constant amplitude stress reversals with equivalent fatigue damage. The method successively extracts the smaller interruption cycles from a sequence, which models the material memory effect seen with stress-strain hysteresis cycles. [ 1 ] This simplification allows the number of cycles until failure of a component to be determined for each rainflow cycle using either Miner's rule to calculate the fatigue damage , or in a crack growth equation to calculate the crack increments. [ 2 ] Both methods give an estimate of the fatigue life of a component. In cases of multiaxial loading, critical plane analysis can be used together with rainflow counting to identify the uniaxial history associated with the plane that maximizes damage. The algorithm was developed by Tatsuo Endo and M. Matsuishi in 1968. [ 3 ]
The rainflow method is compatible with the cycles obtained from examination of the stress-strain hysteresis cycles. When a material is cyclically strained, a plot of stress against strain shows loops forming from the smaller interruption cycles. At the end of the smaller cycle, the material resumes the stress-strain path of the original cycle, as if the interruption had not occurred. The closed loops represent the energy dissipated by the material. [ 1 ]
The rainflow algorithm was developed by T. Endo and M. Matsuishi (an M.S. student at the time) in 1968 and presented in a Japanese paper. The first English presentation by the authors was in 1974. They communicated the technique to N. E. Dowling and J. Morrow in the U.S. who verified the technique and further popularised its use. [ 1 ]
Downing and Socie created one of the more widely referenced and utilized rainflow cycle-counting algorithms in 1982, [ 4 ] which was included as one of many cycle-counting algorithms in ASTM E1049-85. [ 5 ]
Igor Rychlik gave a mathematical definition for the rainflow counting method, [ 6 ] thus enabling closed-form computations from the statistical properties of the load signal.
There are a number of different algorithms for identifying the rainflow cycles within a sequence. They all find the closed cycles and may be left with half closed residual cycles at the end. All methods start with the process of eliminating non turning points from the sequence. A completely closed set of rainflow cycles can be obtained for a repeated load sequence such as used in fatigue testing by starting at the largest peak and continue to the end and wrapping around to the beginning.
This method evaluates each set of 4 adjacent turning points A-B-C-D in turn: [ 7 ]
This method considers the flow of water down of a series of pagoda roofs. Regions where the water will not flow identify the rainflow cycles which are seen as an interruption to the main cycle.
The stress history in Figure 2 is reduced to tensile peaks in Figure 3 and compressive valleys in Figure 4. From the tensile peaks in Figure 3:
Similar half-cycles are calculated for compressive stresses (Figure 4) and the half-cycles are then matched. | https://en.wikipedia.org/wiki/Rainflow-counting_algorithm |
A rainout is the process of precipitation causing the removal of radioactive particles from the atmosphere onto the ground, [ 1 ] creating nuclear fallout by rain. The rainclouds of the rainout are often formed by the particles of a nuclear explosion itself and because of this, the decontamination of rainout is more difficult than a "dry" fallout.
In atmospheric science, rainout also refers to the removal of soluble species—not necessarily radioactive—from the atmosphere by precipitation. [ 2 ]
A rainout could occur in the vicinity of ground zero or the contamination could be carried aloft before deposition depending on the current atmospheric conditions and how the explosion occurred. The explosion, or burst, can be air, surface, subsurface, or seawater . An air burst will produce less fallout than a comparable explosion near the ground due to less particulate being contaminated. Detonations at the surface will tend to produce more fallout material. In case of water surface bursts, the particles tend to be rather lighter and smaller, producing less local fallout but extending over a greater area. The particles contain mostly sea salts with some water; these can have a cloud seeding effect causing local rainout and areas of high local fallout. Fallout from a seawater burst is difficult to remove once it has soaked into porous surfaces because the fission products are present as metallic ions which become chemically bonded to many surfaces. For subsurface bursts, there is an additional phenomenon present called "base surge". The base surge is a cloud that rolls outward from the bottom of the subsiding column, which is caused by an excessive density of dust or water droplets in the air. This surge is made up of small solid particles, but it still behaves like a fluid. A soil earth medium favors base surge formation in an underground burst. Although the base surge typically contains only about 10% of the total bomb debris in a subsurface burst, it can create larger radiation doses than fallout near the detonation, because it arrives sooner than fallout, before much radioactive decay has occurred. For underwater bursts, the visible surge is, in effect, a cloud of liquid (usually water) droplets with the property of flowing almost as if it were a homogeneous fluid. After the water evaporates, an invisible base surge of small radioactive particles may persist.
Meteorogically, snow and rain will accelerate local fallout. Under special meteorological conditions, such as a local rain shower that originates above the radioactive cloud, limited areas of heavy contamination just downwind of a nuclear blast may be formed. Rain on an area contaminated by a surface burst changes the pattern of radioactive intensities by washing off higher elevations, buildings, equipment, and vegetation. This reduces intensities in some areas and possibly increases intensities in drainage systems; on low ground; and in flat, poorly drained areas. [ 3 ]
This radioactivity –related article is a stub . You can help Wikipedia by expanding it .
This article about atmospheric science is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Rainout_(radioactivity) |
A rainscreen is an exterior wall detail where the siding (wall cladding) stands off from the moisture - resistant surface of an air/water barrier applied to the sheathing to create a capillary break and to allow drainage and evaporation. The rainscreen is the cladding or siding itself [ 1 ] but the term rainscreen implies a system of building. Ideally the rainscreen prevents the wall air/water barrier from getting wet but because of cladding attachments and penetrations (such as windows and doors) water is likely to reach this point, and hence materials are selected to be moisture tolerant and integrated with flashing. In some cases a rainscreen wall is called a pressure-equalized rainscreen wall where the ventilation openings are large enough for the air pressure to nearly equalize on both sides of the rain screen, [ 2 ] but this name has been criticized as being redundant [ 3 ] and is only useful to scientists and engineers.
A screen in general terms is a barrier. [ 4 ] The rainscreen in a wall is sometimes defined as the first layer of material on the wall, the siding itself. [ 2 ] Also, rainscreen is defined as the entire system of the siding, drainage plane and a moisture/air barrier . [ 5 ] [ 6 ] A veneer that does not stand off from the wall sheathing to create a cavity is not a rainscreen. However, a masonry veneer can be a rainscreen wall if it is ventilated. [ 7 ]
Many terms have been applied to rain screen walls including basic, open, conventional, pressure-equalized, pressure-moderated rainscreen systems or assemblies. These terms have caused confusion as to what a rain screen is but all reflect the rainscreen principle of a primary and secondary line of defense. One technical difference is between a plane (a gap of 3 ⁄ 8 inch (9.5 mm) or less) and a channel (a gap of more than 3 ⁄ 8 inch (9.5 mm)). [ citation needed ]
In general terms a rainscreen wall may be called a cavity or drained wall . [ 8 ] The two other basic types of exterior walls in terms of water resistance are barrier walls which rely on the one exterior surface to prevent ingress and mass walls which allow but absorb some leakage. [ 8 ]
In the early 1960s research was conducted in Norway on rain penetration of windows and walls, and Øivind Birkeland published a treatise referring to a "rain barrier". In 1963 the Canadian National Research Council published a pamphlet titled "Rain Penetration and its Control" using the term "open rain screen". [ 9 ]
Rainscreen cladding is a kind of double-wall construction that utilizes a surface to help keep the rain out, as well as an inner layer to offer thermal insulation , prevent excessive air leakage and carry wind loading. The surface breathes just like a skin as the inner layer reduces energy losses. [ 10 ]
For water to enter a wall first the water must get onto the wall and the wall must have openings. Water can then enter the wall by capillary action, gravity, momentum, and air pressure (wind). [ 2 ] The rainscreen system provides for two lines of defense against the water intrusion into the walls: The rainscreen and a means to dissipate leakage [ 11 ] often referred to as a channel.
In a rainscreen the air gap allows the circulation of air on the moisture barrier . (These may or may not serve as a vapour barrier , which can be installed on the interior or exterior side of the insulation depending on the climate). This helps direct water away from the main exterior wall which in many climates is insulated. Keeping the insulation dry helps prevent problems such as mold formation and water leakage. The vapour-permeable air/weather barrier prevents water molecules from entering the insulated cavity but allows the passage of vapour, thus reducing the trapping of moisture within the main wall assembly.
The air gap (or cavity) can be created in several ways. One method is to use furring (battens, strapping) fastened vertically to the wall. Ventilation openings are made at the bottom and top of the wall so air can naturally rise through the cavity. Wall penetrations including windows and doors require special care to maintain the ventilation. In the pressure-equalized system the ventilation openings must be large enough to allow air-flow to equalize the pressure on both sides of the cladding. A ratio of 10:1 cladding leakage area to ventilation area has been suggested. [ 2 ]
A water/air resistant membrane is placed between the furring and the sheathing to prevent rain water from entering the wall structure. The membrane directs water away and toward special drip edge flashings which protect other parts of the building.
Insulation may be provided beneath the membrane. The thickness of insulation is determined by building code requirements as well as performance requirements set out by the architect.
The system is a form of double-wall construction that uses an outer layer to keep out the rain and an inner layer to provide thermal insulation, prevent excessive air leakage and carry wind loading. The outer layer breathes like a skin while the inner layer reduces energy losses. The structural frame of the building is kept absolutely dry, as water never reaches it or the thermal insulation. Evaporation and drainage in the cavity removes water that penetrates between panel joints. Water droplets are not driven through the panel joints or openings because the rainscreen principle means that wind pressure acting on the outer face of the panel is equalized in the cavity. Therefore, there is no significant pressure differential to drive the rain through joints. During extreme weather, a minimal amount of water may penetrate the outer cladding. This, however, will run as droplets down the back of the cladding sheets and be dissipated through evaporation and drainage.
A rainscreen drainage plane is an air gap and the water resistant barrier of a rainscreen. Together they provide a predictable, unobstructed path drainage for liquid moisture to drain from a high point of the wall (where it enters) to a low point of the wall (where it exits) the wall detail. The drainage plane must move the water out of the wall system quickly to prevent absorption and consequential rot, mold, and structural degradation.
A drainage plane
is designed to shed bulk rainwater and/or condensation downward and outward in a manner that will prevent uncontrolled water penetration into the conditioned spaces of a building or structure. In a barrier wall system, the exterior cladding also serves as the principal drainage plane and primary line of defense against bulk rainwater penetration. In cavity wall construction, however, the principal drainage plane and primary line of defense against bulk rainwater penetration is located inside the wall cavity, generally on the inboard side of the air space (either directly applied to the outboard surface of the exterior sheathing layer or, in the case of insulated cavity walls, on the outboard surface of the rigid or otherwise moisture-impervious insulation layer). [ 12 ]
Air pressure difference is one of the forces for driving a rainwater into wall systems but gravity is more often the cause of practical problems. [ 13 ] A rainscreen drainage plane that works as a predictable pressure equalization plane creates a separation (an air chamber) between the backside of a rainscreen and the exterior surface of the weather-resistant barrier that is installed on the exterior sheeting of the structural back up wall. This separation allows air contaminated with water vapor from all points in that wall system to exit the interior of the wall system. Moisture laden air that is allowed to pressurize will attempt to move to a lower pressure area that may be deeper into the interior of a wall detail.
Once moisture has penetrated deep into a wall system through the weather resistant barrier and into the exterior sheathing, the wall is deep wet. The air flow that exists in most wall systems is a slight draft that will not dry this condition out in a timely manner. The result is a compromised wall system with rot, rust, and mold potential. The structural integrity of the wall is at stake, as is the health of the occupants. The longer the wall remains wet, the greater the risk. 50% percent of homes suffer from mold problems. [ 21 ] Billions of dollars are spent annually on litigation involving mold and rot problems stemming from entrapped moisture; this has created an entire industry centered around construction litigation. Such litigation has caused insurance premiums for contractors to increase significantly and has made it difficult for contractors involved in moisture related lawsuits to obtain insurance at all. [ 22 ] An effective rainscreen drainage plane system mitigates this risk.
Dampness levels in construction are measured in wood moisture equivalent (WME) percentages and is calculated as follows:
A normal range is 8–13% WME, with fungal growth beginning at the 16% threshold. A 20% WME is enough to promote wood rot. [ 24 ] It logically follows that the more time a part of a wall system exceeds one of these thresholds the greater chance of damage from fungal growth or rot. | https://en.wikipedia.org/wiki/Rainscreen |
In mathematics, the Rainville polynomials p n ( z ) are polynomials introduced by Rainville (1945) given by the generating function
Boas & Buck (1958 , p.46).
This polynomial -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Rainville_polynomials |
Rainwater management is a series of countermeasures to reduce runoff volume and improve water quality by replicating the natural hydrology and water balance of a site, with consideration of rainwater harvesting , urban flood management and rainwater runoff pollution control.
The continuous growth of human populations and the consequent growing need for drinking water is a global problem. [ 1 ] Rainwater is an important source of drinking water, and as a free source of water, considerable quantities can be collected from roof catchments and other surface areas for various uses. [ 2 ] Due to water shortages, rainfall events and flooding, attention has been given to rainwater management. Rainwater management re-conceptualizes urban rainwater, transforming it from a community risk to a resource for urban development, [ 3 ] a good rainwater management is important for the design of sanitation systems and the environment, nowadays different methods of rainwater management have been developed, [ 4 ] including reduction of impervious surfaces , separation of rainwater and sanitary sewers , collection and reuse of rainwater, and Low-impact development (LID) .
[ [1] ].
Rainwater harvesting (RWH) is the process of collecting and storing rainwater rather than letting it run off. Rainwater harvesting systems are increasingly becoming an integral part of the sustainable rainwater management "toolkit" [ 5 ] and are widely used in homes, home-scale projects, schools and hospitals for a variety of purposes including watering gardens , livestock , [ 6 ] irrigation , home use with proper treatment and home heating. For households it is effective in reducing electricity and greenhouse gas emissions and providing domestic water; for urban agriculture , it is effective in reducing rainwater runoff and related issues; and for industry, it provides sustainability of facilities and low financial resource utilization.
Rainwater harvested from roof structures or other compact surfaces is discharged through drains into storage tank , processed by treatment systems and then deployed in use facilities to complete the beneficial use of rainwater. Rainwater so treated is mainly used for irrigation, washing, laundry, and in some countries it is also considered as drinking water after the necessary purification. [ 1 ]
Urban flood management has now become one of the highest priorities in urban development, Urban flooding has a major impact on both public transportation systems and supply chains and is an important topic in rainwater management [ 7 ]
The use of combined sewer systems to treat excess rainwater runoff is common in older urban areas. [ 8 ] The Combined Sewer System (CSS) collects rainwater runoff, domestic sewage and industrial wastewater into a single pipe. [ 9 ] Combined sewer overflows (CSOs) occur when untreated wastewater is discharged to surface water beyond its hydraulic capacity, when this occurs, untreated rainwater and wastewater are discharged directly into nearby streams, rivers and other water bodies. Combined sewer overflows (CSOs) contain untreated or partially treated human and industrial waste, toxic materials and debris, and rainwater. [ 9 ] a problem that is currently a key challenge for rainwater management and can lead to public health incidents. [ 10 ] Gray-green infrastructure is the key technology to solve this problem and is the core technology of the currently introduced " sponge city ". The implementation of gray infrastructure, such as upgrading drainage networks, storage facilities or pumping stations with large diameter pipes, is critical to drain rainwater from urban catchments, while most green infrastructure handles the storage and infiltration of rainwater and drainage of gray infrastructure [ 8 ]
Constructed wetlands for sewer overflows treatment are currently an effective and less costly option to prevent untreated wastewater from overflowing from polluted natural water bodies, and constructed wetlands that act as retention ponds during the rainy season can collect and treat rainwater due to their natural purification function, and produce high quality water for reuse after treatment by constructed wetlands with aeration system and soils infiltration system. [ 4 ]
The conversion of Combined Sewer System (CSS) to separate sewer systems with retention ponds will not only increase rainwater drainage and reduce the potential for urban flooding, but their own retention ponds will also retain pollutants, thereby reducing or preventing unnecessary pollution of a single receiving waters.
The ratio of pervious to impervious surfaces is important in flood management. [ 11 ] [ 12 ] Building vegetated spaces, such as parks integrated with urban facilities, can increase the amount of pervious area. [ 13 ] For new and redevelopment projects, reduce the amount of impervious surfaces, such as buildings, roads, parking lots, and other structures. [ 14 ]
Low-impact development (LID) refers to systems and practices that use or mimic natural processes that result in the infiltration, evapotranspiration or use of stormwater in order to protect water quality and associated aquatic habitat. [ 15 ] Low-impact development (LID) practices provide more sustainable solutions than traditional piping and storm ponds in rainwater management. [ 16 ] The sustainability of LID practices is achieved primarily through the use of porous pavement , bioretention , green roofs , rainwater harvesting , and other rainwater management strategies. Bioretention can effectively retain large amounts of runoff, porous pavement can effectively infiltrate rainwater runoff, [ 17 ] and green roofs can retain rainwater under a variety of climatic conditions. [ 18 ] These methods create and restore green space and reduce the impact of built-up areas at the site and regional scales, promoting the natural flow of water within an ecosystem or watershed. Applied over a wide range of scales, LID can maintain or restore the hydrologic and ecological functions of a watershed. [ 15 ]
Applying rainwater management, surface runoff can be collected and stored in hand-dug farm ponds. [ 19 ] To enhance irrigation in dry conditions, earthen ridges were constructed to collect and prevent rainwater from flowing down the hillsides and slopes. Even during periods of low rainfall, enough water can be collected for crop growth. [ 20 ] Rainwater management can increase the productivity of smallholder farmers in arid environments. Productivity of rainfed agriculture is improved through supplemental irrigation, especially when combined with soil fertility management. [ 21 ]
Rainwater management as a means of multi-stage control and improvement of rainwater systems needs to go through multiple steps of analysis and design, and in the new era of Low-impact development , rainwater management has become more than just a task for engineers, rainwater management projects have tended to become Integrated project delivery (IPD) , designers need to consider rainwater management issues at a much earlier stage to avoid The development and use of software such as Rainwater+ is now helping designers to implement rainwater management at the design stage, its more intuitive GUI and simple workflow ensures that designers with little to no experience in hydrology can use Rainwater+, which will reduce later building construction conflicts to facilitate communication between all parties and improve construction quality.
The term Low-impact development is commonly used in North America and New Zealand, and was first used in the United States by Barlow et al. [ 22 ]
Water sensitive urban design (WSUD) is a concept widely accepted and partially acted on throughout Australia's federal and state governments. [ 23 ]
IUWM derives from the broader term, Integrated Water Management, which involves the integrated management of all parts of the water cycle within a watershed. [ 24 ]
SUDS established in a similar but separate design manual that includes Scotland and Northern Ireland as well as England and Wales, [ 25 ] SUDS consists of a range of techniques and technologies based on the concept of replicating the natural, pre-development drainage of the site as closely as possible, culminating in a management system. [ 26 ]
Best management practices are structural, vegetative or managerial practices used to treat, prevent or reduce water pollution. Structural BMPs. Extended Detention Ponds.
[ 1 ] [ 2 ] | https://en.wikipedia.org/wiki/Rainwater_management |
A raise borer is a machine used in underground mining , to excavate a circular hole between two levels of a mine without the use of explosives .
The raise borer is set up on the upper level of the two levels to be connected, on an evenly laid platform (typically a concrete pad). A small-diameter hole ( pilot hole ) is drilled to the level required; the diameter of this hole is typically 230mm – 445mm (9" - 17.5"), large enough to accommodate the drill string . Once the drill has broken into the opening on the target level, the bit is removed and a reamer head, of the required diameter of the excavation, is attached to the drill string and raised back towards the machine. The drill cuttings from the reamer head fall to the floor of the lower level. The finished raise has smooth walls and may not require rock bolting or other forms of ground support. [ 1 ] One impressive use of raise boring is the 7.1 m diameter shafts for Sasol's Middelbult and Bosjesspruit Mines in South Africa. [ 2 ]
The boxhole borer (or machine roger) is a variant of a raise borer that is used when there is not enough space on the higher of the two levels to be connected. The boxhole borer is set up on the lower level, drills a pilot hole as a guide, then drives the reamer bit along the pilot hole from the lower level to the upper. Precautions have to be taken to redirect falling drill cuttings away from the machine, and to reinforce the drill string.
This article about mining is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Raise_borer |
Raised bogs , also called ombrotrophic bogs , are acidic, wet habitats that are poor in mineral salts and are home to flora and fauna that can cope with such extreme conditions. Raised bogs, unlike fens , are exclusively fed by precipitation ( ombrotrophy ) and from mineral salts introduced from the air. They thus represent a special type of bog , hydrologically , ecologically and in terms of their development history, in which the growth of peat mosses over centuries or millennia plays a decisive role. They also differ in character from blanket bogs which are much thinner and occur in wetter, cloudier climatic zones. [ 1 ]
Raised bogs are very threatened by peat cutting and pollution by mineral salts from the surrounding land (due to agriculture and industry ). The last great raised bog regions are found in western Siberia and Canada .
The term raised bog derives from the fact that this type of bog rises in height over time as a result of peat formation. They are like sponges of peat moss, full of water, that form a more or less dome shape in the landscape. In Germany, the term Hochmoor ( lit. ' high bog ' ) strictly refers only to the classical, lens-shaped bogs of northwest Germany . The bogs are not influenced by mineral-rich groundwater or surface water, but are fed exclusively by precipitation — mainly rainwater, hence their alternative German designation of Regenmoor or "rain-fed bog". Thus the latter refers to all bogs, not just those that are arched or only slightly arched, but which nevertheless are characterized by an extreme mineral salt deficiency and other resulting ecological properties.
A living raised bog needs a moist, balanced climate in which to grow. The quantity of precipitation has to be greater than the water losses through discharge and evaporation. In addition, the precipitation must be evenly spread through the year.
Raised bogs in Europe have been developing for about 11,000 years, since the beginning of the Holocene and after the retreat of the last ice sheet . As far as their origins are concerned, a distinction is made between lake mires or 'siltation-formed raised bogs' ( Verlandungshochmoore ) and 'mire-formed raised bogs' ( wurzelechte Hochmoore ). The former emerged in a secondary process after the silting up of lakes or oxbows (see illustration on the right in the sequence). At first, fens emerged under the influence of groundwater ( minerotrophy ). Oxygen deficiencies and high acidity in the constantly moist substrate inhibited the decomposition of dead plant parts and led to peat formation.
Thus the raised bog rises very slowly above the groundwater level, hence its name. As the resulting peat slowly rises above the influence of mineral salts in the groundwater, it reaches a point where the development of the raised bog begins to change in nature; that is, the bog now becomes fed solely by rainwater, which is low in salt. By contrast, mire-formed raised bogs are created directly on the mineral substrate of low-salt areas without having been initially formed as fens (see figure on the left in the sequence). They are formed either as a primary bog due to the erosion of previously dry mineral soils, for example due to clearing, climate change or infiltration, or as a secondary process as a result of the growth of a raised bog on neighbouring mineral soil. The formation of a typical raised bog is a very slow process, which lasts from centuries to a thousand years even in favourable, undisturbed conditions. Furthermore, there are a number of transitional and intermediate bogs , which in different ways combine characteristics of both raised bogs and fens. (See bog .)
The main constituents of the peat are rootless peat mosses that grow slowly in height whilst at the same time the lower layer becomes peat as the air is excluded. Depending on the geographical location, various species of peat moss are involved in making a raised bog. The growth rate of the peat layer is only about a millimetre per year.
Growing bogs can be divided into two layers. The ' acrotelm ' ( Greek : akros = highest; telma = bog) is the upper part and includes the vegetation layer and the bog 'floor'. Here fresh organic substances (peat formation horizon) are created by the growth and dying of plant elements. The "catotelm" (Greek: kato = below) is the underlying water-saturated part with less biological activity. This layer is counted as a geological subsoil due to the small earth-forming processes that are still going on and is known as the peat preservation horizon ( Torferhaltungshorizont ). In raised bogs, the upper peat layer is called white peat, since it consists of largely undecomposed light brown peat mosses. The lower layer is black peat, which is already well humified and has a black-brown colour with still recognizable plant remains.
The formation of raised bogs is dependent on the climate, that is to say the amount of precipitation and rate of evaporation, which in turn are decisively determined by the temperature. In addition, the relief of the terrain has an influence on the water discharge behaviour and thus the shape of a raised bog. This results in geographical limitations to the formation of raised bogs. Favourable conditions for the development of raised bogs are found mainly in North America ( Canada and Alaska ), Northern Europe and Western Siberia , South America , Southeast Asia and in the Amazon Basin . In these regions, bogs of all kinds and peat deposits of four million square kilometres have been formed, covering three percent of the Earth's surface. In the southern hemisphere low-mineral-rich bogs are rarely formed from peat mosses. Only in the Tierra del Fuego do peat moss raised bogs exist. The most peaty countries in the tropics are found in Southeast Asia. In many cases it is not yet clear how these bogs have emerged as mosses are entirely absent here.
Coastal bogs ( Planregenmoore ) or Atlantic bogs, as their names suggest, tend to form close to the sea. In addition, in regions covered by blanket bog, there are also lightly convex coastal bogs with low energy surface relief in level locations. The distribution of coastal bogs in Europe extends from Ireland to the east via South Norway to Southwest Sweden and north to the Lofoten . In North America there are coastal bogs in the area of the Great Lakes (especially in Minnesota and Ontario ). Coastal bogs are also fed exclusively by rain.
In the less oceanically influenced climatic regions of North-West Europe (lower precipitation), raised bogs take on the classical lens shape and are called plateau bogs or plateau raised bogs ( Plateauregenmoore ). They grow more strongly in the centre than at the margins. This results in the centre of the bog bulging, hence the name "raised bog". This bulging can be several metres high. As a result, the perimeter of the bog is more or less inclined, and is known as the rand . The sloping bog sides of larger bogs are traversed by drainage channels or soaks ( Rüllen ) through which excess water is discharged.
Other characteristic structures of these raised bogs are the flat, treeless raised bog core with its characteristic microrelief of shallow wet depressions or flarks ( Schlenken ) alternating with hummocks ( Bülten ) of drier peat moss. Larger accumulations of water in the middle of the bogs are called kolks or bog ponds (of humic acid -rich water); the wet area on the outer margins is known as a moat or lagg .
Genuine ombrotrophic bogs on the North German Plain are usually sharply divided into two layers: an underlying black peat layer, which is strongly decomposed, and an overlying white peat layer which is less decomposed. This difference is a result of changes in the hydrology of the bog. The white peat grew more rapidly under humid conditions than the black peat. This is attributed to a climate change with high precipitation and low evaporation around 1000 to 500 BC. As a result, the peat moss growth grew locally and the black peat/white peat boundary layer was formed, although this did not develop simultaneously in all raised bogs.
Raised bogs also occur in precipitation-rich upland regions at the montane and, more rarely, alpine levels (i.e. above the tree line ). As a result of the sloping terrain, they often have a characteristic, asymmetric or non-concentric appearance. Mountain or upland bogs may be topographically divided into: [ 2 ]
All these bog types may occur on the margins of lowland bogs i.e. fens , or transition into them.
Kermi bogs ( Kermimoore, Schildhochmoore ) or kermi raised bogs have only a slightly domed shape. The surface of the bog rises steadily from the broad lagg zone. Kermis have ridge-shaped hummocks of peat moss, that are aligned with the contours of the bog. The flarks or elongated depressions are generally tub-shaped and hardly distinguishable externally from kolks . In the central area of these bogs, there are always large kolks. In northern Russia and western Siberia, kermis frequently occur in giant complexes where the bogs have grown into one another. Kermis are also found in Finland in the central and northern boreal forest zone.
String bogs or aapa fens ( Aapamoore or Strangmoore ) are typically found on the northern fringes of the distribution area for raised bogs, in the sub-polar zone, north of the 66th latitude in the northern hemisphere. Here, raised bogs only occur as islands within wetlands supplied by mineral soil water. On level ground these islands are irregularly distributed; on hillsides they form ridges parallel to the contours and at right angles to line of slope. The ridges separate boggy hollows of mineral soil known by the Finnish word, rimpis . The main distribution area for string bogs are the Scandinavian hills, central Finland, Karelia and north Siberia. In North America, Alaska is the main location for string bogs, thanks to its cold continental climate. Frost action plays an important role in these bogs. On the ridges or hummocks, ground ice is found until early summer.
Palsa bogs ( Palsamoore or Palsenmoore ) are found on the margins of the Arctic permafrost soils ( tundra ). Here the ridges of the string bogs can grow into hummocks several metres high. Like string bogs, the so-called palsas frequently lie within peatlands fed by mineral soil water. Some are surrounded by water-filled, ditch-like hollows. Peat formation is limited; these bogs are peat deposits from warmer, interglacial periods and did not experience frost heaving of their inner core of ice until the climate became colder. These ice lenses increase in size from year to year as a result of freeze-thaw processes of the surrounding water. The low temperatures prevent full decomposition of the organic material.
Polygonal bogs ( Polygonmoore ) are widespread on the Arctic and sub-Arctic plains of Siberia and North America and cover vast areas. They are associated with patterned peatland and ice wedges . A scanty layer of peat-forming vegetation can occur in the inner honeycomb-shaped areas of this frost pattern terrain ( cryoturbation ) and are fed during the short summers with sufficient moisture, because the meltwater is prevented from draining away by the raised polygonal margins. The peat layers can attain a thickness of 0.3 to 1 m (1.0–3.3 ft).
The west Siberian raised bog area covers 700,000 km 2 (270,000 sq mi). The large bogs have domes in the centre up to 10 m (33 ft) high. They are predominantly of the kermi bog type. They represent probably the most important type of raised bog on earth. The Vasyugan Swamp in this region, is the largest bog system on earth and covers more than 50,000 km 2 (19,000 sq mi). It is estimated to contain over 14 billion tonnes of peat deposits.
The largest central European raised bog areas are the southern North Sea coastal area and the Alpine Foreland . As in North America there is a succession of raised bog types along the line of descent towards the ocean, from northwest to southeast. As a result of peat use, raised bogs have been harvested for peat and cultivated, apart from a few remnants (less than 10% of the original area). The largest contiguous raised bog in central Europe was the Bourtange Moor , which originally covered an area of about 2,300 km 2 including the Dutch portion, but only small sections remain. The largest remaining raised bog in northern Europe is the 76 km 2 Lille Vildmose . [ 3 ] Other large raised bogs are the Teufelsmoor northeast of Bremen, the Vehnemoor (exhausted) and the Esterweger Dose (formerly about 80 km 2 , exhausted) between Oldenburg and Papenburg. The raised bogs of the Central Uplands of the Harz , Solling , Thuringian Forest ( Großer Beerberg , Schneekopf - Teufelsbad, Fichtenkopf, Saukopf), Giant Mountains , Ore Mountains , Fichtel and Rhön ( Black Moor , Red Moor ) are, by contrast, comparatively small. In the Black Forest the Wildseemoor has been protected and, in the Vosges on le Tanet , north of the Col de la Schlucht a large area has been protected. The Alpine Foreland , which was formed by ice-age glaciation, is also rich in peatland. The Wurzacher Ried (Haidgauer Regenmoorschild) is considered the largest and best preserved raised bog in central Europe. Other raised bogs and peatland areas include the Federsee , the High Fens on the Germano-Belgian border, the Ewiges Meer near Aurich and the Lengener Meer near Wiesmoor. In 2003, Estonia exported 3.6 million m³ of peat for west European garden use, more than 60% of the state production. In Lithuania 60% of the usable peat area has been prepared for extraction or is already exhausted. [ 4 ]
Lough Lurgeen Bog and Glenamaddy Turlough Bog contains very good examples of the Annex 1 habitats : active raised bog, turlough (both priority habitats), degraded raised bog (capable of regeneration) and vegetation of depressions (rhynchosporion). These habitats are considered to be among the best examples in Ireland due to their relatively large size and the generally low levels of disturbance. In the Natura form compiled for the site active raised bog was given a rating of A (Excellent value) which emphasises the importance of the site. Raised bog habitats are now very rare in Europe and it has recently been estimated that the Republic of Ireland contains 50% of the relatively intact oceanic raised bog systems in Europe. [ 5 ]
The site contains the second largest area of intact raised bog surface in Ireland. The combination of raised bog, oligotrophic lake and turlough habitats is unique in Ireland and thus the entire system is very important from both a hydrological and ecological perspective. [ 6 ]
A region of peatland extends from Alaska in the west to the coast of the Atlantic in the east, and is comparable in size to that of West Siberia. A zone of domed raised bogs adjoins the zones of palsa bogs and string fens. In the direction of descent towards the ocean, blanket bogs occur east of Hudson Bay. These are superseded towards the west by plateau bogs in the area of the large lakes and, eventually, by kermi bogs. | https://en.wikipedia.org/wiki/Raised_bog |
During the 1850s and 1860s, engineers carried out a piecemeal raising of the grade of central Chicago to lift the city out of its low-lying swampy ground. Buildings and sidewalks were physically raised on jackscrews . The work was funded by private property owners and public funds.
During the 19th century, the elevation of the Chicago area was little higher than the shoreline of Lake Michigan . For two decades following the city's incorporation, drainage from the city surface was inadequate, resulting in large bodies of standing and pathogenic water. These conditions caused numerous epidemics, including typhoid fever and dysentery , which blighted Chicago six years in a row culminating in the 1854 outbreak of cholera that killed six percent of the city’s population. [ 2 ] [ 3 ] [ 4 ] [ 5 ]
The crisis forced the city's engineers and aldermen to take the drainage problem seriously and after many heated discussions [ 6 ] [ 7 ] —and following at least one false start—a solution eventually materialized. In 1856, engineer Ellis S. Chesbrough drafted a plan for the installation of a citywide sewerage system and submitted it to the Common Council, which adopted the plan. Workers then laid drains, covered and refinished roads and sidewalks with several feet of soil, and raised most buildings on screwjacks to the new grade.
Many of the city's old wooden buildings were considered not worth raising, so instead the owners of these wooden buildings had them either demolished or else placed on rollers and moved to the outskirts of Chicago. Business activities in such buildings continued, as they were being moved. [ 8 ]
In January 1858, the first masonry building in Chicago to be thus raised—a four-story, 70-foot-long (21 m), 750-ton (680 metric tons) brick structure situated at the north-east corner of Randolph Street and Dearborn Street—was lifted on two hundred jackscrews to its new grade, which was 6 feet 2 inches (1.88 m) higher than the old one, “without the slightest injury to the building.” [ 9 ] It was the first of more than fifty comparably large masonry buildings to be raised that year. [ 10 ] The contractor was an engineer from Boston, James Brown, who went on to partner with Chicago engineer James Hollingsworth; Brown and Hollingsworth became the first and, it seems, the busiest building raising partnership in the city. By the year-end, they were lifting brick buildings more than 100 feet (30 m) long, [ 11 ] and the following spring they took the contract to raise a brick block of more than twice that length. [ 12 ]
In 1860, a consortium of no fewer than six engineers—including Brown, Hollingsworth and George Pullman —co-managed a project to raise half a city block on Lake Street , between Clark Street and LaSalle Street completely and in one go. This was a solid masonry row of shops, offices, printeries, etc., 320 feet (98 m) long, comprising brick and stone buildings, some four stories high, some five. [ 13 ] It had a footprint taking up almost one acre (4,000 m 2 ) of space, and an estimated total weight—including hanging sidewalks—of 35,000 tons. [ 14 ] Businesses operating in these premises were not closed down during the operation; as the buildings were being raised, people came, went, shopped and worked in them as they would ordinarily do. In five days the entire assembly was elevated 4 feet 8 inches (1.42 m), by a team consisting of six hundred men using six thousand jackscrews, [ 15 ] which made it ready for new foundation walls to be built underneath. The spectacle drew crowds of thousands, who were, on the final day, permitted to walk at the old ground level, among the jacks. [ 16 ]
The following year the consortium of engineers Ely, Smith and Pullman led a team that raised the Tremont House hotel on the south-east corner of Lake Street and Dearborn Street. [ 17 ] This six-story brick building was luxuriously appointed, and had an area of over 1 acre (4,000 m 2 ). Once again business as usual was maintained as this large hotel ascended. [ 18 ] [ 19 ] Some of the guests staying there at the time—among whose number were several VIPs and a US Senator — [ 20 ] were oblivious to the process as five hundred men worked under covered trenches operating their five thousand jackscrews. [ 21 ] One patron was puzzled to note that the front steps leading from the street into the hotel were becoming steeper every day, and that when he checked out, the windows were several feet above his head, whereas before they had been at eye level. [ 22 ] This hotel building, which until just the previous year had been the tallest building in Chicago, was raised 6 feet (1.8 m) without incident. [ 23 ] [ 24 ] [ 25 ]
On the corner of South Water Street and Wells Street stood the Robbins Building, an iron building 150 feet (46 m) long, 80 feet (24 m) wide and five stories high. This was a very heavy building; its ornate iron frame , its twelve-inch (305 mm) thick masonry wall filling, and its “floors filled with heavy goods” made for a weight estimated at 27,000 tons (24,000 metric tons), a large load to raise over a relatively small area. Hollingsworth and Coughlin took the contract, and in November 1865 lifted not only the building but also the 230 feet (70 m) of stone sidewalk outside it. The complete mass of iron and masonry was raised 27.5 inches (0.70 m), “without the slightest crack or damage.” [ 26 ] [ 27 ] [ 28 ] [ 29 ] [ 30 ]
In 1860 the Franklin House, a four story brick building on Franklin Street, was raised with hydraulic apparatus by the engineer John C. Lane, [ 31 ] [ 32 ] of the Lane and Stratton partnership of San Francisco . Californian engineers had been using hydraulic jacks to raise brick buildings in and around San Francisco as early as 1853. [ 33 ] [ 34 ] [ 35 ]
Many of central Chicago’s hurriedly-erected wooden frame buildings were now considered inappropriate to the burgeoning and increasingly wealthy city. Rather than raise them several feet, proprietors often preferred to relocate these old frame buildings, replacing them with new masonry blocks built to the latest grade. Consequently, the practice of putting the old multi-story, intact and furnished wooden buildings—sometimes entire rows of them en bloc —on rollers and moving them to the outskirts of town or to the suburbs was so common as to be considered nothing more than routine traffic.
Traveller David Macrae wrote, “Never a day passed during my stay in the city that I did not meet one or more houses shifting their quarters. One day I met nine. Going out Great Madison Street in the horse cars we had to stop twice to let houses get across.” The function for which such a building had been constructed would often be maintained during the move, with people dining, shopping and working in these buildings as they were rollered down the street. [ 39 ] [ 40 ] [ 41 ] [ 42 ] Brick buildings also were moved from one location to another, and in 1866, the first of these—a brick building of two and a half stories—made the short move from Madison Street out to Monroe Street. [ 43 ] Later, many other much larger brick buildings were rolled much greater distances across Chicago. [ 44 ] | https://en.wikipedia.org/wiki/Raising_of_Chicago |
Raj Chandra Bose (or Basu) (19 June 1901 – 31 October 1987) was an Indian American mathematician and statistician best known for his work in design theory , finite geometry and the theory of error-correcting codes in which the class of BCH codes is partly named after him. He also invented the notions of partial geometry , association scheme , and strongly regular graph and started a systematic study of difference sets to construct symmetric block designs .
He was notable for his work along with S. S. Shrikhande and E. T. Parker in their disproof of the famous conjecture made by Leonhard Euler dated 1782 that for no n do there exist two mutually orthogonal Latin squares of order 4 n + 2.
Bose was born in Hoshangabad , India into a Bengali family; he was the first of five children. His father was a physician and life was good until 1918 when his mother died in the influenza pandemic . His father died of a stroke the following year. Despite difficult circumstances, Bose continued to study securing first class in both the Masters examinations in Pure and Applied mathematics in 1925 and 1927 respectively at the Rajabazar Science College campus of University of Calcutta . His research was performed under the supervision of the geometry Professor Syamadas Mukhopadhyaya from Calcutta. Bose worked as a lecturer at Asutosh College, Calcutta . He published his work on the differential geometry of convex curves.
Bose's course changed in December 1932 when P. C. Mahalanobis , director of the new (1931) Indian Statistical Institute , offered Bose a part-time job. Mahalanobis had seen Bose's geometrical work and wanted him to work on statistics. The day after Bose moved in, the secretary brought him all the volumes of Biometrika with a list of 50 papers to read and also Ronald Fisher 's Statistical Methods for Research Workers . Mahalanobis told him, "You were saying that you do not know much statistics. You master the 50 papers ... and Fisher's book . This will suffice for your statistical education for the present." With Samarendra Nath Roy , who joined the ISI a little later, Bose was the chief mathematician at the Institute.
He first worked with multivariate analysis where he collaborated with Mahalanobis and Roy. In 1938–39 Fisher visited India and talked about the design of experiments. Roy had the idea of using the theory of finite fields and finite geometry to solve problems in design. The development of a mathematical theory of design would be Bose's main preoccupation until the mid-1950s.
In 1935 Bose had become full-time at the Institute. In 1940 joined the University of Calcutta where C. R. Rao and H. K. Nandi were in the first group of students he taught. In 1945 Bose became Head of the Department of Statistics.
University authorities in the United States told him he needed to have a doctorate. So he submitted his published papers on multivariate analysis and the design of experiments and was awarded a D. Litt. in 1947.
In 1947 Bose went to the United States as a visiting professor at Columbia University and the University of North Carolina at Chapel Hill . He received offers from American universities and he was also offered positions in India. The Indian jobs involved very heavy administration, which he saw as the end of his research work and in March 1949 he joined the University of North Carolina at Chapel Hill as Professor of Statistics.
In the years at Chapel Hill Bose made important discoveries on coding theory (with D.K. Ray-Chaudhuri ) and constructed (with S. S. Shrikhande and E. T. Parker) a Graeco-Latin square of size 10, a counterexample to Euler's conjecture that no Graeco-Latin square of size 4 k + 2 exists. In 1971, he retired at the age of 70. He then accepted a chair at Colorado State University of Fort Collins from which he retired in 1980. His final doctoral student finished after this second retirement.
Bose died in Colorado , aged 86, in 1987. He is survived by two daughters. The elder, Purabi Schur, is retired from the Library of Congress and the younger, Sipra Bose Johnson, is retired as a professor of anthropology from the State University of New York at New Paltz .
This has a chapter in which Bose tells the story of his life. | https://en.wikipedia.org/wiki/Raj_Chandra_Bose |
Rake describes the angle made by a sloped surface with respect to a horizontal or vertical reference. The usages of this term include: | https://en.wikipedia.org/wiki/Rake_(angle) |
Ralava Beboarimisa (born 1977) is a Malagasy politician . He was Minister of Environment, Ecology, Sea, and Forest from 2015 to 2016. He was then Ministry of Transport and Meteorology of Madagascar from 2017 to 2019, firstly during two Governments of Jean Ravelonarivo and Olivier Solonandrasana , and then during transition Government led by Christian Ntsay because of the April 21, 2018 crisis.
Beboarimisa studied finance and international relationship. He acquired his first professional experiences in investment banks in France before returning to Madagascar in 2011. He then held the post of executive director of the Foundation for Protected Areas and Biodiversity of Madagascar for 4 years (FAPBM). FAPBM is one of the largest environmental foundation in Africa and also founding member of the Consortium of African Funds for Environment (CAFE) that Beboarimisa chaired. During his contract with FAPBM, Madagascar was particularly highlighted internationally as FAPBM led a delegation of more than 60 people from many environmental associations, NGOs and communities at the IUCN World Parks Congress 2014 in Sydney Australia.
One of the biggest problems Beboarimisa faced during his tenure as minister of the environment was the rapid deforestation and threat to the flora and fauna of the island that Madagascar is undergoing. [ 1 ] The first law he helped pass was the so-called "Beboarimisa law", which toughened sanctions for cutting down rosewoods in Madagascar. [ 2 ]
Beboarimisa's hard tactics toward combating deforestation made him a popular figure in the country, and for a brief period of time it was rumored that he might succeed Jean Ravelonarivo as the next prime minister . [ 3 ] However, Beboarimisa came under scrutiny in April 2016 after more than 1,000 tons of rosewood were discovered in the possession of a Hong Kong businessman in Singapore, leading to questions of how such a large amount could have been smuggled out of the country. [ 4 ] [ 5 ] Following the effervescence of traffics, a law was even drawn up, called the "Beboarimisa" law to strengthen the fight at a legal level. [ 6 ] United States support for international legal proceedings. [ 7 ] In 2019 the Court of Appeal in Singapore quashed all convictions related to the case. Ruling that the logs had only been intransit through Singapore, and not imported into Singapore. [ 8 ] In August 2017, following a government reshuffle, Beboarimisa returned to government ministry to be at the head of the Ministry of Transport and Meteorology. [ 9 ]
In October 2018, the 60th anniversary of the Republic of Madagascar, he decided to create a non-profit organization called "Bâtir la République" to encourage citizens' involvement and empowerment in the democratic debate, [ 10 ] mindful of the importance of citizen involvement observed during the first edition in 2018, further debates were held in the following years. [ 11 ] The 1st Republic of Madagascar was born on October 14, 1958, while independence was obtained two years later on June 26, 1960. October 14 is generally a forgotten day however "Batir la République" decided to put it forward. [ 12 ] [ 13 ] [ 14 ] | https://en.wikipedia.org/wiki/Ralava_Beboarimisa |
Raleigh plots , or Rayleigh plots (also called circlegrams [ 1 ] and closely related to circular histograms, [ 2 ] phasor diagrams, [ 3 ] and wind roses [ 4 ] ), are statistical graphics that serve as graphical representations for a Raleigh test that map a mean vector to a circular plot. Raleigh plots have many applications in the field of chronobiology , such as in studying butterfly migration patterns or protein and gene expression, and in other fields such as geology, cognitive psychology, and physics.
Raleigh plots was first introduced by Lord Rayleigh . The concept of Raleigh plots evolved from Raleigh tests, also introduced by Lord Rayleigh in 1880. The Rayleigh test is a popular statistical test used to measure the concentration of data points around a circle, identifying any unimodal bias in the distribution. [ 5 ] Rayleigh plots emerged from this analysis as a means to illustrate the nature of the distribution.
In a Raleigh plot, each individual is assigned a unit vector with a corresponding angle . These unit vectors are averaged together in a Raleigh plot into the mean vector. The length of the mean vector is determined by r (or R ), the mean resultant length. r is a measure of concentration, ranging in value between 0 and 1. If the individual angles of the unit vectors are tightly clustered, then the r value will be closer to 1, while if they are widely scattered, then r will be closer to zero. [ 6 ] The mean vector is positioned in the center of a circle. Dashes along the circumference of this circle denote desired values. Examples include angles from magnetic north (zero degrees) going clockwise (e.g., 90 degrees from magnetic north, or eastward); times of day, which can also be described in zeitgeber time and circadian time; and phase. Dots on the circumference are usually used to indicate individual unit vectors and their respective angle in regard to the values being measured. Raleigh plots can also use more than one mean vector, particularly if one wants to display the mean vector for different tested groups in the study or to compare mean vectors between groups. [ 7 ]
The example to the left is a Raleigh plot that has a high r value. Blue and yellow dots indicate individuals from different groups being tested, and the position of the dots indicate in which angle from magnetic north each tested individual is traveling. Due to the high overall concentration of individuals going at an angle between zero degrees and ninety degrees, the mean vector is much longer. Compare the figure to the left with the figure below:
In this second example (to the right), the Raleigh plot has a low r value. Both yellow and blue dots are spread along the circumference of the circle, indicating that many individuals are traveling at different angles. The largest cluster of individuals, a group traveling between 180 degrees and 270 degrees, causes the mean vector to be pointed at an angle in that direction. Notably, due to the variability in the direction within this group, the mean vector is much smaller.
Raleigh plots have been used in chronobiology studies on the biological clocks behind monarch butterfly migration patterns. They are particularly relevant for studying sun compass orientation in migrating butterflies.
In butterfly migration studies, the Raleigh plot maps the orientation of the butterfly when allowed to fly, where the circumference is marked as a compass, with north (N) at the top position. Given the plotted data points, a mean r vector is drawn to indicate the mean orientation of the butterflies in a particular condition. [ 8 ] [ 9 ]
In his studies on the neurobiology of butterfly migration, Steven M. Reppert observes the oriented flight behavior of monarch butterflies. Reppert explains how Raleigh plots are used to handle butterfly orientation data and as tools for the data analysis. [ 10 ]
In a 2012 study by Reppert and colleagues on the sufficiency of an antenna for proper time compensation and sun compass orientation in the monarch butterfly, Raleigh plots were used to present the mean flight orientation of butterflies subjected to different study conditions. Along the edge of the circle, degrees 0º ( magnetic north ) through 360º are shown, the orientation of each butterfly is marked with a dot, and a mean vector is drawn to represent the mean flight orientation recorded. [ 7 ] In a 2016 annual review on the neurobiology of monarch butterfly migration, Reppert, Guerra, and Merlin also use Raleigh plots to present butterfly orientation data. The plots were used in the study of the time-compensated sun compass in monarch butterflies. [ 10 ] A 2018 review by Reppert and de Roode on the mechanisms of monarch butterfly migration also used Raleigh plots, or circlegrams, to represent butterfly orientation data. Each dot indicates the orientation in which a butterfly individual flew continuously for 5 minutes or longer, and the vector points in the mean direction (some degrees from north) with a magnitude proportional to the mean orientation. [ 1 ]
Raleigh plots can be used to visualize circadian rhythms in protein or gene expression, and how their phases are affected by other variables or induced conditions.
Jennifer Mohawk, then a postdoc at the University of Texas Southwestern Medical Center , used multiple Raleigh plots to illustrate PER2 :: LUC expression in her 2013 paper " Methamphetamine and Dopamine Receptor D1 Regulate Entrainment of Murine Circadian Oscillators ." [ 11 ] Specifically, Mohawk investigated how injections of methamphetamine and D1 antagonist SCH-23390 would shift the peak time of PER2 expression in the liver, lung, pituitary gland , and salivary gland . In these plots, the Raleigh plot can be interpreted as a 24 hour clock with CT 0 at the top of the circle and CT 12 at the bottom of the circle. Each arrow represents the average peak phase of PER2::LUC expression of each group. The strength of the phase clustering is symbolized by the length of the arrow, meaning stronger clustering or closer data points resulting in longer arrows. The individual data points are plotted on the outside of the circle and their unique color and shape resemble the different groups of conditions. At ZT 7 is a pink box that shows the timing of the methamphetamine injection. Mohawk and collaborators compared the angle of the vector, or the mean phase, between the different groups in order to determine if methamphetamine injections induced statistically significant phase changes of PER2::LUC expression within the different glands and organs. [ 11 ]
Similarly, Tsedey Mekbib, then a PhD student at the Morehouse School of Medicine , utilized Raleigh plots to depict how the knockdown of SIAH2 impacted the rhythmic expression of all other genes in both males and females. After profiling the entire transcriptome via RNA sequence on the liver at frequent time intervals, the expression of peak timing for all rhythmically expressed genes was plotted on Raleigh plots for each group. These Raleigh plots contain vectors that represent the average peak phase. However, instead of differing the length of the vectors to illustrate the variability in the data points, Mekbib and the other collaborators added a +/- 95% confidence interval that is represented by red range along the circle. In addition to the typical Raleigh plot, the left half of the circle is shaded darker to better visualize the night phase occurring between CT 12 and CT 24. [ 12 ]
Raleigh plots can be used to visualize the circadian rhythms in protein or gene expression in the suprachiasmatic nucleus (SCN) specifically, and how they might influence other peripheral tissues.
Raleigh plots were used by Elizabeth Maywood , an English researcher at the MRC Laboratory of Molecular Biology , to visualize how pacemaking activity and synchrony between host SCN cells lacking vasoactive intestinal peptide (VIP) can be restored with a wild-type SCN graft. These plots show vectors that represent the phase of the host SCN cells, measured by PER2::LUC expression. Each plot has a value representing the mean vector length with time points where the cell phases are closer in sync having a value closer to 1. Maywood and collaborators showed that VIP-null host SCN cells synchrony deteriorated over time based on the mean vector length of the Raleigh plots decreasing, and concluded that paracrine signaling from an introduced wild-type SCN graft is sufficient to restore the synchrony between SCN cell pacemakers based on the mean vector length increasing after the graft was introduced. [ 13 ]
Mariko Izumo, while working at the University of Texas Southwestern Medical Center , used Raleigh plots to assess the effect of knocking out BMAL1 in the SCN on the circadian expression of PER2, measured using PER2::LUC expression, in the SCN and in peripheral tissues. Izumo and others found that knocking out BMAL1 led to the desynchronization and dampening of PER2 expression in peripheral tissues with Raleigh plots showing different mean phases of the rhythm of PER2 expression. They also show that light/dark cycles and feeding can restore synchrony in peripheral tissues with Raleigh plots showing the same mean phases of the rhythm of PER2 expression. [ 14 ]
Similarly, Yongli Shan, also while working at the University of Texas Southwestern Medical Center, used Raleigh plots to show that BMAL1 knockout AVP SCN neurons and VIP SCN neurons show a loss in rhythm in expression of PER2. BMAL1 knockout neurons have data points around the circular diagram and a small mean vector r , while wild-type neurons have a larger mean vector r and data points closer together. Additionally, Shan and others show that intercellular connections to the rest of the SCN was sufficient in restoring rhythmicity in BMAL1 knockout VIP neurons but not AVP neurons with an increase in the mean vector r in VIP neurons but not in AVP neurons. [ 15 ]
Raleigh plots or variations on Raleigh plots are used in fields beyond chronobiology. While Raleigh plots visualize a mean vector for data, the variational plots that are closely related to Raleigh plots may visualize histogram data in spokes on a circular chart.
In geology , circular histogram plots or rose diagrams can be used to characterize tectonic plate movements . For example, they may be used to visualize the frequency and direction of fault line motion. [ 16 ] In meteorology and climate studies, wind roses are used to present data on the direction, duration, and speed of winds that occurred at a given location. For example, in wind roses released by the Midwestern Regional Climate Center, the length of a spoke in a particular direction, representing a histogram bin, is proportional to the duration of time for which the wind was blowing in that direction, with different colors to show wind speed categories. [ 4 ]
Additionally, Raleigh plots can be used in cognitive psychology . Joëlle Provasi, professor at École pratique des hautes études , used them to explain the response of children with or without a lesion in their cerebellum due to surgically removed tumor to a rhythmic stimulus. Provasi and others show a Raleigh plot depicting responses that are close to the stimulus as data points around the top at 0 degrees with a mean vector value close to 1, and a Raleigh plot depicting responses that are irregular with dots spread around the circular plot and a mean vector value closer to 0. [ 17 ] | https://en.wikipedia.org/wiki/Raleigh_plot |
Ralf Brown's Interrupt List (aka RBIL , x86 Interrupt List , MS-DOS Interrupt List or INTER ) is a comprehensive list of interrupts , calls , hooks , interfaces , data structures , CMOS settings , memory and port addresses, as well as processor opcodes for x86 machines from the 1981 IBM PC up to 2000 (including many clones ), [ 1 ] [ 2 ] [ nb 1 ] most of it still applying to IBM PC compatibles today. It also lists some special function registers for the NEC V25 and V35 microcontrollers .
The list covers operating systems , device drivers , and application software ; both documented and undocumented information including bugs , incompatibilities, shortcomings, and workarounds, with version, locale, and date information, often at a detail level far beyond that found in the contemporary literature. [ 3 ] [ 4 ] [ 5 ] A large part of it covers system BIOSes and internals of operating systems such as DOS , OS/2 , and Windows , as well as their interactions. [ 3 ] [ 6 ]
It has been a widely used resource by IBM PC system developers, [ 7 ] [ 4 ] [ 5 ] analysts, [ 8 ] as well as application programmers in the pre- Windows era. [ 3 ] [ 6 ] Parts of the compiled information have been used for and in the creation of several books on systems programming, [ 3 ] [ 6 ] [ 9 ] [ 10 ] [ 11 ] [ 12 ] some of which have also been translated into Chinese, [ 13 ] [ 14 ] [ 15 ] [ 6 ] Japanese [ 3 ] and Russian. [ 16 ] [ 17 ] As such the compilation has proven to be an important resource in developing various closed and open source operating systems, including Linux and FreeDOS . [ 18 ] Today it is still used as a reference to BIOS calls and to develop programs for DOS as well as other system-level software.
The project is the result of the research and collaborative effort of more than 650 listed contributors worldwide over a period of 15 years, of which about 290 provided significant information (and some 55 of them even more than once). [ 1 ] The original list was created in January 1985 by Janet Jack and others, [ 19 ] and, named "Interrupt List for MS-DOS", it was subsequently maintained and mailed to requestors on Usenet by Ross M. Greenberg until 1986. [ 20 ] [ 21 ] [ 22 ] Since October 1987 it is maintained by Ralf D. Brown, [ 23 ] a researcher at Carnegie Mellon University 's Language Technologies Institute . [ 3 ] [ 6 ] [ 24 ] Information from several other interrupt listings was merged into the list in order to establish one comprehensive reference compilation. Over the years, Michael A. Shiels, Timothy Patrick Farley , Matthias R. Paul, Robin Douglas Howard Walker, Wolfgang Lierz and Tamura Jones became major contributors to the project, providing information all over the list. [ 1 ] The project was also expanded to include other PC development-related information and therefore absorbed a number of independently maintained lists on PC I/O ports (by Wim Osterholt and Matthias R. Paul), BIOS CMOS memory contents (by Atley Padgett Peterson ), processor opcodes (by Alex V. Potemkin) and bugs (by Harald Feldmann). [ 1 ] [ nb 1 ] Brown and Paul also conducted several systematic surveys on specific hard- and software details among a number of dedicated user groups in order to validate some info and to help fill some gaps in the list. [ 25 ] [ 26 ] [ 27 ]
Originally, the list was distributed in an archive named INTERRUP in various compression formats as well as in the form of diffs . The distribution file name was changed to include a version in the form INTERnyy (with n = issue number, and yy = 2-digit release year) in 1988. In mid 1989 the distribution settled to only use ZIP compression. [ 28 ] When the archive reached the size of a 360 KB floppy in June 1991, the distribution split into several files following an INTERrrp.ZIP naming scheme (with rr = revision starting with 26 for version 91.3, and p = part indicator of the package starting with letter A). Officially named "MS-DOS Interrupt List" and "x86 Interrupt List" (abbreviated as "INTER") by its maintainer, the community coined the unofficial name "Ralf Brown's Interrupt List" (abbreviated as "RBIL") in the 1990s.
The publication is currently at revision 61 as of 17 July 2000 with almost 8 MB of ASCII text including close to 9600 entries plus about 5400 tables, [ 1 ] fully cross linked, which would result in more than 3700 pages (at 60 lines per page) of condensed information when printed. Of this, the interrupt list itself makes up some 5.5 MB for more than 2500 pages printed. [ nb 1 ]
While the project is not officially abandoned and the website is still maintained (as of 2025 [update] ), new releases have not been forthcoming for a very long time, despite the fact that information was still pending for release even before the INTER61 release in 2000. [ 29 ] New releases were planned for at several times in 2001 [ 30 ] [ 31 ] and 2002, [ 32 ] [ 33 ] [ 34 ] [ 35 ] [ 26 ] [ 27 ] but when they did not materialize, portions of the new information on DOS and PC internals provided by Paul were circulated in preliminary form in the development community for peer-review and to assist in operating system development. [ 31 ] [ 36 ] [ 37 ] [ 33 ] [ 38 ] [ 39 ] [ 40 ] [ 41 ] [ 26 ] [ 42 ] [ 43 ] [ 44 ] [ 45 ] | https://en.wikipedia.org/wiki/Ralf_Brown's_Interrupt_List |
Ralf Riedel (born 11 February 1956) is a German professor of Materials Science at the Technical University of Darmstadt (TU Darmstadt) in Germany. [ 1 ] He is known for his contributions to ceramics, polymer-derived ceramics (PDCs), and high-performance materials, which has advanced the understanding and application of ceramic materials in fields such as aerospace, automotive, and energy technologies. [ 2 ]
Riedel studied chemistry at the University of Stuttgart with his Diploma Thesis concerning "Versuche zur Reduktion von Aldehyden mit weißem Phosphor". [ 1 ] [ 3 ] From 1984, he pursued a Ph.D. in the field of Inorganic Chemistry at the University of Stuttgart. In 1986, he graduated with his dissertation Weißer Phosphor als Edukt für die Synthese phosphororganischer Verbindungen . [ 1 ] [ 3 ]
After education, Riedel undertook postdoctoral research at Max Planck- Institute for Metals Research, Institute for Materials Research, PML, Stuttgart in materials processing and characterization techniques. [ 1 ] [ 3 ] Between 1986 and 1992, he worked on his habilitation concerning "Nicht-oxidische Keramiken aus anorganischen Vorstufen" under supervision of Prof. Dr. G. Becker and Prof. F. Aldinger. [ 1 ] [ 3 ] [ 4 ]
Riedel was establishing and leading the Dispersive Solids Group at the Institute of Materials Science, Technical University of Darmstadt (TU Darmstadt) as professor from 1993 until his retirement in 2022. His research in the Dispersive Solids Group focused on the development of polymer-derived ceramics, high- temperature materials, and functional ceramics for structural and electronic applications. [ 1 ]
Ralf Riedel's career spans several decades with contributions to materials science, particularly in the development and application of polymer-derived ceramics (PDCs) as well as high pressure materials synthesis. His work bridges theoretical research and practical applications. Below is a detailed exploration of his professional journey. [ 5 ]
Riedel´s early research focused on developing ceramic materials through synthesis routes, Highlights of Riedel´s research at the Dispersive Solids Group are as follows: [ 6 ]
Riedel is known for his work on PDCs. He has developed methods to design ceramics at the molecular level, enabling the production of materials with tailored properties. These advances have applications in high-performance coatings, lightweight structural materials, and energy storage technologies. His research into PDCs has been on extending their use to fields like aerospace engineering and microelectronics. [ 7 ]
Riedel's work on ceramics designed for high-temperature environments has advanced the understanding of the thermal stability, creep resistance, and oxidation behavior of ceramics under extreme conditions. [ 8 ]
In addition to PDCs, Riedel has contributed to the field of ceramic composites, where he has developed lightweight, high-strength materials by integrating ceramic matrices with other reinforcing materials. These composites are used in applications requiring exceptional mechanical properties, such as turbine blades and wear-resistant components. [ 9 ]
In recent years, Riedel has focused on using sustainable materials and processes in ceramics manufacturing, contributing to the development of environmentally friendly materials for energy-efficient systems. [ 10 ]
Throughout his career, Riedel has worked closely with industrial partners to ensure the translation of his research into practical applications. He has collaborated with companies in sectors such aerospace, automotive and energy [ 7 ]
1. Li Lu, Tonghui Wen, Wei Li, Qingbo Wen, Zhaoju Yu, Shasha Tao, Jincan Yang, Yalei Wang, Xingang Luan, Xiang Xiong, Ralf Riedel, Single-source-precursor synthesis of dense monolithic SiC/(Ti 0 . 25 Zr 0.25 Hf 0.25 Ta 0.25 )C ceramic nanocomposite with excellent high-temperature oxidation resistance, J. Eur. Ceram. Soc. 44 (2024) 556-609.
2. Honghong Tian, Magdalena Graczyk-Zajac, Alois Kessler, Anke Weidenkaff, Ralf Riedel, Recycling and Reusing of Graphite from Retired Lithium-ion Batteries: A Review, Adv. Mater. 2023, 2308494
3. Liu, Jiongjie; Dong, Changyu; Lu, Xuefeng; Qiao, Zhuhui; Zhou, Feng; Liu, Weimin; Riedel, Ralf, Sn-containing Si 3 N 4 -based composites for adaptive excellent friction and wear in a wide temperature range, Journal of the European Ceramic Society, 42 (2022), 913-920.
4. Shrikant Bhat, Leonore Wiehl, Shariq Haseen, Peter Kroll, Konstantin Glazyrin, Philipp Gollé Leidreiter, Ute Kolb, Robert Farla, Jo-Chi Tseng, Emanuel Ionescu, Tomoo Katsura, and Ralf Riedel, A Novel High-Pressure Tin Oxynitride Sn 2 N 2 O, Chem. Eur. J. 0.1002/chem. 201904529.
5. Takashi Taniguchi, Dmytro Dzivenko, Ralf Riedel, Thierry Chauyeau, Andreas Zerr, Synthesis of cubic zirconium (IV) nitride, c-Zr 3 N 4 , in the 6-8 GPa pressure region, Ceramics international 45 (2019) 20028-20032.
6. Reinold, L.M.; Yamada, Y.; Graczyk-Zajac, M.; Munakata, H.; Kanamura, K.; Riedel, R.; "The influence of the pyrolysis temperature on the electrochemical behavior of carbon-rich SiCN polymer-derived ceramics as anode materials in lithium-ion batteries", J. Power Sources 282 (2015) 409-415.
7. Maged F. Bekheet, Marcus Schwarz, Stefan Lauterbach, Hans-Joachim Kleebe, Peter Kroll, Ralf Riedel, Aleksander Gurlo, "Orthorhombic In2O3: A metastable polymorph of indium sesquioxide", Angew. Chem. Int. Ed. 52 (2013) 6531-6535.
8. S. Sen, S. J. Widgeon, A. Navrotsky, G. Mera, A. Tavakoli, E. Ionescu, R. Riedel, "Can carbon substitute for oxygen in silicates in planetary interiors?", Proceedings of the National Academy of Sciences (PNAS) 110 (2013) 15904 – 15907.
9. E. Horvath-Bordon, R. Riedel, P. F. McMillan, P. Kroll, G. Miehe, P.A. van Aken, A. Zerr, P. Hoppe, O. Shebanova, I. McLaren, S. Lauterbach, E. Kroke, R. Boehler, High-pressure synthesis of crystalline carbon nitride imide, C2N2(NH). Angew. Chem. Int. Ed. 46 (2007) 1476.
10. A. Zerr, G. Miehe, G. Serghiou, M. Schwarz, E. Kroke, R. Riedel, H. Fueß, P. Kroll, R. Boehler, Synthesis of cubic silicon nitride. Nature 400 (1999) 340. | https://en.wikipedia.org/wiki/Ralf_Riedel |
Ralink Technology, Corp. is a Wi-Fi chipset manufacturer mainly known for their IEEE 802.11 ( Wireless LAN ) chipsets. Ralink was founded in 2001 in Cupertino, California , then moved its headquarters to Hsinchu , Taiwan . On 5 May 2011, Ralink was acquired by MediaTek .
Some of Ralink's 802.11n RT2800 chipsets have been accepted into the Wi-Fi Alliance 802.11n draft 2.0 core technology testbed. They have also been selected in the Wi-Fi Protected Setup (WPS) and Wireless Multimedia Extensions Power Save (WMM-PS) testbeds. Ralink was a participant in the Wi-Fi Alliance and the IEEE 802.11 standards committees. [ 1 ] Ralink chipsets are used in various consumer-grade routers made by Gigabyte Technology , Linksys , D-Link , Asus and Belkin , as well as Wi-Fi adaptors for USB , PCI , ExpressCard , PC Card , and PCI Express interfaces. An example of an adapter is the Nintendo Wi-Fi USB Connector which uses the Ralink RT2570 chipset to allow a Nintendo DS or Wii to be internetworked via a home computer.
Ralink provides some documentation without a non-disclosure agreement . [ 2 ] This includes datasheets of their PCI and PCIe chipsets, but for now does not include documentation of their system on a chip used in Wireless routers .
Drivers for MediaTek Ralink wireless network interface controllers were mainlined into the Linux kernel version 2.6.24. (See Comparison of open-source wireless drivers .) Ralink provides GNU General Public License -licensed (GPL) drivers for the Linux kernel . While Linux drivers for the older RT2500 chipsets are no longer updated by Ralink, these are now being maintained by Serialmonkey's rt2x00 project. Current Ralink chipsets require a firmware to be loaded. Ralink allows the use and redistribution of firmware, but does not allow its modification.
In February 2011 Greg Kroah-Hartman praised Ralink for their change in attitude towards the Linux kernel developer community:
As you can see in these posts, Ralink is sending patches for the upstream rt2x00 driver for their new chipsets, and not just dumping a huge, stand-alone tarball driver on the community, as they have done in the past. This shows a huge willingness to learn how to deal with the kernel community, and they should be strongly encouraged and praised for this major change in attitude. | https://en.wikipedia.org/wiki/Ralink |
Raluca Ripan (27 June 1894 – 5 December 1972) was a Romanian chemist , and a titular member of the Romanian Academy . She wrote many treatises, especially in the field of analytical chemistry .
She was born in Iași , in the Moldavia region of Romania; her parents were Constantin and Smaranda Ripan, both originally from Huși . She attended the local girl's high school, after which she enrolled in the Faculty of Science of the University of Iași , graduating in 1919. For her graduate studies she went to the University of Cluj in Transylvania , obtaining her PhD in 1922 under the direction of Gheorghe Spacu , [ 1 ] with thesis "Double amines corresponding to double sulphates in the magnesium series". She is recognized as the first woman from Romania to earn a Ph.D. in the chemical sciences. [ 1 ] [ 2 ]
After obtaining in 1930 her Habilitation and the title of Docent , Ripan became an associate professor of analytic chemistry at the Faculty of Science of the University of Cluj. During World War II , when Cluj passed under Hungarian administration under the terms of the Second Vienna Award , the university moved to Timișoara . In July 1942 (by which time she had 53 publications), she was promoted to full professor through a decree published in Monitorul Oficial . [ 3 ] After the war she returned to Cluj, where she served as Dean of the Faculty of Chemistry from 1948 to 1952.
In 1948, Ripan was elected titular member of the Romanian Academy , thus becoming the first woman to be inducted in that academy. In 1951 she founded the Institute of Chemistry, consisting of three sections (inorganic chemistry, organic chemistry, and physical chemistry); she headed the institute until 1970. From 1951 to 1955 she served as Rector of the University of Cluj, the first woman to hold a rectorship in Romania. [ 1 ] [ 2 ] In 1952 she was elected deputy to the Great National Assembly for the Cluj-Nord constituency of the Cluj Region , serving in this capacity until 1957. In 1963 she was awarded an honorary degree by the Nicolaus Copernicus University in Toruń .
Ripan worked in the domain of complex combinations and their use in analytical chemistry. She discovered and studied new classes of complex combinations used in the determination of metals, as well as new methods of assay for thallium , lead, tellurium , selenic acid , and selenocyanates . [ 4 ] One of her students at the University of Cluj was Ionel Haiduc (a future President of the Romanian Academy), who wrote an undergraduate thesis on polyoxometalates under her direction in 1959. [ 5 ]
She died in Cluj-Napoca in 1972, and is buried at the city's Hajongard Cemetery . The "Raluca Ripan Institute for Research in Chemistry" is now part of Babeș-Bolyai University . [ 6 ] A vocational high school in Cluj-Napoca also bears her name, [ 7 ] as does a national Chemistry competition for high school students. [ 8 ] | https://en.wikipedia.org/wiki/Raluca_Ripan |
Ram Charan Mehrotra (16 February 1922 – 11 July 2004) was an Indian analytical and organometallic chemist, academic, educationist and the vice chancellor of the Universities of Delhi and Allahabad . [ 1 ] He was known for his studies on the chemical theory of indicators, alkoxides and carboxylates of many elements. [ 2 ] He was an elected fellow of the Indian National Science Academy , Indian Chemical Society , Chemical Society of London , Royal Institute of Chemistry , National Academy of Sciences, India [ 3 ] and Indian Academy of Sciences . [ 4 ] The Council of Scientific and Industrial Research , the apex agency of the Government of India for scientific research, awarded him the Shanti Swarup Bhatnagar Prize for Science and Technology , one of the highest Indian science awards, in 1965, for his contributions to chemical sciences. [ 5 ]
Ram Charan Mehrotra was born in a middle-class family on 16 February 1922 in Kanpur in the Indian state of Uttar Pradesh to Ram Bharose Mehrotra, a small-time cloth merchant and his homemaker wife, Chameli Devi. [ 6 ] He lost both his parents before he turned 10 and had to continue his studies depending on merit scholarships and part-time jobs like private tuition. [ 7 ] His primary schooling was at Municipal School, Kanpur and later he joined Christ Church School (present-day Christ Church College, Kanpur ) from where he passed the intermediate course , standing first in the state. Joining the University of Allahabad in 1939 for his graduate studies, he completed the course on the strength of three scholarships [ note 1 ] and passed BSc with Mathematics, Physics and Chemistry as optional subjects. He continued at the university for MSc in chemistry which he passed with first rank in 1943. During this period, he was also involved in student politics in connection with the Quit India Movement of 1942 and had to stay away from studies for four months. [ 7 ]
Before starting his formal academic career by joining Allahabad University in 1944 as a member of faculty of inorganic chemistry, Mehrotra worked at Vigyan Kala Bhawan, Daurala, a local learning centre involved in teaching science to prospective young entrepreneurs, for ten months during 1943–44 and was also associated with Vigyan Pragati , a science magazine published by National Institute of Science Communication and Information Resources (NISCAIR) of the Council of Scientific and Industrial Research. [ 7 ] He served the university till 1954; in between, he had a short stint of two years at Birkbeck College from 1950 to 1952 as a British Council Fellow and part-time faculty, working with Donald Charlton Bradley ; he utilised this period to secure a PhD from the University of London in 1952. He returned to India the same year and resumed his service at Allahabad University when he was offered the position of a reader at Lucknow University in 1954. After serving four years there, he moved to Gorakhpur University in 1958 as a professor where, a year later, he was promoted as the dean of the faculty of science. [ 6 ] It was during this time, he served as a member of the Review Committee in Chemistry of the University Grants Commission of India under the chairmanship of T. R. Seshadri , where his colleagues included Asima Chatterjee , a noted chemist. [ 8 ]
In 1962, on invitation of Mohan Sinha Mehta , the then vice chancellor of the University of Rajasthan , he took up the post of a professor and head of the newly formed chemistry department and served the institution for two decades. In between, he had a five-year stint as the vice chancellor of Delhi University (from 1974 to 1979) [ 9 ] and a short assignment as a UGC National Fellow in December 1979 but on completion of those assignments, he returned to Rajasthan University, where he stayed till 1982; on his move from the university, he was made an emeritus professor. That year, he became associated with the activities of the University Grants Commission , first as the chairman of the Commission on Revision of Pay Scales to Teachers which submitted its report to UGC in 1986. [ 10 ] [ 11 ] Simultaneously, when the National Commission on Teachers was constituted by the Government of India in 1983 under the chairmanship of D. P. Chattopadhyaya , he was appointed as a member of the Research Advisory Committee. [ 12 ] After his assignment with the committee, he took up the chair of the Book Writing Project of the National Council of Educational Research and Training (NCERT) and in 1991, he was appointed as the vice chancellor of the University of Allahabad, a position he held in 1993. [ 13 ]
Mehrotra was married to Suman, a Hindi scholar, whom he married in 1944 around the same time when he joined Allahabad University. The couple had two daughters, Rashmi and Shalini and one son, Piyush Mehrotra, in between. [ 6 ] He died on 11 July 2004, reportedly due to chronic obstructive pulmonary disease , at the age of 82. [ 14 ]
Mehrotra, during his early years in research, made notable contributions in analytical chemistry which included studies on tin, gold and hydrated copper
oxide. [ 7 ] Through his researches on the chemical theory of indicators, he elucidated the applicability of universal type of indicators, ceramic salts and of hypobromites and widened the understanding of alkoxides and carboxylates of many elements. [ 15 ] His work covered the synthesis of several metallic compounds such as polymetaphosphates, alkoxides , beta-diketonates, carboxylates , thiolates and dialky 1 dithiophosphates . [ 1 ]
While serving Rajasthan University as a professor, Mehrotra was known to have contributed in organizing a research school there and successfully tried to obtain Special Assistance Program as well as University Leadership Program from UGC. [ 7 ] The research school has since published several original research papers in international journals. Similarly, he established research schools on inorganic and organometallic chemistry at the universities of Allahabad, Lucknow, and Delhi. [ 1 ] During 1971–72, as a UGC National Professor, he delivered lectures at many Indian universities and he was a pioneer in popularizing science through Hindi medium for which he was awarded a cash prize by the Government of India in 1985. Besides over 800 articles published in peer-reviewed international journals, [ 16 ] [ note 2 ] he authored five books viz. Metal alkoxides , [ 17 ] Metal [beta] [beta]-diketonates and Allied Derivatives , [ 18 ] Metal Carboxylates , [ 19 ] Alkoxo and Aryloxo Derivatives of Metals [ 20 ] and Organometallic Chemistry . [ 21 ] He has also prepared texts for Indira Gandhi National Open University as a member of the Block Preparation Team. [ 22 ] [ 23 ]
Mehrotra was involved in policy-making bodies from early stages of his career when he sat in the Review Committee in Chemistry in 1960 and the committee made a number of recommendations on improvement of curriculum, research environment, and examination procedures of chemistry education in India. [ 8 ] During 1963–67, he sat in the Chemical Advisory Committee of the Atomic Energy Commission of India . [ 6 ] The Commission on Revision of Pay Scales to Teachers which he chaired in 1983 recommended that the procedure for selection of teachers should also include an assessment of the physical and mental abilities of the candidates. [ 24 ] The commission also recommended for pay scale revision of the teaching staff ranging from over 200 to more than 300 per cent which was subsequently accepted by the Government of India and the revision was implemented in 1987 with retrospective effective from 1 January 1986. [ 10 ]
Mehrotra served as the president of the chemistry section of the Indian Science Congress Association in 1967, he would also serve as its national president in 1979. [ 25 ] Besides participating in the UGC ad-hoc commissions, he was also associated with the body as a convener of its chemistry panel and his association with the Council of Scientific and Industrial Research (CSIR) included the chair of the Chemical Research Committee (1975) and membership in CSIR Society and CSIR Governing Body (1963–66 and 1976–80). [ 6 ] He served as the president of the Indian Chemical Society (1976–77) and Vigyan Parishad, Allahabad, as the vice president of the Indian National Science Academy - INSA (1977–78) and as a member of the International Union of Pure and Applied Chemistry (1977–81). He was also a member of the INSA council from 1979 to 1981. [ 1 ]
During his early years at Allahabad University, Basu received the E. G. Hill Memorial Prize of the university in 1949 for the best research work by a member of the science faculty. [ 7 ] The Indian National Science Academy elected Basu as a fellow in 1964 and the University of London honored him with the degree of Doctor of Science in 1965. The ensuing years would see him receive several honoris causa doctorates from Indian universities viz. Meerut University (1976), Kanpur University (1996), Jhansi University (2000) and Banares Hindu University (2000). The Council of Scientific and Industrial Research awarded him the Shanti Swarup Bhatnagar Prize , one of the highest Indian science awards, in 1965. [ 26 ] The Federation of Indian Chambers of Commerce & Industry awarded him the FICCI Award for Science and Technology in 1975 and he received the Professor T. R. Seshadri Seventieth Birthday Commemoration Medal of the Indian National Science Academy in 1976 [ 27 ] and the P. C. Ray Award of the Indian Chemical Society in 1977. He was awarded the National Fellowship by the University Grants Commission in 1980 and the Golden Jubilee Medal by the Institute of Science, Mumbai in 1984. [ 1 ]
The J. C. Ghosh Medal of the Indian Chemical Society reached Mehrotra in 1986, followed by the Academic Achievements Award of the Sōka University in 1987. [ 7 ] The Indian Science Congress Association honored him with four awards; starting with the Platinum Jubilee Distinguished Service Award in 1988; followed by G. P. Chatterjee Award in 1991, Acharya Narendra Dev Award in 1992 and Ashutosh Mukherjee Award in 1993. In between, he received the inaugural Atmaram Award of the Central Institute of Hindi . [ 28 ] The Chemical Research Society of India awarded him Lifetime Achievement Award in 1999 and the Indian Chemical Society awarded him the Platinum Jubilee Award in 2000. [ 7 ] He was an elected fellow of the Indian Academy of Sciences, [ 4 ] Indian National Science Academy and National Academy of Sciences, India [ 3 ] and a fellow of the Chemical Society of London , Royal Institute of Chemistry and the Indian Chemical Society . [ 1 ] He also delivered several award orations and featured lectures; Special lecture at the XVII International Conference on Coordination Chemistry (1977), Plenary lecture at the XIX International Conference on Coordination Chemistry (1978), Plenary lecture at the IV International Conference on Solute-Solvent Interaction (1978), Clarence Karcher Memorial Lecture of University of Oklahoma (1982), the inaugural Foundation Lecture of the Federation of Asian Chemical Societies (1987) and N. R. Dhar Memorial Award Lecture of the National Academy of Science, India (1991) are some of the notable ones. [ 7 ] | https://en.wikipedia.org/wiki/Ram_Charan_Mehrotra |
Ram Prakash Bambah (born 17 September 1925) [ 1 ] [ 2 ] is an Indian mathematician working in number theory and discrete geometry .
Bambah earned a bachelor's degree from Government College University, Lahore , and a master's degree from the University of the Punjab, Lahore . [ 2 ] He then went to England for his doctoral studies, earning his Ph.D. in 1950 from St John's College, Cambridge under the supervision of Louis J. Mordell . [ 2 ] [ 3 ] Returning to India, he became a reader at Panjab University, Chandigarh , in 1952, and was promoted to professor there in 1957. [ 2 ] Maintaining his position at Panjab University, he also held a position as professor at Ohio State University in the US from 1964 to 1969. [ 2 ] He retired from Punjab University in 1993. [ 2 ]
Bambah was president of the Indian Mathematical Society in 1969, and vice chancellor of Panjab University from 1985 to 1991. [ 2 ]
He was elected to the Indian National Science Academy in 1955. [ 2 ] In 1979 he was awarded the Srinivasa Ramanujan Medal , [ 2 ] and in 1974 was elected to the Indian Academy of Sciences . [ 1 ] In 1988 he received the Aryabhata Medal of the Indian National Science Academy [ 2 ] and the Padma Bhushan award. [ 4 ] | https://en.wikipedia.org/wiki/Ram_Prakash_Bambah |
Ram pressure is a pressure exerted on a body moving through a fluid medium, caused by relative bulk motion of the fluid rather than random thermal motion. [ 1 ] It causes a drag force to be exerted on the body. Ram pressure is given in tensor form as
where ρ {\displaystyle \rho } is the density of the fluid; P ram {\displaystyle P_{\text{ram}}} is the momentum flux per second in the i {\displaystyle i} direction through a surface with normal in the j {\displaystyle j} direction. u i , u j {\displaystyle u_{i},u_{j}} are the components of the fluid velocity in these directions. The total Cauchy stress tensor σ i j {\displaystyle \sigma _{ij}} is the sum of this ram pressure and the isotropic thermal pressure (in the absence of viscosity ).
In the simple case when the relative velocity is normal to the surface, and momentum is fully transferred to the object, the ram pressure becomes
The Eulerian form of the Cauchy momentum equation for a fluid is [ 1 ]
for isotropic pressure p {\displaystyle p} , where u → {\displaystyle {\vec {u}}} is fluid velocity, ρ {\displaystyle \rho } the fluid density, and g → {\displaystyle {\vec {g}}} the gravitational acceleration. The Eulerian rate of change of momentum in direction i {\displaystyle i} at a point is thus (using Einstein notation ):
Substituting the conservation of mass, expressed as
this is equivalent to
using the product rule and the Kronecker delta δ i j {\displaystyle \delta _{ij}} . The first term in the brackets is the isotropic thermal pressure, and the second is the ram pressure.
In this context, ram pressure is momentum transfer by advection (flow of matter carrying momentum across a surface into a body). The mass per unit second flowing into a volume V {\displaystyle V} bounded by a surface S {\displaystyle S} is
and the momentum per second it carries into the body is
equal to the ram pressure term. This discussion can be extended to 'drag' forces; if all matter incident upon a surface transfers all its momentum to the volume, this is equivalent (in terms of momentum transfer) to the matter entering the volume (the context above). On the other hand, if only velocity perpendicular to the surface is transferred, there are no shear forces, and the effective pressure on that surface increases by
where u n {\displaystyle u_{n}} is the velocity component perpendicular to the surface.
What is the sea level ram air pressure at 100 mph ?
Within astronomy and astrophysics, James E. Gunn and J. Richard Gott first suggested that galaxies in a galaxy cluster moving through a hot intracluster medium would experience a pressure of
where P r {\displaystyle P_{r}} is the ram pressure, ρ e {\displaystyle \rho _{e}} the intracluster gas density, and v {\displaystyle v} the speed of the galaxy relative to the medium. [ 5 ] This pressure can strip gas out of the galaxy where, essentially, the gas is gravitationally bound to the galaxy less strongly than the force from the intracluster medium 'wind' due to the ram pressure. [ 6 ] [ 5 ] Evidence of this ram pressure stripping can be seen in the image of NGC 4402 . [ 7 ] These ram pressure stripped galaxies will often have a large trailing tail and because of this they are commonly called "Jellyfish galaxies." [ 8 ]
Ram pressure stripping is thought to have profound effects on the evolution of galaxies. As galaxies fall toward the center of a cluster, more and more of their gas is stripped out, including the cool, denser gas that is the source of continued star formation . Spiral galaxies that have fallen at least to the core of both the Virgo and Coma clusters have had their gas (neutral hydrogen) depleted in this way [ 9 ] and simulations suggest that this process can happen relatively quickly, with 100% depletion occurring in 100 million years [ 10 ] to a more gradual few billion years. [ 11 ]
Recent radio observation of carbon monoxide (CO) emission from three galaxies ( NGC 4330 , NGC 4402 , and NGC 4522 ) in the Virgo cluster point to the molecular gas not being stripped but instead being compressed by the ram pressure. Increased Hα emission, a sign of star formation, corresponds to the compressed CO region, suggesting that star formation may be accelerated, at least temporarily, while ram pressure stripping of neutral hydrogen is ongoing. [ 12 ]
More recently, it has been shown that ram pressure can also lead to the removal of gas in isolated dwarf galaxies that plunge through the cosmic web (the so-called cosmic web stripping process). [ 13 ] Although the typical overdensity within the cosmic web is significantly lower than that found in the environment of galaxy clusters , the high relative speed between a dwarf and the cosmic web renders ram pressure efficient. This is an attractive mechanism to explain not only the presence of isolated dwarf galaxies away from galaxy clusters with particularly low hydrogen abundance to stellar mass ratio, [ 14 ] [ 15 ] but also the compression of gas in the centre of a dwarf galaxy and the subsequent reignition of star formation . [ 16 ]
Meteoroids enter Earth's atmosphere from outer space traveling at hypersonic speeds of at least 11 km/s (7 mi/s) and often much faster. Despite moving through the rarified upper reaches of Earth's atmosphere the immense speed at which a meteor travels nevertheless rapidly compresses the air in its path, creating a shock wave . The meteoroid then experiences what is known as ram pressure. As the air in front of the meteoroid is compressed its temperature quickly rises. This is not due to friction , rather it is simply a consequence of many molecules and atoms being made to occupy a smaller space than formerly. Ram pressure and the very high temperatures it causes are the reasons few meteors make it all the way to the ground and most simply burn up or are ablated into tiny fragments . Larger or more solid meteorites may explode instead in a meteor airburst . [ 17 ] [ 18 ]
The use of the term explosion is somewhat loose in this context, and can be confusing. This confusion is exacerbated by the tendency for airburst energies to be expressed in terms of nuclear weapon yields, as when the Tunguska airburst is given a rating in megatons of TNT . Large meteoroids do not explode in the sense of chemical or nuclear explosives. Rather, at a critical moment in its atmospheric entry the enormous ram pressure experienced by the leading face of the meteoroid converts the body's immense momentum into a force blowing it apart over a nearly instantaneous span of time. [ 18 ]
In essence, the meteoroid is ripped apart by its own speed. This occurs when fine tendrils of superheated air force their way into cracks and faults in the leading face's surface. Once this high pressure plasma gains entry to the meteoroid's interior it exerts tremendous force on the body's internal structure. This occurs because the superheated air now exerts its force over a much larger surface area, as when the wind suddenly fills a sail . This sudden rise in the force exerted on the meteoroid overwhelms the body's structural integrity and it begins to break up. The breakup of the meteoroid yields an even larger total surface area for the superheated air to act upon and a cycle of amplification rapidly occurs. This is the explosion, and it causes the meteoroid to disintegrate with hypersonic velocity , a speed comparable to that of explosive detonation . [ 18 ]
Harry Julian Allen and Alfred J. Eggers of NACA used an insight about ram pressure to propose the blunt-body concept : a large, blunt body entering the atmosphere creates a boundary layer of compressed air which serves as a buffer between the body surface and the compression-heated air. In other words, kinetic energy is converted into heated air via ram pressure, and that heated air is quickly moved away from object surface with minimal physical interaction, and hence minimal heating of the body. This was counter-intuitive at the time, when sharp, streamlined profiles were assumed to be better. [ 19 ] [ 20 ] This blunt-body concept was used in Apollo -era capsules. | https://en.wikipedia.org/wiki/Ram_pressure |
In biochemistry , a Ramachandran plot (also known as a Rama plot , a Ramachandran diagram or a [φ,ψ] plot ), originally developed in 1963 by G. N. Ramachandran , C. Ramakrishnan, and V. Sasisekharan , [ 1 ] is a way to visualize energetically allowed regions for backbone dihedral angles ( also called as torsional angles , phi and psi angles ) ψ against φ of amino acid residues in protein structure . The figure on the left illustrates the definition of the φ and ψ backbone dihedral angles [ 2 ] (called φ and φ' by Ramachandran). The ω angle at the peptide bond is normally 180°, since the partial-double-bond character keeps the peptide bond planar. [ 3 ] The figure in the top right shows the allowed φ,ψ backbone conformational regions from the Ramachandran et al. 1963 and 1968 hard-sphere calculations: full radius in solid outline, reduced radius in dashed, and relaxed tau (N-Cα-C) angle in dotted lines. [ 4 ] Because dihedral angle values are circular and 0° is the same as 360°, the edges of the Ramachandran plot "wrap" right-to-left and bottom-to-top. For instance, the small strip of allowed values along the lower-left edge of the plot are a continuation of the large, extended-chain region at upper left.
A Ramachandran plot can be used in two somewhat different ways. One is to show in theory which values, or conformations , of the ψ and φ angles are possible for an amino-acid residue in a protein (as at top right). A second is to show the empirical distribution of datapoints observed in a single structure (as at right, here) in usage for structure validation , or else in a database of many structures (as in the lower 3 plots at left). It's used to predict about Drug-ligand interaction and helpful in pharmaceutical industries. Either case is usually shown against outlines for the theoretically favored regions.
One might expect that larger side chains would result in more restrictions and consequently a smaller allowable region in the Ramachandran plot, but the effect of side chains is small. [ 5 ] In practice, the major effect seen is that of the presence or absence of the methylene group at Cβ. [ 5 ] Glycine has only a hydrogen atom for its side chain, with a much smaller van der Waals radius than the CH 3 , CH 2 , or CH group that starts the side chain of all other amino acids. Hence it is least restricted, and this is apparent in the Ramachandran plot for glycine (see Gly plot in gallery ) for which the allowable area is considerably larger. In contrast, the Ramachandran plot for proline , with its 5-membered-ring side chain connecting Cα to backbone N, shows a limited number of possible combinations of ψ and φ (see Pro plot in gallery ). The residue preceding proline ("pre-proline") also has limited combinations compared to the general case.
The first Ramachandran plot was calculated just after the first protein structure at atomic resolution was determined ( myoglobin , in 1960 [ 6 ] ), although the conclusions were based on small-molecule crystallography of short peptides. Now, many decades later, there are tens of thousands of high-resolution protein structures determined by X-ray crystallography and deposited in the Protein Data Bank (PDB) . Many studies have taken advantage of this data to produce more detailed and accurate φ,ψ plots (e.g., Morris et al. 1992; [ 7 ] Kleywegt & Jones 1996; [ 8 ] Hooft et al. 1997; [ 9 ] Hovmöller et al. 2002; [ 10 ] Lovell et al. 2003; [ 11 ] Anderson et al. 2005 . [ 12 ] Ting et al. 2010 [ 13 ] ).
The four figures below show the datapoints from a large set of high-resolution structures and contours for favored and for allowed conformational regions for the general case (all amino acids except Gly, Pro, and pre-Pro), for Gly, and for Pro. [ 11 ] The most common regions are labeled: α for α helix , Lα for left-handed helix, β for β-sheet , and ppII for polyproline II. Such a clustering is alternatively described in the ABEGO system, where each letter stands for α (and 3 10 ) helix, right-handed β sheets (and extended structures), left-handed helixes, left-handed sheets, and finally unplottable cis peptide bonds sometimes seen with proline; it has been used in the classification of motifs [ 14 ] and more recently for designing proteins. [ 15 ]
While the Ramachandran plot has been a textbook resource for explaining the structural behavior of peptide bond, an exhaustive exploration of how a peptide behaves in every region of the Ramachandran plot was only recently published (Mannige 2017 [ 16 ] ).
The Molecular Biophysics Unit at Indian Institute of Science celebrated 50 years of Ramachandran Map [ 17 ] by organizing International Conference on Biomolecular Forms and Functions from 8–11 January 2013. [ 18 ]
One can also plot the dihedral angles in polysaccharides (e.g. with CARP Archived 2019-05-05 at the Wayback Machine ). [ 19 ] | https://en.wikipedia.org/wiki/Ramachandran_plot |
Raman Laser Spectrometer ( RLS ) is a miniature Raman spectrometer that is part of the science payload on board the European Space Agency 's Rosalind Franklin rover , [ 2 ] tasked to search for biosignatures and biomarkers on Mars. The rover is planned to be launched not earlier than 2028 and land on Mars in 2029.
Raman spectroscopy is a technique employed to identify mineral phases produced by water-related processes. [ 3 ] [ 4 ] [ 5 ] RLS will help to identify organic compounds and search for microbial life by identifying the mineral products and indicators of biologic activities. RLS will provide geological and mineralogical context information that will be scientifically cross-correlated with that obtained by other instruments. [ 6 ]
Raman spectroscopy is sensitive to the composition and structure of any organic compound , making it a powerful tool for the definitive identification and characterisation of biomarkers , and providing direct information of potential biosignatures of past microbial life on Mars . [ 3 ] This instrument will also provide general mineralogical information for igneous, metamorphous, and sedimentary processes. [ 3 ]
RST will also correlate its spectral information with other spectroscopic and imaging instruments such as the Infrared Spectrometer and MicrOmega-IR . [ 3 ] This will be the first Raman analyser to be deployed for a planetary exploration. [ 6 ] The first version for the rover was presented by Fernando Rull-Perez and Sylvestre Maurice in 2003. [ 6 ] The RLS is being developed by a European consortium integrated by Spanish, French, German and UK partners. [ 6 ] The Principal Investigator is Fernando Rull-Perez, from Spanish Astrobiology Center . [ 3 ] The co-investigator is from Observatoire Midi-Pyrénées (LAOMP), France. [ 8 ]
The three major components are the Spectrometer Unit , the Control and Excitation Unit (includes the power converters), and Optical head . [ 9 ]
The RLS instrument provides a structural fingerprint by which molecules can be identified. It is used to analyse the vibrational modes of a substance either in the solid, liquid or gas state. [ 6 ] The technique relies on Raman scattering of a photon by molecules which are excited to higher vibrational or rotational energy levels. In more detail, it will collect and analyse the scattered light emitted by a laser on a crushed Mars rock sample; the spectrum observed (number of peaks, position and relative intensities) is determined by the molecular structure and composition of a compound, enabling the identification and characterisation of the compounds in the sample. [ 3 ]
Some advantages of RLS over other analysers are that it is nondestructive, analysis is completed in a fraction of a second, and the spectral bands provide definitive composition of the material. [ 6 ] RLS measurements will be conducted on the resulting crushed sample powder and it will be a useful tool for flagging the presence of organic molecules for further biomarker search by the MOMA analyser. [ citation needed ]
The processor board carries out several key functions for the Raman spectrometer control, spectral operation, data storage, and communications with the rover. The complete instrument has a mass of 2.4 kg (5.29 lb) and consumes about 30 W while operating. [ 3 ] [ 6 ] [ 7 ]
The goal of RLS is to seek signs of past life on Mars ( biosignatures and biomarkers ) by analysing drilled samples acquired from 2 meters below the Martian surface by the Rosalind Franklin rover core drill . The science objectives of RLS are: [ 6 ] | https://en.wikipedia.org/wiki/Raman_Laser_Spectrometer |
Raman Parimala (born 21 November 1948) [ 1 ] is an Indian mathematician known for her contributions to algebra . She is the Arts & Sciences Distinguished Professor of mathematics at Emory University . [ 2 ] For many years, she was a professor at Tata Institute of Fundamental Research (TIFR), Mumbai .
She was on the Mathematical Sciences jury for the Infosys Prize 2019—2022 [ 3 ] and was on the Abel prize selection Committee 2021–2023. [ 4 ]
Parimala was born and raised in Tamil Nadu , India. [ 5 ] She studied in Saradha Vidyalaya Girls' High School and Stella Maris College at Chennai . She received her M.Sc. from Madras University (1970) and Ph.D. from the University of Mumbai (1976); her advisor was R. Sridharan from TIFR. [ 6 ]
In 1987, she won the highest science award in India: The Shanti Swarup Bhatnagar Prize . [ 7 ]
She is a fellow of the Indian National Science Academy (New Delhi). [ 7 ]
On National Science Day in 2020, Smriti Irani , head of the Ministry of Women and Child Development of the Government of India , announced the establishment of chairs at institutes across India in the names of Raman Parimala and other ten Indian women scientists. [ 9 ] Parimala was an invited speaker at the International Congress of Mathematicians in Zurich in 1994 and gave a talk Study of quadratic forms — some connections with geometry Archived 3 October 2016 at the Wayback Machine . She gave a plenary address Arithmetic of linear algebraic groups over two dimensional fields at the Congress in Hyderabad in 2010. | https://en.wikipedia.org/wiki/Raman_Parimala |
The Raman microscope is a laser-based microscopic device used to perform Raman spectroscopy . [ 1 ] The term MOLE (molecular optics laser examiner) is used to refer to the Raman-based microprobe. [ 1 ] The technique used is named after C. V. Raman , who discovered the scattering properties in liquids. [ 2 ]
The Raman microscope begins with a standard optical microscope , and adds an excitation laser , laser rejection filters , a spectrometer or monochromator , and an optical sensitive detector such as a charge-coupled device (CCD), or photomultiplier tube , (PMT). Traditionally Raman microscopy was used to measure the Raman spectrum of a point on a sample, more recently the technique has been extended to implement Raman spectroscopy for direct chemical imaging over the whole field of view on a 3D sample.
In direct imaging , the whole field of view is examined for scattering over a small range of wavenumbers (Raman shifts). For instance, a wavenumber characteristic for cholesterol could be used to record the distribution of cholesterol within a cell culture.
The other approach is hyperspectral imaging or chemical imaging , in which thousands of Raman spectra are acquired from all over the field of view. The data can then be used to generate images showing the location and amount of different components. Taking the cell culture example, a hyperspectral image could show the distribution of cholesterol, [ 3 ] as well as proteins, nucleic acids, and fatty acids. [ 4 ] [ 5 ] [ 6 ] Sophisticated signal- and image-processing techniques can be used to ignore the presence of water, culture media, buffers, and other interference.
Raman microscopy, and in particular confocal microscopy , can reach down to sub-micrometer lateral spatial resolution. [ 7 ] Because a Raman microscope is a diffraction-limited system , its spatial resolution depends on the wavelength of light and the numerical aperture of the focusing element. In confocal Raman microscopy, the diameter of the confocal aperture is an additional factor. As a rule of thumb, the lateral spatial resolution can reach approximately the laser wavelength when using air objective lenses, while oil or water immersion objectives can provide lateral resolutions of around half the laser wavelength. This means that when operated in the visible to near-infrared range, a Raman microscope can achieve lateral resolutions of approx. 1 µm down to 250 nm, while the depth resolution (if not limited by the optical penetration depth of the sample) can range from 1-6 µm with the smallest confocal pinhole aperture to tens of micrometers when operated without a confocal pinhole. [ 8 ] [ 9 ] [ 10 ] Since the objective lenses of microscopes focus the laser beam down to the micrometer range, the resulting photon flux is much higher than achieved in conventional Raman setups. This has the added effect of increased photobleaching of molecules emitting interfering fluorescence. However, the high photon flux can also cause sample degradation, and thus, for each type of sample, the laser wavelength and laser power have to be carefully selected.
Another tool that is becoming more popular is global Raman imaging. This technique is being used for the characterization of large scale devices, mapping of different compounds and dynamics study. It has already been used for the characterization of graphene layers, [ 11 ] J-aggregated dyes inside carbon nanotubes and multiple other 2D materials such as MoS 2 [ 12 ] and WSe 2 . Since the excitation beam is dispersed over the whole field of view, those measurements can be done without damaging the sample.
By using Raman microspectroscopy, in vivo time- and space-resolved Raman spectra of microscopic regions of samples can be measured. As a result, the fluorescence of water, media, and buffers can be removed. Consequently, it is suitable to examine proteins, cells and organelles.
Raman microscopy for biological and medical specimens generally uses near-infrared (NIR) lasers (785 nm diodes and 1064 nm Nd:YAG are especially common). This reduces the risk of damaging the specimen by applying higher energy wavelengths. However, the intensity of NIR Raman scattering is low (owing to the ω 4 dependence of Raman scattering intensity), and most detectors require very long collection times. Recently, more sensitive detectors have become available, making the technique better suited
to general use. Raman microscopy of inorganic specimens, such as rocks, ceramics and polymers, [ 13 ] can use a broader range of excitation wavelengths.
A related technique, tip-enhanced Raman spectroscopy , can produce high-resolution hyperspectral images of single molecules [ 14 ] and DNA. [ 15 ]
Confocal Raman microscopy can be combined with numerous other microscopy techniques. By using different methods and correlating the data, the user attains a more comprehensive understanding of the sample. Common examples of correlative microscopy techniques are Raman-AFM , [ 16 ] [ 13 ] Raman- SNOM , [ 17 ] and Raman- SEM . [ 18 ]
Correlative SEM-Raman imaging is the integration of a confocal Raman microscope into an SEM chamber which allows correlative imaging of several techniques, such as SE, BSE, EDX , EBSD , EBIC , CL , AFM . [ 19 ] The sample is placed in the vacuum chamber of the electron microscope. Both analysis methods are then performed automatically at the same sample location. The obtained SEM and Raman images can then be superimposed. [ 20 ] [ 21 ] Moreover, adding a focused ion beam (FIB) on the chamber allows removal of the material and therefore 3D imaging of the sample. Low-vacuum mode allows analysis on biological and non-conductive samples.
By using Raman microspectroscopy, in vivo time- and space-resolved Raman spectra of microscopic regions of samples can be measured. Sampling is non-destructive and water, media, and buffers typically do not interfere with the analysis. Consequently, in vivo time- and space-resolved Raman spectroscopy is suitable to examine proteins , cells and organs . In the field of microbiology, confocal Raman microspectroscopy has been used to map intracellular distributions of macromolecules, such as proteins, polysaccharides, and nucleic acids and polymeric inclusions, such as poly-β-hydroxybutyric acid and polyphosphates in bacteria and sterols in microalgae. Combining stable isotopic probing (SIP) experiments with confocal Raman microspectroscopy has permitted determination of assimilation rates of 13 C and 15 N-substrates as well as D 2 O by individual bacterial cells. [ 22 ] | https://en.wikipedia.org/wiki/Raman_microscope |
Raman spectroelectrochemistry (Raman-SEC) is a technique that studies the inelastic scattering or Raman scattering of monochromatic light related to chemical compounds involved in an electrode process. This technique provides information about vibrational energy transitions of molecules, using a monochromatic light source, usually from a laser that belongs to the UV, Vis or NIR region. Raman spectroelectrochemistry provides specific information about structural changes, composition and orientation of the molecules on the electrode surface involved in an electrochemical reaction, being the Raman spectra registered a real fingerprint of the compounds. [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ]
When a monochromatic light beam samples the electrode/solution interface, most of the photons are scattered elastically, with the same energy than the incident light. However, a small fraction is scattered inelastically, being the energy of the laser photons shifted up or down. When the scattering is elastic, the phenomenon is denoted as Rayleigh scattering , while when it is inelastic it is called Raman scattering . Raman spectroscopy combined with electrochemical techniques, makes Raman spectroelectrochemistry a powerful technique in the identification, characterization and quantification of molecules.
The main advantage of Raman spectroelectrochemistry is that it is not limited to the selected solvent, and aqueous and organic solutions can be used. However, the main disadvantage is the intrinsic low Raman signal intensity. Different methods as well as new substrates were developed to improve the sensitivity and selectivity of this multirresponse technique. [ 4 ]
For researchers, a few experimental considerations related to Raman spectroelectrochemistry include electrode preparation, cell design, laser parameters, electrochemical sequence and data process. [ 8 ]
The Raman resonance effect produces an increase in Raman intensity up to 10 6 times. In this phenomenon, the monochromatic light interaction with the sample produces the transition of the molecules from the fundamental state to an excited electronic state, instead of a virtual state as in normal Raman spectroscopy. This phenomenon of increased intensity could be observed in materials such as carbon nanotubes. [ 9 ]
Surface-Enhanced Raman Scattering (SERS) is a technique capable of increasing Raman signal intensity up to 10 11 times. This phenomenon is based on the interaction of monochromatic light with materials that exhibit plasmonic properties. The most common metals used in SERS are nanostructured metals with plasmonic band ( gold , silver or copper ). Nanostructured electrode surfaces can be generated by depositing metallic nanostructures of these materials. A disadvantage of this phenomenon is, sometimes, the lack of reproducibility of the spectra due to the difficulty of obtaining identical nanostructured surfaces in each experiment. [ 1 ] [ 3 ] [ 5 ] [ 6 ] [ 7 ] [ 10 ] [ 11 ]
Surface-oxidation enhanced Raman scattering (SOERS) is a process similar to SERS, which allows the Raman signal to be enhanced when a silver electrode is oxidized in a particular electrolyte composition. This process is carried out at sufficiently positive potentials to ensure the oxidation of the electrode surface. There are significant differences with the SERS effect, but it is a phenomenon that also enhances the Raman signal. [ 1 ] [ 5 ]
In SHINERS, metallic nanoparticles with plasmonic properties are coated with ultra-thin homogeneous silica or alumina layers, forming isolated nanoparticles . The metallic nucleus (Au or Ag) is responsible of the enhancement of the Raman signals of the nearby molecules, while the coating layers eliminate the influence of the metallic nucleus on the Raman and electrochemical signals by preventing the molecules from being directly adsorbed onto them. Silica and alumina coating can improve the chemical and thermal stability of nanoparticles. This fact has great importance in the in-situ study of catalytic reactions. The high sensitivity of the SHINERS surfaces makes these nanostructures a promising tool for the study of liquid-solid interfaces, especially in spectroelectrochemistry . [ 3 ] [ 12 ] [ 13 ] [ 14 ]
Tip-enhanced Raman scattering (TERS) is a technique that provides molecular information at nanoscale. In these experiments, metal nanostructures are replaced by a sharp metal tip of nanometric size, concentrating the roughness directly on a small region that improves the spatial resolution of scanning techniques in Raman spectroscopy. [ 3 ] [ 11 ] [ 15 ] [ 16 ] [ 17 ]
Different configurations can be used to perform Raman-SEC experiments. Raman scattering provides spectra with very weak Raman bands, therefore, a very well aligned optical configuration is required. Laser has to be focused on the electrode surface and an efficient collection of the scattered photons is mandatory. Many of the instruments used for Raman-SEC are based on the combination of a spectrometer , a potentiostat and a confocal microscope , since it is possible to focus and collect the scattered photons in a highly efficient way. [ 4 ] [ 18 ] Low resolution Raman spectrometers can be also used, providing suitable results. Using this setup, the sampling area is larger and average information about the electrode surface is obtained.
Typical configurations in Raman-SEC:
The experimental setup to perform Raman spectroelectrochemistry consists of a light source, a spectrometer , a potentiostat , a spectroelectrochemical cell, a three-electrode system, radiation beam conducting devices, data collection and analysis devices. Nowadays, there are commercial instruments that integrate all these elements in a single instrument, significantly simplifying the performance of spectroelectrochemical experiments. [ 5 ] [ 19 ]
In recent years Raman-SEC has become an important tool in the study of electrochemical processes and in the characterization of many molecules, providing specific in situ information about them. Some applications are: [ 1 ] [ 10 ] [ 14 ] [ 20 ] | https://en.wikipedia.org/wiki/Raman_spectroelectrochemistry |
In mathematics , Ramanujan's congruences are the congruences for the partition function p ( n ) discovered by Srinivasa Ramanujan :
In plain words, the first congruence means that if a number is 4 more than a multiple of 5, i.e. it is in the sequence
then the number of its partitions is a multiple of 5.
Later, other congruences of this type were discovered, for numbers and for Tau-functions .
In his 1919 paper, [ 1 ] he proved the first two congruences using the following identities (using q-Pochhammer symbol notation):
He then stated that "It appears there are no equally simple properties for any moduli involving primes other than these".
After Ramanujan died in 1920, G. H. Hardy extracted proofs of all three congruences from an unpublished manuscript of Ramanujan on p ( n ) (Ramanujan, 1921). The proof in this manuscript employs the Eisenstein series .
In 1944, Freeman Dyson defined the rank function for a partition and conjectured the existence of a "crank" function for partitions that would provide a combinatorial proof of Ramanujan's congruences modulo 11. Forty years later, George Andrews and Frank Garvan found such a function, and proved the celebrated result that the crank simultaneously "explains" the three Ramanujan congruences modulo 5, 7 and 11.
In the 1960s, A. O. L. Atkin of the University of Illinois at Chicago discovered additional congruences for small prime moduli. For example:
Extending the results of A. Atkin, Ken Ono in 2000 proved that there are such Ramanujan congruences modulo every integer coprime to 6. For example, his results give
Later Ken Ono conjectured that the elusive crank also satisfies exactly the same types of general congruences. This was proved by his Ph.D. student Karl Mahlburg in his 2005 paper Partition Congruences and the Andrews–Garvan–Dyson Crank , linked below. This paper won the first Proceedings of the National Academy of Sciences Paper of the Year prize. [ 2 ]
A conceptual explanation for Ramanujan's observation was finally discovered in January 2011 [ 3 ] by considering the Hausdorff dimension of the following P {\displaystyle P} function in the l-adic topology:
It is seen to have dimension 0 only in the cases where ℓ = 5, 7 or 11 and since the partition function can be written as a linear combination of these functions [ 4 ] this can be considered a formalization and proof of Ramanujan's observation.
In 2001, R.L. Weaver gave an effective algorithm for finding congruences of the partition function, and tabulated 76,065 congruences. [ 5 ] This was extended in 2012 by F. Johansson to 22,474,608,014 congruences, [ 6 ] one large example being | https://en.wikipedia.org/wiki/Ramanujan's_congruences |
In number theory , a Heegner number (as termed by Conway and Guy ) is a square-free positive integer d such that the imaginary quadratic field Q [ − d ] {\displaystyle \mathbb {Q} \left[{\sqrt {-d}}\right]} has class number 1. Equivalently, the ring of algebraic integers of Q [ − d ] {\displaystyle \mathbb {Q} \left[{\sqrt {-d}}\right]} has unique factorization . [ 1 ]
The determination of such numbers is a special case of the class number problem , and they underlie several striking results in number theory.
According to the (Baker–) Stark–Heegner theorem there are precisely nine Heegner numbers:
This result was conjectured by Gauss and proved up to minor flaws by Kurt Heegner in 1952. Alan Baker and Harold Stark independently proved the result in 1966, and Stark further indicated that the gap in Heegner's proof was minor. [ 2 ]
Euler's prime-generating polynomial n 2 + n + 41 , {\displaystyle n^{2}+n+41,} which gives (distinct) primes for n = 0, ..., 39, is related to the Heegner number 163 = 4 · 41 − 1.
Rabinowitsch [ 3 ] proved that n 2 + n + p {\displaystyle n^{2}+n+p} gives primes for n = 0 , … , p − 2 {\displaystyle n=0,\dots ,p-2} if and only if this quadratic's discriminant 1 − 4 p {\displaystyle 1-4p} is the negative of a Heegner number.
(Note that p − 1 {\displaystyle p-1} yields p 2 {\displaystyle p^{2}} , so p − 2 {\displaystyle p-2} is maximal.)
1, 2, and 3 are not of the required form, so the Heegner numbers that work are 7, 11, 19, 43, 67, 163, yielding prime generating functions of Euler's form for 2, 3, 5, 11, 17, 41; these latter numbers are called lucky numbers of Euler by F. Le Lionnais . [ 4 ]
Ramanujan's constant is the transcendental number [ 5 ] e π 163 {\displaystyle e^{\pi {\sqrt {163}}}} , which is an almost integer : [ 6 ] e π 163 = 262 537 412 640 768 743.999 999 999 999 25 … ≈ 640 320 3 + 744. {\displaystyle e^{\pi {\sqrt {163}}}=262\,537\,412\,640\,768\,743.999\,999\,999\,999\,25\ldots \approx 640\,320^{3}+744.}
This number was discovered in 1859 by the mathematician Charles Hermite . [ 7 ] In a 1975 April Fool article in Scientific American magazine, [ 8 ] "Mathematical Games" columnist Martin Gardner made the hoax claim that the number was in fact an integer, and that the Indian mathematical genius Srinivasa Ramanujan had predicted it – hence its name. In this wise it has as a spurious provenance as the Feynman point .
This coincidence is explained by complex multiplication and the q -expansion of the j-invariant .
In what follows, j(z) denotes the j-invariant of the complex number z. Briefly, j ( 1 + − d 2 ) {\displaystyle \textstyle j\left({\frac {1+{\sqrt {-d}}}{2}}\right)} is an integer for d a Heegner number, and e π d ≈ − j ( 1 + − d 2 ) + 744 {\displaystyle e^{\pi {\sqrt {d}}}\approx -j\left({\frac {1+{\sqrt {-d}}}{2}}\right)+744} via the q -expansion.
If τ {\displaystyle \tau } is a quadratic irrational, then its j -invariant j ( τ ) {\displaystyle j(\tau )} is an algebraic integer of degree | C l ( Q ( τ ) ) | {\displaystyle \left|\mathrm {Cl} {\bigl (}\mathbf {Q} (\tau ){\bigr )}\right|} , the class number of Q ( τ ) {\displaystyle \mathbf {Q} (\tau )} and the minimal (monic integral) polynomial it satisfies is called the 'Hilbert class polynomial'. Thus if the imaginary quadratic extension Q ( τ ) {\displaystyle \mathbf {Q} (\tau )} has class number 1 (so d is a Heegner number), the j -invariant is an integer.
The q -expansion of j , with its Fourier series expansion written as a Laurent series in terms of q = e 2 π i τ {\displaystyle q=e^{2\pi i\tau }} , begins as: j ( τ ) = 1 q + 744 + 196 884 q + ⋯ . {\displaystyle j(\tau )={\frac {1}{q}}+744+196\,884q+\cdots .}
The coefficients c n {\displaystyle c_{n}} asymptotically grow as ln ( c n ) ∼ 4 π n + O ( ln ( n ) ) , {\displaystyle \ln(c_{n})\sim 4\pi {\sqrt {n}}+O{\bigl (}\ln(n){\bigr )},} and the low order coefficients grow more slowly than 200 000 n {\displaystyle 200\,000^{n}} , so for q ≪ 1 200 000 {\displaystyle \textstyle q\ll {\frac {1}{200\,000}}} , j is very well approximated by its first two terms. Setting τ = 1 + − 163 2 {\displaystyle \textstyle \tau ={\frac {1+{\sqrt {-163}}}{2}}} yields q = − e − π 163 ∴ 1 q = − e π 163 . {\displaystyle q=-e^{-\pi {\sqrt {163}}}\quad \therefore \quad {\frac {1}{q}}=-e^{\pi {\sqrt {163}}}.} Now j ( 1 + − 163 2 ) = ( − 640 320 ) 3 , {\displaystyle j\left({\frac {1+{\sqrt {-163}}}{2}}\right)=\left(-640\,320\right)^{3},} so, ( − 640 320 ) 3 = − e π 163 + 744 + O ( e − π 163 ) . {\displaystyle \left(-640\,320\right)^{3}=-e^{\pi {\sqrt {163}}}+744+O\left(e^{-\pi {\sqrt {163}}}\right).} Or, e π 163 = 640 320 3 + 744 + O ( e − π 163 ) {\displaystyle e^{\pi {\sqrt {163}}}=640\,320^{3}+744+O\left(e^{-\pi {\sqrt {163}}}\right)} where the linear term of the error is, − 196 884 e π 163 ≈ − 196 884 640 320 3 + 744 ≈ − 0.000 000 000 000 75 {\displaystyle {\frac {-196\,884}{e^{\pi {\sqrt {163}}}}}\approx {\frac {-196\,884}{640\,320^{3}+744}}\approx -0.000\,000\,000\,000\,75} explaining why e π 163 {\displaystyle e^{\pi {\sqrt {163}}}} is within approximately the above of being an integer.
The Chudnovsky brothers found in 1987 that 1 π = 12 640 320 3 2 ∑ k = 0 ∞ ( 6 k ) ! ( 163 ⋅ 3 344 418 k + 13 591 409 ) ( 3 k ) ! ( k ! ) 3 ( − 640 320 ) 3 k , {\displaystyle {\frac {1}{\pi }}={\frac {12}{640\,320^{\frac {3}{2}}}}\sum _{k=0}^{\infty }{\frac {(6k)!(163\cdot 3\,344\,418k+13\,591\,409)}{(3k)!(k!)^{3}(-640\,320)^{3k}}},} a proof of which uses the fact that j ( 1 + − 163 2 ) = − 640 320 3 . {\displaystyle j\left({\frac {1+{\sqrt {-163}}}{2}}\right)=-640\,320^{3}.} For similar formulas, see the Ramanujan–Sato series .
For the four largest Heegner numbers, the approximations one obtains [ 9 ] are as follows. e π 19 ≈ 000 0 96 3 + 744 − 0.22 e π 43 ≈ 000 960 3 + 744 − 0.000 22 e π 67 ≈ 00 5 280 3 + 744 − 0.000 0013 e π 163 ≈ 640 320 3 + 744 − 0.000 000 000 000 75 {\displaystyle {\begin{aligned}e^{\pi {\sqrt {19}}}&\approx {\phantom {000\,0}}96^{3}+744-0.22\\e^{\pi {\sqrt {43}}}&\approx {\phantom {000\,}}960^{3}+744-0.000\,22\\e^{\pi {\sqrt {67}}}&\approx {\phantom {00}}5\,280^{3}+744-0.000\,0013\\e^{\pi {\sqrt {163}}}&\approx 640\,320^{3}+744-0.000\,000\,000\,000\,75\end{aligned}}}
Alternatively, [ 10 ] e π 19 ≈ 12 3 ( 3 2 − 1 ) 3 00 + 744 − 0.22 e π 43 ≈ 12 3 ( 9 2 − 1 ) 3 00 + 744 − 0.000 22 e π 67 ≈ 12 3 ( 21 2 − 1 ) 3 0 + 744 − 0.000 0013 e π 163 ≈ 12 3 ( 231 2 − 1 ) 3 + 744 − 0.000 000 000 000 75 {\displaystyle {\begin{aligned}e^{\pi {\sqrt {19}}}&\approx 12^{3}\left(3^{2}-1\right)^{3}{\phantom {00}}+744-0.22\\e^{\pi {\sqrt {43}}}&\approx 12^{3}\left(9^{2}-1\right)^{3}{\phantom {00}}+744-0.000\,22\\e^{\pi {\sqrt {67}}}&\approx 12^{3}\left(21^{2}-1\right)^{3}{\phantom {0}}+744-0.000\,0013\\e^{\pi {\sqrt {163}}}&\approx 12^{3}\left(231^{2}-1\right)^{3}+744-0.000\,000\,000\,000\,75\end{aligned}}} where the reason for the squares is due to certain Eisenstein series . For Heegner numbers d < 19 {\displaystyle d<19} , one does not obtain an almost integer; even d = 19 {\displaystyle d=19} is not noteworthy. [ 11 ] The integer j -invariants are highly factorisable, which follows from the form
and factor as, j ( 1 + − 19 2 ) = 000 0 − 96 3 = − ( 2 5 ⋅ 3 ) 3 j ( 1 + − 43 2 ) = 000 − 960 3 = − ( 2 6 ⋅ 3 ⋅ 5 ) 3 j ( 1 + − 67 2 ) = 00 − 5 280 3 = − ( 2 5 ⋅ 3 ⋅ 5 ⋅ 11 ) 3 j ( 1 + − 163 2 ) = − 640 320 3 = − ( 2 6 ⋅ 3 ⋅ 5 ⋅ 23 ⋅ 29 ) 3 . {\displaystyle {\begin{aligned}j\left({\frac {1+{\sqrt {-19}}}{2}}\right)&={\phantom {000\,0}}-96^{3}=-\left(2^{5}\cdot 3\right)^{3}\\j\left({\frac {1+{\sqrt {-43}}}{2}}\right)&={\phantom {000\,}}-960^{3}=-\left(2^{6}\cdot 3\cdot 5\right)^{3}\\j\left({\frac {1+{\sqrt {-67}}}{2}}\right)&={\phantom {00}}-5\,280^{3}=-\left(2^{5}\cdot 3\cdot 5\cdot 11\right)^{3}\\j\left({\frac {1+{\sqrt {-163}}}{2}}\right)&=-640\,320^{3}=-\left(2^{6}\cdot 3\cdot 5\cdot 23\cdot 29\right)^{3}.\end{aligned}}}
These transcendental numbers , in addition to being closely approximated by integers (which are simply algebraic numbers of degree 1), can be closely approximated by algebraic numbers of degree 3, [ 12 ] e π 19 ≈ x 24 − 24.000 31 ; x 3 − 2 x − 2 = 0 e π 43 ≈ x 24 − 24.000 000 31 ; x 3 − 2 x 2 − 2 = 0 e π 67 ≈ x 24 − 24.000 000 0019 ; x 3 − 2 x 2 − 2 x − 2 = 0 e π 163 ≈ x 24 − 24.000 000 000 000 0011 ; x 3 − 6 x 2 + 4 x − 2 = 0 {\displaystyle {\begin{aligned}e^{\pi {\sqrt {19}}}&\approx x^{24}-24.000\,31;&x^{3}-2x-2&=0\\e^{\pi {\sqrt {43}}}&\approx x^{24}-24.000\,000\,31;&x^{3}-2x^{2}-2&=0\\e^{\pi {\sqrt {67}}}&\approx x^{24}-24.000\,000\,0019;&x^{3}-2x^{2}-2x-2&=0\\e^{\pi {\sqrt {163}}}&\approx x^{24}-24.000\,000\,000\,000\,0011;&\quad x^{3}-6x^{2}+4x-2&=0\end{aligned}}}
The roots of the cubics can be exactly given by quotients of the Dedekind eta function η ( τ ), a modular function involving a 24th root, and which explains the 24 in the approximation. They can also be closely approximated by algebraic numbers of degree 4, [ 13 ] e π 19 ≈ 3 5 ( 3 − 2 ( 1 − 96 24 + 1 3 ⋅ 19 ) ) − 2 − 12.000 06 … e π 43 ≈ 3 5 ( 9 − 2 ( 1 − 960 24 + 7 3 ⋅ 43 ) ) − 2 − 12.000 000 061 … e π 67 ≈ 3 5 ( 21 − 2 ( 1 − 5 280 24 + 31 3 ⋅ 67 ) ) − 2 − 12.000 000 000 36 … e π 163 ≈ 3 5 ( 231 − 2 ( 1 − 640 320 24 + 2 413 3 ⋅ 163 ) ) − 2 − 12.000 000 000 000 000 21 … {\displaystyle {\begin{aligned}e^{\pi {\sqrt {19}}}&\approx 3^{5}\left(3-{\sqrt {2\left(1-{\tfrac {96}{24}}+1{\sqrt {3\cdot 19}}\right)}}\right)^{-2}-12.000\,06\dots \\e^{\pi {\sqrt {43}}}&\approx 3^{5}\left(9-{\sqrt {2\left(1-{\tfrac {960}{24}}+7{\sqrt {3\cdot 43}}\right)}}\right)^{-2}-12.000\,000\,061\dots \\e^{\pi {\sqrt {67}}}&\approx 3^{5}\left(21-{\sqrt {2\left(1-{\tfrac {5\,280}{24}}+31{\sqrt {3\cdot 67}}\right)}}\right)^{-2}-12.000\,000\,000\,36\dots \\e^{\pi {\sqrt {163}}}&\approx 3^{5}\left(231-{\sqrt {2\left(1-{\tfrac {640\,320}{24}}+2\,413{\sqrt {3\cdot 163}}\right)}}\right)^{-2}-12.000\,000\,000\,000\,000\,21\dots \end{aligned}}}
If x {\displaystyle x} denotes the expression within the parenthesis (e.g. x = 3 − 2 ( 1 − 96 24 + 1 3 ⋅ 19 ) {\displaystyle x=3-{\sqrt {2\left(1-{\tfrac {96}{24}}+1{\sqrt {3\cdot 19}}\right)}}} ), it satisfies respectively the quartic equations x 4 − 00 4 ⋅ 3 x 3 + 000 0 2 3 ( 96 + 3 ) x 2 − 000 000 2 3 ⋅ 3 ( 96 − 6 ) x − 3 = 0 x 4 − 00 4 ⋅ 9 x 3 + 000 2 3 ( 960 + 3 ) x 2 − 000 00 2 3 ⋅ 9 ( 960 − 6 ) x − 3 = 0 x 4 − 0 4 ⋅ 21 x 3 + 00 2 3 ( 5 280 + 3 ) x 2 − 000 2 3 ⋅ 21 ( 5 280 − 6 ) x − 3 = 0 x 4 − 4 ⋅ 231 x 3 + 2 3 ( 640 320 + 3 ) x 2 − 2 3 ⋅ 231 ( 640 320 − 6 ) x − 3 = 0 {\displaystyle {\begin{aligned}x^{4}-{\phantom {00}}4\cdot 3x^{3}+{\phantom {000\,0}}{\tfrac {2}{3}}(96+3)x^{2}-{\phantom {000\,000}}{\tfrac {2}{3}}\cdot 3(96-6)x-3&=0\\x^{4}-{\phantom {00}}4\cdot 9x^{3}+{\phantom {000\,}}{\tfrac {2}{3}}(960+3)x^{2}-{\phantom {000\,00}}{\tfrac {2}{3}}\cdot 9(960-6)x-3&=0\\x^{4}-{\phantom {0}}4\cdot 21x^{3}+{\phantom {00}}{\tfrac {2}{3}}(5\,280+3)x^{2}-{\phantom {000}}{\tfrac {2}{3}}\cdot 21(5\,280-6)x-3&=0\\x^{4}-4\cdot 231x^{3}+{\tfrac {2}{3}}(640\,320+3)x^{2}-{\tfrac {2}{3}}\cdot 231(640\,320-6)x-3&=0\\\end{aligned}}}
Note the reappearance of the integers n = 3 , 9 , 21 , 231 {\displaystyle n=3,9,21,231} as well as the fact that 2 6 ⋅ 3 ( − ( 1 − 96 24 ) 2 + 1 2 ⋅ 3 ⋅ 19 ) = 96 2 2 6 ⋅ 3 ( − ( 1 − 960 24 ) 2 + 7 2 ⋅ 3 ⋅ 43 ) = 960 2 2 6 ⋅ 3 ( − ( 1 − 5 280 24 ) 2 + 31 2 ⋅ 3 ⋅ 67 ) = 5 280 2 2 6 ⋅ 3 ( − ( 1 − 640 320 24 ) 2 + 2413 2 ⋅ 3 ⋅ 163 ) = 640 320 2 {\displaystyle {\begin{aligned}2^{6}\cdot 3\left(-\left(1-{\tfrac {96}{24}}\right)^{2}+1^{2}\cdot 3\cdot 19\right)&=96^{2}\\2^{6}\cdot 3\left(-\left(1-{\tfrac {960}{24}}\right)^{2}+7^{2}\cdot 3\cdot 43\right)&=960^{2}\\2^{6}\cdot 3\left(-\left(1-{\tfrac {5\,280}{24}}\right)^{2}+31^{2}\cdot 3\cdot 67\right)&=5\,280^{2}\\2^{6}\cdot 3\left(-\left(1-{\tfrac {640\,320}{24}}\right)^{2}+2413^{2}\cdot 3\cdot 163\right)&=640\,320^{2}\end{aligned}}} which, with the appropriate fractional power, are precisely the j -invariants.
Similarly for algebraic numbers of degree 6, e π 19 ≈ ( 5 x ) 3 − 6.000 010 … e π 43 ≈ ( 5 x ) 3 − 6.000 000 010 … e π 67 ≈ ( 5 x ) 3 − 6.000 000 000 061 … e π 163 ≈ ( 5 x ) 3 − 6.000 000 000 000 000 034 … {\displaystyle {\begin{aligned}e^{\pi {\sqrt {19}}}&\approx \left(5x\right)^{3}-6.000\,010\dots \\e^{\pi {\sqrt {43}}}&\approx \left(5x\right)^{3}-6.000\,000\,010\dots \\e^{\pi {\sqrt {67}}}&\approx \left(5x\right)^{3}-6.000\,000\,000\,061\dots \\e^{\pi {\sqrt {163}}}&\approx \left(5x\right)^{3}-6.000\,000\,000\,000\,000\,034\dots \end{aligned}}}
where the x s are given respectively by the appropriate root of the sextic equations , 5 x 6 − 000 0 96 x 5 − 10 x 3 + 1 = 0 5 x 6 − 000 960 x 5 − 10 x 3 + 1 = 0 5 x 6 − 00 5 280 x 5 − 10 x 3 + 1 = 0 5 x 6 − 640 320 x 5 − 10 x 3 + 1 = 0 {\displaystyle {\begin{aligned}5x^{6}-{\phantom {000\,0}}96x^{5}-10x^{3}+1&=0\\5x^{6}-{\phantom {000\,}}960x^{5}-10x^{3}+1&=0\\5x^{6}-{\phantom {00}}5\,280x^{5}-10x^{3}+1&=0\\5x^{6}-640\,320x^{5}-10x^{3}+1&=0\end{aligned}}}
with the j -invariants appearing again. These sextics are not only algebraic, they are also solvable in radicals as they factor into two cubics over the extension Q 5 {\displaystyle \mathbb {Q} {\sqrt {5}}} (with the first factoring further into two quadratics ). These algebraic approximations can be exactly expressed in terms of Dedekind eta quotients. As an example, let τ = 1 + − 163 2 {\displaystyle \textstyle \tau ={\frac {1+{\sqrt {-163}}}{2}}} , then, e π 163 = ( e π i 24 η ( τ ) η ( 2 τ ) ) 24 − 24.000 000 000 000 001 05 … e π 163 = ( e π i 12 η ( τ ) η ( 3 τ ) ) 12 − 12.000 000 000 000 000 21 … e π 163 = ( e π i 6 η ( τ ) η ( 5 τ ) ) 6 − 6.000 000 000 000 000 034 … {\displaystyle {\begin{aligned}e^{\pi {\sqrt {163}}}&=\left({\frac {e^{\frac {\pi i}{24}}\eta (\tau )}{\eta (2\tau )}}\right)^{24}-24.000\,000\,000\,000\,001\,05\dots \\e^{\pi {\sqrt {163}}}&=\left({\frac {e^{\frac {\pi i}{12}}\eta (\tau )}{\eta (3\tau )}}\right)^{12}-12.000\,000\,000\,000\,000\,21\dots \\e^{\pi {\sqrt {163}}}&=\left({\frac {e^{\frac {\pi i}{6}}\eta (\tau )}{\eta (5\tau )}}\right)^{6}-6.000\,000\,000\,000\,000\,034\dots \end{aligned}}}
where the eta quotients are the algebraic numbers given above.
The three numbers 88, 148, 232, for which the imaginary quadratic field Q [ − d ] {\displaystyle \mathbb {Q} \left[{\sqrt {-d}}\right]} has class number 2, are not Heegner numbers but have certain similar properties in terms of almost integers . For instance, [ 14 ] e π 88 + 8 744 ≈ 00 00 2 508 952 2 − 0.077 … e π 148 + 8 744 ≈ 00 199 148 648 2 − 0.000 97 … e π 232 + 8 744 ≈ 24 591 257 752 2 − 0.000 0078 … {\displaystyle {\begin{aligned}e^{\pi {\sqrt {88}}}+8\,744&\approx {\phantom {00\,00}}2\,508\,952^{2}-0.077\dots \\e^{\pi {\sqrt {148}}}+8\,744&\approx {\phantom {00\,}}199\,148\,648^{2}-0.000\,97\dots \\e^{\pi {\sqrt {232}}}+8\,744&\approx 24\,591\,257\,752^{2}-0.000\,0078\dots \\\end{aligned}}} and e π 22 − 24 ≈ 00 ( 6 + 4 2 ) 6 + 0.000 11 … e π 37 + 24 ≈ ( 12 + 2 37 ) 6 − 0.000 0014 … e π 58 − 24 ≈ ( 27 + 5 29 ) 6 − 0.000 000 0011 … {\displaystyle {\begin{aligned}e^{\pi {\sqrt {22}}}-24&\approx {\phantom {00}}\left(6+4{\sqrt {2}}\right)^{6}+0.000\,11\dots \\e^{\pi {\sqrt {37}}}+24&\approx \left(12+2{\sqrt {37}}\right)^{6}-0.000\,0014\dots \\e^{\pi {\sqrt {58}}}-24&\approx \left(27+5{\sqrt {29}}\right)^{6}-0.000\,000\,0011\dots \\\end{aligned}}}
Given an odd prime p , if one computes k 2 mod p {\displaystyle k^{2}\mod p} for k = 0 , 1 , … , p − 1 2 {\displaystyle \textstyle k=0,1,\dots ,{\frac {p-1}{2}}} (this is sufficient because ( p − k ) 2 ≡ k 2 mod p {\displaystyle \left(p-k\right)^{2}\equiv k^{2}\mod p} ), one gets consecutive composites, followed by consecutive primes, if and only if p is a Heegner number. [ 15 ]
For details, see "Quadratic Polynomials Producing Consecutive Distinct Primes and Class Groups of Complex Quadratic Fields" by Richard Mollin . [ 16 ] | https://en.wikipedia.org/wiki/Ramanujan's_constant |
In number theory , Ramanujan's sum , usually denoted c q ( n ), is a function of two positive integer variables q and n defined by the formula
where ( a , q ) = 1 means that a only takes on values coprime to q .
Srinivasa Ramanujan mentioned the sums in a 1918 paper. [ 1 ] In addition to the expansions discussed in this article, Ramanujan's sums are used in the proof of Vinogradov's theorem that every sufficiently large odd number is the sum of three primes . [ 2 ]
For integers a and b , a ∣ b {\displaystyle a\mid b} is read " a divides b " and means that there is an integer c such that b a = c . {\displaystyle {\frac {b}{a}}=c.} Similarly, a ∤ b {\displaystyle a\nmid b} is read " a does not divide b ". The summation symbol
means that d goes through all the positive divisors of m , e.g.
( a , b ) {\displaystyle (a,\,b)} is the greatest common divisor ,
ϕ ( n ) {\displaystyle \phi (n)} is Euler's totient function ,
μ ( n ) {\displaystyle \mu (n)} is the Möbius function , and
ζ ( s ) {\displaystyle \zeta (s)} is the Riemann zeta function .
These formulas come from the definition, Euler's formula e i x = cos x + i sin x , {\displaystyle e^{ix}=\cos x+i\sin x,} and elementary trigonometric identities.
and so on ( OEIS : A000012 , OEIS : A033999 , OEIS : A099837 , OEIS : A176742 ,.., OEIS : A100051 ,...). c q ( n ) is always an integer.
Let ζ q = e 2 π i q . {\displaystyle \zeta _{q}=e^{\frac {2\pi i}{q}}.} Then ζ q is a root of the equation x q − 1 = 0 . Each of its powers,
is also a root. Therefore, since there are q of them, they are all of the roots. The numbers ζ q n {\displaystyle \zeta _{q}^{n}} where 1 ≤ n ≤ q are called the q -th roots of unity . ζ q is called a primitive q -th root of unity because the smallest value of n that makes ζ q n = 1 {\displaystyle \zeta _{q}^{n}=1} is q . The other primitive q -th roots of unity are the numbers ζ q a {\displaystyle \zeta _{q}^{a}} where ( a , q ) = 1. Therefore, there are φ( q ) primitive q -th roots of unity.
Thus, the Ramanujan sum c q ( n ) is the sum of the n -th powers of the primitive q -th roots of unity.
It is a fact [ 3 ] that the powers of ζ q are precisely the primitive roots for all the divisors of q .
Example. Let q = 12. Then
Therefore, if
is the sum of the n -th powers of all the roots, primitive and imprimitive,
and by Möbius inversion ,
It follows from the identity x q − 1 = ( x − 1)( x q −1 + x q −2 + ... + x + 1) that
and this leads to the formula
published by Kluyver in 1906. [ 4 ]
This shows that c q ( n ) is always an integer. Compare it with the formula
It is easily shown from the definition that c q ( n ) is multiplicative when considered as a function of q for a fixed value of n : [ 5 ] i.e.
From the definition (or Kluyver's formula) it is straightforward to prove that, if p is a prime number,
and if p k is a prime power where k > 1,
This result and the multiplicative property can be used to prove
This is called von Sterneck's arithmetic function. [ 6 ] The equivalence of it and Ramanujan's sum is due to Hölder. [ 7 ] [ 8 ]
For all positive integers q ,
For a fixed value of q the absolute value of the sequence { c q ( 1 ) , c q ( 2 ) , … } {\displaystyle \{c_{q}(1),c_{q}(2),\ldots \}} is bounded by φ( q ), and for a fixed value of n the absolute value of the sequence { c 1 ( n ) , c 2 ( n ) , … } {\displaystyle \{c_{1}(n),c_{2}(n),\ldots \}} is bounded by n .
If q > 1
Let m 1 , m 2 > 0, m = lcm( m 1 , m 2 ). Then [ 9 ] Ramanujan's sums satisfy an orthogonality property :
Let n , k > 0. Then [ 10 ]
known as the Brauer - Rademacher identity.
If n > 0 and a is any integer, we also have [ 11 ]
due to Cohen.
If f ( n ) is an arithmetic function (i.e. a complex-valued function of the integers or natural numbers), then a convergent infinite series of the form:
or of the form:
where the a k ∈ C , is called a Ramanujan expansion [ 12 ] of f ( n ) .
Ramanujan found expansions of some of the well-known functions of number theory. All of these results are proved in an "elementary" manner (i.e. only using formal manipulations of series and the simplest results about convergence). [ 13 ] [ 14 ] [ 15 ]
The expansion of the zero function depends on a result from the analytic theory of prime numbers, namely that the series
converges to 0, and the results for r ( n ) and r ′( n ) depend on theorems in an earlier paper. [ 16 ]
All the formulas in this section are from Ramanujan's 1918 paper.
The generating functions of the Ramanujan sums are Dirichlet series :
is a generating function for the sequence c q (1) , c q (2) , ... where q is kept constant, and
is a generating function for the sequence c 1 ( n ) , c 2 ( n ) , ... where n is kept constant.
There is also the double Dirichlet series
The polynomial with Ramanujan sum's as coefficients can be expressed with cyclotomic polynomial [ 17 ]
σ k ( n ) is the divisor function (i.e. the sum of the k -th powers of the divisors of n , including 1 and n ). σ 0 ( n ) , the number of divisors of n , is usually written d ( n ) and σ 1 ( n ) , the sum of the divisors of n , is usually written σ( n ) .
If s > 0 ,
Setting s = 1 gives
If the Riemann hypothesis is true, and − 1 2 < s < 1 2 , {\displaystyle -{\tfrac {1}{2}}<s<{\tfrac {1}{2}},}
d ( n ) = σ 0 ( n ) is the number of divisors of n , including 1 and n itself.
where γ = 0.5772... is the Euler–Mascheroni constant .
Euler's totient function φ( n ) is the number of positive integers less than n and coprime to n . Ramanujan defines a generalization of it, if
is the prime factorization of n , and s is a complex number, let
so that φ 1 ( n ) = φ ( n ) is Euler's function. [ 18 ]
He proves that
and uses this to show that
Letting s = 1 ,
Note that the constant is the inverse [ 19 ] of the one in the formula for σ( n ) .
Von Mangoldt's function Λ( n ) = 0 unless n = p k is a power of a prime number, in which case it is the natural logarithm log p .
For all n > 0 ,
This is equivalent to the prime number theorem . [ 20 ] [ 21 ]
r 2 s ( n ) is the number of ways of representing n as the sum of 2 s squares , counting different orders and signs as different (e.g., r 2 (13) = 8 , as 13 = (±2) 2 + (±3) 2 = (±3) 2 + (±2) 2 .)
Ramanujan defines a function δ 2 s ( n ) and references a paper [ 22 ] in which he proved that r 2 s ( n ) = δ 2 s ( n ) for s = 1, 2, 3, and 4 . For s > 4 he shows that δ 2 s ( n ) is a good approximation to r 2 s ( n ) .
s = 1 has a special formula:
In the following formulas the signs repeat with a period of 4.
and therefore,
r 2 s ′ ( n ) {\displaystyle r'_{2s}(n)} is the number of ways n can be represented as the sum of 2 s triangular numbers (i.e. the numbers 1, 3 = 1 + 2, 6 = 1 + 2 + 3, 10 = 1 + 2 + 3 + 4, 15, ...; the n -th triangular number is given by the formula n n + 1 / 2 .)
The analysis here is similar to that for squares. Ramanujan refers to the same paper as he did for the squares, where he showed that there is a function δ 2 s ′ ( n ) {\displaystyle \delta '_{2s}(n)} such that r 2 s ′ ( n ) = δ 2 s ′ ( n ) {\displaystyle r'_{2s}(n)=\delta '_{2s}(n)} for s = 1, 2, 3, and 4 , and that for s > 4 , δ 2 s ′ ( n ) {\displaystyle \delta '_{2s}(n)} is a good approximation to r 2 s ′ ( n ) . {\displaystyle r'_{2s}(n).}
Again, s = 1 requires a special formula:
If s is a multiple of 4,
Therefore,
Let
Then for s > 1 ,
These sums are obviously of great interest, and a few of their properties have been discussed already. But, so far as I know, they have never been considered from the point of view which I adopt in this paper; and I believe that all the results which it contains are new.
The majority of my formulae are "elementary" in the technical sense of the word — they can (that is to say) be proved by a combination of processes involving only finite algebra and simple general theorems concerning infinite series | https://en.wikipedia.org/wiki/Ramanujan's_sum |
In number theory , a branch of mathematics , Ramanujan's ternary quadratic form is the algebraic expression x 2 + y 2 + 10 z 2 with integral values for x , y and z . [ 1 ] [ 2 ] Srinivasa Ramanujan considered this expression in a footnote in a paper [ 3 ] published in 1916 and briefly discussed the representability of integers in this form. After giving necessary and sufficient conditions that an integer cannot be represented in the form ax 2 + by 2 + cz 2 for certain specific values of a , b and c , Ramanujan observed in a footnote: "(These) results may tempt us to suppose that there are similar simple results for the form ax 2 + by 2 + cz 2 whatever are the values of a , b and c . It appears, however, that in most cases there are no such simple results." [ 3 ] To substantiate this observation, Ramanujan discussed the form which is now referred to as Ramanujan's ternary quadratic form.
In his 1916 paper [ 3 ] Ramanujan made the following observations about the form x 2 + y 2 + 10 z 2 .
By putting an ellipsis at the end of the list of odd numbers not representable as x 2 + y 2 + 10 z 2 , Ramanujan indicated that his list was incomplete. It was not clear whether Ramanujan intended it to be a finite list or infinite list. This prompted others to look for such odd numbers. In 1927, Burton W. Jones and Gordon Pall [ 2 ] discovered that the number 679 could not be expressed in the form x 2 + y 2 + 10 z 2 and they also verified that there were no other such numbers below 2000. This led to an early conjecture that the seventeen numbers – the sixteen numbers in Ramanujan's list and the number discovered by them – were the only odd numbers not representable as x 2 + y 2 + 10 z 2 . However, in 1941, H Gupta [ 4 ] showed that the number 2719 could not be represented as x 2 + y 2 + 10 z 2 . He also verified that there were no other such numbers below 20000. Further progress in this direction took place only after the development of modern computers. W. Galway wrote a computer program to determine odd integers not expressible as x 2 + y 2 + 10 z 2 . Galway verified that there are only eighteen numbers less than 2 × 10 10 not representable in the form x 2 + y 2 + 10 z 2 . [ 1 ] Based on Galway's computations, Ken Ono and K. Soundararajan formulated the following conjecture: [ 1 ]
The conjecture of Ken Ono and Soundararajan has not been fully resolved. However, besides the results enunciated by Ramanujan, a few more general results about the form have been established. The proofs of some of them are quite simple while those of the others involve quite complicated concepts and arguments. [ 1 ] | https://en.wikipedia.org/wiki/Ramanujan's_ternary_quadratic_form |
In the mathematical field of spectral graph theory , a Ramanujan graph is a regular graph whose spectral gap is almost as large as possible (see extremal graph theory ). Such graphs are excellent spectral expanders . As Murty's survey paper [ 1 ] notes, Ramanujan graphs "fuse diverse branches of pure mathematics, namely, number theory , representation theory , and algebraic geometry ".
These graphs are indirectly named after Srinivasa Ramanujan ; their name comes from the Ramanujan–Petersson conjecture , which was used in a construction of some of these graphs.
Let G {\displaystyle G} be a connected d {\displaystyle d} -regular graph with n {\displaystyle n} vertices, and let λ 1 ≥ λ 2 ≥ ⋯ ≥ λ n {\displaystyle \lambda _{1}\geq \lambda _{2}\geq \cdots \geq \lambda _{n}} be the eigenvalues of the adjacency matrix of G {\displaystyle G} (or the spectrum of G {\displaystyle G} ). Because G {\displaystyle G} is connected and d {\displaystyle d} -regular, its eigenvalues satisfy d = λ 1 > λ 2 {\displaystyle d=\lambda _{1}>\lambda _{2}} ≥ ⋯ ≥ λ n ≥ − d {\displaystyle \geq \cdots \geq \lambda _{n}\geq -d} .
Define λ ( G ) = max i ≠ 1 | λ i | = max ( | λ 2 | , … , | λ n | ) {\displaystyle \lambda (G)=\max _{i\neq 1}|\lambda _{i}|=\max(|\lambda _{2}|,\ldots ,|\lambda _{n}|)} . A connected d {\displaystyle d} -regular graph G {\displaystyle G} is a Ramanujan graph if λ ( G ) ≤ 2 d − 1 {\displaystyle \lambda (G)\leq 2{\sqrt {d-1}}} .
Many sources uses an alternative definition λ ′ ( G ) = max | λ i | < d | λ i | {\displaystyle \lambda '(G)=\max _{|\lambda _{i}|<d}|\lambda _{i}|} (whenever there exists λ i {\displaystyle \lambda _{i}} with | λ i | < d {\displaystyle |\lambda _{i}|<d} ) to define Ramanujan graphs. [ 2 ] In other words, we allow − d {\displaystyle -d} in addition to the "small" eigenvalues. Since λ n = − d {\displaystyle \lambda _{n}=-d} if and only if the graph is bipartite , we will refer to the graphs that satisfy this alternative definition but not the first definition bipartite Ramanujan graphs . If G {\displaystyle G} is a Ramanujan graph, then G × K 2 {\displaystyle G\times K_{2}} is a bipartite Ramanujan graph, so the existence of Ramanujan graphs is stronger.
As observed by Toshikazu Sunada , a regular graph is Ramanujan if and only if its Ihara zeta function satisfies an analog of the Riemann hypothesis . [ 3 ]
Mathematicians are often interested in constructing infinite families of d {\displaystyle d} -regular Ramanujan graphs for every fixed d {\displaystyle d} . Such families are useful in applications.
Several explicit constructions of Ramanujan graphs arise as Cayley graphs and are algebraic in nature. See Winnie Li's survey on Ramanujan's conjecture and other aspects of number theory relevant to these results. [ 5 ]
Lubotzky , Phillips and Sarnak [ 2 ] and independently Margulis [ 6 ] showed how to construct an infinite family of ( p + 1 ) {\displaystyle (p+1)} -regular Ramanujan graphs, whenever p {\displaystyle p} is a prime number and p ≡ 1 ( mod 4 ) {\displaystyle p\equiv 1{\pmod {4}}} . Both proofs use the Ramanujan conjecture , which led to the name of Ramanujan graphs. Besides being Ramanujan graphs, these constructions satisfies some other properties, for example, their girth is Ω ( log p ( n ) ) {\displaystyle \Omega (\log _{p}(n))} where n {\displaystyle n} is the number of nodes.
Let us sketch the Lubotzky-Phillips-Sarnak construction. Let q ≡ 1 mod 4 {\displaystyle q\equiv 1{\bmod {4}}} be a prime not equal to p {\displaystyle p} . By Jacobi's four-square theorem , there are p + 1 {\displaystyle p+1} solutions to the equation p = a 0 2 + a 1 2 + a 2 2 + a 3 2 {\displaystyle p=a_{0}^{2}+a_{1}^{2}+a_{2}^{2}+a_{3}^{2}} where a 0 > 0 {\displaystyle a_{0}>0} is odd and a 1 , a 2 , a 3 {\displaystyle a_{1},a_{2},a_{3}} are even. To each such solution associate the PGL ( 2 , Z / q Z ) {\displaystyle \operatorname {PGL} (2,\mathbb {Z} /q\mathbb {Z} )} matrix α ~ = ( a 0 + i a 1 a 2 + i a 3 − a 2 + i a 3 a 0 − i a 1 ) , i a fixed solution to i 2 = − 1 mod q . {\displaystyle {\tilde {\alpha }}={\begin{pmatrix}a_{0}+ia_{1}&a_{2}+ia_{3}\\-a_{2}+ia_{3}&a_{0}-ia_{1}\end{pmatrix}},\qquad i{\text{ a fixed solution to }}i^{2}=-1{\bmod {q}}.} If p {\displaystyle p} is not a quadratic residue modulo q {\displaystyle q} let X p , q {\displaystyle X^{p,q}} be the Cayley graph of PGL ( 2 , Z / q Z ) {\displaystyle \operatorname {PGL} (2,\mathbb {Z} /q\mathbb {Z} )} with these p + 1 {\displaystyle p+1} generators, and otherwise, let X p , q {\displaystyle X^{p,q}} be the Cayley graph of PSL ( 2 , Z / q Z ) {\displaystyle \operatorname {PSL} (2,\mathbb {Z} /q\mathbb {Z} )} with the same generators. Then X p , q {\displaystyle X^{p,q}} is a ( p + 1 ) {\displaystyle (p+1)} -regular graph on n = q ( q 2 − 1 ) {\displaystyle n=q(q^{2}-1)} or q ( q 2 − 1 ) / 2 {\displaystyle q(q^{2}-1)/2} vertices depending on whether or not p {\displaystyle p} is a quadratic residue modulo q {\displaystyle q} . It is proved that X p , q {\displaystyle X^{p,q}} is a Ramanujan graph.
Morgenstern [ 7 ] later extended the construction of Lubotzky, Phillips and Sarnak. His extended construction holds whenever p {\displaystyle p} is a prime power .
Arnold Pizer proved that the supersingular isogeny graphs are Ramanujan, although they tend to have lower girth than the graphs of Lubotzky, Phillips, and Sarnak. [ 8 ] Like the graphs of Lubotzky, Phillips, and Sarnak, the degrees of these graphs are always a prime number plus one.
Adam Marcus , Daniel Spielman and Nikhil Srivastava [ 9 ] proved the existence of infinitely many d {\displaystyle d} -regular bipartite Ramanujan graphs for any d ≥ 3 {\displaystyle d\geq 3} . Later [ 10 ] they proved that there exist bipartite Ramanujan graphs of every degree and every number of vertices. Michael B. Cohen [ 11 ] showed how to construct these graphs in polynomial time.
The initial work followed an approach of Bilu and Linial . They considered an operation called a 2-lift that takes a d {\displaystyle d} -regular graph G {\displaystyle G} with n {\displaystyle n} vertices and a sign on each edge, and produces a new d {\displaystyle d} -regular graph G ′ {\displaystyle G'} on 2 n {\displaystyle 2n} vertices. Bilu & Linial conjectured that there always exists a signing so that every new eigenvalue of G ′ {\displaystyle G'} has magnitude at most 2 d − 1 {\displaystyle 2{\sqrt {d-1}}} . This conjecture guarantees the existence of Ramanujan graphs with degree d {\displaystyle d} and 2 k ( d + 1 ) {\displaystyle 2^{k}(d+1)} vertices for any k {\displaystyle k} —simply start with the complete graph K d + 1 {\displaystyle K_{d+1}} , and iteratively take 2-lifts that retain the Ramanujan property.
Using the method of interlacing polynomials, Marcus, Spielman, and Srivastava [ 9 ] proved Bilu & Linial's conjecture holds when G {\displaystyle G} is already a bipartite Ramanujan graph, which is enough to conclude the existence result. The sequel [ 10 ] proved the stronger statement that a sum of d {\displaystyle d} random bipartite matchings is Ramanujan with non-vanishing probability. Hall, Puder and Sawin [ 12 ] extended the original work of Marcus, Spielman and Srivastava to r -lifts.
It is still an open problem whether there are infinitely many d {\displaystyle d} -regular (non-bipartite) Ramanujan graphs for any d ≥ 3 {\displaystyle d\geq 3} . In particular, the problem is open for d = 7 {\displaystyle d=7} , the smallest case for which d − 1 {\displaystyle d-1} is not a prime power and hence not covered by Morgenstern's construction.
The constant 2 d − 1 {\displaystyle 2{\sqrt {d-1}}} in the definition of Ramanujan graphs is asymptotically sharp. More precisely, the Alon-Boppana bound states that for every d {\displaystyle d} and ϵ > 0 {\displaystyle \epsilon >0} , there exists n {\displaystyle n} such that all d {\displaystyle d} -regular graphs G {\displaystyle G} with at least n {\displaystyle n} vertices satisfy λ ( G ) > 2 d − 1 − ϵ {\displaystyle \lambda (G)>2{\sqrt {d-1}}-\epsilon } . This means that Ramanujan graphs are essentially the best possible expander graphs .
Due to achieving the tight bound on λ ( G ) {\displaystyle \lambda (G)} , the expander mixing lemma gives excellent bounds on the uniformity of the distribution of the edges in Ramanujan graphs, and any random walks on the graphs has a logarithmic mixing time (in terms of the number of vertices): in other words, the random walk converges to the (uniform) stationary distribution very quickly. Therefore, the diameter of Ramanujan graphs are also bounded logarithmically in terms of the number of vertices.
Confirming a conjecture of Alon , Friedman [ 13 ] showed that many families of random graphs are weakly-Ramanujan . This means that for every d {\displaystyle d} and ϵ > 0 {\displaystyle \epsilon >0} and for sufficiently large n {\displaystyle n} , a random d {\displaystyle d} -regular n {\displaystyle n} -vertex graph G {\displaystyle G} satisfies λ ( G ) < 2 d − 1 + ϵ {\displaystyle \lambda (G)<2{\sqrt {d-1}}+\epsilon } with high probability. While this result shows that random graphs are close to being Ramanujan, it cannot be used to prove the existence of Ramanujan graphs. It is conjectured, [ 14 ] though, that random graphs are Ramanujan with substantial probability (roughly 52%). In addition to direct numerical evidence, there is some theoretical support for this conjecture: the spectral gap of a d {\displaystyle d} -regular graph seems to behave according to a Tracy-Widom distribution from random matrix theory, which would predict the same asymptotic.
In 2024 a preprint by Jiaoyang Huang, Theo McKenzieand and Horng-Tzer Yau proved that λ ( G ) ≤ 2 d − 1 {\displaystyle \lambda (G)\leq 2{\sqrt {d-1}}} with the fraction of eigenvalues that hit the Alon-Boppana bound approximately 69% from proving that edge universality holds, that is they follow a Tracy-Widom distribution associated with the Gaussian Orthogonal Ensemble [ 15 ] [ 16 ]
Expander graphs have many applications to computer science, number theory, and group theory, see e.g Lubotzky's survey on applications to pure and applied math and Hoory, Linial, and Wigderson's survey which focuses on computer science. Ramanujan graphs are in some sense the best expanders, and so they are especially useful in applications where expanders are needed. Importantly, the Lubotzky, Phillips, and Sarnak graphs can be traversed extremely quickly in practice, so they are practical for applications.
Some example applications include | https://en.wikipedia.org/wiki/Ramanujan_graph |
In number theory , the Ramanujan–Nagell equation is an equation between a square number and a number that is seven less than a power of two . It is an example of an exponential Diophantine equation , an equation to be solved in integers where one of the variables appears as an exponent .
The equation is named after Srinivasa Ramanujan , who conjectured that it has only five integer solutions, and after Trygve Nagell , who proved the conjecture. It implies non-existence of perfect binary codes with the minimum Hamming distance 5 or 6.
The equation is
and solutions in natural numbers n and x exist just when n = 3, 4, 5, 7 and 15 (sequence A060728 in the OEIS ).
This was conjectured in 1913 by Indian mathematician Srinivasa Ramanujan , proposed independently in 1943 by the Norwegian mathematician Wilhelm Ljunggren , and proved in 1948 by the Norwegian mathematician Trygve Nagell . The values of n correspond to the values of x as:-
The problem of finding all numbers of the form 2 b − 1 ( Mersenne numbers ) which are triangular is equivalent:
The values of b are just those of n − 3, and the corresponding triangular Mersenne numbers (also known as Ramanujan–Nagell numbers ) are:
for x = 1, 3, 5, 11 and 181, giving 0, 1, 3, 15, 4095 and no more (sequence A076046 in the OEIS ).
An equation of the form
for fixed D , A , B and variable x , n is said to be of Ramanujan–Nagell type . The result of Siegel [ 2 ] implies that the number of solutions in each case is finite. [ 3 ] By representing n = 3 m + r {\displaystyle n=3m+r} with r ∈ { 0 , 1 , 2 } {\displaystyle r\in \{0,1,2\}} and B n = B r y 3 {\displaystyle B^{n}=B^{r}y^{3}} with y = B m {\displaystyle y=B^{m}} , the equation of Ramanujan–Nagell type is reduced to three Mordell curves (indexed by r {\displaystyle r} ), each of which has a finite number of integer solutions:
The equation with A = 1 , B = 2 , D > 0 {\displaystyle A=1,\ B=2,\ D>0} has at most two solutions, except in the case D = 7 {\displaystyle D=7} corresponding to the Ramanujan–Nagell equation. This does not hold for D < 0 {\displaystyle D<0} , such as D = − 17 {\displaystyle D=-17} , where x 2 − 17 = 2 n {\displaystyle x^{2}-17=2^{n}} has the four solutions ( x , n ) = ( 5 , 3 ) , ( 7 , 5 ) , ( 9 , 6 ) , ( 23 , 9 ) {\displaystyle (x,n)=(5,3),(7,5),(9,6),(23,9)} . In general, if D = − ( 4 k − 3 ⋅ 2 k + 1 + 1 ) {\displaystyle D=-(4^{k}-3\cdot 2^{k+1}+1)} for an integer k ⩾ 3 {\displaystyle k\geqslant 3} there are at least the four solutions
and these are the only four if D > − 10 12 {\displaystyle D>-10^{12}} . [ 4 ] There are infinitely many values of D for which there are exactly two solutions, including D = 2 m − 1 {\displaystyle D=2^{m}-1} . [ 1 ]
An equation of the form
for fixed D , A and variable x , y , n is said to be of Lebesgue–Nagell type . This is named after Victor-Amédée Lebesgue , who proved that the equation
has no nontrivial solutions. [ 5 ]
Results of Shorey and Tijdeman [ 6 ] imply that the number of solutions in each case is finite. [ 7 ] Bugeaud, Mignotte and Siksek [ 8 ] solved equations of this type with A = 1 and 1 ≤ D ≤ 100. In particular, the following generalization of the Ramanujan–Nagell equation:
has positive integer solutions only when x = 1, 3, 5, 11, or 181. | https://en.wikipedia.org/wiki/Ramanujan–Nagell_equation |
In mathematics , a Ramanujan–Sato series [ 1 ] [ 2 ] generalizes Ramanujan 's pi formulas such as,
to the form
by using other well-defined sequences of integers s ( k ) {\displaystyle s(k)} obeying a certain recurrence relation , sequences which may be expressed in terms of binomial coefficients ( n k ) {\displaystyle {\tbinom {n}{k}}} , and A , B , C {\displaystyle A,B,C} employing modular forms of higher levels.
Ramanujan made the enigmatic remark that there were "corresponding theories", but it was only in 2012 that H. H. Chan and S. Cooper found a general approach that used the underlying modular congruence subgroup Γ 0 ( n ) {\displaystyle \Gamma _{0}(n)} , [ 3 ] while G. Almkvist has experimentally found numerous other examples also with a general method using differential operators . [ 4 ]
Levels 1–4A were given by Ramanujan (1914), [ 5 ] level 5 by H. H. Chan and S. Cooper (2012), [ 3 ] 6A by Chan, Tanigawa, Yang, and Zudilin, [ 6 ] 6B by Sato (2002), [ 7 ] 6C by H. Chan, S. Chan, and Z. Liu (2004), [ 1 ] 6D by H. Chan and H. Verrill (2009), [ 8 ] level 7 by S. Cooper (2012), [ 9 ] part of level 8 by Almkvist and Guillera (2012), [ 2 ] part of level 10 by Y. Yang, and the rest by H. H. Chan and S. Cooper.
The notation j n ( τ ) is derived from Zagier [ 10 ] and T n refers to the relevant McKay–Thompson series .
Examples for levels 1–4 were given by Ramanujan in his 1917 paper. Given q = e 2 π i τ {\displaystyle q=e^{2\pi i\tau }} as in the rest of this article. Let,
with the j-function j ( τ ), Eisenstein series E 4 , and Dedekind eta function η ( τ ). The first expansion is the McKay–Thompson series of class 1A ( OEIS : A007240 ) with a(0) = 744. Note that, as first noticed by J. McKay , the coefficient of the linear term of j ( τ ) almost equals 196883, which is the degree of the smallest nontrivial irreducible representation of the monster group , a relationship called monstrous moonshine . Similar phenomena will be observed in the other levels. Define
Then the two modular functions and sequences are related by
if the series converges and the sign chosen appropriately, though squaring both sides easily removes the ambiguity. Analogous relationships exist for the higher levels.
Examples:
where 645 = 43 × 15 , {\displaystyle 645=43\times 15,} and U n {\displaystyle U_{n}} is a fundamental unit . The first belongs to a family of formulas which were rigorously proven by the Chudnovsky brothers in 1989 [ 11 ] and later used to calculate 10 trillion digits of π in 2011. [ 12 ] The second formula, and the ones for higher levels, was established by H.H. Chan and S. Cooper in 2012. [ 3 ]
Using Zagier's notation [ 10 ] for the modular function of level 2,
Note that the coefficient of the linear term of j 2A ( τ ) is one more than 4371 which is the smallest degree greater than 1 of the irreducible representations of the Baby Monster group . Define,
Then,
if the series converges and the sign chosen appropriately.
Examples:
The first formula, found by Ramanujan and mentioned at the start of the article, belongs to a family proven by D. Bailey and the Borwein brothers in a 1989 paper. [ 13 ]
Define,
where 782 is the smallest degree greater than 1 of the irreducible representations of the Fischer group Fi 23 and,
Examples:
Define,
where the first is the 24th power of the Weber modular function f ( 2 τ ) {\displaystyle {\mathfrak {f}}(2\tau )} . And,
Examples:
Define,
and,
where the first is the product of the central binomial coefficients and the Apéry numbers ( OEIS : A005258 ) [ 9 ]
Examples:
In 2002, Takeshi Sato [ 7 ] established the first results for levels above 4. It involved Apéry numbers which were first used to establish the irrationality of ζ ( 3 ) {\displaystyle \zeta (3)} . First, define,
The phenomenon of j 6 A {\displaystyle j_{6A}} being squares or a near-square of the other functions will also be manifested by j 10 A {\displaystyle j_{10A}} . Another similarity between levels 6 and 10 is J. Conway and S. Norton showed there are linear relations between the McKay–Thompson series T n , [ 14 ] one of which was,
or using the above eta quotients j n ,
A similar relation exists for level 10.
For the modular function j 6A , one can associate it with three different sequences. (A similar situation happens for the level 10 function j 10A .) Let,
The three sequences involve the product of the central binomial coefficients c ( k ) = ( 2 k k ) {\displaystyle c(k)={\tbinom {2k}{k}}} with: first, the Franel numbers ∑ j = 0 k ( k j ) 3 {\displaystyle \textstyle \sum _{j=0}^{k}{\tbinom {k}{j}}^{3}} ; second, OEIS : A002893 , and third, ( − 1 ) k {\displaystyle (-1)^{k}} OEIS : A093388 . Note that the second sequence, α 2 ( k ) is also the number of 2 n -step polygons on a cubic lattice . Their complements,
There are also associated sequences, namely the Apéry numbers,
the Domb numbers (unsigned) or the number of 2 n -step polygons on a diamond lattice ,
and the Almkvist-Zudilin numbers,
where
The modular functions can be related as,
if the series converges and the sign chosen appropriately. It can also be observed that,
which implies,
and similarly using α 3 and α' 3 .
One can use a value for j 6A in three ways. For example, starting with,
and noting that 3 ⋅ 17 = 51 {\displaystyle 3\cdot 17=51} then,
as well as,
though the formulas using the complements apparently do not yet have a rigorous proof. For the other modular functions,
Define
and,
Example:
No pi formula has yet been found using j 7B .
Levels 2 , 4 , 8 {\displaystyle 2,4,8} are related since they are just powers of the same prime. Define,
Just like for level 6, five of these functions have a linear relationship,
But this is not one of the nine Conway-Norton-Atkin linear dependencies since j 8 A ′ {\displaystyle j_{8A'}} is not a moonshine function. However, it is related to one as,
where the first is the product [ 2 ] of the central binomial coefficient and a sequence related to an arithmetic-geometric mean ( OEIS : A081085 ).
The modular functions can be related as,
if the series converges and signs chosen appropriately. Note also the different exponent of ( j 4 D ( τ ) ) 2 k + 1 2 {\displaystyle \left(j_{4D}(\tau )\right)^{2k+{\frac {1}{2}}}} from the others.
Recall that j 2 A ( − 58 2 ) = 396 4 , {\displaystyle j_{2A}\left({\tfrac {\sqrt {-58}}{2}}\right)=396^{4},} while j 4 B ( − 58 4 ) = 396 2 {\displaystyle j_{4B}\left({\tfrac {\sqrt {-58}}{4}}\right)=396^{2}} . Hence,
For another level 8 example,
Define,
The expansion of the first is the McKay–Thompson series of class 3C (and related to the cube root of the j-function ), while the second is that of class 9A. Let,
where the first is the product of the central binomial coefficients and OEIS : A006077 (though with different signs).
Examples:
Define,
Just like j 6 A {\displaystyle j_{6A}} , the function j 10 A {\displaystyle j_{10A}} is a square or a near-square of the others. Furthermore, there are also linear relations between these,
or using the above eta quotients j n ,
Let,
their complements,
and,
though closed forms are not yet known for the last three sequences.
The modular functions can be related as, [ 15 ]
if the series converges. In fact, it can also be observed that,
Since the exponent has a fractional part , the sign of the square root must be chosen appropriately though it is less an issue when j n is positive.
Just like level 6, the level 10 function j 10A can be used in three ways. Starting with,
and noting that 5 ⋅ 19 = 95 {\displaystyle 5\cdot 19=95} then,
as well as,
though the ones using the complements do not yet have a rigorous proof. A conjectured formula using one of the last three sequences is,
which implies there might be examples for all sequences of level 10.
Define the McKay–Thompson series of class 11A,
or sequence ( OEIS : A128525 ) and where,
and,
No closed form in terms of binomial coefficients is yet known for the sequence but it obeys the recurrence relation ,
with initial conditions s (0) = 1, s (1) = 4.
Example: [ 16 ]
As pointed out by Cooper, [ 16 ] there are analogous sequences for certain higher levels.
R. Steiner found examples using Catalan numbers C k {\displaystyle C_{k}} ,
and for this a modular form with a second periodic for k exists:
Other similar series are
with the last (comments in OEIS : A013709 ) found by using a linear combination of higher parts of Wallis -Lambert series for 4 π {\displaystyle {\tfrac {4}{\pi }}} and Euler series for the circumference of an ellipse .
Using the definition of Catalan numbers with the gamma function the first and last for example give the identities
...
The last is also equivalent to,
and is related to the fact that,
which is a consequence of Stirling's approximation . | https://en.wikipedia.org/wiki/Ramanujan–Sato_series |
In mathematics , the Ramanujan–Soldner constant (also called the Soldner constant ) is a mathematical constant defined as the unique positive zero of the logarithmic integral function . It is named after Srinivasa Ramanujan and Johann Georg von Soldner .
Its value is approximately μ ≈ 1.45136923488338105028396848589202744949303228… (sequence A070769 in the OEIS )
Since the logarithmic integral is defined by
then using l i ( μ ) = 0 , {\displaystyle \mathrm {li} (\mu )=0,} we have
thus easing calculation for numbers greater than μ . Also, since the exponential integral function satisfies the equation
the only positive zero of the exponential integral occurs at the natural logarithm of the Ramanujan–Soldner constant, whose value is approximately ln( μ ) ≈ 0.372507410781366634461991866… (sequence A091723 in the OEIS )
This mathematics -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Ramanujan–Soldner_constant |
The Ramberg–Bäcklund reaction is an organic reaction converting an α-halo sulfone into an alkene in presence of a base with extrusion of sulfur dioxide . [1] The reaction is named after the two Swedish chemists Ludwig Ramberg and Birger Bäcklund. The carbanion formed by deprotonation gives an unstable episulfone that decomposes with elimination of sulfur dioxide . This elimination step is considered to be a concerted cheletropic extrusion . [ citation needed ]
The overall transformation is the conversion of the carbon–sulfur bonds to a carbon–carbon double bond. The original procedure involved halogenation of a sulfide , followed by oxidation to the sulfone . Recently, the preferred method has reversed the order of the steps. After the oxidation , which is normally done with a peroxy acid , halogenation is done under basic conditions by use of dibromodifluoromethane for the halogen transfer step. [2] This method was used to synthesize 1,8-diphenyl-1,3,5,7-octatetraene.
The Ramberg–Bäcklund reaction has several applications. Due to the nature of elimination, it can be applied to both small rings [3] ,
and large rings containing a double bond [4] .
This reaction type gives access to 1,2-dimethylenecyclohexane [5]
and the epoxide variation [6] access to allyl alcohols .
A recently developed application of the Ramberg–Bäcklund reaction is the synthesis of C -glycosides. The required thioethers can be prepared easily by exchange with a thiol . The application of the Ramberg–Bäcklund conditions then leads to an exocyclic vinyl ether that can be reduced to the C-nucleoside [7] .
In a variation, oxidation of a sulfamide generates a azo compound . [ 1 ]
The necessary α-halo sulfones are accessible through oxidation of the corresponding α-halo sulfides with peracids such as meta -chloroperbenzoic acid ; oxidation of sulfides takes place selectively in the presence of alkenes and alcohols. α-Halo sulfides may in turn be synthesized through the treatment of sulfides with halogen electrophiles such as N -chlorosuccinimide or N -bromosuccinimide . [8]
The sulfone group contains an acidic proton in one of the α-positions which is abstracted by a strong base ( scheme 1 ). The negative charge placed on this position (formally a carbanion ) is transferred to the halogen residing on the other α-position in a nucleophilic displacement temporarily forming a three-membered cyclic sulfone. This intermediate is unstable and releases sulfur dioxide to form the alkene. Mixtures of cis isomer and trans isomer are usually obtained. [9]
The Favorskii rearrangement and the Eschenmoser sulfide contraction are conceptually related reactions. | https://en.wikipedia.org/wiki/Ramberg–Bäcklund_reaction |
The Ramberg–Osgood equation was created to describe the nonlinear relationship between stress and strain —that is, the stress–strain curve —in materials near their yield points . It is especially applicable to metals that harden with plastic deformation (see work hardening ), showing a smooth elastic-plastic transition. As it is a phenomenological model , checking the fit of the model with actual experimental data for the particular material of interest is essential.
In its original form, the equation for strain (deformation) is [ 1 ]
here
The equation is essentially assuming the elastic strain portion of the stress-strain curve, ε e {\displaystyle \varepsilon _{e}} , can be modeled with a line, while the plastic portion, ε p {\displaystyle \varepsilon _{p}} , can be modeled with a power law. The elastic and plastic components are summed to find the total strain.
ε = ε e + ε p {\displaystyle \varepsilon =\varepsilon _{e}+\varepsilon _{p}}
The first term on the right side, σ / E {\displaystyle {\sigma }/{E}\,} , is equal to the elastic part of the strain, while the second term, K ( σ / E ) n {\displaystyle \ K({\sigma }/{E})^{n}} , accounts for the plastic part, the parameters K {\displaystyle K} and n {\displaystyle n} describing the hardening behavior of the material. Introducing the yield strength of the material, σ 0 {\displaystyle \sigma _{0}} , and defining a new parameter, α {\displaystyle \alpha } , related to K {\displaystyle K} as α = K ( σ 0 / E ) n − 1 {\displaystyle \alpha =K({\sigma _{0}}/{E})^{n-1}\,} , it is convenient to rewrite the term on the extreme right side as follows:
Replacing in the first expression, the Ramberg–Osgood equation can be written as
In the last form of the Ramberg–Osgood model, the hardening behavior of the material depends on the material constants α {\displaystyle \alpha \,} and n {\displaystyle n\,} . Due to the power-law relationship between stress and plastic strain, the Ramberg–Osgood model implies that plastic strain is present even for very low levels of stress. Nevertheless, for low applied stresses and for the commonly used values of the material constants α {\displaystyle \alpha } and n {\displaystyle n} , the plastic strain remains negligible compared to the elastic strain. On the other hand, for stress levels higher than σ 0 {\displaystyle \sigma _{0}} , plastic strain becomes progressively larger than elastic strain.
The value α σ 0 E {\displaystyle \alpha {\frac {\sigma _{0}}{E}}} can be seen as a yield offset , as shown in figure 1. This comes from the fact that ε = ( 1 + α ) σ 0 / E {\displaystyle \varepsilon =(1+\alpha ){{\sigma _{0}}/{E}}\,} , when σ = σ 0 {\displaystyle \sigma =\sigma _{0}\,} .
Accordingly, (see Figure 1):
Commonly used values for n {\displaystyle n\,} are ~5 or greater, although more precise values are usually obtained by fitting of tensile (or compressive) experimental data. Values for α {\displaystyle \alpha \,} can also be found by means of fitting to experimental data, although for some materials, it can be fixed in order to have the yield offset equal to the accepted value of strain of 0.2%, which means:
Several slightly different alternative formulations of the Ramberg–Osgood equation can be found. As the models are purely empirical, it is often useful to try different models and check which has the best fit with the chosen material.
The Ramberg–Osgood equation can also be expressed using the Hollomon parameters [ 3 ] where K {\displaystyle K} is the strength coefficient (Pa) and n {\displaystyle n} is the strain hardening coefficient (no units). [ 4 ]
ε = σ E + ( σ K ) 1 / n {\displaystyle \varepsilon ={\frac {\sigma }{E}}+\left({\frac {\sigma }{K}}\right)^{1/n}}
Alternatively, if the yield stress, σ y {\displaystyle \sigma _{y}} , is assumed to be at the 0.2% offset strain, the following relationship can be derived. [ 5 ] Note that n {\displaystyle n} is again as defined in the original Ramberg–Osgood equation and is the inverse of the Hollomon's strain hardening coefficient .
ε = σ E + 0.002 ( σ σ y ) n {\displaystyle \varepsilon ={\frac {\sigma }{E}}+0.002\left({\frac {\sigma }{\sigma _{y}}}\right)^{n}}
The Ramberg-Osgood model provides an explicit formula for obtaining strain ε {\displaystyle \varepsilon } from stress σ {\displaystyle \sigma } , but in general an iterative solve must be performed for the inverse relation from strain to stress. This can be computationally demanding, and is not well suited for applications like Finite element analysis where the inverse mapping from strain to stress is generally required. For this reason, several alternative curves have become common in these contexts. One such example is the curve proposed by [ 6 ]
σ ¯ ( ε ¯ ) = b ε ¯ + ( 1 − b ) ε ¯ ( 1 + | ε ¯ | r ) 1 r {\displaystyle {\bar {\sigma }}({\bar {\varepsilon }})=b{\bar {\varepsilon }}+{\frac {(1-b){\bar {\varepsilon }}}{\left(1+|{\bar {\varepsilon }}|^{r}\right)^{\frac {1}{r}}}}}
where σ ¯ = σ / σ y , ε ¯ = ε / ε y , ( σ y , ε y ) {\displaystyle {\bar {\sigma }}=\sigma /\sigma _{y},{\bar {\varepsilon }}=\varepsilon /\varepsilon _{y},\left(\sigma _{y},\varepsilon _{y}\right)} is the yield point, b {\displaystyle b} is the strain hardening parameter, and the parameter r {\displaystyle r} influences the shape of the transition curve and takes account of the Bauschinger effect. | https://en.wikipedia.org/wiki/Ramberg–Osgood_relationship |
Ramboll Studio Dreiseitl Was one of the leading landscape architecture practices of Germany [ 1 ] specialising in the integration of art , urban hydrology, environmental engineering , and landscape architecture within an urban context. [ 2 ] The practise was founded in 1980 by the German landscape architect Herbert Dreiseitl with a goal to promote sustainable projects with a high aesthetic and social value. [ 2 ] Today it has offices in Germany , Singapore and Beijing . [ 3 ] In May 2013, Atelier Dreiseitl was renamed Ramboll Studio Dreiseitl GmbH and became a partner within the international engineering consultancy, the Ramboll Group A/S , based in Copenhagen . [ 4 ]
On April 3, 2023, Ramboll Studio Dreiseitl joined the international architecture, landscape architecture and urbanism studio Henning Larsen Architects , and is now part of the Henning Larsen team, [ 5 ]
The multidisciplinary practice seeks to raise awareness of the social and ecological value of water in urban design . The scope of the practice's work includes strategic catchment-based urban masterplans, urban parks, rivers, civic space and water playgrounds.
Over the past 40 years, it has accumulated experience in technical water systems, including water storage, treatment and reuse, retention and infiltration techniques, grey and black water systems, climatisation and green roofs. [ 2 ]
The consultancy was described in 2012 in Der Spiegel as “a kind of hidden champion of the German design scene”. [ 6 ]
Ramboll Studio Dreiseitl are responsible for the waterscape on Potsdamer Platz in Berlin. [ 7 ] Water was central to Renzo Piano and Christoph Kohlbecker's original design, but it was Ramboll Studio Dreiseitl that conceived and developed the scheme for rainwater recycling and created the many opportunities for public engagement with water. [ 8 ] The scheme is one of the largest urban rainwater harvesting projects in the world [ 9 ] and in 2011, it became one of the first city quarters to be retrospectively awarded the DGNB Certificate of the German Sustainable Building Council (DGNB) in silver.
Another major project in Germany is Arkadien Winnenden , the ecological city design which was named winner of the Green Dot Award ‘Build’ category in 2011. The firm turned the abandoned factory site into an eco-friendly development which combines dense layout with green space, includes permeable paving and waterways which provide natural flood control and a lake which filters rainwater. [ 10 ]
In 2018, Ramboll Studio Dreiseitl was awarded the German Design Award in the category "Urban Space an Infrastructure" for their design and planning of the project Hafen Offenbach [ 11 ] [ 12 ] in Offenbach am Main , Germany. Studio Dreiseitl has transformed the initial urban plan by reconnecting public open spaces with their scenic context, creating a liveable as well as ecologically enriching neighbourhood. [ 13 ]
In Asia, projects include the blue green infrastructure in the Tianjin Cultural Park near Beijing and the water strategy for the central catchment for the city of Singapore , together with the engineers CH2M Hill, as well as the design of the 60ha Bishan-Ang Mo Kio Park . [ 7 ] The rehabilitation of the previously concreted Kallang River (which became a dangerous torrent in the rainy season) [ 14 ] employed techniques of water collection and flood control which were entirely new to Singapore. Ramboll Studio Dreiseitl built a test area and held workshops to explain the concepts. The designers gave the river gentle banks and recycled the concrete from the old drainage channel to create stairs. [ 3 ] Now Bishan Park is one of the most popular parks in Singapore, where people can have a new and direct connection to nature. [ 14 ] In 2012, the design was awarded the Presidents Design Award Singapore [ 15 ] and the World Architecture Festival “Landscape of the Year”. [ 16 ] | https://en.wikipedia.org/wiki/Ramboll_Studio_Dreiseitl |
Ramesh Jasti is a professor of organic chemistry at the University of Oregon . He was the first person to synthesize the elusive cycloparaphenylene in 2008 [ 1 ] during post doctoral work in the laboratory of Professor Carolyn Bertozzi . He started his laboratory at Boston University where he was the recipient of the NSF CAREER award. [ 2 ] His early lab repeatedly broke the record for the synthesis of the smallest cycloparaphenylene known. In 2014, he moved his laboratory to the University of Oregon where he expanded his focus to apply the molecules he discovered in the areas of organic materials , [ 3 ] mechanically interlocked molecules, [ 4 ] and biology . [ 5 ] He is the Director of the Materials Science Institute at the University of Oregon. [ 6 ]
This biographical article about a chemist is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Ramesh_Jasti |
The Ramesside star clocks are ancient Egyptian star clocks appearing on the ceilings of several royal tombs of the Ramesside period . Two sets of star clocks appear on the tomb Ramesses VII and Ramesses IX . [ 1 ] Although all of the sets are corrupt to some degree, a prototype clock can be reconstructed from them. [ 1 ]
This article about subjects relating to ancient Egypt is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Ramesside_star_clocks |
A ramicolous lichen is one that lives on branches . [ 1 ]
This article about lichens or lichenology is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Ramicolous_lichen |
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