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Rhenium hexafluoride , also rhenium(VI) fluoride , (ReF 6 ) is a compound of rhenium and fluorine and one of the seventeen known binary hexafluorides .
Rhenium hexafluoride is made by combining rhenium heptafluoride with additional rhenium metal at 300 °C in a pressure vessel . [ 2 ]
The compound is a Lewis acid and strong oxidant, adducting potassium fluoride and oxidizing nitric oxide to nitrosyl: [ 3 ]
Rhenium hexafluoride is a liquid at room temperature. At 18.5 °C, it freezes into a yellow solid. The boiling point is 33.7 °C. [ 1 ]
The solid structure measured at −140 °C is orthorhombic space group Pnma . Lattice parameters are a = 9.417 Å , b = 8.570 Å, and c = 4.965 Å. There are four formula units (in this case, discrete molecules) per unit cell , giving a density of 4.94 g·cm −3 . [ 2 ]
The ReF 6 molecule itself (the form important for the liquid or gas phase) has octahedral molecular geometry , which has point group ( O h ). The Re–F bond length is 1.823 Å. [ 2 ]
Rhenium hexafluoride is a commercial material used in the electronics industry for depositing films of rhenium. [ 3 ] | https://en.wikipedia.org/wiki/ReF6 |
Rhenium heptafluoride is the compound with the formula ReF 7 . It is a yellow low melting solid and is the only thermally stable metal heptafluoride. [ 2 ] It has a distorted pentagonal bipyramidal structure similar to IF 7 , which was confirmed by neutron diffraction at 1.5 K. [ 3 ] The structure is non-rigid, as evidenced by electron diffraction studies. [ 4 ]
Rhenium heptafluoride can be prepared from the elements at 400 °C: [ 5 ]
It also can be produced by the explosion of rhenium metal under sulfur hexafluoride . [ 6 ]
It hydrolyzes under a base to form perrhenic acid and hydrogen fluoride : [ 1 ]
With fluoride donors such as CsF, the ReF − 8 anion is formed, which has a square antiprismatic structure . [ 7 ] With antimony pentafluoride , SbF 5 , a fluoride acceptor, the ReF + 6 cation is formed. [ 5 ] | https://en.wikipedia.org/wiki/ReF7 |
ReFLEX is a wireless protocol developed by Motorola , used for two-way paging, messaging, and low-bandwidth data. It is based on the FLEX one-way paging protocol, adding capabilities for multiple forward channels, multiple return channels, and roaming. It originally came in two variants, ReFLEX25 and ReFLEX50 . ReFLEX50 was originally developed to support a messaging service launched by MTEL in the mid 1990s, [ 1 ] while ReFLEX25 was developed several years later to provide an upgrade path for traditional one-way paging carriers. [ 2 ] The 50 and 25 signified 50 kHz and 25kHz channel spacing, although in reality both variants supported flexible channel configurations. The two variants were unified into a single protocol with version 2.7, which was released simply as ReFLEX 2.7 . Devices compliant with ReFLEX 2.7 are backwards compatible with both ReFLEX25 and ReFLEX50 networks, with several new features to improve roaming, performance, and interoperability between different networks. ReFLEX systems support forward channel speeds of 1600, 3200, and 6400 bits per second, and return channel speeds of 800, 1600, 6400, and 9600 bits per second. Like FLEX , ReFLEX is synchronous, based on 1.875 second frames and 4-level FSK modulation.
The Motorola PageWriter released in 1996 was one of the first devices to use the ReFLEX network protocol. Although ReFLEX now has limited viability in the commercial market, it is finding new uses in Automatic Meter Reading , public safety, and low cost/bandwidth M2M applications.
This article about wireless technology is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/ReFLEX |
ReLINE Software was a German game development company founded by Uwe Grabosch and Holger Gehrmann in Hannover in 1987.
The company acted first as a developer for Softgold , Rainbow Arts , Golden Games , Magic Bytes , micro-partner , and Robtek; the company later became significantly more independent and co-published games with Magic Byte .
Titles from the eighties include: Operation Hongkong , Drum Studio , Extensor , Hollywood Poker , Space Port , Amegas , Crystal Hammer , Hollywood Poker Pro , Black Gold (also known as Oil Imperium ), Dyter-07 , and Window Wizard (also known as Window Willy ).
Games of the early nineties include Legend of Faerghail , Fate: Gates of Dawn and Centerbase .
Holger Gehrmann and Olaf Patzenhauer continued reLINE Software as a software label in 1993. The games Biing! and Biing! 2 originated from this time. However, the planned development of Oil Imperium 2 was cancelled.
ReLINE Software closed in 2004. In February 2008, Holger Gehrmann fell to his death from a seven-story office building months before his 40th birthday. Olaf Patzenhauer died some time between late 2011 and mid-2012.
This computing article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/ReLINE_Software |
Rhenium(IV) oxide or rhenium dioxide is the inorganic compound with the formula Re O 2 . This gray to black crystalline solid is a laboratory reagent that can be used as a catalyst . It adopts the rutile structure.
It forms via comproportionation : [ 3 ]
Single crystals are obtained by chemical transport , using iodine as the transporting agent.: [ 4 ]
At high temperatures it undergoes disproportionation :
It forms rhenates with alkaline hydrogen peroxide and oxidizing acids . [ 5 ] In molten sodium hydroxide it forms sodium rhenate: [ 6 ] | https://en.wikipedia.org/wiki/ReO2 |
Rhenium trioxide or rhenium(VI) oxide is an inorganic compound with the formula ReO 3 . It is a red solid with a metallic lustre that resembles copper in appearance. It is the only stable trioxide of the Group 7 elements ( Mn , Tc , Re ).
Rhenium trioxide can be formed by reducing rhenium(VII) oxide with carbon monoxide at 200 °C or elemental rhenium at 400 °C. [ 1 ]
Re 2 O 7 can also be reduced with dioxane . [ 2 ]
Rhenium trioxide crystallizes with a primitive cubic unit cell , with a lattice parameter of 3.742 Å (374.2 pm ). The structure of ReO 3 is similar to that of perovskite (ABO 3 ), without the large A cation at the centre of the unit cell. Each rhenium center is surrounded by an octahedron defined by six oxygen centers. These octahedra share corners to form the 3-dimensional structure. The coordination number of O is 2, because each oxygen atom has 2 neighbouring Re atoms. [ 3 ]
ReO 3 is unusual for an oxide because it exhibits very low resistivity . It behaves like a metal in that its resistivity decreases as its temperature decreases. At 300 K , its resistivity is 100.0 nΩ·m , whereas at 100 K, this decreases to 6.0 nΩ·m, 17 times less than at 300 K. [ 3 ]
Rhenium trioxide is insoluble in water, as well as dilute acids and bases. Heating it in base results in disproportionation to give ReO 2 and ReO − 4 , while reaction with acid at high temperature affords Re 2 O 7 . In concentrated nitric acid, it yields perrhenic acid .
Upon heating to 400 °C under vacuum, it undergoes disproportionation : [ 2 ]
Rhenium trioxide can be chlorinated to give rhenium trioxide chloride : [ 4 ]
Rhenium trioxide serves as host for the intercalation of one and two equivalents of lithium. Lithium can be incorporated using butyl lithium :
Re remains octahedral before and after intercalation, but the framework distorts. [ 5 ]
Rhenium trioxide finds some use in organic synthesis as a catalyst for amide reduction . [ 6 ] | https://en.wikipedia.org/wiki/ReO3 |
Rhenium disulfide is an inorganic compound of rhenium and sulfur with the formula ReS 2 . It has a layered structure where atoms are strongly bonded within each layer. The layers are held together by weak Van der Waals bonds , and can be easily peeled off from the bulk material.
ReS 2 is found in nature as the mineral rheniite . [ 3 ] It can be synthesized from the reaction between rhenium and sulfur at 1000 °C, or the decomposition of rhenium(VII) sulfide at 1100 °C: [ 4 ]
Nanostructured ReS 2 can usually be achieved through mechanical exfoliation, chemical vapor deposition (CVD), and chemical and liquid exfoliations. Larger crystals can be grown with the assistance of liquid carbonate flux at high pressure. It is widely used in electronic and optoelectronic device, energy storage, photocatalytic and electrocatalytic reactions. [ 5 ]
It is a two-dimensional (2D) group VII transition metal dichalcogenide (TMD). ReS 2 was isolated down to monolayers which is only one unit cell in thickness for the first time in 2014. [ 6 ] These monolayers have shown layer-independent electrical, optical, and vibrational properties much different from other TMDs.
Bulk ReS 2 has a layered structure and a platelet-like habit. Different crystal structures were proposed for ReS 2 based on single-crystal X-ray diffraction studies. While all authors agree that the lattice is triclinic, the reported cell parameters and atomic arrangements slightly differ. The earliest work [ 7 ] describes ReS 2 in a triclinic unit cell (sp. gr. P 1 ¯ {\displaystyle {\bar {1}}} , a = 0.6455 nm, b = 0.6362 nm, c = 0.6401 nm, α = 105.04°, β = 91.60°, γ = 118.97°) as a distorted variant of the CdCl 2 prototype (1T structure, trigonal space group R 3 ¯ {\displaystyle {\bar {3}}} m). In comparison with ideal octahedral coordination of the metal atoms in CdCl 2 , the Re atoms in ReS 2 are displaced from the centers of the surrounding Se 6 octahedra and form Re 4 clusters that are linked to chains in the b direction. A later study [ 8 ] proposed a more accurate description of the crystal structure. It reports a different triclinic cell (sp. gr. P 1 ¯ {\displaystyle {\bar {1}}} , a = 0.6352 nm, b = 0.6446 nm, c = 1.2779 nm, α = 91.51°, β = 105.17°, γ = 118.97°) with the doubled c parameter and swapped a and b, α and β. There are two layers in this unit cell, related by symmetry centers, and the chains of clusters run along the a axis. Each layer form parallelogram-shaped connected clusters with Re-Re distances of ca. 0.27-0.28 nm in the cluster, and ca. 0.29 nm between clusters. There is one more structure description of ReS 2 published in [ 9 ] in yet another triclinic cell (sp. gr. P 1 ¯ {\displaystyle {\bar {1}}} , a = 0.6417 nm, b = 0.6510 nm, c = 0.6461 nm, α = 121.10°, β = 88.38°, γ = 106.47°) where only one layer is present and the centers of symmetry are in the Re layer. The current consent is that the latter work might have overlooked the doubling of the c parameter captured in. [ 8 ]
Rhenium disulfide is known in nature as the very rare mineral rheniite . [ 10 ] [ 11 ] | https://en.wikipedia.org/wiki/ReS2 |
Rhenium diselenide is an inorganic compound with the formula ReSe 2 . It has a layered structure where atoms are strongly bonded within each layer. The layers are held together by weak Van der Waals bonds , and can be easily peeled off from the bulk material.
Rhenium diselenide with a thickness as small as a triple-atomic layer can be produced by chemical vapor deposition at ambient pressure. A mixture of Ar and hydrogen gases is flown through a tube whose ends are kept at different temperatures. The substrate and ReO 3 powder are placed at the hot end which is heated to 750 °C, and selenium powder is located at the cold end which is kept at 250 °C. [ 4 ]
As most other dichalcogenides of transition metals, rhenium diselenide has a layered structure where atoms are strongly bonded within each layer and the layers are held together by weak Van der Waals bonds . However, while most other layered dichalcogenides have a high (hexagonal) symmetry, ReSe 2 has a very low triclinic symmetry, and this symmetry does not change from the bulk to monolayers. [ 4 ] | https://en.wikipedia.org/wiki/ReSe2 |
Rhenium ditelluride is an inorganic compound of rhenium and tellurium with the formula ReTe 2 . Contrary to rhenium disulfide and diselenide , it does not have a layered structure. [ 2 ] | https://en.wikipedia.org/wiki/ReTe2 |
A reach is a segment of a stream, river, or arm of the sea, [ citation needed ] usually suggesting a straight, level, uninterrupted stretch. [ 1 ] [ 2 ] They are traditionally defined by the capabilities of sailing boats , as a stretch of a watercourse which, because it is straightish, can be sailed in one " reach " (that is, without tacking ).
Reaches are often named by those using the river, and a reach may be named for landmarks, natural features, and historical reasons (see, for instance, Gallions' Reach , named after the family that once owned its banks).
A reach may be an expanse, or widening, of a stream or river channel. This commonly occurs after the river or stream is dammed. A reach is similar to an arm, though an arm may bend and thus have multiple reaches. The term "reach" can also refer to a level stretch, as between river rapids or locks in a canal . [ citation needed ] The word may also be used more generally to refer to any extended portion or stretch of land or water, or even metaphorically.
In fluvial hydrology , a reach is a convenient subdivision of study; it may be any length of river of fairly uniform characteristics, or the length between gauging stations , or simply the length of a watercourse between any two defined points. [ 3 ] [ 4 ] These may be measured in terms of river miles .
As of 2015, the US Board on Geographic Names records 334 place names in the US with the characterization of a named "reach". [ 5 ] | https://en.wikipedia.org/wiki/Reach_(geography) |
Let X be a subset of R n . Then the reach of X is defined as
Shapes that have reach infinity include
The graph of ƒ ( x ) = | x | has reach zero.
A circle of radius r has reach r . | https://en.wikipedia.org/wiki/Reach_(mathematics) |
Remix (renamed React Router since v7 in November 2024) [ 1 ] is an open source full stack web framework . The software is designed for web applications built with front-end JavaScript frameworks like React and Vue.js . [ 2 ] Remix supports server-side rendering and client-side routing. [ 3 ] Remix has been presented as an alternative to the popular React framework Next.js . [ 4 ]
Initially available through a paid subscription, the software was made open source in October 2021. [ 5 ] The team developing Remix (that also developed React Router) was acquired by Shopify in 2022, but has promised that development will stay open-source and "independent". [ 6 ] [ 7 ] The Remix team announced at React Conf 2024 that the next major version of Remix will be merged into and released as React Router v7. [ 8 ]
This software article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/React_Router |
The reactances of synchronous machines comprise a set of characteristic constants used in the theory of synchronous machines . [ 1 ] Technically, these constants are specified in units of the electrical reactance ( ohms ), although they are typically expressed in the per-unit system and thus dimensionless . Since for practically all (except for the tiniest) machines the resistance of the coils is negligibly small in comparison to the reactance, the latter can be used instead of ( complex ) electrical impedance , simplifying the calculations. [ 2 ]
The air gap of the machines with a salient pole rotor is quite different along the pole axis (so called direct axis ) and in the orthogonal direction (so called quadrature axis ). Andre Blondel in 1899 proposed in his paper "Empirical Theory of Synchronous Generators" the two reactions theory that divided the armature magnetomotive force (MMF) into two components: the direct axis component and the quadrature axis component. The direct axis component is aligned with the magnetic axis of the rotor, while the quadrature (or transverse ) axis component is perpendicular to the direct axis. [ 3 ] The relative strengths of these two components depend on the design of the machine and the operating conditions. Since the equations naturally split into direct and quadrature components, many reactances come in pairs, one for the direct axis X d {\displaystyle X_{d}} (with the index d), one for the quadrature axis X q {\displaystyle X_{q}} (with the index q). This is often using direct-quadrature-zero transformation .
In machines with a cylindrical rotor the air gap is uniform, the reactances along the d and q axes are equal, [ 4 ] and d/q indices are frequently dropped.
The flux linkages of the generator vary with its state. Usually applied for transients after a short circuit current. Three states are considered: [ 5 ]
The sub-transient ( X d ″ {\displaystyle X''_{d}} ) and transient ( X d ′ {\displaystyle X'_{d}} ) states are cheracterized by significantly smaller reactances.
The nature of magnetic flux makes it inevitable that part of the flux deviates from the intended "useful" path. In most designs, the productive flux links the rotor and stator; the flux that links just the stator (or the rotor) to itself is useless for energy conversion and thus is considered to be wasted leakage flux ( stray flux ). The corresponding inductance is called leakage inductance . Due to the presence of air gap , the role of the leakage flux is more important in a synchronous machine in comparison to a transformer . [ 7 ]
The synchronous reactances are exhibited by the armature in the steady-state operation of the machine. [ 8 ] The three-phase system is viewed as a superposition of two: the direct one, where the maximum of the phase current is reached when the pole is oriented towards the winding and the quadrature one, that is 90° offset. [ 9 ]
The per-phase reactance can be determined in a mental experiment where the rotor poles are perfectly aligned with a specific angle of the phase field in the armature (0° for X d {\displaystyle X_{d}} , 90° for the X q {\displaystyle X_{q}} ). In this case, the reactance X will be related with the flux linkage Ψ {\displaystyle \Psi } and the phase current I as X = ω Ψ I {\displaystyle X=\omega {\frac {\Psi }{I}}} , where ω {\displaystyle \omega } is the circular frequency . [ 10 ] The conditions for this mental experiment are hard to recreate in practice, but:
Therefore, the direct synchronous reactance can be determined as a ratio of the voltage in open condition V O P E N {\displaystyle V_{OPEN}} to short-circuit current I S C {\displaystyle I_{SC}} : X d = V O P E N I S C {\displaystyle X_{d}={\frac {V_{OPEN}}{I_{SC}}}} . These current and voltage values can be obtained from the open-circuit saturation curve and the synchronous impedance curve . [ 11 ]
The synchronous reactance is a sum of the leakage reactance X l {\displaystyle X_{l}} and the reactance of the armature itself ( X a {\displaystyle X_{a}} ): X d = X l + X a {\displaystyle X_{d}=X_{l}+X_{a}} . [ 12 ]
When analyzing unbalanced three-phase systems it is common to describe a system of symmetrical components . This models the machine by three components, each with a positive sequence reactance X 1 {\displaystyle X_{1}} , a negative sequence reactance X 2 {\displaystyle X_{2}} and a zero sequence reactance X 0 {\displaystyle X_{0}} .
Das [ 13 ] identifies the following reactances: | https://en.wikipedia.org/wiki/Reactances_of_synchronous_machines |
A reactimeter is a diagnostic device used in nuclear power plants (and other nuclear applications) for measuring the reactivity of the nuclear chain reaction (in inhours ) of fissile materials as they approach criticality . [ 1 ]
This article about nuclear power and nuclear reactors for power generation is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Reactimeter |
The Reacting Gas Dynamics Laboratory (RGD) is a research facility at the Massachusetts Institute of Technology in Cambridge, Massachusetts .
The RGD researches methods for deriving high-efficiency, low-carbon energy from hydrocarbon sources or hybridized with concentrated solar thermal energy through thermochemical conversion and combustion . The RGD receives funding from a number of sources both public and private. These include the U.S. Department of Energy , the Office of Naval Research , the Air Force Office of Scientific Research , BP , ENEL , Bosch GmbH , and the Ford Motor Company . The lab also is in collaborations with the King Fahd University of Petroleum and Minerals , the King Abdullah University of Science and Technology , and Masdar in Abu Dhabi , as well as other departments and faculty within MIT. [ 1 ]
Specifically, the lab develops, validates and applies simulation techniques, from the submicron scale to full system scale , to engineer low- CO 2 energy systems. Examples of the simulation work include studies of thermoacoustic instability and multiphysics multiscale simulations of entrained flow gasification . [ 2 ] [ 3 ] These simulations are supported by high-performance computing systems and high-resolution optical diagnostics. The long-term goals of the lab include innovation in clean combustion for propulsion and power, gasification for power and biofuel production, and oxy-combustion and electrochemical /thermochemical conversion in ion transport membrane reactors and high-temperature fuel cells . [ 1 ]
The chief faculty director of the laboratory is Prof. Ahmed Ghoniem of MIT's Mechanical Engineering Department. [ 4 ] | https://en.wikipedia.org/wiki/Reacting_Gas_Dynamics_Laboratory |
As described by the third of Newton's laws of motion of classical mechanics , all forces occur in pairs such that if one object exerts a force on another object, then the second object exerts an equal and opposite reaction force on the first. [ 1 ] [ 2 ] The third law is also more generally stated as: "To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts." [ 3 ] The attribution of which of the two forces is the action and which is the reaction is arbitrary. Either of the two can be considered the action, while the other is its associated reaction.
When something is exerting force on the ground, the ground will push back with equal force in the opposite direction. In certain fields of applied physics, such as biomechanics , this force by the ground is called ' ground reaction force '; the force by the object on the ground is viewed as the 'action'.
When someone wants to jump, he or she exerts additional downward force on the ground ('action'). Simultaneously, the ground exerts upward force on the person ('reaction'). If this upward force is greater than the person's weight, this will result in upward acceleration. When these forces are perpendicular to the ground, they are also called a normal force .
Likewise, the spinning wheels of a vehicle attempt to slide backward across the ground. If the ground is not too slippery, this results in a pair of friction forces: the 'action' by the wheel on the ground in backward direction, and the 'reaction' by the ground on the wheel in forward direction. This forward force propels the vehicle.
The Earth , among other planets , orbits the Sun because the Sun exerts a gravitational pull that acts as a centripetal force , holding the Earth to it, which would otherwise go shooting off into space. If the Sun's pull is considered an action, then Earth simultaneously exerts a reaction as a gravitational pull on the Sun. Earth's pull has the same amplitude as the Sun but in the opposite direction. Since the Sun's mass is so much larger than Earth's, the Sun does not generally appear to react to the pull of Earth, but in fact it does, as demonstrated in the animation (not to precise scale). A correct way of describing the combined motion of both objects (ignoring all other celestial bodies for the moment) is to say that they both orbit around the center of mass , referred to in astronomy as the barycenter , of the combined system.
Any mass on earth is pulled down by the gravitational force of the earth; this force is also called its weight . The corresponding 'reaction' is the gravitational force that mass exerts on the planet.
If the object is supported so that it remains at rest, for instance by a cable from which it is hanging, or by a surface underneath, or by a liquid on which it is floating, there is also a support force in upward direction ( tension force, normal force , buoyant force, respectively). This support force is an 'equal and opposite' force; we know this not because of Newton's third law, but because the object remains at rest, so that the forces must be balanced.
To this support force there is also a 'reaction': the object pulls down on the supporting cable, or pushes down on the supporting surface or liquid. In this case, there are therefore four forces of equal magnitude:
Forces F 1 and F 2 are equal, due to Newton's third law; the same is true for forces F 3 and F 4 .
Forces F 1 and F 3 are equal if and only if the object is in equilibrium, and no other forces are applied. (This has nothing to do with Newton's third law.)
If a mass is hanging from a spring, the same considerations apply as before. However, if this system is then perturbed (e.g., the mass is given a slight kick upwards or downwards, say), the mass starts to oscillate up and down. Because of these accelerations (and subsequent decelerations), we conclude from Newton's second law that a net force is responsible for the observed change in velocity. The gravitational force pulling down on the mass is no longer equal to the upward elastic force of the spring. In the terminology of the previous section, F 1 and F 3 are no longer equal.
However, it is still true that F 1 = F 2 and F 3 = F 4 , as this is required by Newton's third law.
The terms 'action' and 'reaction' have the misleading suggestion of causality , as if the 'action' is the cause and 'reaction' is the effect. It is therefore easy to think of the second force as being there because of the first, and even happening some time after the first. This is incorrect; the forces are perfectly simultaneous, and are there for the same reason. [ 4 ]
When the forces are caused by a person's volition (e.g. a soccer player kicks a ball), this volitional cause often leads to an asymmetric interpretation, where the force by the player on the ball is considered the 'action' and the force by the ball on the player, the 'reaction'. But physically, the situation is symmetric. The forces on ball and player are both explained by their nearness, which results in a pair of contact forces (ultimately due to electric repulsion). That this nearness is caused by a decision of the player has no bearing on the physical analysis. As far as the physics is concerned, the labels 'action' and 'reaction' can be flipped. [ 4 ]
One problem frequently observed by physics educators is that students tend to apply Newton's third law to pairs of 'equal and opposite' forces acting on the same object. [ 5 ] [ 6 ] [ 7 ] This is incorrect; the third law refers to forces on two different objects. In contrast, a book lying on a table is subject to a downward gravitational force (exerted by the earth) and to an upward normal force by the table, both forces acting on the same book. Since the book is not accelerating, these forces must be exactly balanced, according to Newton's second law. They are therefore 'equal and opposite', yet they are acting on the same object, hence they are not action-reaction forces in the sense of Newton's third law. The actual action-reaction forces in the sense of Newton's third law are the weight of the book (the attraction of the Earth on the book) and the book's upward gravitational force on the earth. The book also pushes down on the table and the table pushes upwards on the book.
Moreover, the forces acting on the book are not always equally strong; they will be different if the book is pushed down by a third force, or if the table is slanted, or if the table-and-book system is in an accelerating elevator. The case of any number of forces acting on the same object is covered by considering the sum of all forces.
A possible cause of this problem is that the third law is often stated in an abbreviated form: For every action there is an equal and opposite reaction, [ 8 ] without the details, namely that these forces act on two different objects. Moreover, there is a causal connection between the weight of something and the normal force: if an object had no weight, it would not experience support force from the table, and the weight dictates how strong the support force will be. This causal relationship is not due to the third law but to other physical relations in the system.
Another common mistake is to state that "the centrifugal force that an object experiences is the reaction to the centripetal force on that object." [ 9 ] [ 10 ]
If an object were simultaneously subject to both a centripetal force and an equal and opposite centrifugal force , the resultant force would vanish and the object could not experience a circular motion. The centrifugal force is sometimes called a fictitious force or pseudo force, to underscore the fact that such a force only appears when calculations or measurements are conducted in non-inertial reference frames. [ 11 ] | https://en.wikipedia.org/wiki/Reaction_(physics) |
The Reaction Research Society (not to be confused with UK-based Reaction Engines ) is the oldest continuously operating amateur experimental rocket group in the United States. Founded by George James on 6 January 1943, originally as the Southern California Rocket Society , the organization's name was changed to the Glendale Rocket Society two months later. Ultimately, the society changed its name to the Reaction Research Society around 1946 to encompass more aspects of propulsion beyond rocketry, however most research and experimentation at the RRS has been with solid, liquid and hybrid rocketry.
The RRS is an educational non-profit group in California based in Los Angeles. The RRS has owned and operated a private testing site, the Mojave Test Area (MTA), north of Edwards Air Force Base and California City in the Mojave desert since 1955.
On September 20, 2003, The Reaction Research Society was part of a team that "conducted the first known flight test of a powered liquid-propellant aerospike engine ." [ 1 ]
This article about an organization in the United States is a stub . You can help Wikipedia by expanding it .
This space - or spaceflight -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Reaction_Research_Society |
Reaction bonded silicon carbide , also known as siliconized silicon carbide or SiSiC , is a type of silicon carbide that is manufactured by a chemical reaction between porous carbon or graphite with molten silicon . Due to the left over traces of silicon, reaction bonded silicon carbide is often referred to as siliconized silicon carbide, or its abbreviation SiSiC. [ 1 ]
If bulk silicon carbide is produced by sintering of silicon carbide powder, it usually contains traces of chemicals called sintering aids , which are added to support the sintering process by allowing lower sintering temperatures. This type of silicon carbide is often referred to as sintered silicon carbide , or abbreviated to SSiC.
The silicon carbide powder is gained from silicon carbide produced as described in the article silicon carbide .
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Reaction_bonded_silicon_carbide |
A reaction calorimeter is a calorimeter that measures the amount of energy released (in exothermic reactions) or absorbed (in endothermic reactions) by a chemical reaction .
Heat flow calorimetry measures the heat flowing across the reactor wall and quantifies this in relation to other energy flows within the reactor.
where:
Heat flow calorimetry allows the user to measure heat while the process temperature remains under control. While the driving force T r − T j is measured with a relatively high resolution, the overall heat transfer coefficient U or the calibration factor UA is determined by calibration before and after the reaction takes place. These factors are affected by the product composition, process temperature, agitation rate, viscosity , and liquid level. [ 1 ]
In heat balance calorimetry, the cooling/heating jacket controls the temperature of the process. Heat is measured by monitoring the heat gained or lost by the heat transfer fluid.
where:
Heat balance calorimetry is considered an effective method for measuring heat, as it involves quantifying the heat entering and leaving the system through the heating/cooling jacket using the heat transfer fluid, whose properties are well known.
This method effectively measures heat loss or gain, circumventing many calibration issues associated with heat flow and power compensation calorimetry. However, it is less effective in traditional batch vessels, where significant heat shifts in the cooling/heating jacket can obscure the process's heat signal. [ 2 ]
Power compensation calorimetry is a variation of the heat flow technique. This method utilizes a cooling jacket operating at constant flow and temperature. The process temperature is regulated by adjusting the power of an electrical heater. At the start of the experiment, the electrical heat and cooling power are balanced. As the process's heat load changes, the electrical power is adjusted to maintain the desired process temperature. [ 3 ] The heat liberated or absorbed by the process is determined from the difference between the initial electrical power and the electrical power required at the time of measurement. While power compensation calorimetry requires less preparation than heat flow calorimetry, it faces similar limitations. Changes in product composition, liquid level, process temperature, agitation, or viscosity can impact the instrument's calibration. Additionally, the presence of an electrical heating element is not optimal for process operations. Another limitation of this method is that the maximum heat it can measure is equal to the initial electrical power applied to the heater. [ 4 ]
where:
Constant flux heating and cooling jackets use variable geometry cooling jackets and can operate with cooling jackets at a substantially constant temperature. These reaction calorimeters are simpler to use and are much more tolerant of changes in the process conditions. [ 5 ]
Constant flux calorimetry is an advanced temperature control mechanism used to generate accurate calorimetry. It operates by controlling the jacket area of a laboratory reactor while maintaining a constant inlet temperature of the thermal fluid . This method allows for precise temperature control, even during strongly exothermic or endothermic events, as additional cooling can be achieved by increasing the area over which heat is exchanged.
This system is generally more accurate than heat balance calorimetry, as changes in the delta temperature (T out - T in ) are magnified by keeping the fluid flow as low as possible.
One of the main advantages of constant flux calorimetry is the ability to dynamically measure heat transfer coefficient (U). According to the heat balance equation:
From the heat flow equation that
These equations can be rearranged to:
This allows for the monitoring of U as a function of time.
Different types of reactors in chemistry have different applications. There are batch reactor and flow reactor .
Batch reactor
In traditional calorimeters, batch reactor are used. In the batch process, one reactant is added continuously in small amounts, to achieve complete conversion of the reaction. [ 6 ] Batch calorimeters operating microreactors are still considered the state-of-the-art. [ 7 ] Microreactors gave high surface-to-volumn ratio, which benefits mixing reactants and enhances heat transfer. This technology enables extended reaction processes, higher yield, conversion rate, selectivity, and automation.
Flow reactor
A continuous flow calorimeter is a similar instrument used to obtain thermodynamic information with continuous process. Continuous flow calorimeters offer significant advantages in the study of continuous processes, particularly in industrial applications where consistent and reproducible reaction conditions are critical. This approach results in more controllable residence times, substance concentrations, and temperature. This increased in control can also help manage risk and be used as scale-up factor. [ 8 ]
It can record an axial temperature profile along the flow reactor , allowing the determination of the specific heat of reaction through heat balances and segmental dynamic parameters. These instruments can provide detailed insights into the thermodynamics and kinetics of reactions under steady-state conditions. The use of precise dosing systems ensures accurate control over reactant flow rates, while preheaters can stabilize the temperature of incoming reactants, minimizing temperature fluctuations that could affect the reaction rate and selectivity.
Continuous flow calorimeters also allow for the study of reaction mechanisms and the identification of intermediate species. By analyzing the heat flow data in conjunction with other analytical techniques, such as spectroscopy or chromatography, researchers can gain a comprehensive understanding of the reaction pathways and the factors influencing selectivity and yield. This information is invaluable for developing efficient and sustainable chemical processes, reducing waste, and minimizing energy consumption. | https://en.wikipedia.org/wiki/Reaction_calorimeter |
In chemistry , a reaction coordinate [ 1 ] is an abstract one-dimensional coordinate chosen to represent progress along a reaction pathway. Where possible it is usually a geometric parameter that changes during the conversion of one or more molecular entities , such as bond length or bond angle . For example, in the homolytic dissociation of molecular hydrogen , an apt choice would be the coordinate corresponding to the bond length . Non-geometric parameters such as bond order are also used, but such direct representation of the reaction process can be difficult, especially for more complex reactions.
In computer simulations collective variables are employed for a target-oriented sampling approach. Plain simulations fail to capture so called rare events, because they are not feasible to occur in realistic computation times. This often stems from to high energy barriers separating the reactants from products, or any two states of interest. A collective variable is as the name states only a set, a collection, of individual variables ( x i ) contracted into one:
with A a transformation matrix. The collective variables reduce many variables to a lower-dimensional set of variables, that still describe the crucial characteristics of the system. Many collective variables than span the reaction coordinate with a continuous function ξ :
An example is the complexation of two molecules. The distance between both of them is the collective variable, where the atomic positions are the individual variables x i and the reaction coordinate ξ would be the full path of association and dissociation. By applying a bias to the collective variables the simulation can be 'steered' towards the desired destination. These kinds of simulations are called enhanced simulations .
Special collective variables that help to distinguish reactants from products are also known as order parameters , terminology that originates in work on phase transitions . [ 3 ] Reaction coordinates are special order parameters that describe the entire pathway from reactants through transition states and on to products. Depending on the application, reaction coordinates may be defined by using chemically intuitive variables like bond lengths, or splitting probabilities (also called committors), or using the eigenfunction corresponding to the reactant-to-product transition as a progress coordinate. [ 4 ]
A reaction coordinate parameterizes reaction process at the level of the molecular entities involved. It differs from extent of reaction , which measures reaction progress in terms of the composition of the reaction system.
(Free) energy is often plotted against reaction coordinate(s) to demonstrate in schematic form the potential energy profile (an intersection of a potential energy surface ) associated with the reaction.
In the formalism of transition-state theory the reaction coordinate for each reaction step is one of a set of curvilinear coordinates obtained from the conventional coordinates for the reactants, and leads smoothly among configurations, from reactants to products via the transition state . It is typically chosen to follow the path defined by potential energy gradient – shallowest ascent/steepest descent – from reactants to products. [ 1 ]
This quantum chemistry -related article is a stub . You can help Wikipedia by expanding it .
This molecular physics –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Reaction_coordinate |
Reaction dynamics is a field within physical chemistry , studying why chemical reactions occur, how to predict their behavior, and how to control them. It is closely related to chemical kinetics , but is concerned with individual chemical events on atomic length scales and over very brief time periods. [ 1 ] It considers state-to-state kinetics between reactant and product molecules in specific quantum states , and how energy is distributed between translational, vibrational , rotational , and electronic modes. [ 2 ]
Experimental methods of reaction dynamics probe the chemical physics associated with molecular collisions. They include crossed molecular beam and infrared chemiluminescence experiments, both recognized by the 1986 Nobel Prize in Chemistry awarded to Dudley Herschbach , Yuan T. Lee , and John C. Polanyi "for their contributions concerning the dynamics of chemical elementary processes", [ 3 ] In the crossed beam method used by Herschbach and Lee, narrow beams of reactant molecules in selected quantum states are allowed to react in order to determine the reaction probability as a function of such variables as the translational, vibrational and rotational energy of the reactant molecules and their angle of approach. In contrast the method of Polanyi measures vibrational energy of the products by detecting the infrared chemiluminescence emitted by vibrationally excited molecules, in some cases for reactants in defined energy states. [ 2 ]
Spectroscopic observation of reaction dynamics on the shortest time scales is known as femtochemistry , since the typical times studied are of the order of 1 femto second = 10 −15 s. This subject has been recognized by the award of the 1999 Nobel Prize in Chemistry to Ahmed Zewail .
In addition, theoretical studies of reaction dynamics involve calculating the potential energy surface for a reaction as a function of nuclear positions, and then calculating the trajectory of a point on this surface representing the state of the system. A correction can be applied to include the effect of quantum tunnelling through the activation energy barrier, especially for the movement of hydrogen atoms. [ 2 ]
Steinfeld J.I., Francisco J.S. and Hase W.L. Chemical Kinetics and Dynamics (2nd ed., Prentice-Hall 1999) chaps.6-13 ISBN 0-13-737123-3 | https://en.wikipedia.org/wiki/Reaction_dynamics |
A reaction engine is an engine or motor that produces thrust by expelling reaction mass (reaction propulsion), [ 1 ] in accordance with Newton's third law of motion . This law of motion is commonly paraphrased as: "For every action force there is an equal, but opposite, reaction force."
Examples include jet engines , rocket engines , pump-jets , and more uncommon variations such as Hall effect thrusters , ion drives , mass drivers , and nuclear pulse propulsion .
The discovery of the reaction engine has been attributed to the Romanian inventor Alexandru Ciurcu and to the French journalist Just Buisson [ fr ; ro ] . [ 2 ]
For all reaction engines that carry on-board propellant (such as rocket engines and electric propulsion drives) some energy must go into accelerating the reaction mass. Every engine wastes some energy, but even assuming 100% efficiency, the engine needs energy amounting to
(where M is the mass of propellent expended and V e {\displaystyle V_{e}} is the exhaust velocity), which is simply the energy to accelerate the exhaust.
Comparing the rocket equation (which shows how much energy ends up in the final vehicle) and the above equation (which shows the total energy required) shows that even with 100% engine efficiency, certainly not all energy supplied ends up in the vehicle – some of it, indeed usually most of it, ends up as kinetic energy of the exhaust.
If the specific impulse ( I s p {\displaystyle I_{sp}} ) is fixed, for a mission delta-v, there is a particular I s p {\displaystyle I_{sp}} that minimises the overall energy used by the rocket. This comes to an exhaust velocity of about two-thirds of the mission delta-v (see the energy computed from the rocket equation ). Drives with a specific impulse that is both high and fixed such as Ion thrusters have exhaust velocities that can be enormously higher than this ideal, and thus end up powersource limited and give very low thrust. Where the vehicle performance is power limited, e.g. if solar power or nuclear power is used, then in the case of a large v e {\displaystyle v_{e}} the maximum acceleration is inversely proportional to it. Hence the time to reach a required delta-v is proportional to v e {\displaystyle v_{e}} . Thus the latter should not be too large.
On the other hand, if the exhaust velocity can be made to vary so that at each instant it is equal and opposite to the vehicle velocity then the absolute minimum energy usage is achieved. When this is achieved, the exhaust stops in space [ NB 1 ] and has no kinetic energy; and the propulsive efficiency is 100% all the energy ends up in the vehicle (in principle such a drive would be 100% efficient, in practice there would be thermal losses from within the drive system and residual heat in the exhaust). However, in most cases this uses an impractical quantity of propellant, but is a useful theoretical consideration.
Some drives (such as VASIMR or electrodeless plasma thruster ) actually can significantly vary their exhaust velocity. This can help reduce propellant usage and improve acceleration at different stages of the flight. However the best energetic performance and acceleration is still obtained when the exhaust velocity is close to the vehicle speed. Proposed ion and plasma drives usually have exhaust velocities enormously higher than that ideal (in the case of VASIMR the lowest quoted speed is around 15 km/s compared to a mission delta-v from high Earth orbit to Mars of about 4 km/s ).
For a mission, for example, when launching from or landing on a planet, the effects of gravitational attraction and any atmospheric drag must be overcome by using fuel. It is typical to combine the effects of these and other effects into an effective mission delta-v . For example, a launch mission to low Earth orbit requires about 9.3–10 km/s delta-v. These mission delta-vs are typically numerically integrated on a computer.
All reaction engines lose some energy, mostly as heat.
Different reaction engines have different efficiencies and losses. For example, rocket engines can be up to 60–70% energy efficient in terms of accelerating the propellant. The rest is lost as heat and thermal radiation, primarily in the exhaust.
Reaction engines are more energy efficient when they emit their reaction mass when the vehicle is travelling at high speed.
This is because the useful mechanical energy generated is simply force times distance, and when a thrust force is generated while the vehicle moves, then:
where F is the force and d is the distance moved.
Dividing by length of time of motion we get:
Hence:
where P is the useful power and v is the speed.
Hence, v should be as high as possible, and a stationary engine does no useful work. [ NB 2 ]
Exhausting the entire usable propellant of a spacecraft through the engines in a straight line in free space would produce a net velocity change to the vehicle; this number is termed delta-v ( Δ v {\displaystyle \Delta v} ).
If the exhaust velocity is constant then the total Δ v {\displaystyle \Delta v} of a vehicle can be calculated using the rocket equation, where M is the mass of propellant, P is the mass of the payload (including the rocket structure), and v e {\displaystyle v_{e}} is the velocity of the rocket exhaust . This is known as the Tsiolkovsky rocket equation :
For historical reasons, as discussed above, v e {\displaystyle v_{e}} is sometimes written as
where I sp {\displaystyle I_{\text{sp}}} is the specific impulse of the rocket, measured in seconds, and g 0 {\displaystyle g_{0}} is the gravitational acceleration at sea level.
For a high delta-v mission, the majority of the spacecraft's mass needs to be reaction mass. Because a rocket must carry all of its reaction mass, most of the initially-expended reaction mass goes towards accelerating reaction mass rather than payload. If the rocket has a payload of mass P , the spacecraft needs to change its velocity by Δ v {\displaystyle \Delta v} , and the rocket engine has exhaust velocity v e , then the reaction mass M which is needed can be calculated using the rocket equation and the formula for I sp {\displaystyle I_{\text{sp}}} :
For Δ v {\displaystyle \Delta v} much smaller than v e , this equation is roughly linear , and little reaction mass is needed. If Δ v {\displaystyle \Delta v} is comparable to v e , then there needs to be about twice as much fuel as combined payload and structure (which includes engines, fuel tanks, and so on). Beyond this, the growth is exponential; speeds much higher than the exhaust velocity require very high ratios of fuel mass to payload and structural mass.
For a mission, for example, when launching from or landing on a planet, the effects of gravitational attraction and any atmospheric drag must be overcome by using fuel. It is typical to combine the effects of these and other effects into an effective mission delta-v . For example, a launch mission to low Earth orbit requires about 9.3–10 km/s delta-v. These mission delta-vs are typically numerically integrated on a computer.
Some effects such as Oberth effect can only be significantly utilised by high thrust engines such as rockets; i.e., engines that can produce a high g-force (thrust per unit mass, equal to delta-v per unit time).
In the ideal case m 1 {\displaystyle m_{1}} is useful payload and m 0 − m 1 {\displaystyle m_{0}-m_{1}} is reaction mass (this corresponds to empty tanks having no mass, etc.). The energy required can simply be computed as
This corresponds to the kinetic energy the expelled reaction mass would have at a speed equal to the exhaust speed. If the reaction mass had to be accelerated from zero speed to the exhaust speed, all energy produced would go into the reaction mass and nothing would be left for kinetic energy gain by the rocket and payload. However, if the rocket already moves and accelerates (the reaction mass is expelled in the direction opposite to the direction in which the rocket moves) less kinetic energy is added to the reaction mass. To see this, if, for example, v e {\displaystyle v_{e}} =10 km/s and the speed of the rocket is 3 km/s, then the speed of a small amount of expended reaction mass changes from 3 km/s forwards to 7 km/s rearwards. Thus, although the energy required is 50 MJ per kg reaction mass, only 20 MJ is used for the increase in speed of the reaction mass. The remaining 30 MJ is the increase of the kinetic energy of the rocket and payload.
In general:
Thus the specific energy gain of the rocket in any small time interval is the energy gain of the rocket including the remaining fuel, divided by its mass, where the energy gain is equal to the energy produced by the fuel minus the energy gain of the reaction mass. The larger the speed of the rocket, the smaller the energy gain of the reaction mass; if the rocket speed is more than half of the exhaust speed the reaction mass even loses energy on being expelled, to the benefit of the energy gain of the rocket; the larger the speed of the rocket, the larger the energy loss of the reaction mass.
We have
where ϵ {\displaystyle \epsilon } is the specific energy of the rocket (potential plus kinetic energy) and Δ v {\displaystyle \Delta v} is a separate variable, not just the change in v {\displaystyle v} . In the case of using the rocket for deceleration; i.e., expelling reaction mass in the direction of the velocity, v {\displaystyle v} should be taken negative.
The formula is for the ideal case again, with no energy lost on heat, etc. The latter causes a reduction of thrust, so it is a disadvantage even when the objective is to lose energy (deceleration).
If the energy is produced by the mass itself, as in a chemical rocket, the fuel value has to be v e 2 / 2 {\displaystyle \scriptstyle {v_{\text{e}}^{2}/2}} , where for the fuel value also the mass of the oxidizer has to be taken into account. A typical value is v e {\displaystyle v_{\text{e}}} = 4.5 km/s, corresponding to a fuel value of 10.1 MJ/kg. The actual fuel value is higher, but much of the energy is lost as waste heat in the exhaust that the nozzle was unable to extract.
The required energy E {\displaystyle E} is
Conclusions:
These results apply for a fixed exhaust speed.
Due to the Oberth effect and starting from a nonzero speed, the required potential energy needed from the propellant may be less than the increase in energy in the vehicle and payload. This can be the case when the reaction mass has a lower speed after being expelled than before – rockets are able to liberate some or all of the initial kinetic energy of the propellant.
Also, for a given objective such as moving from one orbit to another, the required Δ v {\displaystyle \Delta v} may depend greatly on the rate at which the engine can produce Δ v {\displaystyle \Delta v} and maneuvers may even be impossible if that rate is too low. For example, a launch to Low Earth orbit (LEO) normally requires a Δ v {\displaystyle \Delta v} of ca. 9.5 km/s (mostly for the speed to be acquired), but if the engine could produce Δ v {\displaystyle \Delta v} at a rate of only slightly more than g , it would be a slow launch requiring altogether a very large Δ v {\displaystyle \Delta v} (think of hovering without making any progress in speed or altitude, it would cost a Δ v {\displaystyle \Delta v} of 9.8 m/s each second). If the possible rate is only g {\displaystyle g} or less, the maneuver can not be carried out at all with this engine.
The power is given by
where F {\displaystyle F} is the thrust and a {\displaystyle a} the acceleration due to it. Thus the theoretically possible thrust per unit power is 2 divided by the specific impulse in m/s. The thrust efficiency is the actual thrust as percentage of this.
If, e.g., solar power is used, this restricts a {\displaystyle a} ; in the case of a large v e {\displaystyle v_{\text{e}}} the possible acceleration is inversely proportional to it, hence the time to reach a required delta-v is proportional to v e {\displaystyle v_{\text{e}}} ; with 100% efficiency:
Examples:
Thus v e {\displaystyle v_{\text{e}}} should not be too large.
The power to thrust ratio is simply: [ 3 ]
Thus for any vehicle power P, the thrust that may be provided is:
Suppose a 10,000 kg space probe will be sent to Mars. The required Δ v {\displaystyle \Delta v} from LEO is approximately 3000 m/s, using a Hohmann transfer orbit . For the sake of argument, assume the following thrusters are options to be used:
Observe that the more fuel-efficient engines can use far less fuel; their mass is almost negligible (relative to the mass of the payload and the engine itself) for some of the engines. However, these require a large total amount of energy. For Earth launch, engines require a thrust to weight ratio of more than one. To do this with the ion or more theoretical electrical drives, the engine would have to be supplied with one to several gigawatts of power, equivalent to a major metropolitan generating station . From the table it can be seen that this is clearly impractical with current power sources.
Alternative approaches include some forms of laser propulsion , where the reaction mass does not provide the energy required to accelerate it, with the energy instead being provided from an external laser or other beam-powered propulsion system. Small models of some of these concepts have flown, although the engineering problems are complex and the ground-based power systems are not a solved problem.
Instead, a much smaller, less powerful generator may be included which will take much longer to generate the total energy needed. This lower power is only sufficient to accelerate a tiny amount of fuel per second, and would be insufficient for launching from Earth. However, over long periods in orbit where there is no friction, the velocity will be finally achieved. For example, it took the SMART-1 more than a year to reach the Moon, whereas with a chemical rocket it takes a few days. Because the ion drive needs much less fuel, the total launched mass is usually lower, which typically results in a lower overall cost, but the journey takes longer.
Mission planning therefore frequently involves adjusting and choosing the propulsion system so as to minimise the total cost of the project, and can involve trading off launch costs and mission duration against payload fraction. | https://en.wikipedia.org/wiki/Reaction_engine |
The reaction field method is used in molecular simulations to simulate the effect of long-range dipole-dipole interactions for simulations with periodic boundary conditions . Around each molecule there is a 'cavity' or sphere within which the Coulomb interactions are treated explicitly. Outside of this cavity the medium is assumed to have a uniform dielectric constant. The molecule induces polarization in this media which in turn creates a reaction field, sometimes called the Onsager reaction field . Although Onsager 's name is often attached to the technique, because he considered such a geometry in his theory of the dielectric constant, [ 1 ] the method was first introduced by Barker and Watts in 1973. [ 2 ] [ 3 ]
The effective pairwise potential becomes:
where r c {\displaystyle r_{c}} is the cut-off radius.
The reaction field in the center of the cavity is given by :
where M → = ∑ μ i {\displaystyle {\vec {M}}=\sum \mu _{i}} is the total dipole moment of all the molecules in the cavity. The contribution to the potential energy of the molecule i {\displaystyle i} at the center of the cavity is − 1 / 2 μ i ⋅ E R F {\displaystyle -1/2\mu _{i}\cdot E_{RF}} and the torque on molecule i {\displaystyle i} is simply μ i × E R F {\displaystyle \mu _{i}\times E_{RF}} .
When a molecule enters or leaves the sphere defined by the cut-off radius, there is a discontinuous jump in energy. [ 4 ] When all of these jumps in energy are summed, they do not exactly cancel, leading to poor energy conservation, a deficiency found whenever a spherical cut-off is used. The situation can be improved by tapering the potential energy function to zero near the cut-off radius. Beyond a certain radius r t {\displaystyle r_{t}} the potential is multiplied by a tapering function f ( r ) {\displaystyle f(r)} . A simple choice is linear tapering with r t = .95 r c {\displaystyle r_{t}=.95r_{c}} , although better results may be found with more sophisticated tapering functions.
Another potential difficulty of the reaction field method is that the dielectric constant must be known a priori. However, it turns out that in most cases dynamical properties are fairly insensitive to the choice of ε R F {\displaystyle \varepsilon _{RF}} . It can be put in by hand, or calculated approximately using any of a number of well-known relations between the dipole fluctuations inside the simulation box and the macroscopic dielectric constant. [ 4 ]
Another possible modification is to take into account the finite time required for the reaction field to respond to changes in the cavity. This "delayed reaction field method" was investigated by van Gunsteren, Berendsen and Rullmann in 1978. [ 5 ] It was found to give better results—this makes sense, as without taking into account the delay, the reaction field is overestimated. However, the delayed method has additional difficulties with energy conservation and thus is not suitable for simulating an NVE ensemble.
The reaction field method is an alternative to the popular technique of Ewald summation . Today, Ewald summation is the usual technique of choice, but for many quantities of interest both techniques yield equivalent results. For example, in Monte Carlo simulations of liquid crystals, (using both the hard spherocylinder [ 6 ] and Gay-Berne models [ 7 ] ) the results from the reaction field method and Ewald summation are consistent. However, the reaction field presents a considerable reduction in the computer time required. The reaction field should be applied carefully, and becomes complicated or impossible to implement for non-isotropic systems, such as systems dominated by large biomolecules or systems with liquid-vapour or liquid-solid coexistence. [ 8 ]
In section 5.5.5 of his book, Allen [ 4 ] compares the reaction field with other methods, focusing on the simulation of the Stockmayer system (the simplest model for a dipolar fluid, such as water). The work of Adams, et al. (1979) showed that the reaction field produces results with thermodynamic quantities (volume, pressure and temperature) which are in good agreement with other methods, although pressure was slightly higher with the reaction field method compared to the Ewald-Kornfeld method (1.69 vs 1.52). The results show that macroscopic thermodynamic properties do not depend heavily on how long-range forces are treated. Similarly, single particle correlation functions do not depend heavily on the method employed. Several other results also show that the dielectric constant ϵ {\displaystyle \epsilon } can be well estimated with either the reaction field or a lattice summation technique. [ 4 ] | https://en.wikipedia.org/wiki/Reaction_field_method |
A reaction inhibitor is a substance that decreases the rate of, or prevents, a chemical reaction .
A catalyst or an Enzyme activator , in contrast, is a substance that increases the rate of a chemical reaction.
2 H 2 O 2 → 2 H 2 O + O 2 , which is catalyzed by heat, light, and impurities. [ 2 ]
An inhibitor can reduce the effectiveness of a catalyst in a catalysed reaction (either a non-biological catalyst or an enzyme ). E.g., if a compound is so similar to (one of) the reactants that it can bind to the active site of a catalyst but does not undergo a catalytic reaction then that catalyst molecule cannot perform its job because the active site is occupied. When the inhibitor is released, the catalyst is again available for reaction.
Inhibition should be distinguished from catalyst poisoning. An inhibitor only hinders the working of a catalyst without changing it, whilst in catalyst poisoning the catalyst undergoes a chemical reaction that is irreversible in the environment in question (the active catalyst may only be regained by a separate process).
Index inhibitors or simplified as inhibitor predictably inhibit metabolism via a given pathway and are commonly used in prospective clinical drug-drug interaction studies. [ 3 ]
Inhibitors of CYP can be classified by their potency , such as:
This catalysis article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Reaction_inhibitor |
In chemistry , a reaction intermediate , or intermediate , is a molecular entity arising within the sequence of a stepwise chemical reaction . It is formed as the reaction product of an elementary step , from the reactants and/or preceding intermediates, but is consumed in a later step. It does not appear in the chemical equation for the overall reaction. [ 1 ]
For example, consider this hypothetical reaction:
If this overall reaction comprises two elementary steps thus:
then X is a reaction intermediate.
The phrase reaction intermediate is often abbreviated to the single word intermediate , and this is IUPAC 's preferred form of the term. [ 2 ] But this shorter form has other uses. It often refers to reactive intermediates . It is also used more widely for chemicals such as cumene which are traded within the chemical industry but are not generally of value outside it.
The IUPAC Gold Book defines [ 3 ] an intermediate as a compound that has a lifetime greater than a molecular vibration , is formed (directly or indirectly) from the reactants, and reacts further to give (either directly or indirectly) the products of a chemical reaction . The lifetime condition distinguishes true, chemically distinct intermediates, both from vibrational states and from transition states (which, by definition, have lifetimes close to that of molecular vibration).
The different steps of a multi-step reaction often differ widely in their reaction rates . Where the difference is significant, an intermediate consumed more quickly than another may be described as a relative intermediate. A reactive intermediate is one which due to its short lifetime does not remain in the product mixture. Reactive intermediates are usually high-energy, are unstable and are seldom isolated.
Cations , often carbocations , serve as intermediates in various types of reactions to synthesize new compounds.
Carbocations are formed in two major alkene addition reactions . In an HX addition reaction, the pi bond of an alkene acts as a nucleophile and bonds with the proton of an HX molecule, where the X is a halogen atom . This forms a carbocation intermediate, and the X then bonds to the positive carbon that is available, as in the following two-step reaction. [ 4 ]
Similarly, in an H 2 O addition reaction, the pi bond of an alkene acts as a nucleophile and bonds with the proton of an [H 3 O] + molecule. This forms a carbocation intermediate (and an H 2 O atom); the oxygen atom of H 2 O then bonds with the positive carbon of the intermediate. The oxygen finally deprotonates to form a final alcohol product, as follows. [ 4 ]
Nucleophilic substitution reactions occur when a nucleophilic molecule attacks a positive or partially positive electrophilic center by breaking and creating a new bond. S N 1 and S N 2 are two different mechanisms for nucleophilic substitution, and S N 1 involves a carbocation intermediate. In S N 1, a leaving group is broken off to create a carbocation reaction intermediate. Then, a nucleophile attacks and forms a new bond with the carbocation intermediate to form the final, substituted product, as shown in the reaction of 2-bromo-2-methylpropane to form 2-methyl-2-propanol . [ 4 ]
In this reaction, (CH 3 ) 3 C + is the formed carbocation intermediate to form the alcohol product.
β-elimination or elimination reactions occur through the loss of a substituent leaving group and loss of a proton to form a pi bond. E1 and E2 are two different mechanisms for elimination reactions, and E1 involves a carbocation intermediate. In E1, a leaving group detaches from a carbon to form a carbocation reaction intermediate. Then, a solvent removes a proton, but the electrons used to form the proton bond form a pi bond, as shown in the pictured reaction on the right. [ 4 ]
A carboanion is an organic molecule where a carbon atom is not electron deficient but contain an overall negative charge. Carboanions are strong nucleophiles, which can be used to extend an alkene's carbon backbone in the synthesis reaction shown below. [ 5 ]
The alkyne carbanion, CHC − , is a reaction intermediate in this reaction. [ 4 ]
Radicals are highly reactive and short-lived, as they have an unpaired electron which makes them extremely unstable. Radicals often react with hydrogens attached to carbon molecules, effectively making the carbon a radical while stabilizing the former radical in a process called propagation. The formed product, a carbon radical, can react with non-radical molecule to continue propagation or react with another radical to form a new stable molecule such as a longer carbon chain or an alkyl halide. [ 4 ]
The example below of methane chlorination shows a multi-step reaction involving radicals.
Methane chlorination is a chain reaction. If only the products and reactants are analyzed, the result is:
However, this reaction has 3 intermediate reactants which are formed during a sequence of 4 irreversible second order reactions until we arrive at the final product. This is why it is called a chain reaction. Following only the carbon containing species in series:
Reactants: CH 4 + 4 Cl 2
Products: CCl 4 + 4 HCl
The other species are reaction intermediates: CH 3 Cl, CH 2 Cl 2 , CHCl 3
These are the set of irreversible second-order reactions:
These intermediate species' concentrations can be calculated by integrating the system of kinetic equations. The full reaction is a free radical propagation reaction which is filled out in detail below.
Initiation : This reaction can occur by thermolysis (heating) or photolysis (absorption of light) leading to the breakage of a molecular chlorine bond.
When the bond is broken it produces two highly reactive chlorine atoms.
Propagation : This stage has two distinct reaction classes. The first is the stripping of a hydrogen from the carbon species by the chlorine radicals. This occurs because chlorine atoms alone are unstable, and these chlorine atoms react with one the carbon species' hydrogens. The result is the formation of hydrochloric acid and a new radical methyl group.
These new radical carbon containing species now react with a second CHCCl 2 molecule. This regenerates the chlorine radical and the cycle continues. This reaction occurs because while the radical methyl species are more stable than the radical chlorines, the overall stability of the newly formed chloromethane species more than makes up the energy difference.
During the propagation of the reaction, there are several highly reactive species that will be removed and stabilized at the termination step.
Termination : This kind of reaction takes place when the radical species interact directly. The products of the termination reactions are typically very low yield in comparison to the main products or intermediates as the highly reactive radical species are in relatively low concentration in relation to the rest of the mixture. This kind of reaction produces stable side products, reactants, or intermediates and slows the propagation reaction by lowering the number of radicals available to propagate the chain reaction.
There are many different termination combinations, some examples are:
Union of methyl radicals from a C-C bond leading to ethane (a side product).
Union of one methyl radical to a Cl radical forming chloromethane (another reaction forming an intermediate).
Union of two Cl radicals to reform chlorine gas (a reaction reforming a reactant).
Reaction intermediates serve purposes in a variety of biological settings. An example of this is demonstrated with the enzyme reaction intermediate of metallo-β-lactamase, which bacteria can use to acquire resistance to commonly used antibiotics such as penicillin . Metallo-β-lactamase can catalyze β-lactams , a family of common antibiotics. Spectroscopy techniques have found that the reaction intermediate of metallo-β-lactamase uses zinc in the resistance pathway. [ 6 ]
Another example of the importance of reaction intermediates is seen with AAA-ATPase p97, a protein that used in a variety of cellular metabolic processes. p97 is also linked to degenerative disease and cancer . In a study looking at reaction intermediates of the AAA-ATPase p97 function found an important ADP.P i nucleotide intermediate is important in the p97 molecular operation. [ 7 ]
An additional example of biologically relevant reaction intermediates can be found with the RCL enzymes, which catalyzes glycosidic bonds . When studied using methanolysis , it was found that the reaction required the formation of a reaction intermediate. [ 8 ]
In the chemical industry, the term intermediate may also refer to the (stable) product of a reaction that is itself valuable only as a precursor chemical for other industries. A common example is cumene which is made from benzene and propylene and used to make acetone and phenol in the cumene process . The cumene itself is of relatively little value in and of itself, and is typically only bought and sold by chemical companies. [ 9 ] | https://en.wikipedia.org/wiki/Reaction_intermediate |
Reaction kinetics in uniform supersonic flow ( French : Cinétique de Réaction en Ecoulement Supersonique Uniforme , CRESU ) is an experiment investigating chemical reactions taking place at very low temperatures . [ 1 ] [ 2 ] [ 3 ]
The technique involves the expansion of a gas or mixture of gases through a de Laval nozzle from a high-pressure reservoir into a vacuum chamber. As it expands, the nozzle collimates the gas into a uniform supersonic beam, which is essentially collision-free and has a temperature that, in the centre-of-mass frame, can be significantly below that of the reservoir gas. Each nozzle produces a characteristic temperature. This way, any temperature between room temperature and about 10 K can be achieved.
There are relatively few CRESU [ 4 ] apparatuses in existence for the simple reason that the gas throughput and pumping requirements are huge, which makes them expensive to run. Two of the leading centres have been the University of Rennes (France) and the University of Birmingham (UK). A more recent development has been a pulsed version of the CRESU, [ 5 ] which requires far less gas and therefore smaller pumps.
Most species have a negligible vapour pressure at such low temperatures, and this means that they quickly condense on the sides of the apparatus. Essentially, the CRESU technique provides a "wall-less flow tube", which allows the kinetics of gas-phase reactions to be investigated at much lower temperatures than otherwise possible.
Chemical kinetics experiments can then be carried out in a pump–probe fashion, using a laser to initiate the reaction (for example, by preparing one of the reagents by photolysis of a precursor), followed by observation of that same species (for example, by laser-induced fluorescence ) after a known time delay. The fluorescence signal is captured by a photomultiplier a known distance downstream of the de Laval nozzle. The time delay can be varied up to the maximum corresponding to the flow time over that known distance. By studying how quickly the reagent species disappears in the presence of differing concentrations of a (usually stable) co-reagent species, the reaction rate constant at the low temperature of the CRESU flow can be determined.
Reactions studied by the CRESU technique typically have no significant activation energy barrier. In the case of neutral–neutral reactions (i.e., not involving any charged species, ions ), these type of barrier-free reactions usually involve free radical species, such as molecular oxygen (O 2 ), the cyanide radical (CN) or the hydroxyl radical (OH). The energetic driving force for these reactions is typically an attractive long-range intermolecular potential.
CRESU experiments have been used to show deviations from Arrhenius kinetics at low temperatures: as the temperature is reduced, the rate constant actually increases. They can explain why chemistry is so prevalent in the interstellar medium , where many different polyatomic species have been detected (by radio astronomy ). | https://en.wikipedia.org/wiki/Reaction_kinetics_in_uniform_supersonic_flow |
In chemistry , a reaction mechanism is the step by step sequence of elementary reactions by which overall chemical reaction occurs. [ 1 ]
A chemical mechanism is a theoretical conjecture that tries to describe in detail what takes place at each stage of an overall chemical reaction. The detailed steps of a reaction are not observable in most cases. The conjectured mechanism is chosen because it is thermodynamically feasible and has experimental support in isolated intermediates (see next section) or other quantitative and qualitative characteristics of the reaction. It also describes each reactive intermediate , activated complex , and transition state , which bonds are broken (and in what order), and which bonds are formed (and in what order). A complete mechanism must also explain the reason for the reactants and catalyst used, the stereochemistry observed in reactants and products, all products formed and the amount of each.
The electron or arrow pushing method is often used in illustrating a reaction mechanism; for example, see the illustration of the mechanism for benzoin condensation in the following examples section.
Mechanisms also are of interest in inorganic chemistry . A often quoted mechanistic experiment involved the reaction of the labile hexaaquo chromous reductant with the exchange inert pentammine cobalt(III) chloride .
Reaction intermediates are chemical species, often unstable and short-lived. They can, however, sometimes be isolated. They are neither reactants nor products of the overall chemical reaction, but temporary products and/or reactants in the mechanism's reaction steps. Reaction intermediates are often confused with the transition state . The transition states are, in contrast, fleeting, high-energy species that cannot be isolated. The kinetics (relative rates of the reaction steps and the rate equation for the overall reaction) are discussed in terms of the energy required for the conversion of the reactants to the proposed transition states (molecular states that correspond to maxima on the reaction coordinates , and to saddle points on the potential energy surface for the reaction).
Information about the mechanism of a reaction is often provided by analyzing chemical kinetics to determine the reaction order in each reactant. [ 2 ]
Illustrative is the oxidation of carbon monoxide by nitrogen dioxide:
The rate law for this reaction is: r = k [ N O 2 ] 2 {\displaystyle r=k[NO_{2}]^{2}} This form shows that the rate-determining step does not involve CO. Instead, the slow step involves two molecules of NO 2 . A possible mechanism for the overall reaction that explains the rate law is:
Each step is called an elementary step, and each has its own rate law and molecularity . The sum of the elementary steps gives the net reaction.
When determining the overall rate law for a reaction, the slowest step is the step that determines the reaction rate. Because the first step (in the above reaction) is the slowest step, it is the rate-determining step . Because it involves the collision of two NO 2 molecules, it is a bimolecular reaction with a rate r {\displaystyle r} which obeys the rate law r = k [ N O 2 ( t ) ] 2 {\displaystyle r=k[NO_{2}(t)]^{2}} .
Other reactions may have mechanisms of several consecutive steps. In organic chemistry , the reaction mechanism for the benzoin condensation , put forward in 1903 by A. J. Lapworth , was one of the first proposed reaction mechanisms.
A chain reaction is an example of a complex mechanism, in which the propagation steps form a closed cycle.
In a chain reaction, the intermediate produced in one step generates an intermediate in another step.
Intermediates are called chain carriers. Sometimes, the chain carriers are radicals, they can be ions as well. In nuclear fission they are neutrons.
Chain reactions have several steps, which may include: [ 3 ]
Even though all these steps can appear in one chain reaction, the minimum necessary ones are Initiation, propagation, and termination.
An example of a simple chain reaction is the thermal decomposition of acetaldehyde (CH 3 CHO) to methane (CH 4 ) and carbon monoxide (CO). The experimental reaction order is 3/2, [ 4 ] which can be explained by a Rice-Herzfeld mechanism . [ 5 ]
This reaction mechanism for acetaldehyde has 4 steps with rate equations for each step :
For the overall reaction, the rates of change of the concentration of the intermediates •CH 3 and CH 3 CO• are zero, according to the steady-state approximation , which is used to account for the rate laws of chain reactions. [ 6 ]
d[•CH 3 ]/dt = k 1 [CH 3 CHO] – k 2 [•CH 3 ][CH 3 CHO] + k 3 [CH 3 CO•] - 2k 4 [•CH 3 ] 2 = 0
and d[CH 3 CO•]/dt = k 2 [•CH 3 ][CH 3 CHO] – k 3 [CH 3 CO•] = 0
The sum of these two equations is k 1 [CH 3 CHO] – 2 k 4 [•CH 3 ] 2 = 0. This may be solved to find the steady-state concentration of •CH 3 radicals as [•CH 3 ] = (k 1 / 2k 4 ) 1/2 [CH 3 CHO] 1/2 .
It follows that the rate of formation of CH 4 is d[CH 4 ]/dt = k 2 [•CH 3 ][CH 3 CHO] = k 2 (k 1 / 2k 4 ) 1/2 [CH 3 CHO] 3/2
Thus the mechanism explains the observed rate expression, for the principal products CH 4 and CO. The exact rate law may be even more complicated, there are also minor products such as acetone (CH 3 COCH 3 ) and propanal (CH 3 CH 2 CHO).
Many experiments that suggest the possible sequence of steps in a reaction mechanism have been designed, including:
A correct reaction mechanism is an important part of accurate predictive modeling . For many combustion and plasma systems, detailed mechanisms are not available or require development.
Even when information is available, identifying and assembling the relevant data from a variety of sources, reconciling discrepant values and extrapolating to different conditions can be a difficult process without expert help. Rate constants or thermochemical data are often not available in the literature, so computational chemistry techniques or group additivity methods must be used to obtain the required parameters. [ citation needed ]
Computational chemistry methods can also be used to calculate potential energy surfaces for reactions and determine probable mechanisms. [ 19 ]
Molecularity in chemistry is the number of colliding molecular entities that are involved in a single reaction step .
In general, reaction steps involving more than three molecular entities do not occur, because is statistically improbable in terms of Maxwell distribution to find such a transition state.
L.G.WADE, ORGANIC CHEMISTRY 7TH ED, 2010 | https://en.wikipedia.org/wiki/Reaction_mechanism |
In ecology and genetics, a reaction norm , also called a norm of reaction , describes the pattern of phenotypic expression of a single genotype across a range of environments. One use of reaction norms is in describing how different species—especially related species—respond to varying environments. But differing genotypes within a single species may also show differing reaction norms relative to a particular phenotypic trait and environment variable. For every genotype, phenotypic trait, and environmental variable, a different reaction norm can exist; in other words, an enormous complexity can exist in the interrelationships between genetic and environmental factors in determining traits. The concept was introduced by Richard Woltereck in 1909. [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ]
Scientifically analyzing norms of reaction in natural populations can be very difficult, simply because natural populations of sexually reproductive organisms usually do not have cleanly separated or superficially identifiable genetic distinctions. However, seed crops produced by humans are often engineered to contain specific genes, and in some cases seed stocks consist of clones . Accordingly, distinct seed lines present ideal examples of differentiated norms of reaction. In fact, agricultural companies market seeds for use in particular environments based on exactly this.
Suppose the seed line A contains an allele a, and a seed line B of the same crop species contains an allele b, for the same gene . With these controlled genetic groups, we might cultivate each variety (genotype) in a range of environments. This range might be either natural or controlled variations in environment. For example, an individual plant might receive either more or less water during its growth cycle, or the average temperature the plants are exposed to might vary across a range.
A simplification of the norm of reaction might state that seed line A is good for "high water conditions" while a seed line B is good for "low water conditions". But the full complexity of the norm of reaction is a function, for each genotype, relating environmental factor to phenotypic trait. By controlling for or measuring actual environments across which monoclonal seeds are cultivated, one can concretely observe norms of reaction. Normal distributions , for example, are common. Of course, the distributions need not be bell-curves.
One advantage of plants is that the same genotype, such as a recombinant inbred line (RIL), can be repeatedly evaluated in multiple environments, or a multi-environmental trial (MET). The reaction norm can then be explored based on the geographic location, mean trait value summarized from the whole population at each environment, or an explicit performance-free index capturing relevant environment inputs. [ 6 ]
Popular non-scientific or lay-scientific audiences frequently misunderstand or simply fail to recognize the existence of norms of reaction. A widespread conception is that each genotype gives a certain range of possible phenotypic expressions. In popular conception, something which is "more genetic" gives a narrower range, while something which is "less genetic (more environmental)" gives a wider range of phenotypic possibilities. This limited conceptual framework is especially prevalent in discussions of human traits such as IQ , sexual orientation , altruism , or schizophrenia (see Nature versus nurture ).
Popular conception of genotype/phenotype interaction
The problem with this common simplified image is not that it does not represent a possible norm of reaction. Rather, by reducing the picture from two dimensions to just one, it focuses only on discrete, non-overlapping phenotypic expressions, and hides the more common pattern of local minima and maxima in phenotypic expression, with overlapping ranges of phenotypic expression between genotypes. | https://en.wikipedia.org/wiki/Reaction_norm |
In chemistry , reaction progress kinetic analysis ( RPKA ) is a subset of a broad range of kinetic techniques utilized to determine the rate laws of chemical reactions and to aid in elucidation of reaction mechanisms . While the concepts guiding reaction progress kinetic analysis are not new, the process was formalized by Professor Donna Blackmond (currently at Scripps Research Institute ) in the late 1990s and has since seen increasingly widespread use. Unlike more common pseudo-first-order analysis, in which an overwhelming excess of one or more reagents is used relative to a species of interest, RPKA probes reactions at synthetically relevant conditions (i.e. with concentrations and reagent ratios resembling those used in the reaction when not exploring the rate law.) Generally, this analysis involves a system in which the concentrations of multiple reactants are changing measurably over the course of the reaction. As the mechanism can vary depending on the relative and absolute concentrations of the species involved, this approach obtains results that are much more representative of reaction behavior under commonly utilized conditions than do traditional tactics. Furthermore, information obtained by observation of the reaction over time may provide insight regarding unexpected behavior such as induction periods, catalyst deactivation, or changes in mechanism. [ 1 ] [ 2 ]
Reaction progress kinetic analysis relies on the ability to accurately monitor the reaction conversion over time. This goal may be accomplished by a range of techniques, the most common of which are described below. While these techniques are sometimes categorized as differential (monitoring reaction rate over time) or integral (monitoring the amount of substrate and/or product over time), simple mathematical manipulation ( differentiation or integration ) allows interconversion of the data obtained by either of the two. Regardless of the technique implemented, it is generally advantageous to confirm the validity in the system of interest by monitoring with an additional independent method. [ 2 ]
NMR spectroscopy is often the method of choice for monitoring reaction progress, where substrate consumption and/or product formation may be observed over time from the change of peak integration relative to a non-reactive standard. From the concentration data, the rate of reaction over time may be obtained by taking the derivative of a polynomial fit to the experimental curve. [ 3 ] Reaction progress NMR may be classified as an integral technique as the primary data collected are proportional to concentration vs. time. [ 2 ] While this technique is extremely convenient for clearly defined systems with distinctive, isolated product and/or reactant peaks, it has the drawback of requiring a homogeneous system amenable to reaction in an NMR tube. While NMR observation may allow for the identification of a reaction intermediates, the presence of any given species over the course of the reaction does not necessarily implicate it in a productive process. [ 1 ] Reaction progress NMR may, however, often be run at variable temperature, allowing the rate of reaction to be adjusted to a level convenient for observation. Examples of utilization of reaction progress NMR abound, with notable examples including investigation of Buchwald–Hartwig amination (One might note that considerable debate surrounded the best approach to mechanistic development of the Buchwald-Hartwig amination as indicated by a number of contradictory and competing reports published over a short period of time. See the designated article and references therein.) [ 4 ]
In situ infrared spectroscopy may be used to monitor the course of a reaction, provided a reagent or product shows distinctive absorbance in the IR spectral region. The rate of reactant consumption and/or product formation may be abstracted from the change of absorbance over time (by application of Beers' Law ). Even when reactant and product spectra display some degree of overlap, modern instrumentation software is generally able to accurately deconvolute the relative contributions provided there is a dramatic change in the absolute absorbance of the peak of interest over time. In situ IR may be classified as an integral technique as the primary data collected are proportional to concentration vs. time. [ 2 ] From these data, the starting material or product concentration over time may be obtained by simply taking the integral of a polynomial fit to the experimental curve. [ 3 ] With increases in the availability of spectrometers with in situ monitoring capabilities, FT-IR has seen increasing use in recent years. Examples of note include mechanistic analysis of the amido-thiourea catalyzed asymmetric Strecker synthesis of unnatural amino acids and of the Lewis base catalyzed halolactonization and cycloetherification . [ 5 ] [ 6 ]
Analogously to the in situ IR experiments described above, in situ UV-visible absorbance spectroscopy may be used to monitor the course of a reaction, provided a reagent or product shows distinctive absorbance in the UV spectral region . The rate of reactant consumption and/or product formation may be abstracted from the change of absorbance over time (by application of Beer's Law ), again leading to classification as an integral technique. [ 2 ] Due to the spectral region utilized, UV-vis techniques are more commonly utilized on inorganic or organometallic systems than on purely organic reactions, and examples include exploration of the samarium Barbier reaction . [ 7 ]
Calorimetry may be used to monitor the course of a reaction, since the instantaneous heat flux of the reaction, which is directly related to the enthalpy change for the reaction, is monitored. Reaction calorimetry may be classified as a differential technique since the primary data collected are proportional to rate vs. time. From these data, the starting material or product concentration over time may be obtained by simply taking the integral of a polynomial fit to the experimental curve. [ 2 ] [ 8 ] [ 9 ] While reaction calorimetry is less frequently employed than a number of other techniques, it has found use as an effective tool for catalyst screening. [ 10 ] Reaction calorimetry has also been applied as an efficient method for mechanistic study of individual reactions including the prolinate - catalyzed α- amination of aldehydes [ 11 ] and the palladium catalyzed Buchwald-Hartwig amination reaction. [ 4 ] [ 12 ]
While Gas Chromatography , HPLC , and Mass Spectrometry are all excellent techniques for distinguishing mixtures of compounds (and sometimes even enantiomers ), the time resolution of these measurements is less precise than that of the techniques described above. Regardless, these techniques have still seen use, such as in the investigation of the Heck reaction where the heterogeneous nature of the reaction precluded utilization of the techniques described above. [ 13 ] and SOMO-activation by organocatalysts [ 14 ] Despite their shortcomings, these techniques may serve as excellent calibration methods.
Reaction progress data may often most simply be presented as plot of substrate concentration ([A] t ) vs. time ( t ) or fraction conversion ( F ) vs. time ( t ). The latter requires minor algebraic manipulation to convert concentration/absorbance values to fractional conversion ( F ), by:
where [A] 0 is the amount, absorbance, or concentration of substrate initially present and [A] t is the amount, absorbance, or concentration of that reagent at time, t . Normalizing data to fractional conversion may be particularly helpful as it allows multiple reactions run with different absolute amounts or concentrations to be compared on the same plot.
Data may also commonly be presented as a plot of reaction rate ( v ) vs. time ( t ). Again, simple algebraic manipulation is required; for example, calorimetric experiments give:
where q is the instantaneous heat transfer , Δ H is the known enthalpy change of the reaction, and V is the reaction volume . [ 2 ]
Data from reaction progress kinetics experiments are also often presented via a rate ( v ) vs. substrate concentration ([S]) plot. This requires obtaining and combining both the [S] vs. t and the v vs. t plots described above (note that one may be obtained from the other by simple differentiation or integration.) The combination leads to a standard set of curves in which reaction progress is read from right to left along the x -axis and reaction rate is read from bottom to top along the y -axis. [ 2 ] While these plots often provide a visually compelling demonstration of basic kinetic trends, differential methods are generally superior for extracting numerical rate constants. (see below)
In catalytic kinetics, two basic approximations are useful (in different circumstances) to describe the behavior of many systems. The situations in which the pre-equilibrium and steady-state approximations are valid can often be distinguished by reaction progress kinetic analysis, and the two situations are closely related to the resting state of the catalyst.
Under steady-state conditions , the catalyst and substrate undergo reversible association followed by a relatively rapid consumption of the catalyst–substrate complex (by both forward reactions to product and reverse reactions to unbound catalyst.) The steady-state approximation holds that the concentration of the catalyst-substrate complex is not changing over time; the total concentration of this complex remains low as it is whisked away almost immediately after formation. A steady-state rate law contains all of the rate constants and species required to go from starting material to product, while the denominator consists of a sum of terms describing the relative rates of the forward and reverse reactions consuming the steady-state intermediate. For the simplest case where one substrate goes to one product through a single intermediate:
In a slightly more complex situation where two substrates bind in sequence followed by product release:
Increasingly complex systems can be described simply with the algorithm described in this reference. [ 15 ]
In the case of the steady-state conditions described above, the catalyst resting state is the unbound form (because the substrate-bound intermediate is, by definition, only present at a minimal concentration.) [ 16 ]
Under pre-equilibrium conditions, the catalyst and substrate undergo rapid and reversible association prior to a relatively slow step leading to product formation and release. Under these conditions, the system can be described by a "one-plus" rate law where the numerator consists of all rate constants and species required to go from starting material to product, and the denominator consists of a sum of terms describing each of the states in which the catalyst exists (and 1 corresponds to the free catalyst). [ 17 ] For the simplest case where one substrate goes to one product through a single intermediate:
In the slightly more complex situation where two substrates bind in sequence followed by product release:
In the case of the simple pre-equilibrium conditions described above, the catalyst resting state is either entirely or partially (depending on the magnitude of the equilibrium constant) the substrate bound complex.
Saturation conditions can be viewed as a special case of pre-equilibrium conditions. At the concentration of substrate examined, formation of the catalyst-substrate complex is rapid and essentially irreversible. The catalyst resting state consists entirely of the bound complex, and [A] is no longer present in the rate law; changing [A] will have no effect on reaction rate because the catalyst is already completely bound and reacting as rapidly as k 2 allows. The simplest case of saturation kinetics is the well-studied Michaelis-Menten model for enzyme kinetics.
While a reaction may exhibit one set of kinetic behavior at early conversion, that behavior may change due to:
In the case of saturation kinetics described above, provided that [A] is not present in a large excess relative to [B], saturation conditions will only apply at the beginning of the reaction. As the substrate is consumed, the concentration decreases and eventually [A] is no longer sufficient to completely overwhelm [Cat]. This is manifested by a gradual change in rate from 0-order to some higher (i.e. 1st, 2nd, etc.) order in [A]. This can also be described as a change in catalyst resting state from the bound form to the unbound form over the course of the reaction.
In addition to simply slowing the reaction, a change in catalyst resting state over the course of the reaction may result in competing paths or processes. Multiple mechanisms may be present to access the product, in which case the order in catalyst or substrate may change depending on the conditions or point in the reaction. A particularly useful probe for changes in reaction mechanism involves examination of the normalized reaction rate vs. catalyst loading at multiple, fixed conversion points. Note that the normalized reaction rate:
adjusts for the consumption of substrate over the course of the reaction, so only rate changes due to catalyst loading will be observed. A linear dependence on catalyst loading for a given conversion is indicative of a first order dependence on catalyst at that conversion, and one can similarly imagine the non-linear plots resulting from higher order dependence. Changes in the linearity or non-linearity from one set of conversion points to another are indicative of changes in the dependence on catalyst over the course of the reaction. Conversely, changes in the linearity or non-linearity of regions of the plot conserved over multiple conversion points (i.e. at 30, 50, and 70%) are indicative of a change in the dependence on catalyst based on the absolute catalyst concentration.
Catalyst interactions with multiple components of a reaction mixture can lead to a complex kinetic dependence. While off-cycle catalyst-substrate or catalyst-product interactions are generally considered "poisonous" to the system (certainly the case in the event of irreversible complexation) cases do exist in which the off-cycle species actually protects the catalyst from permanent deactivation. [ 19 ] [ 20 ] In either case, it is often essential to understand the role of the catalyst resting state. [ 3 ] [ 11 ]
The variable parameter of greatest interest in reaction progress kinetic analysis is the excess ( e ) of one substrate over another, given in units of molarity. The initial concentrations of two species in a reaction may be defined by:
and, assuming a one-to-one reaction stoichiometry, that excess of one substrate over the other is quantitatively preserved over the course of the entire reaction such that: [ 3 ]
A similar set can be constructed for reactions with higher order stoichiometry in which case the excess varies predictably over the course of the reaction. While e may be any value (positive, negative, or zero) generally positive or negative values smaller in magnitude than one equivalent of substrate are used in reaction progress kinetic analysis. (One might note that pseudo-zero-order kinetics uses excess values much much greater in magnitude than the one equivalent of substrate).
Defining the parameter of excess ( e ) allows for the construction of same-excess experiments in which two or more runs of a kinetic experiment with different initial concentrations, but the same-excess allow one to artificially enter the reaction at any point. These experiments are critical for RPKA of catalytic reactions, as they enable one to probe a number of mechanistic possibilities including catalyst activation (induction periods), catalyst deactivation, and product inhibition described in further detail below. [ 2 ] [ 3 ]
Prior to further mechanistic investigation, it is important to determine the kinetic dependence of the reaction of interest on the catalyst. The turnover frequency (TOF) of the catalyst can be expressed as the reaction rate normalized to the concentration of catalyst:
This TOF is determined by running any two or more same-excess experiments in which the absolute catalyst concentration is varied. Because the catalyst concentration is constant over the course of the reaction, the resulting plots are normalized by an unchanging value. If the resulting plots overlay perfectly, then the reaction is, in fact, first-order in catalyst. If the reaction fails to overlay, higher-order processes are at work and require a more detailed analysis than described here. [ 3 ] It is also worth noting that the normalization-overlay manipulation described here is only one approach for interpretation of the raw data. Equally valid results may be obtained by fitting the observed kinetic behavior to simulated rate laws.
As described above, same-excess experiments are conducted with two or more experiments holding the excess, ( e ) constant while changing the absolute concentrations of the substrates (in this case, the catalyst is also treated as a substrate.) Note that this construction causes the number of equivalents and therefore the mole percentage of each reagent/catalyst to differ between reactions. [ 3 ] These experiments enable one to artificially "enter" the reaction at any point, as the initial concentrations of one experiment (the intercepting reaction) are chosen to map directly onto the anticipated concentrations at some intermediate time, t , in another (the parent reaction). One would expect the reaction progress, described by the rate vs. substrate concentration plots detailed above, to map directly onto each other from that interception point onward. This will hold true, however, only if the rate of the reaction is not altered by changes to the active substrate/catalyst concentration (such as by catalyst activation, catalyst deactivation, or product inhibition) before that interception. [ 2 ] [ 3 ]
A perfect overlay of multiple experiments with the same-excess but different initial substrate loadings suggests that no changes in the active substrate/catalyst concentration occur over the course of the reaction. The failure of the plots to overlay is generally indicative of catalyst activation, deactivation, or product inhibition under the reaction conditions. These cases may be distinguished by the position of the reaction progress curves relative to each other. Intercepting reactions lying below (slower rates at the same substrate concentration) the parent reactions on the rate vs. substrate concentration plot, are indicative of catalyst activation under reaction conditions. Intercepting reactions lying above (faster rates at the same substrate concentration) the parent reactions on the rate vs. substrate concentration plot, are indicative of catalyst deactivation under reaction conditions; further experimentation is necessary to distinguish product inhibition from other forms of catalyst death. [ 2 ]
One key difference between the intercepting reaction and the parent reaction described above is the presence of some amount of product in the parent reaction at the interception point. Product inhibition has long been known to influence catalyst efficiency of many systems, and in the case of same-excess experiments, it prevents the intercepting and parent reactions from overlaying. While same-excess experiments as described above cannot attribute catalyst deactivation to any particular cause, product inhibition can be probed by further experiments in which some initial amount of product is added to the intercepting reaction (designed to mimic the amount of product expected to be present in the parent reaction at the same substrate concentration). A perfect overlay of the rate vs. substrate concentration plots under same-excess-same product conditions indicates that product inhibition does occur under the reaction conditions used. While the failure of the rate vs. substrate concentration plots to overlay under same-excess-same product conditions does not preclude product inhibition, it does, at least, indicate that other catalyst deactivation paths must also be active.
Same-excess experiments probing catalyst deactivation and product inhibition are among the most widely used applications of reaction progress kinetic analysis. Among the numerous examples in the literature, some include investigation of the amino alcohol-catalyzed zinc alkylation of aldehydes, [ 21 ] the amido-thiourea catalyzed asymmetric Strecker synthesis of unnatural amino acids , [ 5 ] and the SOMO-activation of organocatalysts. [ 14 ]
With the wealth of data available from monitoring reaction progress over time paired with the power of modern computing methods, it has become reasonably straightforward to numerically evaluate the rate law, mapping the integrated rate laws of simulated reactions paths onto a fit of reaction progress over time. Due to the principles of the propagation of error, rate constants and rate laws can be determined by these differential methods with significantly lower uncertainty than by the construction of graphical rate equations (above.) [ 9 ]
While RPKA allows observation of rates over the course of the entire reaction, conducting only same-excess experiments does not provide sufficient information for determination of the corresponding rate constants. In order to construct enough independent relationships to solve for all of the unknown rate constants, it is necessary to examine systems with different-excess.
Consider again the simple example discussed above where the catalyst associates with substrate A, followed by reaction with B to form product P and free catalyst. Regardless of the approximation applied, multiple independent parameters ( k 2 and K 1 in the case of pre-equilibrium; k 1 , k −1 , and k 2 in the case of steady-state) are required to define the system. While one could imagine constructing multiple equations to describe the unknowns at different concentrations, when the data is obtained from a same-excess experiment [A] and [B] are not independent:
Multiple experiments using different values of e are necessary to establish multiple independent equations defining the multiple independent rate constants in terms of experimental rates and concentrations. Non-linear least squares analysis may then be employed to obtain best fit values of the unknown rate constants to those equations.
Kineticists have historically relied on linearization of rate data to extrapolate rate constants, perhaps best demonstrated by the widespread use of the standard Lineweaver–Burk linearization of the Michaelis–Menten equation. [ 22 ] Linearization techniques were of particular importance before the advent of computing techniques capable of fitting complex curves, and they remain a staple in kinetics due to their intuitively simple presentation. [ 2 ] It is important to note that linearization techniques should NOT be used to extract numerical rate constants as they introduce a large degree of error relative to alternative numerical techniques. Graphical rate laws do, however, maintain that intuitive presentation of linearized data, such that visual inspection of the plot can provide mechanistic insight regarding the reaction at hand. The basis for a graphical rate law rests on the rate ( v ) vs. substrate concentration ([S]) plots discussed above. For example, in the simple cycle discussed with regard to different-excess experiments a plot of v / [A] vs. [B] and its twin v / [B] vs. [A] can provide intuitive insight about the order of each of the reagents. If plots of v / [A] vs. [B] overlay for multiple experiments with different-excess, the data are consistent with a first-order dependence on [A]. The same could be said for a plot of v / [B] vs. [A]; overlay is consistent with a first-order dependence on [B]. Non-overlaying results of these graphical rate laws are possible and are indicative of higher order dependence on the substrates probed. Blackmond has proposed presenting the results of different-excess experiments with a series of graphical rate equations (that she presents in a flow-chart adapted here), but it is important to note that her proposed method is only one of many possible methods to display the kinetic relationship. Furthermore, while the presentation of graphical rate laws may at times be considered a visually simplified way to present complex kinetic data, fitting the raw kinetic data for analysis by differential or other rigorous numerical methods is necessary to extract accurate and quantitative rate constants and reaction orders. [ 2 ] [ 3 ]
It is important to note that even while kinetic analysis is a powerful tool for determining the stoichiometry of the turn-over limiting transition state relative to the ground state, it cannot answer all mechanistic questions. It is possible for two mechanisms to be kinetically indistinguishable, especially under catalytic conditions. For any thorough mechanistic evaluation it is necessary to conduct kinetic analysis of both the catalytic process and its individual steps (when possible) in concert with other forms of analysis such as evaluation of linear free energy relationships , isotope effect studies, computational analysis , or any number of alternative approaches. Finally, it is important to note that no mechanistic hypothesis can ever be proven; alternative mechanistic hypothesis can only be disproven. It is, therefore, essential to conduct any investigation in a hypothesis-driven manner. Only by experimentally disproving reasonable alternatives can the support for a given hypothesis be strengthened. [ 23 ] | https://en.wikipedia.org/wiki/Reaction_progress_kinetic_analysis |
In chemical thermodynamics , the reaction quotient ( Q r or just Q ) [ 1 ] is a dimensionless quantity that provides a measurement of the relative amounts of products and reactants present in a reaction mixture for a reaction with well-defined overall stoichiometry at a particular point in time. Mathematically, it is defined as the ratio of the activities (or molar concentrations ) of the product species over those of the reactant species involved in the chemical reaction, taking stoichiometric coefficients of the reaction into account as exponents of the concentrations. In equilibrium, the reaction quotient is constant over time and is equal to the equilibrium constant .
A general chemical reaction in which α moles of a reactant A and β moles of a reactant B react to give ρ moles of a product R and σ moles of a product S can be written as
The reaction is written as an equilibrium even though, in many cases, it may appear that all of the reactants on one side have been converted to the other side. When any initial mixture of A, B, R, and S is made, and the reaction is allowed to proceed (either in the forward or reverse direction), the reaction quotient Q r , as a function of time t , is defined as [ 2 ]
where {X} t denotes the instantaneous activity [ 3 ] of a species X at time t .
A compact general definition is
where П j denotes the product across all j -indexed variables, a j ( t ) is the activity of species j at time t , and ν j is the stoichiometric number (the stoichiometric coefficient multiplied by +1 for products and −1 for starting materials).
As the reaction proceeds with the passage of time, the species' activities, and hence the reaction quotient, change in a way that reduces the free energy of the chemical system. The direction of the change is governed by the Gibbs free energy of reaction by the relation
where K is a constant independent of initial composition, known as the equilibrium constant . The reaction proceeds in the forward direction (towards larger values of Q r ) when Δ r G < 0 or in the reverse direction (towards smaller values of Q r ) when Δ r G > 0. Eventually, as the reaction mixture reaches chemical equilibrium, the activities of the components (and thus the reaction quotient) approach constant values. The equilibrium constant is defined to be the asymptotic value approached by the reaction quotient:
The timescale of this process depends on the rate constants of the forward and reverse reactions. In principle, equilibrium is approached asymptotically at t → ∞; in practice, equilibrium is considered to be reached, in a practical sense, when concentrations of the equilibrating species no longer change perceptibly with respect to the analytical instruments and methods used.
If a reaction mixture is initialized with all components having an activity of unity, that is, in their standard states , then
This quantity, Δ r G° , is called the standard Gibbs free energy of reaction . [ 4 ]
All reactions, regardless of how favorable, are equilibrium processes, though practically speaking, if no starting material is detected after a certain point by a particular analytical technique in question, the reaction is said to go to completion.
In biochemistry, the reaction quotient is often referred to as the mass-action ratio with the symbol Γ {\displaystyle \Gamma } .
The reaction quotient can be used to predict the direction and extent of an equilibrium chemical reaction. At equilibrium, the reaction quotient (Q) is equal to the equilibrium constant (K) for the reaction, where Q = K. If Q > K, the formation of reactants is favored. This is because the ratio of the numerator to the denominator in Q is greater than that of K, indicating there are more products than at equilibrium. As Le Chatelier's Principle states systems tend towards equilibrium, the equilibrium shifts in the reverse direction favoring the formation of the products. Similarly, when Q < K, the formation of products is favored and the reaction is progressing in the forwards direction. [ 5 ]
Reaction quotient tutorials | https://en.wikipedia.org/wiki/Reaction_quotient |
The reaction rate or rate of reaction is the speed at which a chemical reaction takes place, defined as proportional to the increase in the concentration of a product per unit time and to the decrease in the concentration of a reactant per unit time. [ 1 ] Reaction rates can vary dramatically. For example, the oxidative rusting of iron under Earth's atmosphere is a slow reaction that can take many years, but the combustion of cellulose in a fire is a reaction that takes place in fractions of a second. For most reactions, the rate decreases as the reaction proceeds. A reaction's rate can be determined by measuring the changes in concentration over time.
Chemical kinetics is the part of physical chemistry that concerns how rates of chemical reactions are measured and predicted, and how reaction-rate data can be used to deduce probable reaction mechanisms . [ 2 ] The concepts of chemical kinetics are applied in many disciplines, such as chemical engineering , [ 3 ] [ 4 ] enzymology and environmental engineering . [ 5 ] [ 6 ] [ 7 ]
Consider a typical balanced chemical reaction:
The lowercase letters ( a , b , p , and q ) represent stoichiometric coefficients , while the capital letters represent the reactants ( A and B ) and the products ( P and Q ).
According to IUPAC 's Gold Book definition [ 8 ] the reaction rate ν {\displaystyle \nu } for a chemical reaction occurring in a closed system at constant volume , without a build-up of reaction intermediates , is defined as:
ν = − 1 a d [ A ] d t = − 1 b d [ B ] d t = 1 p d [ P ] d t = 1 q d [ Q ] d t {\displaystyle \nu =-{\frac {1}{a}}{\frac {d[\mathrm {A} ]}{dt}}=-{\frac {1}{b}}{\frac {d[\mathrm {B} ]}{dt}}={\frac {1}{p}}{\frac {d[\mathrm {P} ]}{dt}}={\frac {1}{q}}{\frac {d[\mathrm {Q} ]}{dt}}}
where [X] denotes the concentration of the substance X (= A, B, P or Q) . The reaction rate thus defined has the units of mol/L/s.
The rate of a reaction is always positive. A negative sign is present to indicate that the reactant concentration is decreasing. The IUPAC [ 8 ] recommends that the unit of time should always be the second. The rate of reaction differs from the rate of increase of concentration of a product P by a constant factor (the reciprocal of its stoichiometric number ) and for a reactant A by minus the reciprocal of the stoichiometric number. The stoichiometric numbers are included so that the defined rate is independent of which reactant or product species is chosen for measurement. [ 9 ] : 349 For example, if a = 1 and b = 3 then B is consumed three times more rapidly than A , but ν = − d [ A ] d t = − 1 3 d [ B ] d t {\displaystyle \nu =-{\tfrac {d[\mathrm {A} ]}{dt}}=-{\tfrac {1}{3}}{\tfrac {d[\mathrm {B} ]}{dt}}} is uniquely defined. An additional advantage of this definition is that for an elementary and irreversible reaction, ν {\displaystyle \nu } is equal to the product of the probability of overcoming the transition state activation energy and the number of times per second the transition state is approached by reactant molecules. When so defined, for an elementary and irreversible reaction, ν {\displaystyle \nu } is the rate of successful chemical reaction events leading to the product.
The above definition is only valid for a single reaction , in a closed system of constant volume . If water is added to a pot containing salty water, the concentration of salt decreases, although there is no chemical reaction.
For an open system, the full mass balance must be taken into account:
F A 0 − F A + ∫ 0 V ν d V = d N A d t in − out + ( generation − consumption ) = accumulation {\displaystyle {\begin{array}{ccccccc}F_{\mathrm {A} _{0}}&-&F_{\mathrm {A} }&+&\displaystyle \int _{0}^{V}\nu \,dV&=&\displaystyle {\frac {dN_{\mathrm {A} }}{dt}}\\{\text{in}}&-&{\text{out}}&+&\left({{\text{generation }}- \atop {\text{consumption}}}\right)&=&{\text{accumulation}}\end{array}}} where
When applied to the closed system at constant volume considered previously, this equation reduces to: ν = d [ A ] d t {\displaystyle \nu ={\frac {d[A]}{dt}}} where the concentration [A] is related to the number of molecules N A by [ A ] = N A N 0 V . {\displaystyle [\mathrm {A} ]={\tfrac {N_{\rm {A}}}{N_{0}V}}.} Here N 0 is the Avogadro constant .
For a single reaction in a closed system of varying volume the so-called rate of conversion can be used, in order to avoid handling concentrations. It is defined as the derivative of the extent of reaction with respect to time.
ν = d ξ d t = 1 ν i d n i d t = 1 ν i d ( C i V ) d t = 1 ν i ( V d C i d t + C i d V d t ) {\displaystyle \nu ={\frac {d\xi }{dt}}={\frac {1}{\nu _{i}}}{\frac {dn_{i}}{dt}}={\frac {1}{\nu _{i}}}{\frac {d(C_{i}V)}{dt}}={\frac {1}{\nu _{i}}}\left(V{\frac {dC_{i}}{dt}}+C_{i}{\frac {dV}{dt}}\right)}
Here ν i is the stoichiometric coefficient for substance i , equal to a , b , p , and q in the typical reaction above. Also, V is the volume of reaction and C i is the concentration of substance i .
When side products or reaction intermediates are formed, the IUPAC [ 8 ] recommends the use of the terms the rate of increase of concentration and rate of the decrease of concentration for products and reactants, properly.
Reaction rates may also be defined on a basis that is not the volume of the reactor. When a catalyst is used, the reaction rate may be stated on a catalyst weight (mol g −1 s −1 ) or surface area (mol m −2 s −1 ) basis. If the basis is a specific catalyst site that may be rigorously counted by a specified method, the rate is given in units of s −1 and is called a turnover frequency.
Factors that influence the reaction rate are the nature of the reaction, concentration, pressure , reaction order , temperature , solvent , electromagnetic radiation , catalyst, isotopes , surface area, stirring , and diffusion limit . Some reactions are naturally faster than others. The number of reacting species, their physical state (the particles that form solids move much more slowly than those of gases or those in solution ), the complexity of the reaction and other factors can greatly influence the rate of a reaction.
Reaction rate increases with concentration, as described by the rate law and explained by collision theory . As reactant concentration increases, the frequency of collision increases. The rate of gaseous reactions increases with pressure, which is, in fact, equivalent to an increase in the concentration of the gas. The reaction rate increases in the direction where there are fewer moles of gas and decreases in the reverse direction. For condensed-phase reactions, the pressure dependence is weak.
The order of the reaction controls how the reactant concentration (or pressure) affects the reaction rate.
Usually conducting a reaction at a higher temperature delivers more energy into the system and increases the reaction rate by causing more collisions between particles, as explained by collision theory. However, the main reason that temperature increases the rate of reaction is that more of the colliding particles will have the necessary activation energy resulting in more successful collisions (when bonds are formed between reactants). The influence of temperature is described by the Arrhenius equation . For example, coal burns in a fireplace in the presence of oxygen, but it does not when it is stored at room temperature . The reaction is spontaneous at low and high temperatures but at room temperature, its rate is so slow that it is negligible. The increase in temperature, as created by a match, allows the reaction to start and then it heats itself because it is exothermic . That is valid for many other fuels, such as methane , butane , and hydrogen .
Reaction rates can be independent of temperature ( non-Arrhenius ) or decrease with increasing temperature ( anti-Arrhenius ). Reactions without an activation barrier (for example, some radical reactions), tend to have anti-Arrhenius temperature dependence: the rate constant decreases with increasing temperature.
Many reactions take place in solution and the properties of the solvent affect the reaction rate. The ionic strength also has an effect on the reaction rate.
Electromagnetic radiation is a form of energy. As such, it may speed up the rate or even make a reaction spontaneous as it provides the particles of the reactants with more energy. [ citation needed ] This energy is in one way or another stored in the reacting particles (it may break bonds, and promote molecules to electronically or vibrationally excited states...) creating intermediate species that react easily. As the intensity of light increases, the particles absorb more energy and hence the rate of reaction increases. For example, when methane reacts with chlorine in the dark, the reaction rate is slow. It can be sped up when the mixture is put under diffused light. In bright sunlight, the reaction is explosive.
The presence of a catalyst increases the reaction rate (in both the forward and reverse reactions) by providing an alternative pathway with a lower activation energy. For example, platinum catalyzes the combustion of hydrogen with oxygen at room temperature.
The kinetic isotope effect consists of a different reaction rate for the same molecule if it has different isotopes, usually hydrogen isotopes, because of the relative mass difference between hydrogen and deuterium .
In reactions on surfaces , which take place, for example, during heterogeneous catalysis , the rate of reaction increases as the surface area does. That is because more particles of the solid are exposed and can be hit by reactant molecules.
Stirring can have a strong effect on the rate of reaction for heterogeneous reactions .
Some reactions are limited by diffusion. All the factors that affect a reaction rate, except for concentration and reaction order, are taken into account in the reaction rate coefficient (the coefficient in the rate equation of the reaction).
For a chemical reaction a A + b B → p P + q Q , the rate equation or rate law is a mathematical expression used in chemical kinetics to link the rate of a reaction to the concentration of each reactant. For a closed system at constant volume, this is often of the form v = k [ A ] n [ B ] m − k r [ P ] i [ Q ] j . {\displaystyle v=k[\mathrm {A} ]^{n}[\mathrm {B} ]^{m}-k_{r}[\mathrm {P} ]^{i}[\mathrm {Q} ]^{j}.}
For reactions that go to completion (which implies very small k r ), or if only the initial rate is analyzed (with initial vanishing product concentrations), this simplifies to the commonly quoted form
v = k ( T ) [ A ] n [ B ] m . {\displaystyle v=k(T)[\mathrm {A} ]^{n}[\mathrm {B} ]^{m}.}
For gas phase reaction the rate equation is often alternatively expressed in terms of partial pressures .
In these equations k ( T ) is the reaction rate coefficient or rate constant , although it is not really a constant, because it includes all the parameters that affect reaction rate, except for time and concentration. Of all the parameters influencing reaction rates, temperature is normally the most important one and is accounted for by the Arrhenius equation .
The exponents n and m are called reaction orders and depend on the reaction mechanism. For an elementary (single-step) reaction, the order with respect to each reactant is equal to its stoichiometric coefficient. For complex (multistep) reactions, however, this is often not true and the rate equation is determined by the detailed mechanism, as illustrated below for the reaction of H 2 and NO.
For elementary reactions or reaction steps, the order and stoichiometric coefficient are both equal to the molecularity or number of molecules participating. For a unimolecular reaction or step, the rate is proportional to the concentration of molecules of reactant, so the rate law is first order. For a bimolecular reaction or step, the number of collisions is proportional to the product of the two reactant concentrations, or second order. A termolecular step is predicted to be third order, but also very slow as simultaneous collisions of three molecules are rare.
By using the mass balance for the system in which the reaction occurs, an expression for the rate of change in concentration can be derived. For a closed system with constant volume, such an expression can look like
d [ P ] d t = k ( T ) [ A ] n [ B ] m . {\displaystyle {\frac {d[\mathrm {P} ]}{dt}}=k(T)[\mathrm {A} ]^{n}[\mathrm {B} ]^{m}.}
For the reaction
2 H 2 ( g ) + 2 NO ( g ) ⟶ N 2 ( g ) + 2 H 2 O ( g ) , {\displaystyle {\ce {2H2_{(g)}}}+{\ce {2NO_{(g)}-> N2_{(g)}}}+{\ce {2H2O_{(g)}}},}
the observed rate equation (or rate expression) is v = k [ H 2 ] [ NO ] 2 . {\displaystyle v=k[{\ce {H2}}][{\ce {NO}}]^{2}.}
As for many reactions, the experimental rate equation does not simply reflect the stoichiometric coefficients in the overall reaction: It is third order overall: first order in H 2 and second order in NO, even though the stoichiometric coefficients of both reactants are equal to 2. [ 10 ]
In chemical kinetics, the overall reaction rate is often explained using a mechanism consisting of a number of elementary steps. Not all of these steps affect the rate of reaction; normally the slowest elementary step controls the reaction rate. For this example, a possible mechanism is
1 ) 2 NO ( g ) ↽ − − ⇀ N 2 O 2 ( g ) ( fast equilibrium ) 2 ) N 2 O 2 + H 2 ⟶ N 2 O + H 2 O ( slow ) 3 ) N 2 O + H 2 ⟶ N 2 + H 2 O ( fast ) . {\displaystyle {\begin{array}{rll}1)&\quad {\ce {2NO_{(g)}<=> N2O2_{(g)}}}&({\text{fast equilibrium}})\\2)&\quad {\ce {N2O2 + H2 -> N2O + H2O}}&({\text{slow}})\\3)&\quad {\ce {N2O + H2 -> N2 + H2O}}&({\text{fast}}).\end{array}}}
Reactions 1 and 3 are very rapid compared to the second, so the slow reaction 2 is the rate-determining step. This is a bimolecular elementary reaction whose rate is given by the second-order equation v = k 2 [ H 2 ] [ N 2 O 2 ] , {\displaystyle v=k_{2}[{\ce {H2}}][{\ce {N2O2}}],} where k 2 is the rate constant for the second step.
However N 2 O 2 is an unstable intermediate whose concentration is determined by the fact that the first step is in equilibrium , so that [ N 2 O 2 ] = K 1 [ NO ] 2 , {\displaystyle {\ce {[N2O2]={\mathit {K}}_{1}[NO]^{2}}},} where K 1 is the equilibrium constant of the first step. Substitution of this equation in the previous equation leads to a rate equation expressed in terms of the original reactants v = k 2 K 1 [ H 2 ] [ NO ] 2 . {\displaystyle v=k_{2}K_{1}[{\ce {H2}}][{\ce {NO}}]^{2}\,.}
This agrees with the form of the observed rate equation if it is assumed that k = k 2 K 1 . In practice the rate equation is used to suggest possible mechanisms which predict a rate equation in agreement with experiment.
The second molecule of H 2 does not appear in the rate equation because it reacts in the third step, which is a rapid step after the rate-determining step, so that it does not affect the overall reaction rate.
Each reaction rate coefficient k has a temperature dependency, which is usually given by the Arrhenius equation :
k = A exp ( − E a R T ) {\displaystyle k=A\exp \left(-{\frac {E_{\mathrm {a} }}{RT}}\right)}
where
Since at temperature T the molecules have energies given by a Boltzmann distribution , one can expect the number of collisions with energy greater than E a to be proportional to exp ( − E a R T ) {\displaystyle \exp \left({\tfrac {-E_{\rm {a}}}{RT}}\right)} .
The values for A and E a are dependent on the reaction. There are also more complex equations possible, which describe the temperature dependence of other rate constants that do not follow this pattern.
Temperature is a measure of the average kinetic energy of the reactants. As temperature increases, the kinetic energy of the reactants increases. That is, the particles move faster. With the reactants moving faster this allows more collisions to take place at a greater speed, so the chance of reactants forming into products increases, which in turn results in the rate of reaction increasing. A rise of ten degrees Celsius results in approximately twice the reaction rate.
The minimum kinetic energy required for a reaction to occur is called the activation energy and is denoted by E a or Δ G ‡ . The transition state or activated complex shown on the diagram is the energy barrier that must be overcome when changing reactants into products. The molecules with an energy greater than this barrier have enough energy to react.
For a successful collision to take place, the collision geometry must be right, meaning the reactant molecules must face the right way so the activated complex can be formed.
A chemical reaction takes place only when the reacting particles collide. However, not all collisions are effective in causing the reaction. Products are formed only when the colliding particles possess a certain minimum energy called threshold energy. As a rule of thumb , reaction rates for many reactions double for every ten degrees Celsius increase in temperature. [ 11 ] For a given reaction, the ratio of its rate constant at a higher temperature to its rate constant at a lower temperature is known as its temperature coefficient , ( Q ). Q 10 is commonly used as the ratio of rate constants that are ten degrees Celsius apart.
The pressure dependence of the rate constant for condensed -phase reactions (that is, when reactants and products are solids or liquid) is usually sufficiently weak in the range of pressures normally encountered in industry that it is neglected in practice.
The pressure dependence of the rate constant is associated with the activation volume. For the reaction proceeding through an activation-state complex:
A + B ↽ − − ⇀ | A ⋯ B | ‡ ⟶ P {\displaystyle {\ce {A + B <=>}}\ |{\ce {A}}\cdots {\ce {B}}|^{\ddagger }\ {\ce {-> P}}}
the activation volume, Δ V ‡ , is:
Δ V ‡ = V ¯ ‡ − V ¯ A − V ¯ B {\displaystyle \Delta V^{\ddagger }={\bar {V}}_{\ddagger }-{\bar {V}}_{\mathrm {A} }-{\bar {V}}_{\mathrm {B} }}
where V̄ denotes the partial molar volume of a species and ‡ (a double dagger ) indicates the activation-state complex.
For the above reaction, one can expect the change of the reaction rate constant (based either on mole fraction or on molar concentration ) with pressure at constant temperature to be: [ 9 ] : 390
In practice, the matter can be complicated because the partial molar volumes and the activation volume can themselves be a function of pressure.
Reactions can increase or decrease their rates with pressure, depending on the value of Δ V ‡ . As an example of the possible magnitude of the pressure effect, some organic reactions were shown to double the reaction rate when the pressure was increased from atmospheric (0.1 MPa) to 50 MPa (which gives Δ V ‡ = −0.025 L/mol). [ 12 ] | https://en.wikipedia.org/wiki/Reaction_rate |
In chemical kinetics , a reaction rate constant or reaction rate coefficient ( k {\displaystyle k} ) is a proportionality constant which quantifies the rate and direction of a chemical reaction by relating it with the concentration of reactants. [ 1 ]
For a reaction between reactants A and B to form a product C,
where
the reaction rate is often found to have the form:
r = k [ A ] m [ B ] n {\displaystyle r=k[\mathrm {A} ]^{m}[\mathrm {B} ]^{n}}
Here k {\displaystyle k} is the reaction rate constant that depends on temperature, and [A] and [B] are the molar concentrations of substances A and B in moles per unit volume of solution, assuming the reaction is taking place throughout the volume of the solution. (For a reaction taking place at a boundary, one would use moles of A or B per unit area instead.)
The exponents m and n are called partial orders of reaction and are not generally equal to the stoichiometric coefficients a and b . Instead they depend on the reaction mechanism and can be determined experimentally.
Sum of m and n, that is, ( m + n ) is called the overall order of reaction.
For an elementary step , there is a relationship between stoichiometry and rate law, as determined by the law of mass action . Almost all elementary steps are either unimolecular or bimolecular. For a unimolecular step
the reaction rate is described by r = k 1 [ A ] {\displaystyle r=k_{1}[\mathrm {A} ]} , where k 1 {\displaystyle k_{1}} is a unimolecular rate constant. Since a reaction requires a change in molecular geometry, unimolecular rate constants cannot be larger than the frequency of a molecular vibration. Thus, in general, a unimolecular rate constant has an upper limit of k 1 ≤ ~10 13 s −1 .
For a bimolecular step
the reaction rate is described by r = k 2 [ A ] [ B ] {\displaystyle r=k_{2}[\mathrm {A} ][\mathrm {B} ]} , where k 2 {\displaystyle k_{2}} is a bimolecular rate constant. Bimolecular rate constants have an upper limit that is determined by how frequently molecules can collide, and the fastest such processes are limited by diffusion . Thus, in general, a bimolecular rate constant has an upper limit of k 2 ≤ ~10 10 M −1 s −1 .
For a termolecular step
the reaction rate is described by r = k 3 [ A ] [ B ] [ C ] {\displaystyle r=k_{3}[\mathrm {A} ][\mathrm {B} ][\mathrm {C} ]} , where k 3 {\displaystyle k_{3}} is a termolecular rate constant.
There are few examples of elementary steps that are termolecular or higher order, due to the low probability of three or more molecules colliding in their reactive conformations and in the right orientation relative to each other to reach a particular transition state. [ 2 ] There are, however, some termolecular examples in the gas phase. Most involve the recombination of two atoms or small radicals or molecules in the presence of an inert third body which carries off excess energy, such as O + O 2 + N 2 → O 3 + N 2 . One well-established example is the termolecular step 2 I + H 2 → 2 HI in the hydrogen-iodine reaction . [ 3 ] [ 4 ] [ 5 ] In cases where a termolecular step might plausibly be proposed, one of the reactants is generally present in high concentration (e.g., as a solvent or diluent gas). [ 6 ]
For a first-order reaction (including a unimolecular one-step process), there is a direct relationship between the unimolecular rate constant and the half-life of the reaction: t 1 / 2 = ln 2 k {\textstyle t_{1/2}={\frac {\ln 2}{k}}} . Transition state theory gives a relationship between the rate constant k ( T ) {\displaystyle k(T)} and the Gibbs free energy of activation Δ G ‡ = Δ H ‡ − T Δ S ‡ {\displaystyle {\Delta G^{\ddagger }=\Delta H^{\ddagger }-T\Delta S^{\ddagger }}} , a quantity that can be regarded as the free energy change needed to reach the transition state. In particular, this energy barrier incorporates both enthalpic ( Δ H ‡ {\displaystyle \Delta H^{\ddagger }} ) and entropic ( Δ S ‡ {\displaystyle \Delta S^{\ddagger }} ) changes that need to be achieved for the reaction to take place: [ 7 ] [ 8 ] The result from transition state theory is k ( T ) = k B T h e − Δ G ‡ / R T {\textstyle k(T)={\frac {k_{\mathrm {B} }T}{h}}e^{-\Delta G^{\ddagger }/RT}} , where h is the Planck constant and R the molar gas constant . As useful rules of thumb, a first-order reaction with a rate constant of 10 −4 s −1 will have a half-life ( t 1/2 ) of approximately 2 hours. For a one-step process taking place at room temperature, the corresponding Gibbs free energy of activation (Δ G ‡ ) is approximately 23 kcal/mol.
The Arrhenius equation is an elementary treatment that gives the quantitative basis of the relationship between the activation energy and the reaction rate at which a reaction proceeds. The rate constant as a function of thermodynamic temperature is then given by:
k ( T ) = A e − E a / R T {\displaystyle k(T)=Ae^{-E_{\mathrm {a} }/RT}}
The reaction rate is given by:
r = A e − E a / R T [ A ] m [ B ] n , {\displaystyle r=Ae^{-E_{\mathrm {a} }/RT}[\mathrm {A} ]^{m}[\mathrm {B} ]^{n},}
where E a is the activation energy , and R is the gas constant, and m and n are experimentally determined partial orders in [A] and [B], respectively. Since at temperature T the molecules have energies according to a Boltzmann distribution , one can expect the proportion of collisions with energy greater than E a to vary with e − E a ⁄ RT . The constant of proportionality A is the pre-exponential factor , or frequency factor (not to be confused here with the reactant A) takes into consideration the frequency at which reactant molecules are colliding and the likelihood that a collision leads to a successful reaction. Here, A has the same dimensions as an ( m + n )-order rate constant ( see Units below ).
Another popular model that is derived using more sophisticated statistical mechanical considerations is the Eyring equation from transition state theory :
k ( T ) = κ k B T h ( c ⊖ ) 1 − M e − Δ G ‡ / R T = ( κ k B T h ( c ⊖ ) 1 − M ) e Δ S ‡ / R e − Δ H ‡ / R T , {\displaystyle k(T)=\kappa {\frac {k_{\mathrm {B} }T}{h}}(c^{\ominus })^{1-M}e^{-\Delta G^{\ddagger }/RT}=\left(\kappa {\frac {k_{\mathrm {B} }T}{h}}(c^{\ominus })^{1-M}\right)e^{\Delta S^{\ddagger }/R}e^{-\Delta H^{\ddagger }/RT},}
where Δ G ‡ is the free energy of activation, a parameter that incorporates both the enthalpy and entropy change needed to reach the transition state. The temperature dependence of Δ G ‡ is used to compute these parameters, the enthalpy of activation Δ H ‡ and the entropy of activation Δ S ‡ , based on the defining formula Δ G ‡ = Δ H ‡ − T Δ S ‡ . In effect, the free energy of activation takes into account both the activation energy and the likelihood of successful collision, while the factor k B T / h gives the frequency of molecular collision.
The factor ( c ⊖ ) 1- M ensures the dimensional correctness of the rate constant when the transition state in question is bimolecular or higher. Here, c ⊖ is the standard concentration, generally chosen based on the unit of concentration used (usually c ⊖ = 1 mol L −1 = 1 M), and M is the molecularity of the transition state. Lastly, κ, usually set to unity, is known as the transmission coefficient , a parameter which essentially serves as a " fudge factor " for transition state theory.
The biggest difference between the two theories is that Arrhenius theory attempts to model the reaction (single- or multi-step) as a whole, while transition state theory models the individual elementary steps involved. Thus, they are not directly comparable, unless the reaction in question involves only a single elementary step.
Finally, in the past, collision theory , in which reactants are viewed as hard spheres with a particular cross-section, provided yet another common way to rationalize and model the temperature dependence of the rate constant, although this approach has gradually fallen into disuse. The equation for the rate constant is similar in functional form to both the Arrhenius and Eyring equations:
k ( T ) = P Z e − Δ E / R T , {\displaystyle k(T)=PZe^{-\Delta E/RT},}
where P is the steric (or probability) factor and Z is the collision frequency, and Δ E is energy input required to overcome the activation barrier. Of note, Z ∝ T 1 / 2 {\displaystyle Z\propto T^{1/2}} , making the temperature dependence of k different from both the Arrhenius and Eyring models.
All three theories model the temperature dependence of k using an equation of the form
k ( T ) = C T α e − Δ E / R T {\displaystyle k(T)=CT^{\alpha }e^{-\Delta E/RT}}
for some constant C , where α = 0, 1 ⁄ 2 , and 1 give Arrhenius theory, collision theory, and transition state theory, respectively, although the imprecise notion of Δ E , the energy needed to overcome the activation barrier, has a slightly different meaning in each theory. In practice, experimental data does not generally allow a determination to be made as to which is "correct" in terms of best fit. Hence, all three are conceptual frameworks that make numerous assumptions, both realistic and unrealistic, in their derivations. As a result, they are capable of providing different insights into a system. [ 9 ]
The units of the rate constant depend on the overall order of reaction . [ 10 ]
If concentration is measured in units of mol·L −1 (sometimes abbreviated as M), then
Calculation of rate constants of the processes of generation and relaxation of electronically and vibrationally excited particles are of significant importance. It is used, for example, in the computer simulation of processes in plasma chemistry or microelectronics . First-principle based models should be used for such calculation. It can be done with the help of computer simulation software.
Rate constant can be calculated for elementary reactions by molecular dynamics simulations.
One possible approach is to calculate the mean residence time of the molecule in the reactant state. Although this is feasible for small systems with short residence times, this approach is not widely applicable as reactions are often rare events on molecular scale.
One simple approach to overcome this problem is Divided Saddle Theory. [ 11 ] Such other methods as the Bennett Chandler procedure , [ 12 ] [ 13 ] and Milestoning [ 14 ] have also been developed for rate constant calculations.
The theory is based on the assumption that the reaction can be described by a reaction coordinate, and that we can apply Boltzmann distribution at least in the reactant state.
A new, especially reactive segment of the reactant, called the saddle domain , is introduced, and the rate constant is factored:
k = k S D ⋅ α R S S D {\displaystyle k=k_{\mathrm {SD} }\cdot \alpha _{\mathrm {RS} }^{\mathrm {SD} }}
where α SD RS is the conversion factor between the reactant state and saddle domain, while k SD is the rate constant from the saddle domain. The first can be simply calculated from the free energy surface, the latter is easily accessible from short molecular dynamics simulations [ 11 ] | https://en.wikipedia.org/wiki/Reaction_rate_constant |
In chemistry , a reaction step of a chemical reaction is defined as: "An elementary reaction , constituting one of the stages of a stepwise reaction in which a reaction intermediate (or, for the first step, the reactants) is converted into the next reaction intermediate (or, for the last step, the products ) in the sequence of intermediates between reactants and products" . [ 1 ] To put it simply, it is an elementary reaction which goes from one reaction intermediate to another or to the final product.
This physical chemistry -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Reaction_step |
Organoboron chemistry or organoborane chemistry studies organoboron compounds , also called organoboranes . These chemical compounds combine boron and carbon ; typically, they are organic derivatives of borane (BH 3 ), as in the trialkyl boranes. [ 1 ] [ 2 ]
Organoboranes and -borates enable many chemical transformations in organic chemistry — most importantly, hydroboration and carboboration . Most reactions transfer a nucleophilic boron substituent to an electrophilic center either inter- or intramolecularly . In particular, α,β -unsaturated borates and borates with an α leaving group are highly susceptible to intramolecular 1,2-migration of a group from boron to the electrophilic α position. Oxidation or protonolysis of the resulting organoboranes generates many organic products, including alcohols, carbonyl compounds, alkenes, and halides. [ 3 ]
The C-B bond has low polarity ( electronegativity 2.55 for carbon and 2.04 for boron). Alkyl boron compounds are in general stable, though easily oxidized.
Boron often forms electron-deficient compounds without a full octet , such as the triorganoboranes. These compounds are strong electrophiles , but typically too sterically hindered to dimerize . Electron donation from vinyl and aryl groups can lend the C-B bond some double bond character.
The most-studied class of organoboron compounds has the formula BR n H 3−n . These compounds are catalysts, reagents, and synthetic intermediates. Except a few bulky derivatives, the primary and secondary hydrides (n = 1 or 2) are, like diborane itself, strongly Lewis acidic and dimerize in condensed phases. The trialkyl and triaryl derivatives, e.g. triethylboron , are typically only weakly Lewis acidic , and form monomers with a trigonal, planar boron center. [ 5 ]
Monoalkyl boranes are relatively rare. When the alkyl group is small, such as methyl, monoalkylboranes often redistribute to mixtures of diborane and di- and trialkylboranes. One example of an isolable (bulky) primary borane is thexylborane (ThxBH 2 ), produced by the hydroboration of tetramethylethylene : [ 6 ] A chiral example is monoisopinocampheylborane, obtained by hydroboration of (−)‐α‐pinene with borane dimethyl sulfide . Although often written as IpcBH 2 , it is a dimer, [IpcBH 2 ] 2 . [ 7 ]
Dialkylboranes are also rare with small alkyls. One common preparation reduces dialkylhalogenoboranes with metal hydrides. [ 8 ] An important application in organic synthesis is transmetallation to form organozinc compounds . [ 9 ] [ 10 ] Nevertheless, some diaryl and dialkylboranes are well known. Dimesitylborane is a dimer (C 6 H 2 Me 3 ) 4 B 2 H 2 ) that reacts only slowly with simple terminal alkenes. It adds to alkynes to give alkenylboranes. [ 11 ] A hindered dialkylborane is disiamylborane , abbreviated Sia 2 BH, also a dimer. Owing to its steric bulk, it selectively hydroborates less hindered, usually terminal alkenes in the presence of more substituted alkenes. [ 12 ] Disiamylborane must be freshly prepared as its solutions can only be stored at 0 °C for a few hours. Dicyclohexylborane Chx 2 BH exhibits improved thermal stability than Sia 2 BH.
A versatile dialkylborane is 9-BBN . Also called "banana borane", it exists as a dimer. It can be distilled without decomposition at 195 °C (12mm Hg). Reactions with 9-BBN typically occur at 60–80 °C, with most alkenes reacting within one hour. Tetrasubstituted alkenes add 9-BBN at elevated temperature. Hydroboration of alkenes with 9-BBN proceeds with excellent regioselectivity. It is more sensitive to steric differences than Sia 2 BH, perhaps because of it rigid C 8 backbone. 9-BBN is more reactive towards alkenes than alkynes. [ 13 ]
Compounds of the type BR n (OR) 3-n are called borinic esters (n = 2), boronic esters (n = 1), and borates (n = 0). Boronic acids are key to the Suzuki reaction . Trimethyl borate , debatably not an organoboron compound, is an intermediate in sodium borohydride production.
Boranes and borinic, boronic, and borate esters all form adducts with appropriate Lewis bases.
Strong bases do not deprotonate boranes of the form R 2 BH. Instead these reactions afford the octet-complete adduct R 2 HB-base. [ 14 ]
NHCs and boranes form stable NHC-borane adducts . [ 15 ] Triethylborane adducts can be synthesised directly from the imidazolium salt and lithium triethylborohydride .
Boron is renowned for cluster species , e.g. dodecaborate [B 12 H 12 ] 2- . Such clusters have many organic derivatives. One example is [B 12 (CH 3 ) 12 ] 2- and its radical derivative [B 12 (CH 3 ) 12 ] − . [ 16 ] Related cluster compounds with carbon vertices are carboranes ; the best known is orthocarborane, C 2 B 10 H 12 . Carboranes have few commercial applications. Anionic derivatives such as [C 2 B 9 H 11 ] 2− , called dicarbollides, ligate similarly to cyclopentadienide .
Borane cluster structures are built from the triangular (BR) 3 unit , which is almost unknown in isolation. However, the corresponding aromatic dianion, (BR) 2− 3 , forms from careful dehalogenation of a RNBCl 2 species. [ 17 ]
Organometallic compounds with metal-boron bonds (M–BR 2 ) are boryl complexes, corresponding to the notional boryl anion R 2 B − , although the latter cannot be produced through deprotonation (see § Adducts ). In one synthesis, the boryl anion moiety arose through lithium-halogen exchange :
As shown, the product is isoelectronic to an N-heterocyclic carbene . [ 18 ] [ 19 ]
Related ligands are borylenes (M–B(R)–M).
Alkylideneboranes (RB=CRR) with a boron–carbon double bond are rare. One example, HB=CH 2 , can be detected at low temperature. The derivative CH 3 B=C(SiMe 3 ) 2 is fairly stable, but prone to cyclodimerisation . [ 20 ]
Some boron-substituted heterocycles are aromatic , but very few such arenes are stable. In borabenzene , boron replaces one CH center in benzene. Borabenzene and derivatives invariably appear as adducts, e.g., C 5 H 5 B-pyridine. The cyclic compound borole , a structural analog of pyrrole , has not been isolated, but substituted derivatives (boroles) are known. The cyclic compound borepin has been isolated and is aromatic.
Boron-boron multiple bonds are rare, although doubly-bonded dianions have been known since the 1990s. [ 21 ] Neutral analogues use NHC adducts, such as the following diborane(2) derivative: [ 22 ] [ 23 ]
Each boron atom has an attached proton and is coordinated to a NHC carbene . [ 24 ] [ 25 ]
A reported diboryne is based on similar chemistry. [ 26 ]
A compound with the B≡C triple bond was synthesized for the first time in 2025. [ 27 ]
Simple organoboranes such as triethylborane or tris(pentafluorophenyl)boron can be prepared from trifluoroborane (in ether ) and the ethyl or pentafluorophenyl Grignard reagent . Further carbanion addition will effect a borate (R 4 B − ).
Boronic acids RB(OH) 2 react with potassium bifluoride K[HF 2 ] to form trifluoroborate salts K[RBF 3 ], [ 28 ] precursors to nucleophilic alkyl and aryl boron difluorides, ArBF 2 : [ 29 ]
In hydroboration , alkenes insert into borane B-H bonds, with anti-Markovnikov stereochemistry. Hydroboration occurs stereospecifically syn — on the same alkene face. The transition state for this concerted reaction can be visualized as a square with the corners occupied by carbon, carbon, hydrogen and boron, maximizing overlap between the olefin p-orbitals and the empty boron orbital.
Hydroboration with borane (BH 3 ) equivalents converts only 33% of the starting olefin to product — boron-containing byproducts consume the remainder. The chelate effect improves that ratio for cyclic boron-containing reagents. One common cyclic organoboron reagent is 9-BBN . [ 30 ] [ 31 ]
Metal-catalyzed borylation reactions produce an organoboron compound from aliphatic or aromatic C-H sigma bonds via a transition-metal catalyst. A common reagent is bis(pinacolato)diboron .
Carbon monoxide reacts with alkylboranes to form an unstable borane carbonyl . Then an alkyl substituent migrates from boron to the carbonyl carbon. For example, homologated primary alcohols result from organoboranes, carbon monoxide, and a reducing agent (here, sodium borohydride ): [ 32 ]
Alkynylboranes attack electrophiles to give trans alkenylboranes, [ 33 ] as in the first step of this olefin synthesis:
The key property of organoboranes (R 3 B) and borates (R 4 B − , generated via addition of R − to R 3 B) is their susceptibility to reorganization. These compounds possess boron–carbon bonds polarized toward carbon. The boron-attached carbon is nucleophilic; [ 34 ] in borates, the nucleophicity suffices for intermolecular transfer to an electrophile. [ 35 ] [ 3 ]
Boranes alone are generally not nucleophilic enough to transfer an R group intermolecularly. Instead, the group 1,2-migrates to an electrophilic carbon attached to boron, especially if that carbon is unsaturated or bears a good leaving group: [ 35 ]
An organic group's migration propensity depends on its ability to stabilize negative charge: alkynyl > aryl ≈ alkenyl > primary alkyl > secondary alkyl > tertiary alkyl. [ 36 ] Bis(norbornyl)borane and 9-BBN are often hydroboration reagents for this reason — only the hydroborated olefin is likely to migrate upon nucleophilic activation.
Migration retains configuration at the migrant carbon [ 37 ] and inverts it at the (presumably sp 3 -hybridized ) terminus. [ 38 ] The resulting reorganized borane can then be oxidized or protolyzed to a final product.
Organoboranes are unstable to Brønsted–Lowry acids , deboronating in favor of a proton. Consequently, organoboranes are easily removed from an alkane or alkene substrate, as in the second step of this olefin synthesis: [ 33 ]
α-Halo enolates are common nucleophiles in borane reorganization. After nucleophilic attack at boron, the resulting ketoboronate eliminates the halogen and tautomerizes to a neutral enolborane. A functionalized carbonyl compound then results from protonolysis, [ 39 ] or quenching with other electrophiles:
Because the migration is stereospecific, this method synthesizes enantiopure α-alkyl or -aryl ketones. [ 40 ]
α-Haloester enolates add similarly to boranes, but with lower yields: [ 41 ]
Diazoesters and diazoketones remove the requirement for external base. [ 42 ] α,α'-Dihalo enolates react with boranes to form α-halo carbonyl compounds that can be further functionalized at the α position. [ 43 ]
In allylboration, an allylborane adds across an aldehyde or ketone with an allylic shift , and can then be converted to a homoallylic alcohol during workup . The reaction is much slower with ketones than aldehydes. [ 44 ] For example, in Nicolaou's epothilones synthesis, asymmetric allylboration (with an allylborane derived from chiral alpha-pinene ) is the first step in a two-carbon homologation to acetogenin : [ 45 ]
Trifluoroborate salts are stabler than boronic acids and selectively alkylate aldehydes : [ 46 ]
The hydroboration-oxidation reaction pair oxidizes the borane to an alcohol with hydrogen peroxide or to a carbonyl group with chromium oxide .
Oxidation of an alkenylborane gives a boron-free enol. [ 47 ]
Organoborane activation with hydroxide or alkoxide and treatment with X 2 yields haloalkanes. With excess base, two of the three alkyl groups attached to the boron atom may convert to halide, but disiamylborane permits only halogenation of the hydroborated olefin: [ 48 ]
Treatment of an alkenylborane with iodine or bromine induces migration of a boron-attached organic group. Alkynyl groups migrate selectively, forming enynes after treatment with sodium acetate and hydrogen peroxide: [ 49 ]
Organoboron compounds also transmetalate easily, especially to organopalladium compounds. In the Suzuki reaction , an aryl - or vinyl - boronic acid couples to an aryl - or vinyl - halide through a palladium(0) complex catalyst: [ 50 ] R 1 − BY 2 + R 2 − X → Base Pd catalyst R 1 − R 2 {\displaystyle {\ce {R1-BY2{}+R2-X->[{} \atop {\underset {\text{catalyst}}{\ce {Pd}}}][{\text{Base}}]R1-R2}}}
Borane hydrides such as 9-BBN and L-selectride (lithium tri( sec-butyl )borohydride) are reducing agents . An asymmetric catalyst for carbonyl reductions is the CBS catalyst , which relies on boron coordination to the carbonyl oxygen.
Homologated primary alcohols result from the treatment of organoboranes with carbon monoxide and a hydride: [ 51 ]
Tertiary alcohols with two identical groups attached to the alcohol carbon may be synthesized through an alkynylborane double migration: [ 47 ]
Organoborates anions reductively eliminate against acyl halides. Here, the borate was generated from tri(cyclopentyl)borane and phenyllithium; the three cyclopentyl groups do not significantly migrate: [ 52 ]
Organoboron chemistry is mainly of commercial value in the pharmaceutical industry.
Triethylborane was used to ignite the JP-7 fuel of the Pratt & Whitney J58 variable cycle engines powering the Lockheed SR-71 Blackbird .
Organoboron compounds have long been discussed for use as boron delivery agents in neutron capture therapy of cancer . [ 53 ] | https://en.wikipedia.org/wiki/Reactions_of_organoborates_and_boranes |
Reactions of organocopper reagents involve species containing copper-carbon bonds acting as nucleophiles in the presence of organic electrophiles . Organocopper reagents are now commonly used in organic synthesis as mild, selective nucleophiles for substitution and conjugate addition reactions. [ 1 ]
Since the discovery that copper(I) halides catalyze the conjugate addition of Grignard reagents in 1941, [ 2 ] organocopper reagents have emerged as weakly basic, nucleophilic reagents for substitution and addition reactions. The constitution of organocopper compounds depends on their method of preparation and the various kinds of organocopper reagents exhibit different reactivity profiles . As a result, the scope of reactions involving organocopper reagents is extremely broad.
The mechanism of nucleophilic substitution by lower-order organocuprates depends in a profound way on the structure of the substrate, organocuprate, and reaction conditions. Early evidence suggested that a direct S N 2 displacement was occurring; [ 6 ] however more recent results suggest that invertive oxidative addition of copper(I) into the carbon-leaving group bond takes place, generating a copper(III) intermediate which then undergoes reductive elimination to generate the coupled product. [ 7 ] Both of these mechanisms predict inversion at the electrophilic carbon, which is observed in a number of cases. [ 8 ] On the other hand, experiments with radical traps and the observation of racemization during substitution suggest a radical mechanism. [ 9 ]
(1)
In 1941, Kharash discovered that Grignard reagents add to cyclohexenone in presence of Cu(I) resulting in 1,4-addition instead of 1,2-addition. [ 10 ] This work foreshadowed extensive studies on the conjugate additions to enones with organocuprates. Note that if a Grignard reagent (such as RMgBr) is used, the reaction with an enone would instead proceed through a 1,2-addition. The 1,4-addition mechanism of cuprates to enones goes through the nucleophilic addition of the Cu(I) species at the beta-carbon of the alkene to form a Cu(III) intermediate, followed by reductive elimination of Cu(I). [ 11 ] In the original paper describing this reaction, methylmagnesium bromide is reacted with isophorone with and without 1 mole percent of added copper(I) chloride (see figure). [ 10 ]
Without added salt the main products are alcohol B (42%) from nucleophilic addition to the carbonyl group and diene C (48%) as its dehydration reaction product. With added salt the main product is 1,4-adduct A (82%) with some C (7%).
A 1,6-addition is also possible, for example in one step of the commercial-scale production of fulvestrant : [ 12 ]
Diastereoselective conjugate addition reactions of chiral organocuprates provide β-functionalized ketones in high yield and diastereoselectivity. A disadvantage of these reactions is the requirement of a full equivalent of enantiopure starting material. [ 13 ]
(3)
More recently, catalytic enantioselective methods have been developed based on the copper(I)-catalyzed conjugate addition of Grignard reactions to enones. The proposed mechanism involves transmetalation from the Grignard reagent to copper, conjugate addition, and rate-determining reductive elimination (see the analogous upper pathway in equation (2)). [ 14 ]
(4)
Vinyl and aryl Grignard reagents couple with primary alkyl halides in the presence of a catalytic amount of a copper(I) halide salt. The use of Li 2 CuCl 4 rather than simple copper(I) halide salts (CuX) improves yields of these coupling reactions. [ 15 ]
(5)
The addition of Grignard reagents to alkynes is facilitated by a catalytic amount of copper halide. Transmetalation to copper and carbocupration are followed by transmetalation of the product alkene back to magnesium . The addition is syn unless a coordinating group is nearby in the substrate, in which case the addition becomes anti and yields improve. [ 16 ]
(6)
Propargyl methanesulfinates are useful substrates for the synthesis of allenes from stoichiometric organocopper complexes. In this case, the complexes were generated in situ through the combination of a Grignard reagent, copper(I) bromide, and lithium bromide. Organocopper complexes very often need Lewis acid activation in order to react efficiently; magnesium bromide generated in situ serves as an activating Lewis acid in this case. [ 17 ]
(7)
Alkenylcopper complexes, easily generated through carbocupration, are useful for the introduction of a vinyl group in the β position of a carbonyl compound. In this case, as above, magnesium bromide is serving as an activating Lewis acid. [ 18 ]
(8)
Epoxide opening with organocuprates is highly selective for the less hindered position. Substitution takes place with complete inversion of configuration at the electrophilic carbon. [ 19 ]
(9)
Generally, organocuprates react with allylic electrophiles in an anti S N 2 fashion. In the reaction below, nearly complete inversion of configuration was observed despite the presence of a second stereocenter in the ring. [ 20 ]
(10)
Conjugate addition of organocuprates is widely used in organic synthesis. Vinyl ether cuprates serve as convenient acyl anion equivalents in conjugate addition reactions to enones. The resulting enol ethers can be hydrolyzed to 1,4-diketones, which are difficult to access using conventional carbonyl chemistry. [ 21 ]
(11)
The use of additives in conjunction with a stoichiometric amount of organocopper complexes enhances the rate and yield of many reactions. Organocopper complexes in particular react sluggishly in the absence of a Lewis acid. Although magnesium bromide generated in situ from the reaction of Grignard reagents and copper(I) halides can serve this role (see above), external Lewis acids are also useful. In the presence of boron trifluoride etherate, organocopper complexes are able to add to sterically congested enones in moderate yield (effecting the same transformation with an organocuprate would be difficult). [ 22 ]
(12)
Boron trifluoride etherate is also useful as an additive in reactions of higher-order cyanocuprates. The use of the 2-thienyl group as a "dummy" substituent in the cyanocuprate conserves the potentially valuable organolithium reagent used to generate the cyanocuprate (as only the dummy group is present in copper-containing byproducts). In the absence of boron trifluoride etherate, no reaction was observed in this case. [ 23 ]
(13)
Conjugate addition reactions of higher-order cyanocuprates represent another useful application for boron trifluoride etherate. The vinyl group is transferred selectively in this reaction (there is a mistake in a scheme); this is in contrast to substitution reactions employing the same reagent, which result in selective transfer of the methyl group. [ 24 ]
(14)
Secondary amines can be alkylated with cuprates. The reaction is based on the oxidative coupling of lithium alkyl copper amide which is reported to form in situ during the reaction between lithium dialkylcuprates and primary or secondary amides. [ 25 ]
Because the stereoselectivity of carbocupration is extremely high, the reaction has been applied to the synthesis of pheromones in which the geometric purity of double bonds is critical. One example is the insect pheromone of Cossus cossus , which is synthesized by syn -selective carbocupration of acetylene and alkylation of the resulting organocuprate in the presence of added phosphite. [ 26 ]
(15) | https://en.wikipedia.org/wiki/Reactions_of_organocopper_reagents |
Reactions on surfaces are reactions in which at least one of the steps of the reaction mechanism is the adsorption of one or more reactants. The mechanisms for these reactions, and the rate equations are of extreme importance for heterogeneous catalysis . Via scanning tunneling microscopy , it is possible to observe reactions at the solid gas interface in real space, if the time scale of the reaction is in the correct range. [ 1 ] [ 2 ] Reactions at the solid–gas interface are in some cases related to catalysis.
If a reaction occurs through these steps:
where A is the reactant and S is an adsorption site on the surface and the respective rate constants for the adsorption, desorption and reaction are k 1 , k −1 and k 2 , then the global reaction rate is:
where:
C S {\displaystyle C_{\mathrm {S} }} is highly related to the total surface area of the adsorbent: the greater the surface area, the more sites and the faster the reaction. This is the reason why heterogeneous catalysts are usually chosen to have great surface areas (in the order of a hundred m 2 /gram)
If we apply the steady state approximation to AS, then:
and
The result is equivalent to the Michaelis–Menten kinetics of reactions catalyzed at a site on an enzyme . The rate equation is complex, and the reaction order is not clear. In experimental work, usually two extreme cases are looked for in order to prove the mechanism. In them, the rate-determining step can be:
The order respect to A is 1. Examples of this mechanism are N 2 O on gold and HI on platinum
The last expression is the Langmuir isotherm for the surface coverage. The adsorption equilibrium constant K 1 = k 1 k − 1 {\displaystyle K_{1}={\frac {k_{1}}{k_{-1}}}} , and the numerator and denominator have each been divided by k − 1 {\displaystyle k_{-1}} . The overall reaction rate becomes r = K 1 k 2 C A C S K 1 C A + 1 {\displaystyle r={\frac {K_{1}k_{2}C_{\mathrm {A} }C_{\mathrm {S} }}{K_{1}C_{\mathrm {A} }+1}}} .
Depending on the concentration of the reactant the rate changes:
In this mechanism, suggested by Irving Langmuir in 1921 and further developed by Cyril Hinshelwood in 1926, two molecules adsorb on neighboring sites and the adsorbed molecules undergo a bimolecular reaction: [ 3 ]
The rate constants are k 1 {\displaystyle k_{1}} and k − 1 {\displaystyle k_{-1}} for adsorption and desorption of A respectively, k 2 {\displaystyle k_{2}} and k − 2 {\displaystyle k_{-2}} for adsorption and desorption of B, and k {\displaystyle k} for the reaction generating the final products. The rate law is: r = k θ A θ B C S 2 {\displaystyle r=k\theta _{\mathrm {A} }\theta _{\mathrm {B} }C_{\mathrm {S} }^{2}}
Proceeding as before we get θ A = k 1 C A θ E k − 1 + k C S θ B {\displaystyle \theta _{\mathrm {A} }={\frac {k_{1}C_{\mathrm {A} }\theta _{E}}{k_{-1}+kC_{\mathrm {S} }\theta _{\mathrm {B} }}}} , where θ E {\displaystyle \theta _{E}} is the fraction of empty sites, so θ A + θ B + θ E = 1 {\displaystyle \theta _{\mathrm {A} }+\theta _{\mathrm {B} }+\theta _{E}=1} . Let us assume now that the rate limiting step is the reaction of the adsorbed molecules, which is easily understood: the probability of two adsorbed molecules colliding is low.
Then θ A = K 1 C A θ E {\displaystyle \theta _{\mathrm {A} }=K_{1}C_{\mathrm {A} }\theta _{E}} , with K i = k i / k − i {\displaystyle K_{i}=k_{i}/k_{-i}} , which is nothing but Langmuir isotherm for two adsorbed gases, with adsorption constants K 1 {\displaystyle K_{1}} and K 2 {\displaystyle K_{2}} .
Calculating θ E {\displaystyle \theta _{E}} from θ A {\displaystyle \theta _{\mathrm {A} }} and θ B {\displaystyle \theta _{\mathrm {B} }} we finally get
The rate law is complex and there is no clear order with respect to either reactant, but we can consider different values of the constants, for which it is easy to measure integer orders:
That means that 1 ≫ K 1 C A , K 2 C B {\displaystyle 1\gg K_{1}C_{\mathrm {A} },K_{2}C_{\mathrm {B} }} , so r = k C S 2 K 1 K 2 C A C B {\displaystyle r=kC_{\mathrm {S} }^{2}K_{1}K_{2}C_{\mathrm {A} }C_{\mathrm {B} }} . The order is one with respect to each reactant, and the overall order is two.
In this case K 1 C A , 1 ≫ K 2 C B {\displaystyle K_{1}C_{\mathrm {A} },1\gg K_{2}C_{\mathrm {B} }} , so r = k C S 2 K 1 K 2 C A C B ( 1 + K 1 C A ) 2 {\displaystyle r=kC_{\mathrm {S} }^{2}{\frac {K_{1}K_{2}C_{\mathrm {A} }C_{\mathrm {B} }}{(1+K_{1}C_{\mathrm {A} })^{2}}}} . The reaction order is 1 with respect to B. There are two extreme possibilities for the order with respect to A:
One of the reactants has very high adsorption and the other one doesn't adsorb strongly.
K 1 C A ≫ 1 , K 2 C B {\displaystyle K_{1}C_{\mathrm {A} }\gg 1,K_{2}C_{\mathrm {B} }} , so r = k C S 2 K 2 C B K 1 C A {\displaystyle r=kC_{\mathrm {S} }^{2}{\frac {K_{2}C_{\mathrm {B} }}{K_{1}C_{\mathrm {A} }}}} . The reaction order is 1 with respect to B and −1 with respect to A. Reactant A inhibits the reaction at all concentrations.
The following reactions follow a Langmuir–Hinshelwood mechanism: [ 4 ]
In this mechanism, proposed in 1922 by Irving Langmuir and later expanded upon by Eric Rideal , only one of the molecules adsorbs and the other one reacts with it directly from the gas phase, without adsorbing (" nonthermal surface reaction "):
Constants are k 1 , k − 1 {\displaystyle k_{1},k_{-1}} and k {\displaystyle k} and rate equation is r = k C S θ A C B {\displaystyle r=kC_{\mathrm {S} }\theta _{\mathrm {A} }C_{\mathrm {B} }} . Applying steady state approximation to AS and proceeding as before (considering the reaction the limiting step once more) we get r = k C S C B K 1 C A K 1 C A + 1 {\displaystyle r=kC_{\mathrm {S} }C_{\mathrm {B} }{\frac {K_{1}C_{\mathrm {A} }}{K_{1}C_{\mathrm {A} }+1}}} . The order is one with respect to B. There are two possibilities, depending on the concentration of reactant A:
The following reactions follow an Langmuir–Rideal mechanism: [ 4 ]
The Langmuir-Rideal mechanism is often, incorrectly, attributed to Dan Eley as the Eley-Rideal mechanism. [ 5 ] The actual Eley-Rideal mechanism, studied in the thesis of Dan Eley and proposed by Eric Rideal in 1939, was the reaction between a chemisorbed and a physisorbed molecule. [ 6 ] As opposed to the Langmuir-Rideal mechanism, in this mechanism the physisorbed molecule is in thermal equilibrium with the surface. | https://en.wikipedia.org/wiki/Reactions_on_surfaces |
Reaction–diffusion systems are mathematical models that correspond to several physical phenomena. The most common is the change in space and time of the concentration of one or more chemical substances: local chemical reactions in which the substances are transformed into each other, and diffusion which causes the substances to spread out over a surface in space.
Reaction–diffusion systems are naturally applied in chemistry . However, the system can also describe dynamical processes of non-chemical nature. Examples are found in biology , geology and physics (neutron diffusion theory) and ecology . Mathematically, reaction–diffusion systems take the form of semi-linear parabolic partial differential equations . They can be represented in the general form
where q ( x , t ) represents the unknown vector function, D is a diagonal matrix of diffusion coefficients , and R accounts for all local reactions. The solutions of reaction–diffusion equations display a wide range of behaviours, including the formation of travelling waves and wave-like phenomena as well as other self-organized patterns like stripes, hexagons or more intricate structure like dissipative solitons . Such patterns have been dubbed " Turing patterns ". [ 1 ] Each function, for which a reaction diffusion differential equation holds, represents in fact a concentration variable .
The simplest reaction–diffusion equation is in one spatial dimension in plane geometry,
is also referred to as the Kolmogorov–Petrovsky–Piskunov equation . [ 2 ] If the reaction term vanishes, then the equation represents a pure diffusion process. The corresponding equation is Fick's second law . The choice R ( u ) = u (1 − u ) yields Fisher's equation that was originally used to describe the spreading of biological populations , [ 3 ] the Newell–Whitehead-Segel equation with R ( u ) = u (1 − u 2 ) to describe Rayleigh–Bénard convection , [ 4 ] [ 5 ] the more general Zeldovich–Frank-Kamenetskii equation with R ( u ) = u (1 − u )e - β (1- u ) and 0 < β < ∞ ( Zeldovich number ) that arises in combustion theory, [ 6 ] and its particular degenerate case with R ( u ) = u 2 − u 3 that is sometimes referred to as the Zeldovich equation as well. [ 7 ]
The dynamics of one-component systems is subject to certain restrictions as the evolution equation can also be written in the variational form
and therefore describes a permanent decrease of the "free energy" L {\displaystyle {\mathfrak {L}}} given by the functional
with a potential V ( u ) such that R ( u ) = d V ( u ) / d u .
In systems with more than one stationary homogeneous solution, a typical solution is given by travelling fronts connecting the homogeneous states. These solutions move with constant speed without changing their shape and are of the form u ( x , t ) = û ( ξ ) with ξ = x − ct , where c is the speed of the travelling wave. Note that while travelling waves are generically stable structures, all non-monotonous stationary solutions (e.g. localized domains composed of a front-antifront pair) are unstable. For c = 0 , there is a simple proof for this statement: [ 8 ] if u 0 ( x ) is a stationary solution and u = u 0 ( x ) + ũ ( x , t ) is an infinitesimally perturbed solution, linear stability analysis yields the equation
With the ansatz ũ = ψ ( x )exp(− λt ) we arrive at the eigenvalue problem
of Schrödinger type where negative eigenvalues result in the instability of the solution. Due to translational invariance ψ = ∂ x u 0 ( x ) is a neutral eigenfunction with the eigenvalue λ = 0 , and all other eigenfunctions can be sorted according to an increasing number of nodes with the magnitude of the corresponding real eigenvalue increases monotonically with the number of zeros. The eigenfunction ψ = ∂ x u 0 ( x ) should have at least one zero, and for a non-monotonic stationary solution the corresponding eigenvalue λ = 0 cannot be the lowest one, thereby implying instability.
To determine the velocity c of a moving front, one may go to a moving coordinate system and look at stationary solutions:
This equation has a nice mechanical analogue as the motion of a mass D with position û in the course of the "time" ξ under the force R with the damping coefficient c which allows for a rather illustrative access to the construction of different types of solutions and the determination of c .
When going from one to more space dimensions, a number of statements from one-dimensional systems can still be applied. Planar or curved wave fronts are typical structures, and a new effect arises as the local velocity of a curved front becomes dependent on the local radius of curvature (this can be seen by going to polar coordinates ). This phenomenon leads to the so-called curvature-driven instability. [ 9 ]
Two-component systems allow for a much larger range of possible phenomena than their one-component counterparts. An important idea that was first proposed by Alan Turing is that a state that is stable in the local system can become unstable in the presence of diffusion . [ 10 ]
A linear stability analysis however shows that when linearizing the general two-component system
a plane wave perturbation
of the stationary homogeneous solution will satisfy
Turing's idea can only be realized in four equivalence classes of systems characterized by the signs of the Jacobian R ′ of the reaction function. In particular, if a finite wave vector k is supposed to be the most unstable one, the Jacobian must have the signs
This class of systems is named activator-inhibitor system after its first representative: close to the ground state, one component stimulates the production of both components while the other one inhibits their growth. Its most prominent representative is the FitzHugh–Nagumo equation
with f ( u ) = λu − u 3 − κ which describes how an action potential travels through a nerve. [ 11 ] [ 12 ] Here, d u , d v , τ , σ and λ are positive constants.
When an activator-inhibitor system undergoes a change of parameters, one may pass from conditions under which a homogeneous ground state is stable to conditions under which it is linearly unstable. The corresponding bifurcation may be either a Hopf bifurcation to a globally oscillating homogeneous state with a dominant wave number k = 0 or a Turing bifurcation to a globally patterned state with a dominant finite wave number. The latter in two spatial dimensions typically leads to stripe or hexagonal patterns.
For the Fitzhugh–Nagumo example, the neutral stability curves marking the boundary of the linearly stable region for the Turing and Hopf bifurcation are given by
If the bifurcation is subcritical, often localized structures ( dissipative solitons ) can be observed in the hysteretic region where the pattern coexists with the ground state. Other frequently encountered structures comprise pulse trains (also known as periodic travelling waves ), spiral waves and target patterns. These three solution types are also generic features of two- (or more-) component reaction–diffusion equations in which the local dynamics have a stable limit cycle [ 13 ]
For a variety of systems, reaction–diffusion equations with more than two components have been proposed, e.g. the Belousov–Zhabotinsky reaction , [ 14 ] for blood clotting , [ 15 ] fission waves [ 16 ] or planar gas discharge systems. [ 17 ]
It is known that systems with more components allow for a variety of phenomena not possible in systems with one or two components (e.g. stable running pulses in more than one spatial dimension without global feedback). [ 18 ] An introduction and systematic overview of the possible phenomena in dependence on the properties of the underlying system is given in. [ 19 ]
In recent times, reaction–diffusion systems have attracted much interest as a prototype model for pattern formation . [ 20 ] The above-mentioned patterns (fronts, spirals, targets, hexagons, stripes and dissipative solitons) can be found in various types of reaction–diffusion systems in spite of large discrepancies e.g. in the local reaction terms. It has also been argued that reaction–diffusion processes are an essential basis for processes connected to morphogenesis in biology [ 21 ] [ 22 ] and may even be related to animal coats and skin pigmentation. [ 23 ] [ 24 ] Other applications of reaction–diffusion equations include ecological invasions, [ 25 ] spread of epidemics, [ 26 ] tumour growth, [ 27 ] [ 28 ] [ 29 ] dynamics of fission waves, [ 30 ] wound healing [ 31 ] and visual hallucinations. [ 32 ] Another reason for the interest in reaction–diffusion systems is that although they are nonlinear partial differential equations, there are often possibilities for an analytical treatment. [ 8 ] [ 9 ] [ 33 ] [ 34 ] [ 35 ] [ 20 ]
Well-controllable experiments in chemical reaction–diffusion systems have up to now been realized in three ways. First, gel reactors [ 36 ] or filled capillary tubes [ 37 ] may be used. Second, temperature pulses on catalytic surfaces have been investigated. [ 38 ] [ 39 ] Third, the propagation of running nerve pulses is modelled using reaction–diffusion systems. [ 11 ] [ 40 ]
Aside from these generic examples, it has turned out that under appropriate circumstances electric transport systems like plasmas [ 41 ] or semiconductors [ 42 ] can be described in a reaction–diffusion approach. For these systems various experiments on pattern formation have been carried out.
A reaction–diffusion system can be solved by using methods of numerical mathematics . There exist several numerical treatments in research literature. [ 43 ] [ 20 ] [ 44 ] Numerical solution methods for complex geometries are also proposed. [ 45 ] [ 46 ] Reaction-diffusion systems are described to the highest degree of detail with particle based simulation tools like SRSim or ReaDDy [ 47 ] which employ among others reversible interacting-particle reaction dynamics. [ 48 ] | https://en.wikipedia.org/wiki/Reaction–diffusion_system |
Reactive & Functional Polymers is a monthly peer-reviewed scientific journal , established in 1982 and published by Elsevier . It covers research on both the science and the technology of reactive polymers (those with functional groups) including polymers and other polymers with specific chemical reactivity or other functionality. The journal publishes both original research and review papers. The editor-in-chief is Alexander Bismarck ( University of Vienna ). [ 1 ]
The journal is abstracted and indexed in:
According to the Journal Citation Reports , the journal has a 2020 impact factor of 3.975. [ 7 ]
This article about a chemistry journal is a stub . You can help Wikipedia by expanding it .
See tips for writing articles about academic journals . Further suggestions might be found on the article's talk page .
This article about a materials science journal is a stub . You can help Wikipedia by expanding it .
See tips for writing articles about academic journals . Further suggestions might be found on the article's talk page . | https://en.wikipedia.org/wiki/Reactive_&_Functional_Polymers |
Reactive armour is a type of vehicle armour used in protecting vehicles, especially modern tanks, against shaped charges and hardened kinetic energy penetrators . The most common type is explosive reactive armour (ERA), but variants include self-limiting explosive reactive armour (SLERA), non-energetic reactive armour (NERA), non-explosive reactive armour (NxRA), and electric armour. NERA and NxRA modules can withstand multiple hits, unlike ERA and SLERA.
When a shaped charge strikes the upper plate of the armour, it detonates the inner explosive, releasing blunt damage that the tank can absorb.
Reactive armour is intended to counteract anti-tank munitions that work by piercing the armour and then either killing the crew inside, disabling vital mechanical systems, or creating spalling that disables the crew—or all three.
Reactive armour can be defeated with multiple hits in the same place, as by tandem-charge weapons, which fire two or more shaped charges in rapid succession. Without tandem charges, hitting precisely the same spot twice is much more difficult.
The Australians were the first recorded to have conceptualized and developed methods to disrupt and spread the jet of a hollow charge shell to reduce its penetrating power. In a June 1944 report from the Explosives Manufacturing Practices Laboratory of the Explosives Factory Maribyrnong, an operational requirement for the defence against shaped charges was laid out. The focus was in regard to Japanese 75 mm hollow charge shells used against Allied tanks in the Pacific. The destructive effect of the shaped charge was identified as caused by a jet moving at high velocities, consisting of particles from the liner. The two methods developed were to destroy the jet by forcing it to act through a layer of explosives, disrupting the jet, and to make it act through a layer of oxidiser, destroying the jet by burning it with oxidising agents.
The earliest trials were done with small charges able to defeat 2 inch of steel plate which were readily defeated by a layer of explosive (Baratol, R.D.X., Cordite, etc.) or a vigorous oxidising medium. Subsequent trials with British No.68 and American M9A1 grenades were carried out. However trials were done in few numbers which caused varied results. A mixture of Sodium and Potassium Nitrates explosives was seen as the most practical option due to their casting properties. The mixture acted as an oxidiser which may explode when dispersed and heated. The Explosives Manufacturing Practices Laboratory seemingly developed a more middle road between chemical armor and explosive reactive armor concepts to counter the hollow charge threat. [ 1 ] [ 2 ]
The idea of counterexplosion ( kontrvzryv in Russian) in armour was proposed in the USSR by the Scientific Research Institute of Steel (NII Stali) in 1949 by academician Bogdan Vjacheslavovich Voitsekhovsky . [ citation needed ] The first pre-production models were produced during the 1960s. However, insufficient theoretical analysis during one of the tests resulted in all of the prototype elements being detonated. [ citation needed ] For a number of reasons, including the aforementioned accident and a belief that Soviet tanks had sufficient armour, the research was ended. No more research was conducted until 1974, when the Ministry of the Defensive Industry announced a contest to find the best tank protection [ citation needed ] .
Picatinny Arsenal , an American military research and manufacturing facility experimented with testing linear cutting charges against anti-tank ammunition in the 1950s, and concluded that they may be effective with an adequate sensing and triggering mechanism, but noted "tactical limitations"; the report was declassified in 1980. [ 3 ]
A West German researcher, Manfred Held, carried out similar work with the IDF in 1967–1969. [ 4 ] Reactive armour created on the basis of the joint research was first installed on Israeli tanks during the 1982 Lebanon war and was judged very effective. [ by whom? ]
An element of explosive reactive armour (ERA) is made of either a sheet or slab of high explosive sandwiched between two metal plates, or multiple "banana shaped" rods filled with high explosive which are referred to as shaped charges. On attack by a penetrating weapon, the explosive detonates, forcibly driving the metal plates apart to damage the penetrator. The shaped charges, in contrast, each detonate individually, launching one spike-shaped plate each, meant to deflect, detonate or cut the incoming projectile.
The disruption is attributed to two mechanisms. First, the moving plates change the effective velocity and angle of impact of the shaped charge jet, reducing the angle of incidence and increasing the effective jet velocity versus the plate element. Second, since the plates are angled compared to the usual impact direction of shaped charge warheads, as the plates move outwards the impact point on the plate moves over time, requiring the jet to cut through fresh plates of material. This second effect greatly increases the effective plate thickness during the impact.
To be effective against kinetic energy projectiles, ERA must use much thicker and heavier plates and a correspondingly thicker explosive layer. Such heavy ERA , such as the Soviet-developed Kontakt-5 , can break apart a penetrating rod that is longer than the ERA is deep, again reducing penetration capability. Such ERA is ineffective against modern armor-piercing fin-stabilized discarding sabot (APFSDS) projectiles, however, due to their depleted uranium construction.
An important aspect of ERA is the brisance , or detonation speed of its explosive element. A more brisant explosive and greater plate velocity will result in more plate material being fed into the path of the oncoming jet, greatly increasing the plate's effective thickness. This effect is especially pronounced in the rear plate receding away from the jet, which triples in effective thickness with double the velocity. [ 5 ]
ERA also counters explosively forged projectiles, as produced by a shaped charge. The counter-explosion must disrupt the incoming projectile so that its momentum is distributed in all directions rather than toward the target, greatly reducing its effectiveness.
Explosive reactive armour has been valued by the Soviet Union and its now-independent component states since the 1980s, and almost every tank in the eastern-European military inventory today has either been manufactured to use ERA or had ERA tiles added to it, including even the T-55 and T-62 tanks built forty to fifty years ago, but still used today by reserve units. The U.S. Army uses reactive armour on its Abrams tanks as part of the TUSK (Tank Urban Survivability Kit) package and on Bradley vehicles and the Israelis use it frequently on their American built M60 tanks.
ERA tiles are used as add-on (or appliqué ) armour to the portions of an armoured fighting vehicle that are most likely to be hit, typically the front ( glacis ) of the hull and the front and sides of the turret. Their use requires that a vehicle be fairly heavily armoured to protect itself and its crew from the exploding ERA.
A further complication to the use of ERA is the inherent danger to anyone near the tank when a plate detonates, though a high-explosive anti-tank (HEAT) warhead explosion would already cause great danger to anyone near the tank. Although ERA plates are intended only to bulge following detonation, the combined energy of the ERA explosive, coupled with the kinetic or explosive energy of the projectile, will frequently cause the plate to explode, creating shrapnel that risks injuring or killing bystanders. Thus, infantry must operate some distance from vehicles protected by ERA in combined arms operations.
ERA is insensitive to impact by kinetic projectiles up to 30 mm in caliber. A 20 mm APIT autocannon round penetrates a Serbian ERA sample but fails to detonate it. However, computer simulations indicate that a small caliber (30 mm) HEAT projectile will detonate an ERA, as would larger shape charges and APFSDS penetrators. [ 6 ]
NERA and NxRA operate similarly to explosive reactive armour, but without the explosive liner. Two metal plates sandwich an inert liner, such as rubber. [ 7 ] When struck by a shaped charge's metal jet, some of the impact energy is dissipated into the inert liner layer, and the resulting high pressure causes a localized bending or bulging of the plates in the area of the impact. As the plates bulge, the point of jet impact shifts with the plate bulging, increasing the effective thickness of the armour. This is almost the same as the second mechanism that explosive reactive armour uses, but it uses energy from the shaped charge jet rather than from explosives. [ 8 ]
Since the inner liner is non-explosive, the bulging is less energetic than on explosive reactive armour, and thus offers less protection than a similarly-sized ERA. However, NERA and NxRA are lighter, safe to handle, and safer for nearby infantry; can theoretically be placed on any part of the vehicle; and can be packaged in multiple spaced layers if needed. A key advantage of this kind of armour is that it cannot be defeated by tandem warhead shaped charges, which employ a small forward warhead to detonate ERA before the main warhead fires.
Electric armour or electromagnetic armour is a proposed reactive armour technology. It is made up of two or more conductive plates separated by an air gap or by an insulating material, creating a high-power capacitor . [ 9 ] [ 10 ] [ 11 ] [ 12 ] [ 13 ] In operation, a high-voltage power source charges the armour. When an incoming body penetrates the plates, it closes the circuit to discharge the capacitor, dumping energy into the penetrator, which may vaporize it or even turn it into a plasma , diffusing the attack. It is not public knowledge whether this is supposed to function against both kinetic energy penetrators and shaped charge jets, or only the latter. As of 2005, this technology had not yet been introduced on any known operational platform.
Another electromagnetic alternative to ERA uses layers of plates of electromagnetic metal with silicone spacers on alternate sides. The damage to the exterior of the armour passes electricity into the plates, causing them to magnetically move together. As the process is completed at the speed of electricity the plates are moving when struck by the projectile, causing the projectile energy to be deflected whilst the energy is also dissipated in parting the magnetically attracted plates. [ citation needed ] | https://en.wikipedia.org/wiki/Reactive_armour |
Reactive carbonyl species (RCS) are molecules with highly reactive carbonyl groups, and often known for their damaging effects on proteins, nucleic acids, and lipids. They are often generated as metabolic products. Important RCSs include 3-deoxyglucosone , glyoxal , and methylglyoxal . RCSs react with amines and thiol groups leading to advanced glycation endproducts (AGEs). AGE's are indicators of diabetes. [ 1 ]
Reactive aldehyde species (RASP), [ 2 ] such as malondialdehyde and 4-hydroxynonenal , are a subset of RCS that are implicated in a variety of human diseases. [ 3 ]
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Reactive_carbonyl_species |
A reactive center , also called a propagating center , in chemistry is a particular location, usually an atom, within a chemical compound that is the likely center of a reaction in which the chemical is involved. In chain-growth polymer chemistry, this is also the point of propagation for a growing chain. The reactive center is commonly radical , anionic , or cationic , but can also take other forms. [ 1 ]
This article about polymer science is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Reactive_center |
In classical mechanics , a reactive centrifugal force forms part of an action–reaction pair with a centripetal force .
In accordance with Newton's first law of motion , an object moves in a straight line in the absence of a net force acting on the object. A curved path ensues when a force that is orthogonal to the object's motion acts on it; this force is often called a centripetal force , as it is directed toward the center of curvature of the path. Then in accordance with Newton's third law of motion , there will also be an equal and opposite force exerted by the object on some other object, [ 1 ] [ 2 ] and this reaction force is sometimes called a reactive centrifugal force , as it is directed in the opposite direction of the centripetal force.
In the case of a ball held in circular motion by a string, the centripetal force is the force exerted by the string on the ball. The reactive centrifugal force on the other hand is the force the ball exerts on the string, placing it under tension .
Unlike the inertial force known as centrifugal force , which exists only in the rotating frame of reference , the reactive force is a real Newtonian force that is observed in any reference frame. The two forces will only have the same magnitude in the special cases where circular motion arises and where the axis of rotation is the origin of the rotating frame of reference. [ 3 ] [ 4 ] [ 5 ] [ 6 ]
The figure at right shows a ball in uniform circular motion held to its path by a string tied to an immovable post. In this system a centripetal force upon the ball provided by the string maintains the circular motion, and the reaction to it, which some refer to as the reactive centrifugal force , acts upon the string and the post.
Newton's first law requires that any body moving along any path other than a straight line be subject to a net non-zero force, and the free body diagram shows the force upon the ball (center panel) exerted by the string to maintain the ball in its circular motion.
Newton's third law of action and reaction states that if the string exerts an inward centripetal force on the ball, the ball will exert an equal but outward reaction upon the string, shown in the free body diagram of the string (lower panel) as the reactive centrifugal force .
The string transmits the reactive centrifugal force from the ball to the fixed post, pulling upon the post. Again according to Newton's third law, the post exerts a reaction upon the string, labeled the post reaction , pulling upon the string. The two forces upon the string are equal and opposite, exerting no net force upon the string (assuming that the string is massless), but placing the string under tension.
The reason the post appears to be "immovable" is because it is fixed to the earth. If the rotating ball was tethered to the mast of a boat, for example, the boat mast and ball would both experience rotation about a central point.
Even though the reactive centrifugal is rarely used in analyses in the physics literature, the concept is applied within some mechanical engineering concepts. An example of this kind of engineering concept is an analysis of the stresses within a rapidly rotating turbine blade. [ 1 ] The blade can be treated as a stack of layers going from the axis out to the edge of the blade. Each layer exerts an outward (centrifugal) force on the immediately adjacent, radially inward layer and an inward (centripetal) force on the immediately adjacent, radially outward layer. At the same time the inner layer exerts an elastic centripetal force on the middle layer, while and the outer layer exerts an elastic centrifugal force, which results in an internal stress. It is the stresses in the blade and their causes that mainly interest mechanical engineers in this situation.
Another example of a rotating device in which a reactive centrifugal force can be identified used to describe the system behavior is the centrifugal clutch . A centrifugal clutch is used in small engine-powered devices such as chain saws, go-karts and model helicopters. It allows the engine to start and idle without driving the device, but automatically and smoothly engages the drive as the engine speed rises. A spring is used to constrain the spinning clutch shoes. At low speeds, the spring provides the centripetal force to the shoes, which move to larger radius as the speed increases and the spring stretches under tension. At higher speeds, when the shoes can't move any further out to increase the spring tension, due to the outer drum, the drum provides some of the centripetal force that keeps the shoes moving in a circular path. The force of tension applied to the spring, and the outward force applied to the drum by the spinning shoes are the corresponding reactive centrifugal forces. The mutual force between the drum and the shoes provides the friction needed to engage the output drive shaft that is connected to the drum. [ 7 ] Thus the centrifugal clutch illustrates both the fictitious centrifugal force and the reactive centrifugal force.
The "reactive centrifugal force" discussed in this article is not the same thing as the centrifugal pseudoforce , which is usually what is meant by the term "centrifugal force".
Reactive centrifugal force, being one-half of the reaction pair together with centripetal force, is a concept which applies in any reference frame. This distinguishes it from the inertial or fictitious centrifugal force, which appears only in rotating frames.
In a two-body rotation, such as a planet and moon rotating about their common center of mass or barycentre , the forces on both bodies are centripetal. In that case, the reaction to the centripetal force of the planet on the moon is the centripetal force of the moon on the planet. [ 6 ] | https://en.wikipedia.org/wiki/Reactive_centrifugal_force |
Reactive compatibilization is the process of modifying a mixed immiscible blend of polymers to arrest phase separation and allow for the formation of a stable, long-term continuous phase. It is done via the addition of a reactive polymer, miscible with one blend component and reactive towards functional groups on the second component, which result in the "in-situ" formation of block or grafted copolymers. [ 1 ]
A large number of commercial polymeric products are derived from the blending of two or more polymers to achieve a favorable balance of physical properties. However, since most polymer blends are immiscible, it is rare to find a pair of polymers that both are miscible and have desired characteristics. An example of such pair is the miscible resin NORYL ™, a mix of poly(phenylene oxide) and polystyrene. [ 2 ] Immiscible blends will phase separate and form a dispersed phase, which may improve physical properties (figure 1). DuPont’s rubber toughened Nylon consists of small particles of poly(cis-isoprene) ( natural rubber ) in a Nylon matrix that toughen the material by arresting crack propagation.
The Gibbs free energy of mixing, Δ G ( m i x ) = Δ H ( m i x ) − T Δ S ( m i x ) {\displaystyle \Delta G_{(}mix)=\Delta H_{(}mix)-T\Delta S_{(}mix)} , must be negative for a blend to be miscible. According to Flory-Huggins theory, a revision of regular solution theory, the entropy change per mole of lattice sites of blending polymer 1 and polymer 2 is
Δ S ( m i x , b l e n d ) = − R ( ϕ 1 x 1 ln ϕ 1 + ϕ 2 x 2 ln ϕ 2 ) {\displaystyle \Delta S_{(}mix,blend)=-R\left({\phi _{1} \over x_{1}}\ln \phi _{1}+{\phi _{2} \over x_{2}}\ln \phi _{2}\right)}
, where ΔS is the change in entropy of mixing, R is the gas constant , Φ is the volume fraction of each polymer, and x is the number of segments of each polymer. [ 3 ] x 1 and x 2 increase with higher degrees of polymerization and thus molecular weight. Since most useful polymers are high in molecular weight, the change in entropy experienced from the mixing of two large polymer chains is very low, and typically does not bring the Gibbs free energy low enough to constitute miscibility.
Most processed polymer mixes consist of a dispersed phase in a more continuous matrix of the other component. The formation, size, and concentration of this disperse phase are typically optimized for specific mechanical properties. If the morphology is not stabilized, the dispersed phase may coalesce under heat or stress from the environment or further processing. [ 4 ] This coalescence may result in diminished properties (brittleness and discoloration) due to the induced phase separation. These morphologies can be stabilized by sufficient interfacial adhesion or lowered interfacial tension between the two phases.
A common technique involves functionalizing one monomer. For example, Nylon-rubber bands are polymerized with functionalized rubber to produce graft or block copolymers. The added structures make it no longer favorable to coalesce and/or increase the steric hindrance in the interfacial area where phase separation would occur. | https://en.wikipedia.org/wiki/Reactive_compatibilization |
Reactive distillation is a process where the chemical reactor is also the still . Separation of the product from the reaction mixture does not need a separate distillation step which saves energy (for heating) and materials. This technique can be useful for equilibrium-limited reactions such as esterification and ester hydrolysis reactions. Conversion can be increased beyond what is expected by the equilibrium due to the continuous removal of reaction products from the reactive zone. This approach can also reduce capital and investment costs. [ 1 ]
The conditions in the reactive column are suboptimal both as a chemical reactor and as a distillation column , since the reactive column combines these. The introduction of an in situ separation process in the reaction zone or vice versa leads to complex interactions between vapor–liquid equilibrium , mass transfer rates, diffusion and chemical kinetics, which poses a great challenge for design and synthesis of these systems. Side reactors, where a separate column feeds a reactor and vice versa, are better for some reactions, if the optimal conditions of distillation and reaction differ too much.
Reactive distillation can be used with a wide variety of chemistries, including the following:
The esterification of acetic acid with alcohols including methanol , [ 2 ] n-butanol , ethanol , isobutanol , and amyl alcohol .
Another interesting feature of this system is that it is associated with the formation of a minimum boiling ternary azeotrope of ester, alcohol and water, which is heterogeneous in nature. Hence, in a typical reactive distillation column that consists of both reactive and non-reactive zones, the heterogeneous azeotrope or a composition close to the azeotrope can be obtained as the distillate product. Moreover, the aqueous phase that forms after the condensation of the vapor is almost pure water. Depending on the requirement either of the phases can be withdrawn as a product and the other phase can be recycled back as reflux. The pure ester i.e. butyl acetate, being the least volatile component in the system, is realized as a bottom product.
Removing organic acids from aqueous alcohol (ethanol, isopropanol) in dewatering columns is a simple example. An aqueous base (NaOH, KOH) is added to the top of the column, acid-base reactions occur in the column, and the resulting organic salts and excess base exit the bottom of the column with the separated water. | https://en.wikipedia.org/wiki/Reactive_distillation |
The reactive empirical bond-order ( REBO ) model is a function for calculating the potential energy of covalent bonds and the interatomic force . In this model, the total potential energy of system is a sum of nearest-neighbour pair interactions which depend not only on the distance between atoms but also on their local atomic environment. A parametrized bond order function was used to describe chemical pair bonded interactions.
The early formulation and parametrization of REBO for carbon systems was done by Tersoff in 1988, [ 1 ] [ 2 ] based on works of Abell. [ 3 ] The Tersoff's model could describe single, double and triple bond energies in carbon structures such as in hydrocarbons and diamonds. A significant step was taken by Brenner in 1990. [ 4 ] [ 5 ] He extended Tersoff's potential function to radical and conjugated hydrocarbon bonds by introducing two additional terms into the bond order function.
Compared to classical first-principle and semi-empirical approaches, the REBO model is less time-consuming, since only the 1st- and 2nd-nearest-neighbour interactions were considered. This advantage of computational efficiency is especially helpful for large-scale atomic simulations (from 1000 to 1000000 atoms). [ 6 ] In recent years, the REBO model has been widely used in the studies concerning mechanical and thermal properties of carbon nanotubes . [ 7 ] [ 8 ]
Despite numerous successful applications of the first-generation REBO potential function, its several drawbacks have been reported. e.g. its form is too restrictive to simultaneously fit equilibrium distances, energies, and force constants for all types of C-C bonds, the possibility of modeling processes involving energetic atomic collisions is limited because both Morse-type terms go to finite values when the atomic distance decreases, and the neglect of a separate pi bond contribution leads to problems with the overbinding of radicals and a poor treatment of conjugacy. [ 9 ] [ 10 ]
To overcome these drawbacks, an extension of Brenner's potential was proposed by Stuart et al. [ 10 ] It is called the adaptive intermolecular reactive bond order (AIREBO) potential, in which both the repulsive and attractive pair interaction functions in REBO function are modified to fit bond properties, and the long-range atomic interactions and single bond torsional interactions are included. The AIREBO model has been used in recent studies using numerical simulations . [ 11 ] [ 12 ] | https://en.wikipedia.org/wiki/Reactive_empirical_bond_order |
Reactive flash volatilization (RFV) is a chemical process that rapidly converts nonvolatile solids and liquids to volatile compounds by thermal decomposition for integration with catalytic chemistries.
The utilization of heavy fossil fuels or biomass rich in carbohydrates , (C 6 H 10 O 5 ) n , for fuels or chemicals requires an initial thermochemical process called pyrolysis which fractures large polymers to mixtures of small volatile organic compounds (VOCs). A specific method of pyrolysis of biomass, termed "fast pyrolysis," converts particles of biomass to about 10% carbon-rich solid called char , about 15% gases such as carbon dioxide, and about 70% a mixture of organic compounds commonly referred to as " bio-oil " at 500 °C in 1–2 seconds. [ 1 ]
Pyrolysis: Biomass + Heat → 0.70VOCs + 0.10Char + 0.15Gases
The volatile organics can be collected as a brown, highly acidic liquid for further thermochemical conversion by traditional processes such as steam reforming , gasification , catalytic partial oxidation , catalytic cracking , combustion , or hydrotreating . [2]
Catalytic steam reforming: VOCs + H 2 O + Heat + Catalyst → H 2 + CO + Catalyst Catalytic partial oxidation: VOCs + O 2 + Catalyst → H 2 + CO + Heat + Catalyst Catalytic combustion : VOCs + O 2 + Catalyst → CO 2 + H 2 O + Heat + Catalyst
These two sets of chemistries, pyrolysis and catalytic processing, are combined to form the reactive flash volatilization process. Solid hydrocarbons or biomass are contacted with high temperature (500–900 °C) catalysts to generate gases and volatile organic compounds . [ 2 ] The volatile species flow into the catalyst with a reactant (H 2 , O 2 , or H 2 O) to convert to desirable products (H 2 , CO, H 2 O, CO 2 , or VOCs).
RFV: Biomass + heat + Reactant + Catalyst → Gases + VOCs + Reactant + Catalyst → Products + Catalyst
Reactive flash volatilization was demonstrated in 2006 in the journal Science by the high temperature (700–800 °C) conversion of soybean oil (triglycerides) and sugar (D-(+)-glucose) to synthesis gas (H 2 + CO) and olefins (ethylene and propylene). [ 3 ] Complete, continuous catalytic conversion of heavy fuels was surprising, because the initial pyrolytic chemistry has been shown to generate significant amounts of solid residue called "char" which was expected to block the necessary interaction between the reactant compounds and the solid metal catalyst. [3] [ dead link ]
The process has been described, "The low volatility of these biofuel feedstocks not only leads to soot production when they are used directly in internal combustion engines but also causes them to coat industrial catalysts with a deactivating layer of carbon, thus hindering their conversion to lighter products. James Richard Salge and colleagues show that if heavy fuels such as soybean oil or biodiesel are sprayed onto hot rhodium-cerium catalysts as fine droplets in the presence of oxygen, the fuels can self-heat and fully react to form hydrogen without carbon formation and catalyst deactivation." [ 4 ] RFV: Triglyceride + O 2 + Catalyst → Ethylene + Propylene + CO 2 + H 2 O + Catalyst
The process converted 70% of the atomic hydrogen in soy-oil triglycerides to molecular H 2 , and 60% of atomic carbon to carbon monoxide on a Rh-based catalyst with Cerium supported on alpha-alumina. [ 5 ] Under different operating conditions, the process can produce a significant amount of ethylene and propylene. [ 6 ]
The first demonstration of reactive flash volatilization occurred by a series of experimental steps: [ 7 ]
An initial supply of heat is necessary to achieve temperatures of 300 °C, after which the reaction initiates, or "lights off," and quickly rises to temperatures of 700–800 °C. Under steady conditions, the reaction generates sufficient heat to maintain the high temperature, extremely fast chemistry. [ 8 ] The total time for conversion of heavy, nonvolatile compounds to volatile or gaseous species occurs in milliseconds (or thousandths of a second). [4]
Reactive flash volatilization of solid particles composed of cellulose , starch , lignin , Quaking Aspen ( Populus tremuloides ) wood chips, and polyethylene was demonstrated in 2007 in the scientific journal Angewandte Chemie . [ 9 ] Particles of cellulose were completely converted to syngas (H 2 and CO) and combustion products (H 2 O and CO 2 ) in as little as 30 milliseconds. Catalytic reforming of all materials occurred without the requirement of an external heat source while operating at 500–900 °C. Under optimal conditions, 50% of all atomic hydrogen and 50% of all atomic carbon can be converted to molecular H 2 and carbon monoxide in as little time as 30 milliseconds. Reaction chemistry was demonstrated on both a Rh-Ce/alumina catalyst and a Ni-Ce/alumina catalyst. [ 9 ]
A publication in the scientific journal Green Chemistry demonstrated that the process of reactive flash volatilization can be considered a combination of several other global chemistries occurring through thermal and chemical integration. [ 10 ] As shown in the diagram at the right, the initial pyrolysis chemistry occurs when the biomass particle (green) physically contacts the hot catalyst (orange). Volatile organic compounds (VOCs) flow into the catalyst with oxygen, adsorb on Rh atoms, and react to form combustion products (H 2 O and CO 2 ) and syngas (H 2 and CO). After this initial chemistry, three main global reactions occur. Combustion products react catalytically with syngas by the water-gas shift reaction . Also, volatile organics react catalytically with steam (H 2 O) to form new combustion products and syngas. Finally, the volatile organics can crack homogeneously in the gas phase to form smaller volatile organics. [ 9 ]
The operating temperature has been shown to vary within the catalyst length while also being a strong function of the biomass-to-oxygen ratio. An experimental examination has shown that the heat required to thermally fracture biomass was generated within the catalyst bed by surface oxidation reactions. The temperature profile (and reaction temperature) was shown to be extremely important to prevent the formation of carbon at equilibrium. [ 10 ] Very fast conversion has been attributed to high operating temperatures, but the maximum cellulose processing rate has not been determined. [ 11 ] However, catalytic partial oxidation of volatile organic compounds has shown that complete conversion can occur in less than 10 milliseconds. [ 12 ] | https://en.wikipedia.org/wiki/Reactive_flash_volatilization |
In chemistry , a reactive intermediate or an intermediate is a short-lived, high-energy, highly reactive molecule . When generated in a chemical reaction , it will quickly convert into a more stable molecule. Only in exceptional cases can these compounds be isolated and stored, e.g. low temperatures, matrix isolation . When their existence is indicated, reactive intermediates can help explain how a chemical reaction takes place. [ 1 ] [ 2 ] [ 3 ] [ 4 ]
Most chemical reactions take more than one elementary step to complete, and a reactive intermediate is a high-energy, hence unstable, product that exists only in one of the intermediate steps. The series of steps together make a reaction mechanism . A reactive intermediate differs from a reactant or product or a simple reaction intermediate only in that it cannot usually be isolated but is sometimes observable only through fast spectroscopic methods. It is stable in the sense that an elementary reaction forms the reactive intermediate and the elementary reaction in the next step is needed to destroy it.
When a reactive intermediate is not observable, its existence must be inferred through experimentation. This usually involves changing reaction conditions such as temperature or concentration and applying the techniques of chemical kinetics , chemical thermodynamics , or spectroscopy . Reactive intermediates based on carbon are radicals , carbenes , carbocations , carbanions , arynes , and carbynes .
Reactive intermediates have several features in common: | https://en.wikipedia.org/wiki/Reactive_intermediate |
A reactive liquid extraction process is a liquid-liquid extraction process that is intensified through a mechanism involving a reversible reaction between the extracted chemical species and a host chemical species constituting, or present in, the extractant . [ 1 ] [ 2 ] | https://en.wikipedia.org/wiki/Reactive_liquid_extraction |
In the U.S. military , reactive materials ( RM ) are a new class of materials currently being investigated by the Office of Naval Research and others as a means to increase the lethality of direct-hit or fragmentation warheads . Reactive materials are similar to insensitive high explosives , but are usually thermite -like pyrotechnic compositions of two or more nonexplosive solid materials, which stay inert and do not react with each other until subjected to a sufficiently strong mechanical, electrical or laser stimulus, after which they undergo fast burning or explosion with release of high amount of chemical energy in addition to their kinetic energy . Fragments or projectiles made of such materials have therefore greater damaging effect than inert ones, with expected lethality increase up to 500%.
The material classes under investigation are thermites , intermetallic compounds, metal-polymer mixtures (e.g., magnesium/teflon/viton -like), metastable intermolecular composites (MIC), matrix materials, and hydrides . [ 1 ] These materials must be strong enough to act as structural components, be sufficiently stable to survive handling and launch, to penetrate a target, and sufficiently unstable to reliably ignite on impact.
The mixtures under investigation include one or more finely powdered (down to nanoparticle size) metalloids or metals like aluminium , magnesium , zirconium , titanium , tungsten , tantalum , uranium [ 2 ] or hafnium , with one or more oxidizers like teflon or other fluoropolymer , pressed or sintered or bonded by other method to a compact, high-density mass. To achieve a suitable reaction rate and insensitivity to impact, friction, and electrostatic discharge , fuel particles have sizes usually between 1-250 μm. [ 3 ] [ 4 ] A standard composition is aluminium-teflon (Al-PTFE).
Metals which can form intermetallic compounds by an exothermic reaction are another class of candidate materials. An example is a laminate of thin alternating layers of aluminum and nickel , commercially available as NanoFoil .
The RM weapons under development include an active protection system defensive grenade for intercepting incoming missiles or grenades and detonating them at a safe distance, and the BattleAxe warhead that covers a wide area with RM fragments with devastating results to soft targets , while the unexploded fragments left behind have very low lethality versus conventional cluster bomb remains.
Under research are materials with high mechanical strength , high density, high energy density , and which can rapidly convert from a consolidated structural material to fine powder with large surface area, be dispersed and then ignited to produce a large thermobaric blast. [ 5 ]
A palladium -clad aluminum wire, known under trademark Pyrofuze , is used as a pyrotechnic initiator .
Reactive materials also have non-weapon uses. Thin layers of reactive materials, clad with a solder , are used for reactive bonding , e.g., in electronics, or for brazing , such as in composite armor plates. | https://en.wikipedia.org/wiki/Reactive_material |
Reactive multi-layer foils are a class of reactive materials , sometimes referred to as a pyrotechnic initiator of two mutually reactive metals, sputtered to form thin layers that create a laminated foil . [ 1 ] On initiation by a heat pulse, delivered by a bridge wire , a laser pulse, an electric spark , a flame , or by other means, the metals undergo self-sustaining exothermic reaction , producing an intermetallic compound. The reaction occurs in solid and liquid phase only, without releasing any gas.
One particular type of such materials is aluminum-nickel multilayered foil, that produces (NiAl). Other similar materials are composed of aluminium- titanium , or titanium- amorphous silicon , are used for joining materials by reactive bonding . Other similar intermetallic compositions used in pyrotechnics are titanium - boron and aluminium - palladium ("Pyrofuze").
These foils are made in a range of thicknesses, e.g. 60, 80, 100, and 150 micrometers. The flame front propagation rate ranges generally between 7.5–9 m/s. The reaction temperature can reach up to 1500 °C for a millisecond. The energy released is approximately 1200 to 1300 joules per gram. [ 2 ] The velocity and temperature of the reaction can be controlled by adjusting the thickness of the layers. Typical thickness is 50 nm per a bilayer. [ 3 ] The thin layers maximize the contact between the metal and lower the activation energy for the reaction, normally too high to allow reaction between bulk aluminium and bulk nickel. The layers are deposited by sequential sputtering of alternately nickel and aluminium.
Nickel aluminide will ignite on heating to at least 250 °C in rate of at least 200 °C/min. Slower heating will anneal the material, causing loss of its pyrotechnic properties. For electrical initiation, a momentary contact at 10A/5V is sufficient; for ohmic contact, 120-150 amperes is needed for a 15 micrometer diameter contact, and 250-300 A for a 300 micrometer contact. [ 4 ] It can be also ignited by a heat paper. When the flame front reaches the edge of the material, particles of molten metal can be ejected, causing voids in the bond; this can be prevented by simultaneous ignition from more sides, so the flame fronts meet in the middle, confined by the substrates. [ 5 ]
The foil can be both cut and ignited by a laser . The pulse width and power determines if the material will be cut or initiated. [ 2 ] It is frequently used as a heat source for soldering and brazing . When sandwiched between the components to be joined, either with a foil of solder on each side, using solder precoated components, or using solder-coated foil, it uniformly delivers significant amount of heat energy across the entire area, melting the solder and only locally heating the surface of the substrates, lowering the heat load on the component in comparison with soldering/brazing in a furnace . An externally applied even pressure during reaction and cooling serves to ensure a good homogeneous joint without voids. [ 4 ] Significantly dissimilar materials can be bonded without cracking: semiconductors, metals, ceramics, and polymers. [ 3 ] The energy is deposited very locally, without significant heating of the bulk of the substrates, which reduces problems with mismatched thermal expansion coefficients between the materials and allows their joining at room temperature.
The bonding process can be used in assembly of electronics , die attachment to heatsinks where high temperature stability is required (e.g. high-power LEDs or concentrated photovoltaics solar panels , soldering together layers of composite armor plates, bonding of large sputtering targets made of ceramics or refractory metals where normal indium based solders cannot be used, and other applications where a uniform joint over large area has to be created. [ 6 ]
The foil can be used as a pyrotechnic heat source , a replacement of potassium chlorate / iron pellets, for thermal batteries . It reacts faster than the conventional composition, reaches higher temperatures, and heat buffers of inert metal (e.g. steel) are needed to lower the peak temperature and prolong the heat delivery. [ 7 ] They can be also used as an electrically initiated pyrotechnic initiator , e.g. to ignite solid propellants , and in decoy flares . They can be employed in weapons as reactive materials , enhancing the energy delivery to the targets by the projectiles or their fragments. | https://en.wikipedia.org/wiki/Reactive_multi-layer_foil |
Reactive nitrogen ("Nr"), also known as fixed nitrogen [ 1 ] , refers to all forms of nitrogen present in the environment except for molecular nitrogen ( N 2 ). [ 2 ] While nitrogen is an essential element for life on Earth, molecular nitrogen is comparatively unreactive, and must be converted to other chemical forms via nitrogen fixation before it can be used for growth. Common Nr species include nitrogen oxides ( NO x ), ammonia ( NH 3 ), nitrous oxide ( N 2 O ), as well as the anion nitrate ( NO − 3 ).
Biologically, nitrogen is "fixed" mainly by the microbes (eg., Bacteria and Archaea) of the soil that fix N 2 into mainly NH 3 but also other species. Legumes, a type of plant in the Fabacae family, are symbionts to some of these microbes that fix N 2 . NH 3 is a building block to Amino acids and proteins amongst other things essential for life. However, just over half of all reactive nitrogen entering the biosphere is attributable to anthropogenic activity such as industrial fertilizer production. [ 3 ] While reactive nitrogen is eventually converted back into molecular nitrogen via denitrification , an excess of reactive nitrogen can lead to problems such as eutrophication in marine ecosystems.
In the environmental context, reactive nitrogen compounds include the following classes:
All of these compounds enter into the nitrogen cycle .
As a consequence, an excess of Nr can affect the environment relatively quickly. This also means that nitrogen-related problems need to be looked at in an integrated manner. [ 4 ] | https://en.wikipedia.org/wiki/Reactive_nitrogen |
Reactive nitrogen species ( RNS ) are a family of antimicrobial molecules derived from nitric oxide (•NO) and superoxide (O 2 •− ) produced via the enzymatic activity of inducible nitric oxide synthase 2 ( NOS2 ) and NADPH oxidase respectively. NOS2 is expressed primarily in macrophages after induction by cytokines and microbial products, notably interferon-gamma (IFN-γ) and lipopolysaccharide (LPS). [ 2 ]
Reactive nitrogen species act together with reactive oxygen species (ROS) to damage cells , causing nitrosative stress . Therefore, these two species are often collectively referred to as ROS/RNS.
Reactive nitrogen species are also continuously produced in plants as by-products of aerobic metabolism or in response to stress. [ 3 ]
RNS are produced in animals starting with the reaction of nitric oxide (•NO) with superoxide (O 2 •− ) to form peroxynitrite (ONOO − ): [ 4 ] [ 5 ]
Superoxide anion (O 2 − ) is a reactive oxygen species that reacts quickly with nitric oxide (NO) in the vasculature. The reaction produces peroxynitrite and depletes the bioactivity of NO. This is important because NO is a key mediator in many important vascular functions including regulation of smooth muscle tone and blood pressure, platelet activation, and vascular cell signaling. [ 6 ]
Peroxynitrite itself is a highly reactive species which can directly react with various biological targets and components of the cell including lipids, thiols, amino acid residues, DNA bases, and low-molecular weight antioxidants. [ 7 ] However, these reactions happen at a relatively slow rate. This slow reaction rate allows it to react more selectively throughout the cell. Peroxynitrite is able to get across cell membranes to some extent through anion channels. [ 8 ] Additionally peroxynitrite can react with other molecules to form additional types of RNS including nitrogen dioxide (•NO 2 ) and dinitrogen trioxide (N 2 O 3 ) as well as other types of chemically reactive free radicals . Important reactions involving RNS include:
Peroxynitrite can react directly with proteins that contain transition metal centers. Therefore, it can modify proteins such as hemoglobin, myoglobin, and cytochrome c by oxidizing ferrous heme into its corresponding ferric forms. Peroxynitrite may also be able to change protein structure through the reaction with various amino acids in the peptide chain. The most common reaction with amino acids is cysteine oxidation. Another reaction is tyrosine nitration; however peroxynitrite does not react directly with tyrosine. Tyrosine reacts with other RNS that are produced by peroxynitrite. All of these reactions affect protein structure and function and thus have the potential to cause changes in the catalytic activity of enzymes, altered cytoskeletal organization, and impaired cell signal transduction. [ 8 ] | https://en.wikipedia.org/wiki/Reactive_nitrogen_species |
In chemistry and biology , reactive oxygen species ( ROS ) are highly reactive chemicals formed from diatomic oxygen ( O 2 ), water , and hydrogen peroxide . Some prominent ROS are hydroperoxide (H 2 O 2 ), superoxide (O 2 − ), [ 1 ] hydroxyl radical (OH . ), and singlet oxygen ( 1 O 2 ). [ 2 ] ROS are pervasive because they are readily produced from O 2 , which is abundant. ROS are important in many ways, both beneficial and otherwise. ROS function as signals, that turn on and off biological functions. They are intermediates in the redox behavior of O 2 , which is central to fuel cells . ROS are central to the photodegradation of organic pollutants in the atmosphere. Most often however, ROS are discussed in a biological context, ranging from their effects on aging and their role in causing dangerous genetic mutations.
ROS are not uniformly defined. All sources include superoxide, singlet oxygen, and hydroxyl radical. Hydrogen peroxide is not nearly as reactive as these species, but is readily activated and is thus included. [ 3 ] Peroxynitrite and nitric oxide are reactive oxygen-containing species as well.
In its fleeting existence, the hydroxyl radical reacts rapidly irreversibly with all organic compounds.
Competing with its formation, superoxide is destroyed by the action of superoxide dismutases , enzymes that catalyze its disproportionation:
In a biological context, ROS are byproducts of the normal metabolism of oxygen . ROS have roles in cell signaling and homeostasis . [ 7 ] [ 8 ] [ 9 ] [ 10 ] ROS are intrinsic to cellular functioning, and are present at low and stationary levels in normal cells. [ 11 ] In plants, ROS are involved in metabolic processes related to photoprotection and tolerance to various types of stress. [ 12 ] However, ROS can cause irreversible damage to DNA as they oxidize and modify some cellular components and prevent them from performing their original functions. This suggests that ROS has a dual role; whether they will act as harmful, protective or signaling factors depends on the balance between ROS production and disposal at the right time and place. [ 13 ] [ 8 ] [ 14 ] In other words, oxygen toxicity can arise both from uncontrolled production and from the inefficient elimination of ROS by the antioxidant system. ROS were also demonstrated to modify the visual appearance of fish . [ 15 ] This potentially affects their behavior and ecology, such as their temperature control, their visual communication, their reproduction and survival.
During times of environmental stress (e.g., UV or heat exposure), ROS levels can increase dramatically. [ 9 ] This may result in significant damage to cell structures. Cumulatively, this is known as oxidative stress . The production of ROS is strongly influenced by stress factor responses in plants, these factors that increase ROS production include drought, salinity, chilling, defense of pathogens, nutrient deficiency, metal toxicity and UV-B radiation. ROS are also generated by exogenous sources such as ionizing radiation [ 16 ] generating irreversible effects in the development of tissues in both animals and plants. [ 17 ]
ROS are produced during the processes of respiration and photosynthesis in organelles such as mitochondria , peroxisomes and chloroplasts . [ 14 ] [ 20 ] [ 21 ] [ 22 ] During the respiration process the mitochondria convert energy for the cell into a usable form, adenosine triphosphate (ATP). The process of ATP production in the mitochondria, called oxidative phosphorylation , involves the transport of protons (hydrogen ions) across the inner mitochondrial membrane by means of the electron transport chain . In the electron transport chain, electrons are passed through a series of proteins via oxidation-reduction reactions, with each acceptor protein along the chain having a greater reduction potential than the previous. The last destination for an electron along this chain is an oxygen molecule. In normal conditions, the oxygen is reduced to produce water; however, in about 0.1–2% of electrons passing through the chain (this number derives from studies in isolated mitochondria, though the exact rate in live organisms is yet to be fully agreed upon), oxygen is instead prematurely and incompletely reduced to give the superoxide radical ( • O − 2 ), most well documented for Complex I and Complex III . [ 23 ]
Another source of ROS production in animal cells is the electron transfer reactions catalyzed by the mitochondrial P450 systems in steroidogenic tissues. [ 24 ] These P450 systems are dependent on the transfer of electrons from NADPH to P450. During this process, some electrons "leak" and react with O 2 producing superoxide. To cope with this natural source of ROS, the steroidogenic tissues, ovary and testis, have a large concentration of antioxidants such as vitamin C (ascorbate) and β-carotene and anti-oxidant enzymes. [ 25 ]
If too much damage is present in mitochondria, a cell undergoes apoptosis or programmed cell death. [ 26 ] [ 27 ]
In addition, ROS are produced in immune cell signaling via the NOX pathway. Phagocytic cells such as neutrophils , eosinophils , and mononuclear phagocytes produce ROS when stimulated. [ 28 ] [ 29 ]
In chloroplasts , the carboxylation and oxygenation reactions catalyzed by rubisco ensure that the functioning of the electron transport chain (ETC) occurs in an environment rich in O 2 . The leakage of electrons in the ETC will inevitably produce ROS within the chloroplasts. [ 14 ] ETC in photosystem I (PSI) was once believed to be the only source of ROS in chloroplasts. The flow of electrons from the excited reaction centers is directed to the NADP and these are reduced to NADPH, and then they enter the Calvin cycle and reduce the final electron acceptor, CO 2 . [ 30 ] In cases where there is an ETC overload, part of the electron flow is diverted from ferredoxin to O 2 , forming the superoxide free radical (by the Mehler reaction ). In addition, electron leakage to O 2 can also occur from the 2Fe-2S and 4Fe-4S clusters in the PSI ETC. However, PSII also provides electron leakage locations (QA, QB) for O 2 -producing O 2 -. [ 31 ] [ 32 ] Superoxide (O 2 -) is generated from PSII, instead of PSI; QB is shown as the location for the generation of O 2 •-. [ 31 ]
The formation of ROS can be stimulated by a variety of agents such as pollutants, heavy metals , [ 19 ] tobacco , smoke, drugs, xenobiotics , microplastics , or radiation. In plants, in addition to the action of dry abiotic factors , high temperature, interaction with other living beings can influence the production of ROS. [ citation needed ]
Ionizing radiation can generate damaging intermediates through the interaction with water, a process termed radiolysis . Since water comprises 55–60% of the human body, the probability of radiolysis is quite high under the presence of ionizing radiation. In the process, water loses an electron and becomes highly reactive. Then through a three-step chain reaction, water is sequentially converted to hydroxyl radical ( • OH), hydrogen peroxide (H 2 O 2 ), superoxide radical ( • O − 2 ), and ultimately oxygen (O 2 ). [ citation needed ]
The hydroxyl radical is extremely reactive and immediately removes electrons from any molecule in its path, turning that molecule into a free radical and thus propagating a chain reaction. However, hydrogen peroxide is actually more damaging to DNA than the hydroxyl radical, since the lower reactivity of hydrogen peroxide provides enough time for the molecule to travel into the nucleus of the cell, subsequently reacting with macromolecules such as DNA. [ citation needed ]
In plants, the production of ROS occurs during events of abiotic stress that lead to a reduction or interruption of metabolic activity. For example, the increase in temperature, drought are factors that limit the availability of CO 2 due to stomatal closure, increasing the production of ROS, such as O 2 ·- and 1 O 2 in chloroplasts. [ 33 ] [ 34 ] The production of 1 O 2 in chloroplasts can cause reprogramming of the expression of nucleus genes leading to chlorosis and programmed cell death . [ 34 ] In cases of biotic stress, the generation of ROS occurs quickly and weakly initially and then becomes more solid and lasting. [ 35 ] The first phase of ROS accumulation is associated with plant infection and is probably independent of the synthesis of new ROS-generating enzymes . However, the second phase of ROS accumulation is associated only with infection by non-virulent pathogens and is an induced response dependent on increased mRNA transcription encoding enzymes.
Superoxide dismutases (SOD) are a class of enzymes that catalyzes the dismutation of superoxide into oxygen and hydrogen peroxide. As such, they are an important antioxidant defense in nearly all cells exposed to oxygen. In mammals and most chordates, three forms of superoxide dismutase are present. SOD1 is located primarily in the cytoplasm, SOD2 in the mitochondria and SOD3 is extracellular. The first is a dimer (consists of two units), while the others are tetramers (four subunits). SOD1 and SOD3 contain copper and zinc ions, while SOD2 has a manganese ion in its reactive centre. The genes are located on chromosomes 21, 6, and 4, respectively (21q22.1, 6q25.3 and 4p15.3-p15.1). [ citation needed ]
The SOD-catalysed dismutation of superoxide may be written with the following half-reactions:
where M = Cu ( n = 1 ); Mn ( n = 2 ); Fe ( n = 2 ); Ni ( n = 2 ). In this reaction the oxidation state of the metal cation oscillates between n and n + 1 .
Catalase , which is concentrated in peroxisomes located next to mitochondria, reacts with the hydrogen peroxide to catalyze the formation of water and oxygen. Glutathione peroxidase reduces hydrogen peroxide by transferring the energy of the reactive peroxides to a sulfur-containing tripeptide called glutathione . The sulfur contained in these enzymes acts as the reactive center, carrying reactive electrons from the peroxide to the glutathione. Peroxiredoxins also degrade H 2 O 2 , within the mitochondria, cytosol, and nucleus.
Effects of ROS on cell metabolism are well documented in a variety of species. [ 19 ] These include not only roles in apoptosis (programmed cell death) but also positive effects such as the induction of host defence [ 36 ] [ 37 ] genes and mobilization of ion transporters . [ citation needed ] This implicates them in control of cellular function. In particular, platelets involved in wound repair and blood homeostasis release ROS to recruit additional platelets to sites of injury . These also provide a link to the adaptive immune system via the recruitment of leukocytes . [ citation needed ]
Reactive oxygen species are implicated in cellular activity to a variety of inflammatory responses including cardiovascular disease . They may also be involved in hearing impairment via cochlear damage induced by elevated sound levels , in ototoxicity of drugs such as cisplatin , and in congenital deafness in both animals and humans. [ citation needed ] ROS are also implicated in mediation of apoptosis or programmed cell death and ischaemic injury. Specific examples include stroke and heart attack . [ citation needed ]
In general, the harmful effects of reactive oxygen species on the cell are the damage of DNA or RNA, oxidation of polyunsaturated fatty acids in lipids ( lipid peroxidation ), oxidation of amino acids in proteins, and oxidative deactivation of specific enzymes by oxidation co-factors. [ 38 ]
When a plant recognizes an attacking pathogen, one of the first induced reactions is to rapidly produce superoxide ( O − 2 ) or hydrogen peroxide ( H 2 O 2 ) to strengthen the cell wall. This prevents the spread of the pathogen to other parts of the plant, essentially forming a net around the pathogen to restrict movement and reproduction.
In the mammalian host, ROS is induced as an antimicrobial defense. [ 28 ] To highlight the importance of this defense, individuals with chronic granulomatous disease who have deficiencies in generating ROS, are highly susceptible to infection by a broad range of microbes including Salmonella enterica , Staphylococcus aureus , Serratia marcescens , and Aspergillus spp.
Studies on the homeostasis of the Drosophila melanogaster ' s intestines have shown the production of ROS as a key component of the immune response in the gut of the fly. ROS acts both as a bactericide, damaging the bacterial DNA, RNA and proteins, as well as a signalling molecule that induces repair mechanisms of the epithelium . [ 39 ] The uracil released by microorganism triggers the production and activity of DUOX, the ROS-producing enzyme in the intestine. DUOX activity is induced according to the level of uracil in the gut; under basal conditions, it is down-regulated by the protein kinase MkP3 . The tight regulation of DUOX avoids excessive production of ROS and facilitates differentiation between benign and damage-inducing microorganisms in the gut. [ 40 ]
The manner in which ROS defends the host from invading microbe is not fully understood. One of the more likely modes of defense is damage to microbial DNA. Studies using Salmonella demonstrated that DNA repair mechanisms were required to resist killing by ROS. A role for ROS in antiviral defense mechanisms has been demonstrated via Rig-like helicase-1 and mitochondrial antiviral signaling protein. Increased levels of ROS potentiate signaling through this mitochondria-associated antiviral receptor to activate interferon regulatory factor (IRF)-3, IRF-7, and nuclear factor kappa B (NF-κB), resulting in an antiviral state. [ 41 ] Respiratory epithelial cells induce mitochondrial ROS in response to influenza infection. This induction of ROS led to the induction of type III interferon and the induction of an antiviral state, limiting viral replication. [ 42 ] In host defense against mycobacteria, ROS play a role, although direct killing is likely not the key mechanism; rather, ROS likely affect ROS-dependent signalling controls, such as cytokine production, autophagy, and granuloma formation. [ 43 ] [ 44 ]
Reactive oxygen species are also implicated in activation, anergy and apoptosis of T cells . [ 45 ]
In aerobic organisms the energy needed to fuel biological functions is produced in the mitochondria via the electron transport chain . Reactive oxygen species (ROS) with the potential to cause cellular damage are produced along with the release of energy. ROS can damage lipids, DNA , RNA , and proteins, which, in theory, contributes to the physiology of aging .
ROS are produced as a normal product of cellular metabolism . In particular, one major contributor to oxidative damage is hydrogen peroxide (H 2 O 2 ), which is converted from superoxide that leaks from the mitochondria. Catalase and superoxide dismutase ameliorate the damaging effects of hydrogen peroxide and superoxide, respectively, by converting these compounds into oxygen and hydrogen peroxide (which is later converted to water), resulting in the production of benign molecules . However, this conversion is not 100% efficient, and residual peroxides persist in the cell. While ROS are produced as a product of normal cellular functioning, excessive amounts can cause deleterious effects. [ 46 ]
Memory capabilities decline with age, evident in human degenerative diseases such as Alzheimer's disease , which is accompanied by an accumulation of oxidative damage. Current studies demonstrate that the accumulation of ROS can decrease an organism's fitness because oxidative damage is a contributor to senescence. In particular, the accumulation of oxidative damage may lead to cognitive dysfunction, as demonstrated in a study in which old rats were given mitochondrial metabolites and then given cognitive tests . Results showed that the rats performed better after receiving the metabolites, suggesting that the metabolites reduced oxidative damage and improved mitochondrial function. [ 47 ] Accumulating oxidative damage can then affect the efficiency of mitochondria and further increase the rate of ROS production. [ 48 ] The accumulation of oxidative damage and its implications for aging depends on the particular tissue type where the damage is occurring. Additional experimental results suggest that oxidative damage is responsible for age-related decline in brain functioning. Older gerbils were found to have higher levels of oxidized protein in comparison to younger gerbils. Treatment of old and young mice with a spin trapping compound caused a decrease in the level of oxidized proteins in older gerbils but did not have an effect on younger gerbils. In addition, older gerbils performed cognitive tasks better during treatment but ceased functional capacity when treatment was discontinued, causing oxidized protein levels to increase. This led researchers to conclude that oxidation of cellular proteins is potentially important for brain function. [ 49 ]
According to the free radical theory of aging , oxidative damage initiated by reactive oxygen species is a major contributor to the functional decline that is characteristic of aging. While studies in invertebrate models indicate that animals genetically engineered to lack specific antioxidant enzymes (such as SOD), in general, show a shortened lifespan (as one would expect from the theory), the converse manipulation, increasing the levels of antioxidant enzymes, has yielded inconsistent effects on lifespan (though some studies in Drosophila do show that lifespan can be increased by the overexpression of MnSOD or glutathione biosynthesizing enzymes). Also contrary to this theory, deletion of mitochondrial SOD2 can extend lifespan in Caenorhabditis elegans . [ 50 ]
In mice, the story is somewhat similar. Deleting antioxidant enzymes, in general, yields shorter lifespan, although overexpression studies have not (with some exceptions) consistently extended lifespan. [ 51 ] Study of a rat model of premature aging found increased oxidative stress , reduced antioxidant enzyme activity and substantially greater DNA damage in the brain neocortex and hippocampus of the prematurely aged rats than in normally aging control rats. [ 52 ] The DNA damage 8-OHdG is a product of ROS interaction with DNA. Numerous studies have shown that 8-OHdG increases with age [ 53 ] (see DNA damage theory of aging ).
ROS are constantly generated and eliminated in the biological system and are required to drive regulatory pathways. [ 54 ] Under normal physiological conditions, cells control ROS levels by balancing the generation of ROS with their elimination by scavenging systems. But under oxidative stress conditions, excessive ROS can damage cellular proteins, lipids and DNA, leading to fatal lesions in the cell that contribute to carcinogenesis.
Cancer cells exhibit greater ROS stress than normal cells do, partly due to oncogenic stimulation, increased metabolic activity and mitochondrial malfunction. ROS is a double-edged sword. On one hand, at low levels, ROS facilitates cancer cell survival since cell-cycle progression driven by growth factors and receptor tyrosine kinases (RTK) require ROS for activation [ 55 ] and chronic inflammation, a major mediator of cancer, is regulated by ROS. On the other hand, a high level of ROS can suppress tumor growth through the sustained activation of cell-cycle inhibitor [ 56 ] [ 57 ] and induction of cell death as well as senescence by damaging macromolecules. In fact, most of the chemotherapeutic and radiotherapeutic agents kill cancer cells by augmenting ROS stress. [ 58 ] [ 59 ] The ability of cancer cells to distinguish between ROS as a survival or apoptotic signal is controlled by the dosage, duration, type, and site of ROS production. Modest levels of ROS are required for cancer cells to survive, whereas excessive levels kill them.
Metabolic adaptation in tumours balances the cells' need for energy with equally important need for macromolecular building blocks and tighter control of redox balance. As a result, production of NADPH is greatly enhanced, which functions as a cofactor to provide reducing power in many enzymatic reactions for macromolecular biosynthesis and at the same time rescuing the cells from excessive ROS produced during rapid proliferation. Cells counterbalance the detrimental effects of ROS by producing antioxidant molecules, such as reduced glutathione (GSH) and thioredoxin (TRX), which rely on the reducing power of NADPH to maintain their activities. [ 60 ]
Most risk factors associated with cancer interact with cells through the generation of ROS. ROS then activate various transcription factors such as nuclear factor kappa-light-chain-enhancer of activated B cells (NF-κB), activator protein-1 (AP-1), hypoxia-inducible factor-1α and signal transducer and activator of transcription 3 (STAT3), leading to expression of proteins that control inflammation; cellular transformation; tumor cell survival; tumor cell proliferation; and invasion, angiogenesis as well as metastasis. And ROS also control the expression of various tumor suppressor genes such as p53, retinoblastoma gene (Rb), and phosphatase and tensin homolog (PTEN). [ 61 ]
ROS-related oxidation of DNA is one of the main causes of mutations, which can produce several types of DNA damage, including non-bulky (8-oxoguanine and formamidopyrimidine) and bulky (cyclopurine and etheno adducts) base modifications, abasic sites, non-conventional single-strand breaks, protein-DNA adducts, and intra/interstrand DNA crosslinks. [ 62 ] It has been estimated that endogenous ROS produced via normal cell metabolism modify approximately 20,000 bases of DNA per day in a single cell. 8-oxoguanine is the most abundant among various oxidized nitrogeneous bases observed. During DNA replication, DNA polymerase mispairs 8-oxoguanine with adenine, leading to a G→T transversion mutation. The resulting genomic instability directly contributes to carcinogenesis. Cellular transformation leads to cancer and interaction of atypical PKC-ζ isoform with p47phox controls ROS production and transformation from apoptotic cancer stem cells through blebbishield emergency program . [ 63 ] [ 64 ]
Uncontrolled proliferation is a hallmark of cancer cells. Both exogenous and endogenous ROS have been shown to enhance proliferation of cancer cells. The role of ROS in promoting tumor proliferation is further supported by the observation that agents with potential to inhibit ROS generation can also inhibit cancer cell proliferation. [ 61 ] Although ROS can promote tumor cell proliferation, a great increase in ROS has been associated with reduced cancer cell proliferation by induction of G2/M cell cycle arrest; increased phosphorylation of ataxia telangiectasia mutated (ATM), checkpoint kinase 1 (Chk 1), Chk 2; and reduced cell division cycle 25 homolog c (CDC25). [ 65 ]
A cancer cell can die in three ways: apoptosis , necrosis , and autophagy . Excessive ROS can induce apoptosis through both the extrinsic and intrinsic pathways. [ 66 ] In the extrinsic pathway of apoptosis, ROS are generated by Fas ligand as an upstream event for Fas activation via phosphorylation, which is necessary for subsequent recruitment of Fas-associated protein with death domain and caspase 8 as well as apoptosis induction. [ 61 ] In the intrinsic pathway, ROS function to facilitate cytochrome c release by activating pore-stabilizing proteins (Bcl-2 and Bcl-xL) as well as inhibiting pore-destabilizing proteins (Bcl-2-associated X protein, Bcl-2 homologous antagonist/killer). [ 67 ] The intrinsic pathway is also known as the caspase cascade and is induced through mitochondrial damage which triggers the release of cytochrome c. DNA damage, oxidative stress, and loss of mitochondrial membrane potential lead to the release of the pro-apoptotic proteins mentioned above stimulating apoptosis. [ 68 ] Mitochondrial damage is closely linked to apoptosis and since mitochondria are easily targeted there is potential for cancer therapy. [ 69 ]
The cytotoxic nature of ROS is a driving force behind apoptosis, but in even higher amounts, ROS can result in both apoptosis and necrosis, a form of uncontrolled cell death, in cancer cells. [ 70 ]
Numerous studies have shown the pathways and associations between ROS levels and apoptosis, but a newer line of study has connected ROS levels and autophagy. [ 71 ] ROS can also induce cell death through autophagy, which is a self-catabolic process involving sequestration of cytoplasmic contents (exhausted or damaged organelles and protein aggregates) for degradation in lysosomes. [ 72 ] Therefore, autophagy can also regulate the cell's health in times of oxidative stress. Autophagy can be induced by ROS levels through many pathways in the cell in an attempt to dispose of harmful organelles and prevent damage, such as carcinogens, without inducing apoptosis. [ 73 ] Autophagic cell death can be prompted by the over expression of autophagy where the cell digests too much of itself in an attempt to minimize the damage and can no longer survive. When this type of cell death occurs, an increase or loss of control of autophagy regulating genes is commonly co-observed. [ 74 ] Thus, once a more in-depth understanding of autophagic cell death is attained and its relation to ROS, this form of programmed cell death may serve as a future cancer therapy.
Autophagy and apoptosis are distinct mechanisms for cell death brought on by high levels of ROS. Aautophagy and apoptosis, however, rarely act through strictly independent pathways. There is a clear connection between ROS and autophagy and a correlation seen between excessive amounts of ROS leading to apoptosis. [ 73 ] The depolarization of the mitochondrial membrane is also characteristic of the initiation of autophagy. When mitochondria are damaged and begin to release ROS, autophagy is initiated to dispose of the damaging organelle. If a drug targets mitochondria and creates ROS, autophagy may dispose of so many mitochondria and other damaged organelles that the cell is no longer viable. The extensive amount of ROS and mitochondrial damage may also signal for apoptosis. The balance of autophagy within the cell and the crosstalk between autophagy and apoptosis mediated by ROS is crucial for a cell's survival. This crosstalk and connection between autophagy and apoptosis could be a mechanism targeted by cancer therapies or used in combination therapies for highly resistant cancers.
After growth factor stimulation of RTKs, ROS can trigger activation of signaling pathways involved in cell migration and invasion such as members of the mitogen activated protein kinase (MAPK) family – extracellular regulated kinase (ERK), c-jun NH-2 terminal kinase (JNK) and p38 MAPK. ROS can also promote migration by augmenting phosphorylation of the focal adhesion kinase (FAK) p130Cas and paxilin. [ 75 ]
Both in vitro and in vivo, ROS have been shown to induce transcription factors and modulate signaling molecules involved in angiogenesis (MMP, VEGF) and metastasis (upregulation of AP-1, CXCR4, AKT and downregulation of PTEN). [ 61 ]
Experimental and epidemiologic research over the past several years has indicated close associations among ROS, chronic inflammation, and cancer. [ 61 ] ROS induces chronic inflammation by the induction of COX-2, inflammatory cytokines (TNFα, interleukin 1 (IL-1), IL-6), chemokines (IL-8, CXCR4) and pro-inflammatory transcription factors (NF-κB). [ 61 ] These chemokines and chemokine receptors, in turn, promote invasion and metastasis of various tumor types.
Both ROS-elevating and ROS-eliminating strategies have been developed with the former being predominantly used. Cancer cells with elevated ROS levels depend heavily on the antioxidant defense system. ROS-elevating drugs further increase cellular ROS stress level, either by direct ROS-generation (e.g. motexafin gadolinium, elesclomol) or by agents that abrogate the inherent antioxidant system such as SOD inhibitor (e.g. ATN-224, 2-methoxyestradiol) and GSH inhibitor (e.g. PEITC, buthionine sulfoximine (BSO)). The result is an overall increase in endogenous ROS, which when above a cellular tolerability threshold, may induce cell death. [ 76 ] On the other hand, normal cells appear to have, under lower basal stress and reserve, a higher capacity to cope with additional ROS-generating insults than cancer cells do. [ 77 ] Therefore, the elevation of ROS in all cells can be used to achieve the selective killing of cancer cells.
Radiotherapy also relies on ROS toxicity to eradicate tumor cells. Radiotherapy uses X-rays, γ-rays as well as heavy particle radiation such as protons and neutrons to induce ROS-mediated cell death and mitotic failure. [ 61 ]
Due to the dual role of ROS, both prooxidant and antioxidant-based anticancer agents have been developed. However, modulation of ROS signaling alone seems not to be an ideal approach due to adaptation of cancer cells to ROS stress, redundant pathways for supporting cancer growth and toxicity from ROS-generating anticancer drugs. Combinations of ROS-generating drugs with pharmaceuticals that can break the redox adaptation could be a better strategy for enhancing cancer cell cytotoxicity. [ 61 ]
James Watson [ 78 ] and others [ 79 ] have proposed that lack of intracellular ROS due to a lack of physical exercise may contribute to the malignant progression of cancer, because spikes of ROS are needed to correctly fold proteins in the endoplasmatic reticulum and low ROS levels may thus aspecifically hamper the formation of tumor suppressor proteins. [ 79 ] Since physical exercise induces temporary spikes of ROS, this may explain why physical exercise is beneficial for cancer patient prognosis. [ 80 ] Moreover, high inducers of ROS such as 2-deoxy-D-glucose and carbohydrate-based inducers of cellular stress induce cancer cell death more potently because they exploit the cancer cell's high avidity for sugars. [ 81 ]
ROS are critical in memory formation. [ 84 ] [ 85 ] [ 86 ] ROS also have a central role in epigenetic DNA demethylation , which is relevant to learning and memory [ 87 ] [ 88 ]
In mammalian nuclear DNA, a methyl group can be added, by a DNA methyltransferase , to the 5th carbon of cytosine to form 5mC (see red methyl group added to form 5mC near the top of the first figure). The DNA methyltransferases most often form 5mC within the dinucleotide sequence "cytosine-phosphate-guanine" to form 5mCpG. This addition is a major type of epigenetic alteration and it can silence gene expression . Methylated cytosine can also be demethylated , an epigenetic alteration that can increase the expression of a gene. A major enzyme involved in demethylating 5mCpG is TET1 . However, TET1 is only able to act on 5mCpG if an ROS has first acted on the guanine to form 8-hydroxy-2'-deoxyguanosine (8-OHdG), resulting in a 5mCp-8-OHdG dinucleotide . [ 82 ] However, TET1 is only able to act on the 5mC part of the dinucleotide when the base excision repair enzyme OGG1 binds to the 8-OHdG lesion without immediate excision. Adherence of OGG1 to the 5mCp-8-OHdG site recruits TET1 and TET1 then oxidizes the 5mC adjacent to 8-OHdG, as shown in the first figure, initiating a demethylation pathway shown in the second figure.
The thousands of CpG sites being demethylated during memory formation depend on ROS in an initial step. The altered protein expression in neurons, controlled in part by ROS-dependent demethylation of CpG sites in gene promoters within neuron DNA, are central to memory formation. [ 89 ] | https://en.wikipedia.org/wiki/Reactive_oxygen_species |
All living cells produce reactive oxygen species (ROS) as a byproduct of metabolism. ROS are reduced oxygen intermediates that include the superoxide radical (O 2 − ) and the hydroxyl radical (OH•), as well as the non-radical species hydrogen peroxide (H 2 O 2 ). These ROS are important in the normal functioning of cells, playing a role in signal transduction [ 1 ] [ 2 ] and the expression of transcription factors. [ 3 ] [ 4 ] However, when present in excess, ROS can cause damage to proteins, lipids and DNA by reacting with these biomolecules to modify or destroy their intended function. As an example, the occurrence of ROS have been linked to the aging process in humans, as well as several other diseases including Alzheimer's , rheumatoid arthritis , Parkinson's , and some cancers. [ 5 ] Their potential for damage also makes reactive oxygen species useful in direct protection from invading pathogens, [ 6 ] as a defense response to physical injury, [ 7 ] [ 8 ] [ 9 ] [ 10 ] and as a mechanism for stopping the spread of bacteria and viruses by inducing programmed cell death . [ 11 ]
Reactive oxygen species are present in low concentrations in seawater and are produced primarily through the photolysis of organic and inorganic matter. [ 12 ] However, the biological production of ROS, generated through algal photosynthesis and subsequently 'leaked' to the environment, can contribute significantly to concentrations in the water column. [ 13 ] [ 14 ] [ 15 ] Although there is very little information on the biological generation of ROS in marine surface waters, several species of marine phytoplankton have recently been shown to release significant amounts of ROS into the environment. [ 16 ] [ 17 ] This ROS has the potential to harm nearby organisms, [ 18 ] [ 19 ] and, in fact, has been implicated as the cause of massive fish, bacteria, and protist mortalities. [ 20 ] [ 21 ] [ 22 ]
In sea water, ROS can be generated through abiotic as well as biotic processes, among which are the radiolysis and photolysis of water molecules and cellular respiration. According to a model proposed by Fan [ 23 ] for the prediction of ROS in surface waters, the biochemistry mediated by phytoplankton may be just as important for the production of ROS as photochemistry. Biological ROS is often synthesized in mitochondrial membranes, as well as the endoplasmic reticulum of animals, plants, and some bacteria. [ 24 ] [ 25 ] In addition, chloroplasts and the organelles peroxisomes and glyoxysomes are also sites for the generation of ROS. [ 24 ] [ 25 ] [ 26 ] The ROS most likely released to the environment are those produced at the cell surface as electrons get "leaked" from the respiratory chain and react with molecular oxygen, O 2 . [ 27 ] The products of this subsequent reduction of molecular oxygen are what are referred to as reactive oxygen species. Thus, the production of ROS is in direct proportion to the concentration of O 2 in the system, with increases of O 2 leading to higher production of ROS. [ 28 ] There are three main reactive oxygen species: the superoxide anion (O 2 − ), hydrogen peroxide (H 2 O 2 ), and the hydroxyl radical (OH•). The superoxide anion is formed directly from the one-electron reduction of molecular oxygen. [ 29 ] Hydrogen peroxide is then formed from the disproportionation of the superoxide anion. This reaction occurs very quickly in seawater. Next, the reduction of hydrogen peroxide yields the hydroxyl radical, H 2 O 2 ↔2OH•, which can then get reduced to the hydroxyl ion and water. [ 1 ] However, the presence of reactive oxygen species in marine systems is hard to detect and measure accurately, for a number of reasons. First, ROS concentrations are generally low (nanomoles) in seawater. Second, they may react with other hard to identify molecules that occur in low quantities, resulting in unknown products. Finally, they are (for the most part) transient intermediates, having lifetimes as little as microseconds. [ 30 ]
According to Blough & Zepp, [ 30 ] superoxide is one of the hardest reactive oxygen species to quantify because it is present in low concentrations: 2×10 −12 M in the open ocean and up to 2×10 −10 M in coastal areas. The main sources of biological superoxide in the ocean come from the reduction of oxygen at the cell surface and metabolites released into the water. [ 27 ] [ 31 ] In marine systems, superoxide most often acts as a one-electron reductant, but it can also serve as an oxidant and may increase the normally slow oxidation rates of environmental compounds. [ 12 ] [ 30 ] Superoxide is very unstable, with between 50 and 80% of its concentration of anions spontaneously disproportionating to hydrogen peroxide. At its peak, this reaction occurs with a rate constant on the order of 2.2×10 4 – 4.5×10 5 L mol −1 sec −1 in seawater. [ 12 ] The dismutation of superoxide to hydrogen peroxide can also be catalyzed by the antioxidant enzyme superoxide dismutase with a rate constant on the order of 2×10 9 L mol −1 sec −1 . [ 32 ] As a result of these fast acting processes, the steady state concentration of superoxide is very small. Since superoxide is also moderately reactive towards trace metals and dissolved organic matter, any remaining superoxide is thought to be removed from the water column through reactions with these species. [ 12 ] [ 30 ] As a result, the presence of superoxide in surface waters has been known to result in an increase of reduced iron. [ 30 ] [ 33 ] This, in turn, serves to enhance the availability of iron to phytoplankton whose growth is often limited by this key nutrient. As a charged radical species, superoxide is unlikely to significantly affect an organism's cellular function since it is not able to easily diffuse through the cell membrane. Instead, its potential toxicity lies in its ability to react with extracellular surface proteins or carbohydrates to inactivate their functions. [ 34 ] Although its lifetime is fairly short (about 50 microseconds), superoxide has the potential to reach cell surfaces since it has a diffusion distance of about 320 nm. [ 1 ] [ 34 ]
The reduction product of superoxide is hydrogen peroxide, one of the most studied reactive oxygen species because it occurs in relatively high concentrations, is relatively stable, and is fairly easy to measure. [ 12 ] It is thought that algal photosynthesis is one of the major modes of hydrogen peroxide production, while the production of H 2 O 2 by stressed organisms is a secondary source. [ 13 ] [ 14 ] [ 15 ] In marine systems, hydrogen peroxide (H 2 O 2 ) exists at concentrations of 10 −8 -10 −9 M in the photic zone, [ 15 ] but has been found in double those concentrations in parts of the Atlantic Ocean. [ 35 ] Its lifetime, ranging from hours to days in coastal waters, can be as long as 15 days in Antarctic seawater. [ 12 ] [ 30 ] H 2 O 2 is important in aquatic environments because it can oxidize dissolved organic matter and affect the redox chemistry of iron, copper, and manganese. [ 33 ] Since hydrogen peroxide, as an uncharged molecule, diffuses easily across biological membranes it can directly damage cellular constituents (DNA and enzymes) by reacting with them and deactivating their functions. [ 2 ] In addition, hydrogen peroxide reduces to the hydroxyl radical, the most reactive radical and the one with the greatest possibility for damage. [ 1 ] [ 2 ] [ 12 ] [ 30 ]
Even though the superoxide and the hydrogen peroxide radicals are toxic in their own right, they become potentially more toxic when they interact to form the hydroxyl radical (OH•). This proceeds through the iron and copper catalyzed Haber–Weiss reaction : [ 36 ] O 2 − + Fe 3+ ↔ O 2 + Fe 2+ H 2 O 2 + Fe 2+ ↔ Fe 3+ + OH• + OH −
Since iron and copper are present in coastal waters, the hydroxyl radical could be formed by reactions with either of the, [ 37 ] [ 38 ] and, in fact, their oxidation does result in significant sources of hydroxyl radicals in the ocean. [ 33 ] The hydroxyl radical is the most unstable of the ROS (lifetime of 10 −7 seconds), reacting with many inorganic and organic species in the surrounding environment at rates near the diffusion limit (rate constants of 10 8 -10 10 L mol −1 sec −1 ). [ 39 ] In seawater, the radical is removed as a result of reactions with bromide ions, while in fresh water it reacts principally with bicarbonate and carbonate ions. [ 12 ] [ 30 ] Because it has such a high reactivity, day time concentrations in surface waters of the hydroxyl radical are generally very low (10 −19 to 10 −17 M). [ 12 ] The hydroxyl radical can oxidize membrane lipids and cause nucleic acids and proteins to denature. However, because the radical is so reactive, there is likely not enough time for transport to the cell surface (mean diffusion distance of 4.5 nm). [ 39 ] Thus, direct effects to organisms of externally generated hydroxyl radicals are expected to be minimal. Indirectly, the hydroxyl radical can result in significant biogeochemical changes in marine systems by influencing the cycling of dissolved organic matter and trace metal speciation. Both intracellular and extracellular reactive oxygen species can be removed from the environment by antioxidants produced biologically as a defense mechanism. Many phytoplankton, for instance, have been found to have numerous superoxide-scavenging (superoxide dismutase) and hydrogen peroxide-scavenging enzymes (catalase, ascorbate peroxidase, and glutathione peroxidase). [ 40 ] [ 41 ] [ 42 ] [ 43 ] [ 44 ] The antioxidant superoxide dismutase catalyses the formation of hydrogen peroxide from the superoxide anion through the following reaction: [ 45 ] 2 O 2 − + 2H + ↔ O 2 + H 2 O 2 . Similarly, catalase increases the formation of water from hydrogen peroxide by catalyzing the reaction: [ 46 ] 2H 2 O 2 ↔ O 2 + 2H 2 O. As a result of this reaction, the hydroxyl radical is prevented from forming. In addition, the presence of large quantities of humics in the water can also act as antioxidants of ROS. [ 47 ] However, it must be noted that certain ROS can inactivate certain enzymes. For instance, the superoxide anion is known to temporarily inhibit the function of catalase at high concentrations. [ 48 ]
Many algal species have been shown to not only produce reactive oxygen species under normal conditions but to increase production of these compounds under stressful situations. In particular, ROS levels have been shown to be influenced by cell size, cell density, growth stage, light intensity, temperature, and nutrient availability.
Oda et al. [ 16 ] found that differences in the production of ROS were due to the size of the cell. By comparing four species of flagellates, they showed that the larger species Ichatonella produced the most superoxide and hydrogen peroxide per cell than Heterosigma akashiwo , Olisthodiscus luteus , and Fibrocapsa japonica . In a comparison of 37 species of marine microalgae, including dinoflagellates, rhaphidophytes, and chlorophytes, Marshall et al. [ 17 ] also found a direct relationship between cell size and the amount of superoxide produced. The largest cells, Chattonella marina , produced up to 100 times more superoxide than most other marine algae (see figure in [ 49 ] ). The authors suggest that since ROS is produced as a byproduct of metabolism, and larger cells are more metabolically active than smaller cells, it follows that larger cells should produce more ROS. Similarly, since photosynthesis also produces ROS, larger cells likely have a greater volume of chloroplasts and would be expected to produce more ROS than smaller cells.
The production of ROS has also been shown to be dependent on algal cell density. Marshall et al. [ 17 ] found that for Chattonella marina , higher concentrations of cells produced less superoxide per cell than those with a lower density. This may explain why some raphydophyte blooms are toxic at low concentration and non-toxic in heavy blooms. [ 50 ] Tang & Gobler [ 51 ] also found that cell density was inversely related to ROS production for the alga Cochlodinium polykrikoides . They found, in addition, that increases of ROS production were also related to the growth phase of algae. In particular, algae in exponential growth were more toxic than those in the stationary or late exponential phase. Many other algal species ( Heterosigma akashiwo , Chattonella marina , and Chattonella antiqua ) have also been shown to produce the highest amounts of ROS during the exponential phase of growth. [ 50 ] [ 52 ] Oda et al. [ 16 ] suggest this is due to actively growing cells having higher photosynthesis and metabolic rates. Resting stage cells of Chattonella antiqua have been shown to generate less superoxide than their motile counterparts. [ 53 ]
Since superoxide is produced through the auto-oxidation of an electron acceptor in photosystem I during photosynthesis, one would expect a positive relationship between light levels and algal ROS production. [ 17 ] This is indeed what has been shown: in the diatom Thallasia weissflogii , an increase in light intensity caused an increase in the production of both superoxide and hydrogen peroxide. [ 54 ] Similarly, in the flagellates Chattonella marina , Prorocentrum minimum , and Cochlodinium polykrikoides , decreases in light levels resulted in decreases in superoxide production, [ 17 ] [ 55 ] [ 56 ] with higher levels produced during the day. However, because many studies have found ROS production to be relatively high even in the dark, metabolic pathways other than photosynthesis are likely more important for production. [ 52 ] For instance, Liu et al. [ 57 ] found that ROS production was regulated by iron concentration and pH. From this evidence they suggest that ROS production is most likely due to a plasma membrane enzyme system dependent on iron availability. Similarly, in Heterosigma akashiwo, the depletion of iron and an increase in temperature, not light intensity, resulted in enhanced production of ROS. [ 50 ] Liu et al. [ 57 ] found the same relationship with temperature.
The active release of reactive oxygen species from cells has a variety of purposes, including a means to deter predators, or a chemical defense for the incapacitation of competitors. [ 58 ] [ 59 ] [ 60 ] In addition, ROS may be involved in cell signaling, as well as the oxidation or reduction of necessary or toxic metals. [ 13 ] [ 61 ]
It is not surprising that ROS production may be a form of chemical defense against predators, since at low levels it can damage DNA and at high levels lead to cell necrosis. [ 25 ] One of the most common mechanisms of cellular injury is the reaction of ROS with lipids, which can disrupt enzyme activity and ATP production, and lead to apoptosis. [ 37 ] Reactions of ROS with proteins can modify amino acids, fragment peptide chains, alter electrical charges, and ultimately inactivate an enzyme's function. [ 62 ] [ 63 ] In DNA, deletions, mutations, and other lethal genetic effects may result from reactions with ROS. [ 64 ] [ 65 ] Reactive oxygen species are especially inexpensive to produce as defense chemicals, simply because they are not composed of metabolically costly elements such as carbon, nitrogen, or phosphate. Reactive oxygen species produced by phytoplankton have been linked to deaths of fish, shellfish, and protists, as well as shown to reduce the viability and growth of bacteria. [ 20 ] [ 50 ] [ 66 ] [ 67 ] In addition, a study by Marshall et al. [ 17 ] showed that four algal species used as bivalve feed produced significantly lower concentrations of superoxide, suggesting that ROS production by other algal species may be a way to decrease grazing by bivalves. The most direct evidence for ROS as a defense mechanism is the fact that many icthyotoxic algae produce greater concentrations of ROS than nonichthyotoxic strains. [ 16 ] [ 17 ] [ 19 ] [ 50 ]
It is possible that ROS may not be the actual toxic substance, but may in fact work to make other exudates more toxic by oxidizing them. [ 17 ] [ 68 ] For instance, ROS from Chattonella marina have been shown to enhance the toxic effects of fatty acid eicosapentaenoic acid (EPA) on exposed fishes. [ 17 ] [ 68 ] Similarly, free-fatty acids released from diatom biofilms as products of ROS oxidation of EPA are known to be toxic to zooplankters. [ 69 ] In addition, Fontana et al. [ 70 ] suggested that the interaction of ROS and diatom exudates (such as fatty acid hydroperoxides) are responsible for inhibiting embryonic development and causing larval abnormalities in copepods. Finally, ROS oxidation of algal polyunsaturated fatty acids have also been shown to deter grazers. [ 71 ]
In addition to impacting predator-prey interactions, the production of ROS may also help an alga get an advantage in the competition for resources against other algae, be a way to prevent fouling bacteria, and act as a signaling mechanism between cells. [ 60 ] [ 67 ] [ 72 ] ROS can inhibit photosynthesis in algae [ 25 ] Thus an alga that is more tolerant of ROS than another may produce and release it as a means of decreasing the other species competitive ability. In addition, Chattonella marina , the most well studied raphydophyte for ROS production, may produce a boundary of ROS that deters other marine microalgae from using nutrients in its vicinity. [ 27 ] Similarly, this boundary could also be a way to discourage bacteria fouling, since the production of ROS is known to inhibit growth and bioluminescent ability in the bacteria Vibrio alginolyticus and Vibrio fischeri , respectively. [ 67 ] [ 72 ] Lastly, Marshall et al. [ 27 ] showed that Chattonella marina cells were able to change their rate of superoxide production in as little as one hour when in different cell densities, increasing the rate from 1.4 to 7.8 times the original. They suggest that this quick response in altering rates of production may be a form of chemical signaling between cells that works to provide information about cell density.
ROS may be useful in the oxidation or reduction of necessary or toxic metals. Since iron is necessary for phytoplankton growth, the auto-reduction of reactive oxygen species may be a way for algae to get usable iron from free or organically bound ferric iron. [ 73 ] For instance, Cakman et al. [ 74 ] showed that ROS may increase the amount of iron available through extracellular ferric reduction. It is thought that the high reducing power of this reaction is maintained through the electron-rich superoxide ion. [ 74 ] In several studies on the ROS production of Heterosigma akashiwo , hydrogen peroxide production was found to be inversely proportional to the concentration of iron available. [ 50 ] [ 75 ] In addition, Cornish and Page in 1998 found that phytoplankton produce more ROS when there are lower levels of extracellular iron. They suggested that when intracellular iron is limiting, the phytoplankton respond by producing more ROS as a way to increase the reducing potential around the cell and thus be better able to reduce that iron to a usable form. Similarly, lower ROS production would suggest that the intracellular iron is at sufficiently high levels for cellular function. | https://en.wikipedia.org/wiki/Reactive_oxygen_species_production_in_marine_microalgae |
Reactive sulfur species (RSS) are a family of sulfur-based chemical compounds that can oxidize and inhibit thiol-proteins and enzymes. They are often formed by the oxidation of thiols and disulfides into higher oxidation states. Examples of RSS include persulfides , polysulfides and thiosulfate . [ 1 ] [ 2 ] | https://en.wikipedia.org/wiki/Reactive_sulfur_species |
Reactive transport modeling in porous media refers to the creation of computer models integrating chemical reaction with transport of fluids through the Earth's crust . Such models predict the distribution in space and time of the chemical reactions that occur along a flowpath. Reactive transport modeling in general can refer to many other processes, including reactive flow of chemicals through tanks, reactors, or membranes; particles and species in the atmosphere; gases exiting a smokestack; and migrating magma.
Reactive transport models are constructed to understand the composition of natural waters; the origin of economic mineral deposits ; the formation and dissolution of rocks and minerals in geologic formations in response to injection of industrial wastes, steam, or carbon dioxide ; and the generation of acidic waters and leaching of metals from mine wastes . They are often relied upon to predict the migration of contaminant plumes; the mobility of radionuclides in waste repositories ; and the biodegradation of chemicals in landfills . When applied to the study of contaminants in the environments, they are known as fate and transport models. [ 1 ]
Modern reactive transport modeling has arisen from several separate schools of thought. [ 2 ] Hydrologists primarily concerned with the physical nature of mass transport assumed relatively simple reaction formulations, such as linear distribution coefficients or linear decay terms, which could be added to the advection-dispersion equation . By assuming linear, equilibrium sorption , for example, the advection-dispersion equation can be modified by a simple retardation factor and solved analytically . Such analytical solutions are limited to relatively simple flow systems and reactions.
Geochemical models , on the other hand, have been developed to provide thermodynamic descriptions of multicomponent systems without regard to transport. Reaction path models were created, for instance, to describe the sequence of chemical reactions resulting from chemical weathering or hydrothermal alteration in batch systems , in terms of the overall reaction progress. By adopting the reference frame of a packet of fluid and treating reaction progress as travel time (or distance along a flowpath), however, a batch reaction path model could be thought of as describing advective transport through an aquifer . [ 3 ]
The most sophisticated multi-component reactive transport models consider both reaction and transport. [ 4 ] [ 5 ] Early studies developed the theoretical basis of reactive transport models, and the numerical tools necessary to solve them, and applied them to problems of reactive contaminant transport [ 6 ] and flow through reacting hydrothermal systems. [ 7 ]
Reactive transport models have found increased application in recent years with improvements in the power of personal computers and modeling software . [ 5 ] [ 8 ]
Reactive transport models couple a large number chemical reactions with mass transport. Certain applications, such as geothermal energy production and ore deposit modeling, require the additional calculation of heat transfer . In modeling carbon sequestration and hydraulic fracturing , moreover, it may be necessary to describe rock deformation resulting from mineral growth or abnormally high fluid pressure. Description of transport through the unsaturated zone and multiphase flow modeling, as applied to transport of petroleum and natural gas ; non-aqueous phase liquids ( DNAPL or LNAPL ); and supercritical carbon dioxide requires increasingly complex models which are prone to considerable uncertainty.
In many cases the processes simulated in reactive transport models are highly related. Mineral dissolution and precipitation, for example, can affect the porosity and permeability of the domain, which in turn affect the flow field and groundwater velocity. Heat transport greatly affects the viscosity of water and its ability to flow. Below are many of the physical and chemical processes which can be simulated with reactive transport models.
Geochemical reactions :
Mass Transport:
Heat transport:
Medium deformation:
Some of the simplest reactive transport problems can be solved analytically. Where equilibrium sorption is described by a linear distribution coefficient, for example, the sorbing solute's velocity is retarded relative to that of a nonreactive tracer; the relative velocities can be described with a retardation factor. Analytical solutions are exact solutions of the governing equations.
Complex reactive transport problems are more commonly solved numerically. In this case, the governing equations are approximated so that they can be solved by computer algorithms. The governing equations, including both reaction and transport terms, can be solved simultaneously using a one-step or global implicit simulator. This technique is straightforward conceptually, but computationally very difficult. [ 9 ]
Instead of solving all the relevant equations together, the transport and chemical reaction equations can be solved separately. Operator splitting , as this technique is known, uses appropriate numerical techniques to solve the reaction and transport equations at each time step. [ 1 ] Various methods exist, including the sequential non-iterative approach (SNIA), Strang splitting , and sequential iterative approach (SIA). [ 9 ] Since the reaction and transport terms are handled separately, separate programs for batch reaction and transport can be linked together. Cross-linkable re-entrant software objects designed for this purpose readily enable construction of reactive transport models of any flow configuration. [ 10 ] [ 11 ]
Reactive transport modeling requires input from numerous fields, including hydrology , geochemistry and biogeochemistry , microbiology , soil physics , and fluid dynamics . [ 2 ] The numerical formulation and solution of reactive transport problems can be especially difficult due to errors arising in the coupling process, beyond those inherent to the individual processes. Valocchi and Malmstead (1992), for example, reported on the potential errors arising from the operator splitting technique. [ 12 ]
Even in the absence of numerical difficulties, the general lack of knowledge available to practitioners creates uncertainty. Field sites are typically heterogeneous , both physically and chemically, and sampling is often sparse. The prevailing assumption of Fickian dispersion is often inadequate. Equilibrium constants and kinetic rate laws for relevant reactions are often poorly known. The complexity of many processes requires expertise in one or more of the aforementioned fields. Many processes, such as long-term nuclear waste storage, cannot be experimentally verified; reactive transport problems can only attempt to predict such long-term behavior. The current descriptions of multi-phase flow and mechanical deformation processes are still being developed. | https://en.wikipedia.org/wiki/Reactive_transport_modeling_in_porous_media |
In chemistry , reactivity is the impulse for which a chemical substance undergoes a chemical reaction , either by itself or with other materials, with an overall release of energy .
Reactivity refers to:
The chemical reactivity of a single substance (reactant) covers its behavior in which it:
The chemical reactivity of a substance can refer to the variety of circumstances (conditions that include temperature, pressure, presence of catalysts) in which it reacts, in combination with the:
The term reactivity is related to the concepts of chemical stability and chemical compatibility .
Reactivity is a somewhat vague concept in chemistry. It appears to embody both thermodynamic factors and kinetic factors (i.e., whether or not a substance reacts, and how fast it reacts). Both factors are actually distinct, and both commonly depend on temperature. For example, it is commonly asserted that the reactivity of alkali metals ( Na , K , etc.) increases down the group in the periodic table, or that hydrogen's reactivity is evidenced by its reaction with oxygen. In fact, the rate of reaction of alkali metals (as evidenced by their reaction with water for example) is a function not only of position within the group but also of particle size. Hydrogen does not react with oxygen—even though the equilibrium constant is very large—unless a flame initiates the radical reaction, which leads to an explosion.
Restriction of the term to refer to reaction rates leads to a more consistent view. Reactivity then refers to the rate at which a chemical substance tends to undergo a chemical reaction in time. In pure compounds , reactivity is regulated by the physical properties of the sample. For instance, grinding a sample to a higher specific surface area increases its reactivity. In impure compounds, the reactivity is also affected by the inclusion of contaminants. In crystalline compounds, the crystalline form can also affect reactivity. However, in all cases, reactivity is primarily due to the sub-atomic properties of the compound.
Although it is commonplace to make statements that "substance X is reactive," each substance reacts with its own set of reagents. For example, the statement that "sodium metal is reactive" suggests that sodium reacts with many common reagents (including pure oxygen, chlorine, hydrochloric acid , and water), either at room temperature or when using a Bunsen burner .
The concept of stability should not be confused with reactivity. For example, an isolated molecule of an electronically excited state of the oxygen molecule spontaneously emits light after a statistically defined period. [ citation needed ] The half-life of such a species is another manifestation of its stability, but its reactivity can only be ascertained via its reactions with other species.
The second meaning of reactivity (i.e., whether or not a substance reacts) can be rationalized at the atomic and molecular level using older and simpler valence bond theory and also atomic and molecular orbital theory. Thermodynamically, a chemical reaction occurs because the products (taken as a group) are at a lower free energy than the reactants; the lower energy state is referred to as the "more stable state." Quantum chemistry provides the most in-depth and exact understanding of the reason this occurs. Generally, electrons exist in orbitals that are the result of solving the Schrödinger equation for specific situations.
All things (values of the n and m l quantum numbers ) being equal, the order of stability of electrons in a system from least to greatest is;
To achieve one of these orders of stability, an atom reacts with another atom to stabilize both. For example, a lone hydrogen atom has a single electron in its 1s orbital. It becomes significantly more stable (as much as 100 kilocalories per mole , or 420 kilojoules per mole ) when reacting to form H 2 .
It is for this same reason that carbon almost always forms four bonds . Its ground-state valence configuration is 2s 2 2p 2 , half-filled. However, the activation energy to go from half-filled to fully-filled p orbitals is negligible, and as such, carbon forms them almost instantaneously. Meanwhile, the process releases a significant amount of energy ( exothermic ). This four equal bond configuration is called sp 3 hybridization .
The above three paragraphs rationalize, albeit very generally, the reactions of some common species, particularly atoms. One approach to generalize the above is the activation strain model [ 1 ] [ 2 ] [ 3 ] of chemical reactivity which provides a causal relationship between, the reactants' rigidity and their electronic structure, and the height of the reaction barrier.
The rate of any given reaction:
is governed by the rate law :
where the rate is the change in the molar concentration in one second in the rate-determining step of the reaction (the slowest step), [A] is the product of the molar concentration of all the reactants raised to the correct order (known as the reaction order), and k is the reaction constant, which is constant for one given set of circumstances (generally temperature and pressure) and independent of concentration. The reactivity of a compound is directly proportional to both the value of k and the rate. For instance, if
then
where n is the reaction order of A , m is the reaction order of B , n + m is the reaction order of the full reaction, and k is the reaction constant. | https://en.wikipedia.org/wiki/Reactivity_(chemistry) |
In chemistry, a reactivity series (or reactivity series of elements ) is an empirical, calculated, and structurally analytical progression [ 1 ] of a series of metals , arranged by their "reactivity" from highest to lowest. [ 2 ] [ 3 ] [ 4 ] It is used to summarize information about the reactions of metals with acids and water , single displacement reactions and the extraction of metals from their ores . [ 5 ]
Going from the bottom to the top of the table the metals:
There is no unique and fully consistent way to define the reactivity series, but it is common to use the three types of reaction listed below, many of which can be performed in a high-school laboratory (at least as demonstrations). [ 6 ]
The most reactive metals, such as sodium , will react with cold water to produce hydrogen and the metal hydroxide :
Metals in the middle of the reactivity series, such as iron , will react with acids such as sulfuric acid (but not water at normal temperatures) to give hydrogen and a metal salt , such as iron(II) sulfate :
There is some ambiguity at the borderlines between the groups. Magnesium , aluminium and zinc can react with water, but the reaction is usually very slow unless the metal samples are specially prepared to remove the surface passivation layer of oxide which protects the rest of the metal. Copper and silver will react with nitric acid ; but because nitric acid is an oxidizing acid , the oxidizing agent is not the H + ion as in normal acids, but the NO 3 − ion.
The reactivity series is sometimes quoted in the strict reverse order of standard electrode potentials , when it is also known as the " electrochemical series ". [ 8 ]
The following list includes the metallic elements of the first six periods. It is mostly based on tables provided by NIST . [ 9 ] [ 10 ] However, not all sources give the same values: there are some differences between the precise values given by NIST and the CRC Handbook of Chemistry and Physics . In the first six periods this does not make a difference to the relative order, but in the seventh period it does, so the seventh-period elements have been excluded. (In any case, the typical oxidation states for the most accessible seventh-period elements thorium and uranium are too high to allow a direct comparison.) [ 11 ]
Hydrogen has been included as a benchmark, although it is not a metal. Borderline germanium , antimony , and astatine have been included. Some other elements in the middle of the 4d and 5d rows have been omitted (Zr–Tc, Hf–Os) when their simple cations are too highly charged or of rather doubtful existence. Greyed-out rows indicate values based on estimation rather than experiment.
The positions of lithium and sodium are changed on such a series.
Standard electrode potentials offer a quantitative measure of the power of a reducing agent, rather than the qualitative considerations of other reactive series. However, they are only valid for standard conditions: in particular, they only apply to reactions in aqueous solution. Even with this proviso, the electrode potentials of lithium and sodium – and hence their positions in the electrochemical series – appear anomalous. The order of reactivity, as shown by the vigour of the reaction with water or the speed at which the metal surface tarnishes in air, appears to be
i.e., alkali metals > alkaline earth metals,
the same as the reverse order of the (gas-phase) ionization energies . This is borne out by the extraction of metallic lithium by the electrolysis of a eutectic mixture of lithium chloride and potassium chloride : lithium metal is formed at the cathode, not potassium. [ 1 ]
The image shows a periodic table extract with the electronegativity values of metals. [ 12 ]
Wulfsberg [ 13 ] distinguishes: very electropositive metals with electronegativity values below 1.4 electropositive metals with values between 1.4 and 1.9; and electronegative metals with values between 1.9 and 2.54.
From the image, the group 1–2 metals and the lanthanides and actinides are very electropositive to electropositive; the transition metals in groups 3 to 12 are very electropositive to electronegative; and the post-transition metals are electropositive to electronegative. The noble metals , inside the dashed border (as a subset of the transition metals) are very electronegative.
Li > Cs > Rb > K > Ba > Sr > Ca > Na > La > Y > Mg > Ce > Sc > Be > Al > Ti > Mn > V > Cr > Zn > Ga > Fe > Cd > In > Tl > Co > Ni > Sn > Pb > ( H ) > Sb > Bi > Cu > Po > Ru > Rh > Ag > Hg > Pd > Ir > Pt > Au | https://en.wikipedia.org/wiki/Reactivity_series |
In chemistry the reactivity–selectivity principle or RSP states that a more reactive chemical compound or reactive intermediate is less selective in chemical reactions. In this context selectivity represents the ratio of reaction rates .
This principle was generally accepted until the 1970s when too many exceptions started to appear. The principle is now considered obsolete. [ 1 ]
A classic example of perceived RSP found in older organic chemistry textbooks concerns the free radical halogenation of simple alkanes . Whereas the relatively unreactive bromine reacts with 2-methylbutane predominantly to 2-bromo-2-methylbutane, the reaction with much more reactive chlorine results in a mixture of all four regioisomers .
Another example of RSP can be found in the selectivity of the reaction of certain carbocations with azides and water . The very stable triphenylmethyl carbocation derived from solvolysis of the corresponding triphenylmethyl chloride reacts 100 times faster with the azide anion than with water. When the carbocation is the very reactive tertiary adamantane carbocation (as judged from diminished rate of solvolysis) this difference is only a factor of 10.
Constant or inverse relationships are just as frequent. For example, a group of 3- and 4-substituted pyridines in their reactivity quantified by their pKa show the same selectivity in their reactions with a group of alkylating reagents.
The reason for the early success of RSP was that the experiments involved very reactive intermediates with reactivities close to kinetic diffusion control and as a result the more reactive intermediate appeared to react slower with the faster substrate.
General relationships between reactivity and selectivity in chemical reactions can successfully be explained by Hammond's postulate .
When reactivity-selectivity relationships do exist they signify different reaction modes. In one study [ 2 ] the reactivity of two different free radical species (A, sulfur, B carbon) towards addition to simple alkenes such as acrylonitrile , vinyl acetate and acrylamide was examined.
The sulfur radical was found to be more reactive (6*10 8 vs. 1*10 7 M −1 .s −1 ) and less selective (selectivity ratio 76 vs 1200) than the carbon radical. In this case, the effect can be explained by extending the Bell–Evans–Polanyi principle with a factor δ {\displaystyle \delta \,} accounting for transfer of charge from the reactants to the transition state of the reaction which can be calculated in silico :
E a = E o + α Δ H r + β δ 2 {\displaystyle E_{a}=E_{o}+\alpha \Delta H_{r}+\beta \delta ^{2}\,}
with E a {\displaystyle E_{a}\,} the activation energy and Δ H r {\displaystyle \Delta H_{r}\,} the reaction enthalpy change. With the electrophilic sulfur radical the charge transfer is largest with electron-rich alkenes such as acrylonitrile but the resulting reduction in activation energy (β is negative) is offset by a reduced enthalpy. With the nucleophilic carbon radical on the other hand both enthalpy and polar effects have the same direction thus extending the activation energy range. | https://en.wikipedia.org/wiki/Reactivity–selectivity_principle |
In clinical trials , reactogenicity is the capacity of a vaccine to produce common, "expected" adverse reactions, especially excessive immunological responses and associated signs and symptoms, including fever and sore arm at the injection site. Other manifestations of reactogenicity typically identified in such trials include bruising , redness , induration , and swelling . [ 1 ]
The term reactogenicity was coined by the US Food and Drug Administration (FDA). All vaccines can induce reactogenicity, but reactogenicity is more likely in vaccines containing an adjuvant , which is a chemical additive intended for enhancing the recipient's immune response to the antigen that is present in a vaccine. Reactogenicity describes the immediate short-term reactions of a system to vaccines and should not be confused with the long-term consequences sequelae . Assessments of reactogenicity are carried out to evaluate the safety and usability of an experimental vaccine (see Investigational New Drug ). It is unclear whether a higher degree of reactogenicity to a vaccine correlates with more severe adverse events , which would require hospitalization or are life-threatening. Adverse events have been linked to a higher degree of reactogenicity; however, the links might have been coincidental. After assessing large databases relating to these events for many years, the FDA has not been able to make such a correlation. [ 1 ]
The US National Institutes of Health (NIH) has provided the following definition of reactogenicity: [ 2 ]
Reactogenicity events are AEs that are common and known to occur for the intervention/investigational product being studied and should be collected in a standard, systematic format using a grading scale based on functional assessment or magnitude of reaction. Provide a definition of expected vs unexpected AEs and local vs systemic events, based on the risk profile of the intervention/investigational product. This information is found on the IB or package insert. Typically, reactogenicity AEs are solicited and collected on memory cards and documented on a reactogenicity CRF. This information comes from the participant who may also have a memory aid to help recollect their symptoms. The following is an example of a functional scale for assessing reactogenicity or other parameters not specifically listed in the toxicity table: 0 = Absence of the indicated symptom 1 = Mild (awareness of a symptom but the symptom is easily tolerated) 2 = Moderate (discomfort enough to cause interference with usual activity) 3 = Severe (incapacitating; unable to perform usual activities; requires absenteeism or bed rest) 4 = Life-threatening | https://en.wikipedia.org/wiki/Reactogenicity |
The reactor software design pattern is an event handling strategy that can respond to many potential service requests concurrently . The pattern's key component is an event loop , running in a single thread or process , which demultiplexes incoming requests and dispatches them to the correct request handler. [ 1 ]
By relying on event-based mechanisms rather than blocking I/O or multi-threading, a reactor can handle many concurrent I/O bound requests with minimal delay. [ 2 ] A reactor also allows for easily modifying or expanding specific request handler routines, though the pattern does have some drawbacks and limitations. [ 1 ]
With its balance of simplicity and scalability , the reactor has become a central architectural element in several server applications and software frameworks for networking . Derivations such as the multireactor and proactor also exist for special cases where even greater throughput, performance, or request complexity are necessary. [ 1 ] [ 2 ] [ 3 ] [ 4 ]
Practical considerations for the client–server model in large networks, such as the C10k problem for web servers , were the original motivation for the reactor pattern. [ 5 ]
A naive approach to handle service requests from many potential endpoints, such as network sockets or file descriptors , is to listen for new requests from within an event loop, then immediately read the earliest request. Once the entire request has been read, it can be processed and forwarded on by directly calling the appropriate handler. An entirely "iterative" server like this, which handles one request from start-to-finish per iteration of the event loop, is logically valid. However, it will fall behind once it receives multiple requests in quick succession. The iterative approach cannot scale because reading the request blocks the server's only thread until the full request is received, and I/O operations are typically much slower than other computations. [ 2 ]
One strategy to overcome this limitation is multi-threading: by immediately splitting off each new request into its own worker thread, the first request will no longer block the event loop, which can immediately iterate and handle another request. This "thread per connection" design scales better than a purely iterative one, but it still contains multiple inefficiencies and will struggle past a point. From a standpoint of underlying system resources , each new thread or process imposes overhead costs in memory and processing time (due to context switching ). The fundamental inefficiency of each thread waiting for I/O to finish isn't resolved either. [ 1 ] [ 2 ]
From a design standpoint, both approaches tightly couple the general demultiplexer with specific request handlers too, making the server code brittle and tedious to modify. These considerations suggest a few major design decisions:
Combining these insights leads to the reactor pattern, which balances the advantages of single-threading with high throughput and scalability. [ 1 ] [ 2 ]
The reactor pattern can be a good starting point for any concurrent, event-handling problem. The pattern is not restricted to network sockets either; hardware I/O, file system or database access, inter-process communication , and even abstract message passing systems are all possible use-cases. [ citation needed ]
However, the reactor pattern does have limitations, a major one being the use of callbacks, which make program analysis and debugging more difficult, a problem common to designs with inverted control . [ 1 ] The simpler thread-per-connection and fully iterative approaches avoid this and can be valid solutions if scalability or high-throughput are not required. [ a ] [ citation needed ]
Single-threading can also become a drawback in use-cases that require maximum throughput, or when requests involve significant processing. Different multi-threaded designs can overcome these limitations, and in fact, some still use the reactor pattern as a sub-component for handling events and I/O. [ 1 ]
The reactor pattern (or a variant of it) has found a place in many web servers, application servers , and networking frameworks:
A reactive application consists of several moving parts and will rely on some support mechanisms: [ 1 ]
The standard reactor pattern is sufficient for many applications, but for particularly demanding ones, tweaks can provide even more power at the price of extra complexity.
One basic modification is to invoke event handlers in their own threads for more concurrency. Running the handlers in a thread pool , rather than spinning up new threads as needed, will further simplify the multi-threading and minimize overhead. This makes the thread pool a natural complement to the reactor pattern in many use-cases. [ 2 ]
Another way to maximize throughput is to partly reintroduce the approach of the "thread per connection" server, with replicated dispatchers / event loops running concurrently. However, rather than the number of connections, one configures the dispatcher count to match the available CPU cores of the underlying hardware.
Known as a multireactor, this variant ensures a dedicated server is fully using the hardware's processing power. Because the distinct threads are long-running event loops, the overhead of creating and destroying threads is limited to server startup and shutdown. With requests distributed across independent dispatchers, a multireactor also provides better availability and robustness; should an error occur and a single dispatcher fail, it will only interrupt requests allocated to that event loop. [ 3 ] [ 4 ]
For particularly complex services, where synchronous and asynchronous demands must be combined, one other alternative is the proactor pattern. This pattern is more intricate than a reactor, with its own engineering details, but it still makes use of a reactor subcomponent to solve the problem of blocking IO. [ 3 ]
Related patterns:
Specific applications:
Sample implementations: | https://en.wikipedia.org/wiki/Reactor_pattern |
A reactor pressure vessel (RPV) in a nuclear power plant is the pressure vessel containing the nuclear reactor coolant , core shroud , and the reactor core .
Russian Soviet era RBMK reactors have each fuel assembly enclosed in an individual 8 cm diameter pipe rather than having a pressure vessel. Whilst most power reactors do have a pressure vessel, they are generally classified by the type of coolant rather than by the configuration of the vessel used to contain the coolant. The classifications are:
Of the main classes of reactor with a pressure vessel, the pressurized water reactor is unique in that the pressure vessel suffers significant neutron irradiation (called fluence ) during operation, and may become brittle over time as a result. In particular, the larger pressure vessel of the boiling water reactor is better shielded from the neutron flux, so although more expensive to manufacture in the first place because of this extra size, it has an advantage in not needing annealing to extend its life.
Annealing of pressurized water reactor vessels to extend their working life is a complex and high-value technology being actively developed by both nuclear service providers ( AREVA ) and operators of pressurized water reactors.
All pressurized water reactor pressure vessels share some features regardless of the particular design.
The reactor vessel body is the largest component and is designed to contain the fuel assembly, coolant, and fittings to support coolant flow and support structures. It is usually cylindrical in shape and is open at the top to allow the fuel to be loaded.
This structure is attached to the top of the reactor vessel body. It contains penetrations to allow the control rod driving mechanism to attach to the control rods in the fuel assembly. The coolant level measurement probe also enters the vessel through the reactor vessel head.
The fuel assembly of nuclear fuel usually consisting of uranium or uranium–plutonium mixes. It is usually a rectangular block of gridded fuel rods.
Protecting the inside of the vessel from fast neutrons escaping from the fuel assembly is a cylindrical shield wrapped around the fuel assembly. Reflectors send the neutrons back into the fuel assembly to better utilize the fuel. The main purpose though is to protect the vessel from fast neutron induced damage that can make the vessel brittle and reduce its useful life.
The RPV provides a critical role in safety of the PWR reactor and the materials used must be able to contain the reactor core at elevated temperatures and pressures. [ 1 ] [ 2 ] The materials used in the cylindrical shell of the vessels have evolved over time, but in general they consist of low-alloy ferritic steels clad with 3–10 mm of austenitic stainless steel . The stainless steel cladding is primarily used in locations that come into contact with coolant in order to minimize corrosion. [ 2 ] Through the mid-1960, SA-302, Grade B, a molybdenum-manganese plate steel, was used in the body of the vessel. [ 2 ] As changing designs required larger pressure vessels, the addition of nickel to this alloy by roughly 0.4-0.7 wt% was required to increase the yield strength. [ 2 ] Other common steel alloys include SA-533 Grade B Class 1 and SA-508 Class 2. Both materials have main alloying elements of nickel, manganese, molybdenum, and silicon, but the latter also includes 0.25-0.45 wt% chromium. [ 2 ] All alloys listed in the reference also have >0.04 wt% sulfur. [ 2 ] Low-alloyed NiMoMn ferritic steels are attractive for this purpose due to their high thermal conductivity and low thermal expansion, properties that make them resistant to thermal shock. [ 3 ] However, when considering the properties of these steels, one must take into account the response it will have to radiation damage. Due to harsh conditions, the RPV cylinder shell material is often the lifetime-limiting component for a nuclear reactor. [ 1 ] Understanding the effects radiation has on the microstructure in addition to the physical and mechanical properties will allow scientists to design alloys more resistant to radiation damage.
In 2018 Rosatom announced it had developed a thermal annealing technique for RPVs which ameliorates radiation damage and extends service life by between 15 and 30 years. This had been demonstrated on unit 1 of the Balakovo Nuclear Power Plant . [ 4 ]
Due to the nature of nuclear energy generation, the materials used in the RPV are constantly bombarded by high-energy particles. These particles can either be neutrons or fragments of an atom created by a fission event. [ 5 ] When one of these particles collides with an atom in the material, it will transfer some of its kinetic energy and knock the atom out of its position in the lattice. When this happens, this primary "knock-on" atom (PKA) that was displaced and the energetic particle may rebound and collide with other atoms in the lattice. This creates a chain reaction that can cause many atoms to be displaced from their original positions. [ 5 ] This atomic movement leads to the creation of many types of defects. [ 5 ] The accumulation of various defects can cause microstructural changes that can lead to a degradation in macroscopic properties. As previously mentioned, the chain reaction caused by a PKA often leaves a trail of vacancies and clusters of defects at the edge. This is called a displacement cascade . [ 6 ] The vacancy-rich core of a displacement cascade can also collapse into dislocation loops. Due to irradiation, materials tend to develop a higher concentration of defects than is present in typical steels, and the high temperatures of operation induce migration of the defects. This can cause things like recombination of interstitials and vacancies and clustering of like defects, which can either create or dissolve precipitates or voids. Examples of sinks, or thermodynamically favorable places for defects to migrate to, are grain boundaries, voids, incoherent precipitates, and dislocations.
Interactions between defects and alloying elements can cause a redistribution of atoms at sinks such as grain boundaries. The physical effect that can occur is that certain elements will be enriched or depleted in these areas, which often leads to embrittlement of grain boundaries or other detrimental property changes. This is because there is a flux of vacancies towards a sink and a flux of atoms away or toward the sink that may have varying diffusion coefficients. The uneven rates of diffusion cause a concentration of atoms that will not necessarily be in the correct alloy proportions. It has been reported that nickel, copper and silicon tend to be enriched at sinks, whereas chromium tends to be depleted. [ 6 ] [ 7 ] The resulting physical effect is changing chemical composition at grain boundaries or around voids/incoherent precipitates, which also serve as sinks.
Voids form due to a clustering of vacancies and generally form more readily at higher temperatures. Bubbles are simply voids filled with gas; they will occur if transmutation reactions are present, meaning a gas is formed due to the breakdown of an atom caused by neutron bombardment. [ 6 ] The biggest issue with voids and bubbles is dimensional instability. An example of where this would be very problematic is areas with tight dimensional tolerances, such as threads on a fastener.
The creation of defects such as voids or bubbles, precipitates, dislocation loops or lines, and defect clusters can strengthen a material because they block dislocation motion. The movement of dislocations is what leads to plastic deformation. While this hardens the material, the downside is that there is a loss of ductility. Losing ductility, or increasing brittleness, is dangerous in RPVs because it can lead to catastrophic failure without warning. When ductile materials fail, there is substantial deformation before failure, which can be monitored. Brittle materials will crack and explode when under pressure without much prior deformation, so there is not much engineers can do to detect when the material is about to fail. A particularly damaging element in steels that can lead to hardening or embrittlement is copper. Cu-rich precipitates are very small (1-3 nm) so they are effective at pinning dislocations. [ 6 ] [ 8 ] It has been recognized that copper is the dominant detrimental element in steels used for RPVs, especially if the impurity level is greater than 0.1 wt%. [ 8 ] Thus, the development of "clean" steels, or ones with very low impurity levels, is important in reducing radiation-induced hardening.
Creep occurs when a material is held under levels of stress below their yield stress that causes plastic deformation over time. This is especially prevalent when a material is exposed to high stresses at elevated temperatures, because diffusion and dislocation motion occur more rapidly. Irradiation can cause creep due to the interaction between stress and the development of the microstructure. [ 6 ] In this case, the increase in diffusivities due to high temperatures is not a very strong factor for causing creep. The dimensions of the material are likely to increase in the direction of the applied stress due to the creation of dislocation loops around defects that formed due to radiation damage. Furthermore, applied stress can allow interstitials to be more readily absorbed in dislocation, which assists in dislocation climb. When dislocations are able to climb, excess vacancies are left, which can also lead to swelling. [ 6 ]
Due to the embrittlement of grain boundaries or other defects that can serve as crack initiators, the addition of radiation attack at cracks can cause intergranular stress corrosion cracking. The main environmental stressor that forms due to radiation is hydrogen embrittlement at crack tips. Hydrogen ions are created when radiation splits water molecules, which is present because water is the coolant in PWRs, into OH − and H + . There are several suspected mechanisms that explain hydrogen embrittlement, three of which are the decohesion mechanism, the pressure theory, and the hydrogen attack method . In the decohesion mechanism, it is thought that the accumulation of hydrogen ions reduces the metal-to-metal bond strength, which makes it easier to cleave atoms apart. [ 6 ] The pressure theory is the idea that hydrogen can precipitate as a gas at internal defects and create bubbles within the material. The stress caused by the expanding bubble in addition to the applied stress is what lowers the overall stress required to fracture the material. [ 6 ] The hydrogen attack method is similar to the pressure theory, but in this case it is suspected that the hydrogen reacts with carbon in the steel to form methane, which then forms blisters and bubbles at the surface. In this case, the added stress by the bubbles is enhanced by the decarburization of the steel, which weakens the metal. [ 6 ] In addition to hydrogen embrittlement, radiation induced creep can cause the grain boundaries to slide against each other. This destabilizes the grain boundaries even further, making it easier for a crack to propagate along its length. [ 6 ]
Very aggressive environments require novel materials approaches in order to combat declines in mechanical properties over time. One method researchers have sought to use is introducing features to stabilize displaced atoms. This can be done by adding grain boundaries, oversized solutes, or small oxide dispersants to minimize defect movement. [ 5 ] [ 6 ] By doing this, there would be less radiation-induced segregation of elements, which would in turn lead to more ductile grain boundaries and less intergranular stress corrosion cracking. Blocking dislocation and defect movement would also help to increase the resistance to radiation assisted creep. Attempts have been reported of instituting yttrium oxides to block dislocation motion, but it was found that technological implementation posed a greater challenge than expected. [ 5 ] Further research is required to continue improving the radiation damage resistance of structural materials used in nuclear power plants.
Because of the extreme requirements needed to build large state-of-the-art reactor pressure vessels and the limited market, as of January 2020 [update] there are only a handful of manufacturers in the world including: [ 9 ] | https://en.wikipedia.org/wiki/Reactor_pressure_vessel |
Read's conjecture is a conjecture, first made by Ronald Read , about the unimodality of the coefficients of chromatic polynomials in the context of graph theory . [ 1 ] [ 2 ] In 1974, S. G. Hoggar tightened this to the conjecture that the coefficients must be strongly log-concave . Hoggar's version of the conjecture is called the Read–Hoggar conjecture . [ 3 ] [ 4 ]
The Read–Hoggar conjecture had been unresolved for more than 40 years before June Huh proved it in 2009, during his PhD studies, using methods from algebraic geometry . [ 1 ] [ 5 ] [ 6 ] [ 7 ]
This graph theory -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Read's_conjecture |
In DNA sequencing , a read is an inferred sequence of base pairs (or base pair probabilities) corresponding to all or part of a single DNA fragment. A typical sequencing experiment involves fragmentation of the genome into millions of molecules, which are size-selected and ligated to adapters . The set of fragments is referred to as a sequencing library, which is sequenced to produce a set of reads. [ 1 ]
Sequencing technologies vary in the length of reads produced. Reads of length 20-40 base pairs (bp) are referred to as ultra-short. [ 2 ] Typical sequencers produce read lengths in the range of 100-500 bp. [ 3 ] However, Pacific Biosciences platforms produce read lengths of approximately 1500 bp. [ 4 ] Read length is a factor which can affect the results of biological studies. [ 5 ] For example, longer read lengths improve the resolution of de novo genome assembly and detection of structural variants. It is estimated that read lengths greater than 100 kilobases (kb) will be required for routine de novo human genome assembly. [ 6 ] Bioinformatic pipelines to analyze sequencing data usually take into account read lengths. [ 7 ]
A genome is the complete genetic information of an organism or a cell. Single or double stranded nucleic acids store this information in a linear or in a circular sequence. To precisely determine this sequence, over time more efficient technologies with increased accuracy, throughput and sequencing speed have been developed. Sanger and Maxam-Gilbert sequencing technologies were classified as the First Generation Sequencing Technology who initiated the field of DNA sequencing with their publication in 1977. [ 8 ] First Generation Sequencing typically has read lengths of 400 to 900 base pairs. [ citation needed ]
In 2005 Roche’s 454 technology introduced new sequencing technology that was capable of high throughput at low cost. [ 9 ] This and similar technologies came to be known as Second Generation Sequencing or Next Generation Sequencing (NGS) . One of the hallmarks of NSG is short sequence reads. NGS methods may sequence millions to billions of reads in a single run, and the time it takes to create GigaBase-sized reads is only a few days or hours, making it superior to first-generation sequencing techniques like Sanger sequencing. All NSG techniques produce short reads, i.e. 80–200 bases, as opposed to longer length reads produced by Sanger sequencing. [ 10 ]
Beginning in the 2010s, revolutionary new technologies ushered in the Third-Generation Sequencing era (TGS) . TGS is a term used to describe methods that are capable of sequencing single DNA molecules without amplification. While Sanger and SRS techniques can only produce read lengths of one kilobase pair, third-generation sequencing technologies can produce read lengths of 5 to 30 kilobase pairs. The longest read length ever generated by a third-generation sequencing technology is 2 million base pairs. [ 11 ]
Historically, only one individual per species was addressed due to time and expense constraints, and its sequence served as the species' "reference" genome .
These reference genomes can be used to guide resequencing efforts in the same species by serving as a read mapping template. Read mapping is the process to align NGS reads on a reference genome. [ 12 ] Any NGS application, such as genome variation calling, transcriptome analysis, transcription factor binding site calling, epigenetic mark calling, metagenomics, and so on, requires read mapping. The performance of these applications is influenced by accurate alignment. Furthermore, because the number of reads is so large, the mapping process must be efficient. There are different methods used to align reads on reference genome depending on how many mismatches and indels are being allowed. Roughly speaking, the methods can be divided into two categories: the seed-and-extension approach and the filtering approach. Many short read aligners use the seed-and-extend strategy, such as BWA-SW, Bowtie 2, BatAlign, LAST, Cushaw2, BWA-MEM, etc. A filter-based approach is used by a number of methods like SeqAlto, GEM, MASAI etc. [ 13 ]
In genomics, reassembling genomes by DNA sequencing is a significant challenge. The retrieved reads span the entire genome uniformly due to random sampling. Reads are stitched together computationally to reconstruct the genome. This process is known as de novo genome assembly .
I Sanger sequencing has larger read length compared to NGS. Two assemblers were developed for assembling Sanger sequencing reads - the OLC assembler Celera and the de Bruijn graph assembler Euler. These two methods were used to put together our human reference genome. However, since Sanger sequencing is low throughput and expensive, only a few
genomes are assembled with Sanger sequencing.
Second-generation sequencing reads are short, and these sequencing techniques can efficiently and cost-effectively sequence hundreds of millions of reads.
For rebuilding genomes from short sequences, some custom genome assemblers have been built. Their success spawned several de novo genome assembly projects. Although this method is cost-effective, the reads are short and the repeat sections are long, resulting in fragmented genomes.
We now have very long reads (of 10,000 bp) thanks to the arrival of third-generation sequencing. Long reads are capable of resolving the ordering of repeat regions, although they have a high error rate (15–18%). To correct errors in third-generation sequencing reads, a number of computational methods have been devised.
Assembling with short reads and assembling with long reads have different advantages and disadvantages owing to error rates and ease of assembly. Sometimes a hybrid method is preferred, and short reads and long reads are combined to get better result. There are two approaches, the first one is using mate-pair reads and long reads to improve the assembly from the short reads. Second approach is using short reads to correct the errors in long reads.
Second-generation sequencing generates short reads (of length < 300bp) and these are highly accurate (sequencing error rate equals ~1%). Short read sequencing technologies have made sequencing much easier, a lot faster and much cheaper than Sanger sequencing. The August 2019 report from the National Human Genome Research Institute put the cost of sequencing a complete human genome at $942.00 United States dollars (USD). [ 14 ] [ 15 ]
The inability to sequence lengthy sections of DNA is a drawback shared by all second-generation sequencing technology.
To use NGS to sequence a big genome like human DNA, the DNA must be fragmented and amplified in clones ranging from 75 to 400 base pairs, that is why NGS is also known as "shortread sequencing" (SRS). After sequencing short reads, it then becomes a computational problem and many computer programs and techniques have been developed to assemble the random clones into a contiguous sequence. [ 16 ]
A necessary step in SRS is polymerase chain reaction which causes preferential amplification of repetitive DNA. SRS also fails to generate sufficient overlap sequence from the DNA fragments. This constitutes a major challenge for de novo sequencing of a highly complex and repetitive genome like the human genome. [ 17 ] Another challenge with SRS is the detection of large sequence changes, which is a major roadblock to studying structural variations. [ 18 ]
The third-generation sequencing sequences long reads and is often referred to as long read sequencing (LRS). LRS technologies are capable of sequencing single DNA molecules without amplification. The availability of long reads constitutes a great advantage, because it is often difficult to generate long continuous consensus sequence using NGS because of the difficulty of detecting overlaps between NGS short reads, thus impacting the overall quality of assembly. LRS has been shown to considerably improve the quality of genome assemblies in several studies. [ 19 ] [ 20 ] Another advantage of LRS over NGS is that it provides the simultaneous capability of characterizing a variety of epigenetic marks along with DNA sequencing. [ 21 ] [ 22 ]
Major challenge of LRS is accuracy and cost. Though with LRS is improving fast in those areas too. | https://en.wikipedia.org/wiki/Read_(biology) |
Reading is an action performed by computers , to acquire data from a source and place it into their volatile memory for processing . Computers may read information from a variety of sources, such as magnetic storage , the Internet , or audio and video input ports . Reading is one of the core functions of a Turing machine .
A read cycle is the act of reading one unit of information (e.g. a byte). A read channel is an electrical circuit that transforms the physical magnetic flux changes into abstract bits. A read error occurs when the physical part of the process fails for some reason, such as dust or dirt entering the drive.
For example, a computer may read information off a floppy disk and store it temporarily in random-access memory before it is written to the hard drive to be processed at a future date.
Complementary metal–oxide–semiconductor (CMOS) is a non-volatile medium . [ 1 ] It is used in microprocessors , microcontrollers , static RAM , and other digital logic circuits. Memory is read through the use of a combination of p-type and n-type metal–oxide–semiconductor field-effect transistors (MOSFETs). In CMOS logic, a collection of n-type MOSFETs are arranged in a pull-down network between the output node and the lower-voltage power supply rail , named V ss , which often has ground potential. By asserting or de-asserting the inputs to the CMOS circuit, individual transistors along the pull-up and pull-down networks become conductive and resistive to electric current, and results in the desired path connecting from the output node to one of the voltage rails.
Flash memory stores information in an array of memory cells made from floating-gate transistors . Flash memory utilizes either NOR logic or NAND logic.
In NOR gate flash, each cell resembles a standard MOSFET , except the transistor has two gates instead of one. On top is the control gate (CG), as in other MOS transistors, but below this, there is a floating gate (FG) insulated all around by an oxide layer. The FG is interposed between the CG and the MOSFET channel, and because the FG is electrically isolated by its insulating layer, any electrons placed on it are trapped there and, under normal conditions, will not discharge for many years. When current flow through the MOSFET channel binary code is generated, reproducing the stored data .
NAND gate flash utilizes tunnel injection for writing and tunnel release for erasing. NAND flash memory forms the core of the removable USB storage devices known as USB flash drives , as well as most memory card formats available today.
The magnetic medium is found in magnetic tape, hard disk drives, floppy disks, and so on. This medium uses different patterns of magnetization in a magnetizable material to store data and is a form of non-volatile memory . Magnetic storage media can be classified as either sequential access memory or random-access memory .
Magnetic-core memory uses toroids (rings) of a hard magnetic material (usually a semi-hard ferrite) as transformer cores, where each wire threaded through the core serves as a transformer winding. Two or more wires pass through each core. Magnetic hysteresis allows each of the cores to store a state.
The mechanical medium utilizes one of the oldest methods of computing and has largely become obsolete. The earliest known method of memory storage and subsequent computerized reading is the Antikythera mechanism (c. 100–150 BCE ) which utilizes over thirty gears that spin a dial indicator. Following the Antikythera mechanism, Hero of Alexandria (c. 10–70 CE ) designed an entirely mechanical play almost ten minutes in length, powered by a binary-like system of ropes, knots, and simple machines operated by a rotating cylindrical cogwheel.
Punched cards were a common storage medium for computers from 1900 to 1950. The information was read through a method of identifying the holes in the card.
Optical discs refer to the non-volatile flat, circular, usually polycarbonate discs. Data is stored in pits or bumps arranged sequentially on the continuous, spiral track extending from the innermost track to the outermost track, covering the entire disc surface. Data is read by a means of a laser; when the laser enters a pit, the focus of the laser is changed and interpenetrated by the reader's software.
Random-access memory (RAM) is a form of computer data storage. A random-access device allows stored data to be accessed directly in any random order. In contrast, other data storage media such as hard disks, CDs, DVDs and magnetic tape, as well as early primary memory types such as drum memory, read and write data only in a predetermined order, consecutively, because of mechanical design limitations. Therefore, the time to access a given data location varies significantly depending on its physical location. Today, random-access memory takes the form of integrated circuits. Strictly speaking, modern types of DRAM are not random access, as data is read in bursts, although the name DRAM / RAM has stuck. However, many types of SRAM, ROM, OTP, and NOR flash are still random access even in a strict sense. RAM is normally associated with volatile types of memory (such as DRAM memory modules), where its stored information is lost if the power is removed. Many other types of non-volatile memory are RAM as well, including most types of ROM and a type of flash memory called NOR-Flash. The first RAM modules to come into the market were created in 1951 and were sold until the late 1960s and early 1970s. | https://en.wikipedia.org/wiki/Reading_(computer) |
In molecular biology , a reading frame is a specific choice out of the possible ways to read the sequence of nucleotides in a nucleic acid ( DNA or RNA ) molecule as a sequence of triplets. Where these triplets equate to amino acids or stop signals during translation , they are called codons .
A single strand of a nucleic acid molecule has a phosphoryl end, called the 5′-end , and a hydroxyl or 3′-end . These define the 5′→3′ direction . There are three reading frames that can be read in this 5′→3′ direction, each beginning from a different nucleotide in a triplet. In a double stranded nucleic acid, an additional three reading frames may be read from the other, complementary strand in the 5′→3′ direction along this strand. As the two strands of a double-stranded nucleic acid molecule are antiparallel, the 5′→3′ direction on the second strand corresponds to the 3′→5′ direction along the first strand. [ 1 ] [ 2 ]
In general, at the most, one reading frame in a given section of a nucleic acid, is biologically relevant ( open reading frame ). Some viral transcripts can be translated using multiple, overlapping reading frames. There is one known example of overlapping reading frames in mammalian mitochondrial DNA : coding portions of genes for 2 subunits of ATPase overlap.
DNA encodes protein sequence by a series of three-nucleotide codons . Any given sequence of DNA can therefore be read in six different ways: Three reading frames in one direction (starting at different nucleotides) and three in the opposite direction. During transcription , the RNA polymerase read the template DNA strand in the 3′→5′ direction, but the mRNA is formed in the 5′ to 3′ direction. [ 3 ] The mRNA is single-stranded and therefore only contains three possible reading frames, of which only one is translated . The codons of the mRNA reading frame are translated in the 5′→3′ direction into amino acids by a ribosome to produce a polypeptide chain .
An open reading frame (ORF) is a reading frame that has the potential to be transcribed into RNA and translated into protein. It requires a continuous sequence of DNA which may include a start codon , through a subsequent region which has a length that is a multiple of 3 nucleotides, to a stop codon in the same reading frame. [ 4 ]
When a putative amino acid sequence resulting from the translation of an ORF remained unknown in mitochondrial and chloroplast genomes, the corresponding open reading frame was called an unidentified reading frame (URF). For example, the MT-ATP8 gene was first described as URF A6L when the complete human mitochondrial genome was sequenced. [ 5 ]
The usage of multiple reading frames leads to the possibility of overlapping genes ; there may be many of these in viral, prokaryote, and mitochondrial genomes . [ 6 ] Some viruses, e.g. hepatitis B virus and BYDV , use several overlapping genes in different reading frames.
In rare cases, a ribosome may shift from one frame to another during translation of an mRNA ( translational frameshift ). This causes the first part of the mRNA to be translated in one reading frame, and the latter part to be translated in a different reading frame. This is distinct from a frameshift mutation , as the nucleotide sequence (DNA or RNA) is not altered—only the frame in which it is read. | https://en.wikipedia.org/wiki/Reading_frame |
Ready-mix concrete ( RMC ) is concrete that is manufactured in a batch plant , according to each specific job requirement, then delivered to the job site "ready to use". [ 1 ]
There are two types with the first being the barrel truck or in–transit mixers . This type of truck delivers concrete in a plastic state to the site. [ 2 ] The second is the volumetric concrete mixer . This delivers the ready mix in a dry state and then mixes the concrete on site. However, other sources divide the material into three types: Transit Mix, Central Mix or Shrink Mix concrete. [ 3 ] [ 4 ]
Ready-mix concrete refers to concrete that is specifically manufactured for customers' construction projects, and supplied to the customer on site as a single product. It is a mixture of Portland or other cements, water and aggregates: sand, gravel, or crushed stone. [ 5 ] All aggregates should be of a washed type material with limited amounts of fines or dirt and clay. An admixture is often added to improve workability of the concrete and/or increase setting time of concrete (using retarders) to factor in the time required for the transit mixer to reach the site. The global market size is disputed depending on the source. It was estimated at 650 billion dollars in 2019. [ 6 ] However it was estimated at just under 500 billion dollars in 2018. [ 7 ]
There is some dispute as to when the first ready-mix delivery was made and when the first factory was built. Some sources suggest as early as 1913 in Baltimore . By 1929 there were over 100 plants operating in the United States . [ 8 ] The industry did not expand significantly until the 1960s, and has continued to grow since then.
Batch plants combine a precise amount of gravel, sand, water and cement by weight (as per a mix design formulation for the grade of concrete recommended by the structural engineer or architect), allowing specialty concrete mixtures to be developed and implemented on construction sites.
Ready-mix concrete is often used instead of other materials due to the cost and wide range of uses in building, particularly in large projects like high-rise buildings and bridges. [ 9 ] It has a long life span when compared to other products of a similar use, like roadways. It has an average life span of 30 years under high traffic areas compared to the 10 to 12 year life of asphalt concrete with the same traffic.
Ready-mixed concrete is used in construction projects where the construction site is not willing, or is unable, to mix concrete on site. Using ready-mixed concrete means product is delivered finished, on demand, in the specific quantity required, in the specific mix design required. For a small to medium project, the cost and time of hiring mixing equipment, labour, plus purchase and storage for the ingredients of concrete, added to environmental concerns (cement dust is an airborne health hazard) [ 10 ] may simply be not worthwhile when compared to the cost of ready-mixed concrete, where the customer pays for what they use, and allows others do the work up to that point. For a large project, outsourcing concrete production to ready-mixed concrete suppliers means delegating the quality control and testing, material logistics and supply chain issues and mix design, to specialists who are already established for those tasks, trading off against introducing another contracted external supplier who needs to make a profit, and losing the control and immediacy of on-site mixing.
Ready-mix concrete is bought and sold by volume – usually expressed in cubic meters (cubic yards in the US). Batching and mixing is done under controlled conditions. In the UK, ready-mixed concrete is specified either informally, by constituent weight or volume (1-2-4 or 1-3-6 being common mixes) or using the formal specification standards of the European standard EN 206+ A1 , which is supplemented in the UK by BS 8500. This allows the customer to specify what the concrete has to be able to withstand in terms of ground conditions, exposure, and strength, and allows the concrete manufacturer to design a mix that meets that requirement using the materials locally available to a batching plant. This is verified by laboratory testing, such as performing cube tests to verify compressive strength, [ 11 ] flexural tests, [ 12 ] and supplemented by field testing, such as slump tests done on site to verify plasticity of the mix.
The performance of a concrete mix can be altered by use of admixtures. Admixtures can be used to reduce water requirements, entrain air into a mixture, to improve surface durability, or even superplasticise concrete to make it self-levelling, as self-consolidating concrete , [ 13 ] the use of admixtures requires precision in dosing and mix design, which is more difficult without the dosing/measuring equipment and laboratory backing of a batching plant, which means they are not easily used outside of ready-mixed concrete.
Concrete has a limited lifespan between batching / mixing and curing. This means that ready-mixed concrete should be placed within 30 to 45 minutes of the batching process to hold slump and mix design specifications in the US, [ 14 ] though in the UK, environmental and material factors, plus in-transit mixing, allow for up two hours to elapse. [ 15 ] Modern admixtures and water reducers can modify that time span to some degree. [ 16 ]
Ready-mixed concrete can be transported and placed at site using a number of methods. The most common and simplest is the chute fitted to the back of transit mixer trucks (as in picture), which is suitable for placing concrete near locations where a truck can back in. Dumper trucks, crane hoppers, truck-mounted conveyors, and, in extremis , wheelbarrows, can be used to place concrete from trucks where access is not direct. Some concrete mixes are suitable for pumping with a concrete pump .
In 2011, there were 2,223 companies employing 72,925 workers that produced ready-mix concrete in the United States. [ 17 ]
As an alternative to centralized batch plant system is the volumetric mobile mixer. This is often referred to as on-site concrete, site mixed concrete or mobile mix concrete. This is a mobile miniaturized version of the large stationary batch plant. They are used to provide ready mix concrete utilizing a continuous batching process or metered concrete system. The volumetric mobile mixer is a truck that holds sand, rock, cement, water, fiber, and some add mixtures and color depending on how the batch plant is outfitted. These trucks mix or batch the ready mix on the job site. This type of truck can mix as much or as little amount of concrete as needed. The on-site mixing eliminates the travel time hydration that can cause the transit mixed concrete to become unusable. These trucks are as precise as the centralized batch plant system, since the trucks are scaled and tested using the same ASTM (American standard test method) [ 23 ] like all other ready mix manufactures. This is a hybrid approach between centralized batch plants and traditional on-site mixing . [ 24 ] Each type of system has advantages and disadvantages, depending on the location, size of the job, and mix design set forth by the engineer. | https://en.wikipedia.org/wiki/Ready-mix_concrete |
In chemistry , a reagent ( / r i ˈ eɪ dʒ ən t / ree- AY -jənt ) or analytical reagent is a substance or compound added to a system to cause a chemical reaction , or test if one occurs. [ 1 ] The terms reactant and reagent are often used interchangeably, but reactant specifies a substance consumed in the course of a chemical reaction. [ 1 ] Solvents , though involved in the reaction mechanism , are usually not called reactants. Similarly, catalysts are not consumed by the reaction, so they are not reactants. In biochemistry , especially in connection with enzyme -catalyzed reactions, the reactants are commonly called substrates .
In organic chemistry , the term "reagent" denotes a chemical ingredient (a compound or mixture, typically of inorganic or small organic molecules) introduced to cause the desired transformation of an organic substance. Examples include the Collins reagent , Fenton's reagent , and Grignard reagents .
In analytical chemistry , a reagent is a compound or mixture used to detect the presence or absence of another substance, e.g. by a color change, or to measure the concentration of a substance, e.g. by colorimetry . Examples include Fehling's reagent , Millon's reagent , and Tollens' reagent .
In commercial or laboratory preparations, reagent-grade designates chemical substances meeting standards of purity that ensure the scientific precision and reliability of chemical analysis , chemical reactions or physical testing. Purity standards for reagents are set by organizations such as ASTM International or the American Chemical Society . For instance, reagent-quality water must have very low levels of impurities such as sodium and chloride ions, silica , and bacteria, as well as a very high electrical resistivity . Laboratory products which are less pure, but still useful and economical for undemanding work, may be designated as technical , practical , or crude grade to distinguish them from reagent versions.
In the field of biology, the biotechnology revolution in the 1980s grew from the development of reagents that could be used to identify and manipulate the chemical matter in and on cells. [ 2 ] [ 3 ] These reagents included antibodies ( polyclonal and monoclonal ), oligomers , all sorts of model organisms and immortalised cell lines , reagents and methods for molecular cloning and DNA replication , and many others. [ 3 ] [ 4 ]
Tool compounds are an important class of reagent in biology. They are small molecules or biochemicals like siRNA or antibodies that are known to affect a given biomolecule [ ambiguous ] —for example a drug target —but are unlikely to be useful as drugs themselves, and are often starting points in the drug discovery process. [ 5 ] [ 6 ]
However, many natural substances are hits in almost any assay in which they are tested, and therefore not useful as tool compounds. Medicinal chemists class them instead as pan-assay interference compounds . One example is curcumin . [ 7 ] [ 8 ] [ 9 ] | https://en.wikipedia.org/wiki/Reagent |
Reagent Chemicals [ a ] is a publication of the American Chemical Society (ACS) Committee on Analytical Reagents, [ 1 ] detailing standards of purity for over four hundred of the most widely used chemicals in laboratory analyses and chemical research. Chemicals that meet this standard may be sold as "ACS Reagent Grade" materials.
Reagent standards relieve chemists of concern over chemical purity. "ACS Reagent Grade", is regarded as a gold standard measure and is in some cases required for use in chemical manufacturing, usually where stringent quality specifications and a purity of equal to or greater than 95% are required. [ 2 ] The American Chemical Society does not validate the purity of chemicals sold with this designation, but it relies on suppliers, acting in their self-interest, to meet these standards. In practice, the reliability of supplier stated purity is at times questionable. [ 3 ]
In addition to specifications for each chemical, Reagent Chemicals provides detailed methods for determining how to measure the properties and impurities listed in the specifications. Included are detailed explanations for numerous common analytical methods such as gas , liquid , ion , and headspace chromatography , atomic absorption spectroscopy , and optical emission spectroscopy .
Reagent Chemicals is primarily of interest to manufacturers and suppliers of chemicals to laboratories worldwide, and less so to research laboratories. Many standards organizations and federal agencies that set guidelines require the use of ACS-grade regent chemicals for many test procedures. This includes the United States Pharmacopeia (USP) and the U.S. Environmental Protection Agency (EPA). [ 4 ] An exception would be those working on trace analyses (measuring contaminants in the environment, for example), where small impurities in reagents would be significant.
After eleven paper editions over 68 years, Reagent Chemicals became an electronic resource in 2017. [ 5 ] The publication is updated several times a year to include new reagents and methods of analysis. Changes are published online six months prior to becoming an official standard, allowing manufacturers to adjust their labels or processes. [ 6 ]
While the full details of most reagents are behind a paywall , that for acetone is publicly available to showcase a typical entry.
The ACS Committee on Analytical Reagents is responsible for the Reagent Chemicals publication and standards included within. The committee includes members from chemical and pharmaceutical manufacturers, academia , and government organizations ( NIST , EPA , USGS ). [ 1 ] | https://en.wikipedia.org/wiki/Reagent_Chemicals |
Reagent testing is one of the processes used to identify substances contained within a pill, usually illicit substances.
With the increased prevalence of drugs being available in their pure forms, the terms "drug checking" or "pill testing" [ 1 ] may also be used, although these terms usually refer to testing with a wider variety of techniques covered by drug checking .
A test is done by taking a small scraping from a pill and placing it in the reagent testing liquid or dropping the reagent onto the scraping. [ 3 ] The liquid will change colour when reacting with different chemicals to indicate the presence of certain substances.
Testing with a reagent kit does not indicate the pill is safe. While the testing process does show some particular substances are present, it may not show a harmful substance that is also present and unaccounted for by the testing process. Some substances that cause strong colour changes can also mask the presence of other substances that cause weaker colour changes. Thin layer chromatography is used with reagent testing to separate substances before testing and prevent this "masking" effect. [ 4 ]
Ehrlich reagent can only detect drugs with an indole moiety, but this is useful because drugs from the NBOMe class do not have an indole and are often sold as LSD which does. The Ehrlich reagent has an additional benefit over other reagents in that it does not react with the paper on which LSD is often distributed.
Reagent tests are often limited to target specific chemicals, and when these substances are mis-sold it is usually by substitution of a different substance in the same chemical family, rendering the test unuseful for consumers. However, reagent tests for chemicals families also exist.
Lacing agents are often used to cut the weight of substances. Some of the most available and non-suspicious cutting agents are reducing sugars : The common dietary monosaccharides galactose , glucose and fructose are all reducing sugars. Sugar is the generic name for sucrose , a disaccharide composed of glucose and fructose.
As reagent testing has become more popular, vendors have begun to offer a greater range of tests. This increases the likelihood that a substance might have a unique profile of results, making the tests more useful.
Other reagents are discussed in scientific literature, but limited applications mean they may not be sold for consumer testing.
The National Institute of Justice provides information about "Color Test Reagents/Kits for Preliminary Identification
of Drugs of Abuse" in NIJ Standard–0604.01. [ 5 ]
Several products are in early phases of development that are intended to allow their users to covertly detect (without using droppers, etc.) date-rape drugs , for instance reusable straws with components that change color in the presence of GHB , Rohypnol , or ketamine – see Date rape drug § Detection .
Results will vary depending on sample adulteration, quantity, temperature, lighting, exposure to air, storage, as well as reagent quality and degradation. Colorimetric techniques have been developed. [ 6 ]
If more than one bottle are open at the same time and the cap are put on the wrong reagent bottle, this may cross-contaminate the reagents and ruin them.
According to a 2003 research published in Pharmacotherapy , neither the Marquis, Mecke, nor Simon's reagents should be used by the public for harm reduction purposes. These agents do not help identify pure MDMA tablets. The research team suggests using gas chromatography-mass spectrometry as the most sensitive and specific testing method for identifying MDMA and its contaminants [ 7 ] but this is out of reach for users in most countries and reagent tests remain popular, often distributed by harm-reduction organisations due to their low cost and high utility when multiple test reagents are used. [ 8 ] [ 9 ] [ 10 ]
Home pill testing equipment is illegal in the US state of Illinois where the (720 ILCS 600/) Drug Paraphernalia Control Act specifically outlaws "testing equipment intended to be used unlawfully in a private home for identifying or in analyzing the strength, effectiveness or purity of cannabis or controlled substances;" [ 11 ]
Rapid fentanyl test strips are decriminalized in Tennessee. Representative William Lamberth, R-Portland, introduced HB2177 in the Tennessee General Assembly on January 31, 2022, followed by the introduction of SB2427 by Senator Jack Johnson, R-Franklin, the following day. The bill was eventually passed by Governor Bill Lee on March 31. Fentanyl test strips were previously considered drug paraphernalia by Tennessee Code Annotated §39-17-402, which defines terms such as controlled substance and drug paraphernalia in Tennessee state law. Per TCA §39-17-425, possession of fentanyl test strips was previously a Class A misdemeanor, punishable by up to 11 months, 29 days in jail and fines of up to $2,500; distributing them was previously a Class E felony, punishable by prison sentences of one to six years and fines of up to $3,000. [ 12 ] [ 13 ] [ 14 ]
Bases (e.g. sodium bicarbonate ) or acids (e.g. citric acid ) are sometimes used as cutting agents. An individual base solution and acid solution can help determine if the substance contains an acid or base respectively, if an acid–base reaction will occur.
Common cutting agents: | https://en.wikipedia.org/wiki/Reagent_testing |
Real-Time Messaging Protocol ( RTMP ) is a communication protocol for streaming audio, video, and data over the Internet. Originally developed as a proprietary protocol by Macromedia for streaming between Flash Player and the Flash Communication Server, Adobe (which acquired Macromedia) has released an incomplete version of the specification of the protocol for public use.
The RTMP protocol has multiple variations:
While the primary motivation for RTMP was to be a protocol for playing Flash video , it is also used in some other applications, such as the Adobe LiveCycle Data Services ES .
RTMP is a TCP-based protocol which maintains persistent connections and allows low-latency communication. To deliver streams smoothly and transmit as much information as possible, it splits streams into fragments, and their size is negotiated dynamically between the client and server. Sometimes, it is kept unchanged; the default fragment sizes are 64 bytes for audio data, and 128 bytes for video data and most other data types. Fragments from different streams may then be interleaved, and multiplexed over a single connection. With longer data chunks, the protocol thus carries only a one-byte header per fragment, so incurring very little overhead . However, in practice, individual fragments are not typically interleaved. Instead, the interleaving and multiplexing is done at the packet level, with RTMP packets across several different active channels being interleaved in such a way as to ensure that each channel meets its bandwidth, latency, and other quality-of-service requirements. Packets interleaved in this fashion are treated as indivisible, and are not interleaved on the fragment level.
The RTMP defines several virtual channels on which packets may be sent and received, and which operate independently of each other. For example, there is a channel for handling RPC requests and responses, a channel for video stream data, a channel for audio stream data, a channel for out-of-band control messages (fragment size negotiation, etc.), and so on. During a typical RTMP session, several channels may be active simultaneously at any given time. When RTMP data is encoded, a packet header is generated. The packet header specifies, amongst other matters, the ID of the channel on which it is to be sent, a timestamp of when it was generated (if necessary), and the size of the packet's payload. This header is then followed by the actual payload content of the packet, which is fragmented according to the currently agreed-upon fragment size before it is sent over the connection. The packet header itself is never fragmented, and its size does not count towards the data in the packet's first fragment. In other words, only the actual packet payload (the media data) is subject to fragmentation.
At a higher level, the RTMP encapsulates MP3 or AAC audio and FLV1 video multimedia streams, and can make remote procedure calls (RPCs) using the Action Message Format . Any RPC services required are made asynchronously, using a single client/server request/response model, such that real-time communication is not required. [ clarification needed ] [ 3 ] [ 4 ]
RTMP sessions may be encrypted using either of two methods:
In RTMP Tunneled (RTMPT), RTMP data is encapsulated and exchanged via HTTP , and messages from the client (the media player, in this case) are addressed to port 80 (the default for HTTP) on the server.
While the messages in RTMPT are larger than the equivalent non-tunneled RTMP messages due to HTTP headers, RTMPT may facilitate the use of RTMP in scenarios where the use of non-tunneled RTMP would otherwise not be possible, such as when the client is behind a firewall that blocks non-HTTP and non-HTTPS outbound traffic.
The protocol works by sending commands through the POST URL, and AMF messages through the POST body. An example is
for a connection to be opened.
Adobe has released a specification for version 1.0 of the protocol, dated 21 December 2012. [ 5 ] The web landing page leading to that specification notes that "To benefit customers who want to protect their content, the open RTMP specification does not include Adobe's unique secure RTMP measures". [ 6 ]
A document accompanying the Adobe specification grants "non-exclusive, royalty-free, nontransferable, non-sublicensable, personal, worldwide" patent license to all implementations of the protocol, with two restrictions: one forbids use for intercepting streaming data ("any technology that intercepts streaming video, audio and/or data content for storage in any device or medium"), and another prohibits circumvention of "technological measures for the protection of audio, video and/or data content, including any of Adobe’s secure RTMP measures". [ 7 ]
Stefan Richter, author of some books on Flash , noted in 2008 that while Adobe is vague as to which patents apply to RTMP, U.S. patent 7,246,356 appears to be one of them. [ 3 ]
In 2011, Adobe did sue Wowza Media Systems claiming, among other things, infringement of their RTMP patents. [ 8 ] [ 9 ] [ 10 ] In 2015, Adobe and Wowza announced that the lawsuits have been settled and dismissed with prejudice. [ 11 ]
Packets are sent over a TCP connection, which is established first between client and server. They contain a header and a body which, in the case of connection and control commands, is encoded using the Action Message Format (AMF). The header is split into the Basic Header (shown as detached from the rest, in the diagram) and Chunk Message Header . The Basic Header is the only constant part of the packet and is usually composed of a single composite byte, where the two most significant bits are the Chunk Type ( fmt in the specification) and the rest form the Stream ID. Depending on the value of the former, some fields of the Message Header can be omitted, and their value derived from previous packets while depending on the value of the latter, the Basic Header can be extended with one or two extra bytes (as in the case of the diagramme that has three bytes in total (c)). If the value of the remaining six bits of the Basic Header (BH) (least significant) is 0 then the BH is two bytes and represents from Stream ID 64 to 319 (64+255); if the value is 1, then the BH is three bytes (with last two bytes encoded as 16bit Little Endian) and represents from Stream ID 64 to 65599 (64+65535); if the value is 2, then BH is one byte and is reserved for low-level protocol control messages and commands. The Chunk Message Header contains meta-data information such as the message size (measured in bytes), the Timestamp Delta and Message Type . This last value is a single byte and defines whether the packet is an audio, video, command or "low level" RTMP packet such as an RTMP Ping.
An example is shown below as captured when a flash client executes the following code:
this will generate the following Chunk:
The packet starts with a Basic Header of a single byte (0x03) where the two most significant bits (b 00 000011) define a chunk header type of 0 while the rest (b00 000011 ) define a Chunk Stream ID of 3. The four possible values of the header type and their significance are:
The last type (b11) is always used in the case of aggregate messages where, in the example above, the second message will start with an id of 0xC3 (b11000011) and would mean that all Message Header fields should be derived from the message with a stream Id of 3 (which would be the message right above it). The six least significant bits that form the Stream ID can take values between 3 and 63. Some values have special meaning, like 1 that stands for an extended ID format, in which case there will be two bytes following that. A value of two is for low level messages such as Ping and Set Client Bandwidth.
The next bytes of the RTMP Header (including the values in the example packet above) are decoded as follows:
The Message Type ID byte defines whether the packet contains audio/video data, a remote object or a command. Some possible values for are:
Following the header, 0x02 denotes a string of size 0x000C and values 0x63 0x72 ... 0x6D ("createStream" command). Following that we have a 0x00 (number) which is the transaction id of value 2.0. The last byte is 0x05 (null) which means there are no arguments.
Some of the message types shown above, such as Ping and Set Client/Server Bandwidth, are considered low level RTMP protocol messages which do not use the AMF encoding format. Command messages on the other hand, whether AMF0 (Message Type of 0x14) or AMF3 (0x11), use the format and have the general form shown below:
The transaction id is used for commands that can have a reply. The value can be either a string like in the example above or one or more objects, each composed of a set of key/value pairs where the keys are always encoded as strings while the values can be any AMF data type, including complex types like arrays.
Control messages are not AMF encoded. They start with a stream Id of 0x02 which implies a full (type 0) header and have a message type of 0x04. The header is followed by six bytes, which are interpreted as such:
The first two bytes of the message body define the Ping Type, which can apparently [ 12 ] take six possible values.
Pong is the name for a reply to a Ping, with the values used as seen above.
This relates to messages that have to do with the client up-stream and server down-stream bit-rate. The body is composed of four bytes showing the bandwidth value, with a possible extension of one byte which sets the Limit Type. This can have one of three possible values which can be: hard, soft or dynamic (either soft or hard).
The value received in the four bytes of the body. A default value of 128 bytes exists, and the message is sent only when a change is wanted.
After establishing a TCP connection, an RTMP connection is established first, performing a handshake through the exchange of three packets from each side (also referred to as Chunks in the official documentation). These are referred in the official spec as C0-2 for the client sent packets and S0-2 for the server side respectively and are not to be confused with RTMP packets that can be exchanged only after the handshake is complete. These packets have a structure of their own and C1 contains a field setting the "epoch" timestamp, but since this can be set to zero, as is done in third party implementations, the packet can be simplified. The client initialises the connection by sending the C0 packet with a constant value of 0x03 representing the current protocol version. It follows straight with C1 without waiting for S0 to be received first which contains 1536 bytes, with the first four representing the epoch timestamp, the second four all being 0, and the rest being random (and which can be set to 0 in third party implementations). C2 and S2 are an echo of S1 and C1 respectively, except with the second four bytes being the time the respective message was received (instead of 0). After C2 and S2 are received, the handshake is considered complete.
At this point, the client, and server can negotiate a connection by exchanging AMF encoded messages. These include key value pairs which relate to variables that are needed for a connection to be established. An example message from the client is:
The Flash Media Server and other implementations uses the concept of an "app" to conceptually define a container for audio/video and other content, implemented as a folder on the server root which contains the media files to be streamed. The first variable contains the name of this app as "sample" which is the name provided by the Wowza Server for their testing. The flashVer string is the same as returned by the Action-script getversion() function. The audioCodec and videoCodec are encoded as doubles and their meaning can be found in the original spec. The same is true for the videoFunction variable, which in this case is the self-explanatory SUPPORT_VID_CLIENT_SEEK constant. Of special interest is the objectEncoding which will define whether the rest of the communication will make use of the extended AMF3 format or not. As version 3 is the current default, the flash client has to be told explicitly in Action-script code to use AMF0 if that is requested. The server then replies with a ServerBW, a ClientBW and a SetPacketSize message sequence, finally followed by an Invoke, with an example message.
Some values above are serialised into properties of a generic Action-script Object, which is then passed to the NetConnection event listener. The clientId will establish a number for the session to be started by the connection. Object encoding must match the value previously set.
To start a video stream, the client sends a "createStream" invocation followed by a ping message, followed by a "play" invocation with the file name as argument. The server will then reply with a series of "onStatus" commands followed by the video data as encapsulated within RTMP messages.
After a connection is established, media is sent by encapsulating the content of FLV tags into RTMP messages of type 8 and 9 for audio and video, respectively.
This refers to the HTTP tunneled version of the protocol. It communicates over port 80 and passes the AMF data inside HTTP POST request and responses. The sequence for connection is as follows:
The first request has an /fcs/ident2 path, and the correct reply is a 404 Not Found error. The client then sends an /open/1 request where the server must reply with a 200 ok appending a random number that will be used as the session identifier for the said communication. In this example, 1728724019 is returned in the response body.
From now on, the /idle/<session id>/<sequence #> is a polling request where the session id has been generated and returned from the server and the sequence is just a number that increments by one for every request. The appropriate response is a 200 OK, with an integer returned in the body signifying the interval time. AMF data is sent through /send/<session id>/<sequence #>
RTMP is implemented at these three stages:
The open-source RTMP client command-line tool rtmpdump is designed to play back or save to disk the full RTMP stream, including the RTMPE protocol Adobe uses for encryption. RTMPdump runs on Linux, Android, Solaris, Mac OS X , and most other Unix-derived operating systems, as well as Microsoft Windows. Originally supporting all versions of 32-bit Windows including Windows 98, from version 2.2 the software will run only on Windows XP and above (although earlier versions remain fully functional).
Packages of the rtmpdump suite of software are available in the major open-source repositories (Linux distributions). These include the front-end apps "rtmpdump", "rtmpsrv" and "rtmpsuck."
Development of RTMPdump was restarted in October 2009, outside the United States, at the MPlayer site. [ 13 ] The current version features greatly improved functionality, and has been rewritten to take advantage of the benefits of the C programming language . In particular, the main functionality was built into a library (librtmp) which can easily be used by other applications. The RTMPdump developers have also written support for librtmp for MPlayer , FFmpeg , XBMC , cURL , VLC and a number of other open source software projects. Use of librtmp provides these projects with full support of RTMP in all its variants without any additional development effort.
FLVstreamer is a fork of RTMPdump, without the code, which Adobe claims violates the DMCA in the USA. This was developed as a response to Adobe's attempt in 2008 to suppress RTMPdump. FLVstreamer is an RTMP client that will save a stream of audio or video content from any RTMP server to disk, if encryption (RTMPE) is not enabled on the stream.
Enhanced RTMP (E-RTMP) is an enhancement to the Real-Time Messaging Protocol (RTMP) and FLV specifications, modernizing streaming workflows while maintaining compatibility with existing RTMP infrastructure. [ 2 ] Developed as an open specification, E-RTMP was published by the Veovera Software Organization, with contributions from Adobe , Google , Twitch , and others.
Enhancements introduced in E-RTMP include:
E-RTMP enhances RTMP’s capabilities while ensuring seamless interoperability with existing RTMP implementations. | https://en.wikipedia.org/wiki/Real-Time_Messaging_Protocol |
Real-Time Object-Oriented Modeling ( ROOM ) is a domain-specific language .
ROOM was developed in the early 1990s for modeling real-time systems . [ 1 ] The initial focus was on telecommunications , even though ROOM can be applied to any event-driven real-time system.
ROOM was supported by ObjecTime Developer (commercial) and is now implemented by the official Eclipse project eTrice [ 2 ]
When UML2 was defined (version 2 of UML with real time extensions), many elements of ROOM were adopted.
ROOM is a modeling language for the definition of software systems. It allows the complete code generation for the whole system from the model. ROOM comes with a textual as well as with a graphical notation.
Typically the generated code is accompanied with manually written code, e.g. for graphical user interfaces ( GUI ).
The code is compiled and linked against a runtime library which provides base classes and basic services (e.g. messaging).
ROOM describes a software system along three dimensions: structure, behavior and inheritance. The following sections will explain these three aspects in more detail.
The structural view in ROOM is composed of actors or capsules . Actors can communicate with each other using ports . Those ports are connected by bindings . Actors do exchange messages asynchronously via ports and bindings. To each port a unique protocol is assigned. A protocol in ROOM defines a set of outgoing and a set of incoming messages. Ports can be connected with a binding if they belong to the same protocol and are conjugate to each other. That means that one port is sending the outgoing messages of the protocol and receiving the incoming ones. This port is called the regular port. Its peer port, the conjugated port, receives the outgoing messages and sends the incoming ones of the protocol. In other words, a port is the combination of a required and a provided interface in a role (since one and the same protocol can be used by several ports of an actor).
An actor can contain other actors (as a composition ). In ROOM these are called actor references or actor refs for short. This allows to create structural hierarchies of arbitrary depth.
The actor's ports can be part of its interface (visible from the exterior) or part of its structure (used by itself) or both. Ports that are part of the interface only are called relay ports . They are directly connected to a port of a sub actor (they are delegating to the sub actor). Ports that are part of the structure only are called internal end ports . Ports that belong to both, structure and interface, are called external end ports .
Each actor in ROOM has a behavior which is defined by means of a hierarchical finite-state machine , or just state machine for short. A state machine is a directed graph consisting of nodes called states and edges called transitions . State transitions are triggered by incoming messages from an internal or external end port. In this context the messages sometimes are also called events or signals . If a transition specifies a certain trigger then it is said to fire if the state machine is in the source state of the transition and a message of the type specified by the trigger arrives. Afterwards the state is changed to the target state of the transition.
During the state change certain pieces of code are executed. The programmer (or modeler) can attach them to the states and transitions. In ROOM this code is written in the so called detail level language , usually the target language of the code generation. A state can have entry code and exit code . During a state change first the exit code of the source state is executed. Then the action code of the firing transition is executed and finally the entry code of the target state. A typical part of those codes is the sending of messages through ports of the actor.
State machines in ROOM also have a graphical notation similar to the UML state charts . An example is shown in the diagram in this section.
A state machine can also have a hierarchy in the sense that states can have sub state machines. Similar to the structure this can be extended to arbitrary depth. For details of the semantics of hierarchical state machines we refer to the original book. [ 3 ]
An important concept in the context of state machines is the execution model of run-to-completion . That means that an actor is processing a message completely before it accepts the next message. Since the run-to-completion semantics is guaranteed by the execution environment, the programmer/modeler doesn't have to deal with classical thread synchronization. And this despite the fact that typical ROOM systems are highly concurrent because of the asynchronous communication. And maybe its worth to stress that the asynchronous nature of ROOM systems is not by accident but reflects the inherent asynchronicity of e.g. the machine being controlled by the software. Definitely this requires another mind set than the one that is needed for functional programming of synchronous systems.
But after a short while of getting accustomed it will be evident that asynchronously communicating state machines are perfectly suited for control software.
Like other object-oriented programming languages ROOM uses the concept of classes . Actors are classes which can be instantiated as objects several times in the system. Of course each instance of an actor class tracks its own state and can communicate with other instances of the same (and other) classes.
Similar to other modern programming languages ROOM allows inheritance of actor classes. It is a single inheritance as an actor class can be derived from another actor class (its base class ).
It inherits all features of the base class like ports and actor refs, but also the state machine.
The derived actor class can add further states and transitions to the inherited one.
A last powerful concept of ROOM is layering . This notion refers to the vertical layers of a software system consisting of services and their clients. ROOM introduces the notions of service access point (SAP) for the client side and service provision point (SPP) for the server side. From the point of view of an actor implementation the SAPs and SPPs work like ports. Like ports they are associated with a protocol. But other than ports they don't have to (and even cannot) be bound explicitly. Rather, an actor is bound to a concrete service by a layer connection and this binding of a service is propagated recursively to all sub actors of this actor.
This concept is very similar to dependency injection . | https://en.wikipedia.org/wiki/Real-Time_Object-Oriented_Modeling |
In mathematics , and, more specifically in numerical analysis and computer algebra , real-root isolation of a polynomial consist of producing disjoint intervals of the real line , which contain each one (and only one) real root of the polynomial, and, together, contain all the real roots of the polynomial.
Real-root isolation is useful because usual root-finding algorithms for computing the real roots of a polynomial may produce some real roots, but, cannot generally certify having found all real roots. In particular, if such an algorithm does not find any root, one does not know whether it is because there is no real root. Some algorithms compute all complex roots, but, as there are generally much fewer real roots than complex roots, most of their computation time is generally spent for computing non-real roots (in the average, a polynomial of degree n has n complex roots, and only log n real roots; see Geometrical properties of polynomial roots § Real roots ). Moreover, it may be difficult to distinguish the real roots from the non-real roots with small imaginary part (see the example of Wilkinson's polynomial in next section).
The first complete real-root isolation algorithm results from Sturm's theorem (1829). However, when real-root-isolation algorithms began to be implemented on computers it appeared that algorithms derived from Sturm's theorem are less efficient than those derived from Descartes' rule of signs (1637).
Since the beginning of 20th century there has been much research activity for improving the algorithms derived from Descartes' rule of signs, getting very efficient implementations, and determining their computational complexities . The best implementations can routinely isolate real roots of polynomials of degree more than 1,000. [ 1 ] [ 2 ]
For finding real roots of a polynomial, the common strategy is to divide the real line (or an interval of it where root are searched) into disjoint intervals until having at most one root in each interval. Such a procedure is called root isolation , and a resulting interval that contains exactly one root is an isolating interval for this root.
Wilkinson's polynomial shows that a very small modification of one coefficient of a polynomial may change dramatically not only the value of the roots, but also their nature (real or complex). Also, even with a good approximation, when one evaluates a polynomial at an approximate root, one may get a result that is far to be close to zero. For example, if a polynomial of degree 20 (the degree of Wilkinson's polynomial) has a root close to 10, the derivative of the polynomial at the root may be of the order of 10 20 ; {\displaystyle 10^{20};} this implies that an error of 10 − 10 {\displaystyle 10^{-10}} on the value of the root may produce a value of the polynomial at the approximate root that is of the order of 10 10 . {\displaystyle 10^{10}.} It follows that, except maybe for very low degrees, a root-isolation procedure cannot give reliable results without using exact arithmetic. Therefore, if one wants to isolate roots of a polynomial with floating-point coefficients, it is often better to convert them to rational numbers , and then take the primitive part of the resulting polynomial, for having a polynomial with integer coefficients.
For this reason, although the methods that are described below work theoretically with real numbers, they are generally used in practice with polynomials with integer coefficients, and intervals ending with rational numbers. Also, the polynomials are always supposed to be square free . There are two reasons for that. Firstly Yun's algorithm for computing the square-free factorization is less costly than twice the cost of the computation of the greatest common divisor of the polynomial and its derivative. As this may produce factors of lower degrees, it is generally advantageous to apply root-isolation algorithms only on polynomials without multiple roots, even when this is not required by the algorithm. The second reason for considering only square-free polynomials is that the fastest root-isolation algorithms do not work in the case of multiple roots.
For root isolation, one requires a procedure for counting the real roots of a polynomial in an interval without having to compute them, or, at least a procedure for deciding whether an interval contains zero, one or more roots. With such a decision procedure, one may work with a working list of intervals that may contain real roots. At the beginning, the list contains a single interval containing all roots of interest, generally the whole real line or its positive part. Then each interval of the list is divided into two smaller intervals. If one of the new intervals does not contain any root, it is removed from the list. If it contains one root, it is put in an output list of isolating intervals. Otherwise, it is kept in the working list for further divisions, and the process may continue until all roots are eventually isolated
The first complete root-isolation procedure results of Sturm's theorem (1829), which expresses the number of real roots in an interval in terms of the number of sign variations of the values of a sequence of polynomials, called Sturm's sequence , at the ends of the interval. Sturm's sequence is the sequence of remainders that occur in a variant of Euclidean algorithm applied to the polynomial and its derivatives. When implemented on computers, it appeared that root isolation with Sturm's theorem is less efficient than the other methods that are described below. [ 3 ] Consequently, Sturm's theorem is rarely used for effective computations, although it remains useful for theoretical purposes.
Descartes' rule of signs asserts that the difference between the number of sign variations in the sequence of the coefficients of a polynomial and the number of its positive real roots is a nonnegative even integer. It results that if this number of sign variations is zero, then the polynomial does not have any positive real roots, and, if this number is one, then the polynomial has a unique positive real root, which is a single root. Unfortunately the converse is not true, that is, a polynomial which has either no positive real root or has a single positive simple root may have a number of sign variations greater than 1.
This has been generalized by Budan's theorem (1807), into a similar result for the real roots in a half-open interval ( a , b ] : If f ( x ) is a polynomial, and v is the difference between of the numbers of sign variations of the sequences of the coefficients of f ( x + a ) and f ( x + b ) , then v minus the number of real roots in the interval, counted with their multiplicities, is a nonnegative even integer. This is a generalization of Descartes' rule of signs, because, for b sufficiently large, there is no sign variation in the coefficients of f ( x + b ) , and all real roots are smaller than b .
Budan's may provide a real-root-isolation algorithm for a square-free polynomial (a polynomial without multiple root): from the coefficients of polynomial, one may compute an upper bound M of the absolute values of the roots and a lower bound m on the absolute values of the differences of two roots (see Properties of polynomial roots ). Then, if one divides the interval [– M , M ] into intervals of length less than m , then every real root is contained in some interval, and no interval contains two roots. The isolating intervals are thus the intervals for which Budan's theorem asserts an odd number of roots.
However, this algorithm is very inefficient, as one cannot use a coarser partition of the interval [– M , M ] , because, if Budan's theorem gives a result larger than 1 for an interval of larger size, there is no way for insuring that it does not contain several roots.
Vincent's theorem (1834) [ 4 ] provides a method for real-root isolation, which is at the basis of the most efficient real-root-isolation algorithms. It concerns the positive real roots of a square-free polynomial (that is a polynomial without multiple roots). If a 1 , a 2 , … , {\displaystyle a_{1},a_{2},\ldots ,} is a sequence of positive real numbers, let
be the k th convergent of the continued fraction
Vincent's theorem — Let p 0 ( x ) {\displaystyle p_{0}(x)} be a square-free polynomial of degree n , and a 1 , a 2 , … , {\displaystyle a_{1},a_{2},\ldots ,} be a sequence of real numbers. For i = 1, 2,..., consider the polynomial
Then, there is an integer k such that either p k ( 0 ) = 0 , {\displaystyle p_{k}(0)=0,} or the sequence of the coefficients of p k {\displaystyle p_{k}} has at most one sign variation.
In the first case, the convergent c k is a positive root of p 0 . {\displaystyle p_{0}.} Otherwise, this number of sign variations (either 0 or 1) is the number of real roots of p 0 {\displaystyle p_{0}} in the interval defined by c k − 1 {\displaystyle c_{k-1}} and c k . {\displaystyle c_{k}.}
For proving his theorem, Vincent proved a result that is useful on its own: [ 4 ]
Vincent's auxiliary theorem — If p ( x ) is a square-free polynomial of degree n , and a , b , c , d are nonnegative real numbers such that | a c − b d | {\displaystyle \left|{\frac {a}{c}}-{\frac {b}{d}}\right|} is small enough (but not 0), then there is at most one sign variation in the coefficients of the polynomial
and this number of sign variations is the number of real roots of p ( x ) in the open interval defined by a c {\displaystyle {\frac {a}{c}}} and b d . {\displaystyle {\frac {b}{d}}.}
For working with real numbers, one may always choose c = d = 1 , but, as effective computations are done with rational numbers , it is generally convenient to suppose that a , b , c , d are integers.
The "small enough" condition has been quantified independently by Nikola Obreshkov , [ 5 ] and Alexander Ostrowski : [ 6 ]
Theorem (Obreschkoff–Ostrowski) — The conclusion of Vincent's auxiliary result holds if the polynomial p ( x ) has at most one root α + iβ such that
In particular the conclusion holds if
where sep( p ) is the minimal distance between two roots of p .
For polynomials with integer coefficients, the minimum distance sep( p ) may be lower bounded in terms of the degree of the polynomial and the maximal absolute value of its coefficients; see Properties of polynomial roots § Root separation . This allows the analysis of worst-case complexity of algorithms based on Vincent's theorems. However, Obreschkoff–Ostrowski theorem shows that the number of iterations of these algorithms depend on the distances between roots in the neighborhood of the working interval; therefore, the number of iterations may vary dramatically for different roots of the same polynomial.
James V. Uspensky gave a bound on the length of the continued fraction (the integer k in Vincent's theorem), for getting zero or one sign variations: [ 1 ] [ 7 ]
Theorem (Uspensky) — Let p ( x ) be a polynomial of degree n , and sep( p ) be the minimal distance between two roots of p . Let
Then the integer k , whose existence is asserted in Vincent's theorem, is not greater than the smallest integer h such that
where F h {\displaystyle F_{h}} is the h th Fibonacci number .
The use of continued fractions for real-root isolation has been introduced by Vincent, although he credited Joseph-Louis Lagrange for this idea, without providing a reference. [ 4 ] For making an algorithm of Vincent's theorem, one must provide a criterion for choosing the a i {\displaystyle a_{i}} that occur in his theorem. Vincent himself provided some choice (see below). Some other choices are possible, and the efficiency of the algorithm may depend dramatically on these choices. Below is presented an algorithm, in which these choices result from an auxiliary function that will be discussed later.
For running this algorithm one must work with a list of intervals represented by a specific data structure. The algorithm works by choosing an interval, removing it from the list, adding zero, one or two smaller intervals to the list, and possibly outputs an isolation interval.
For isolating the real roots of a polynomial p ( x ) of degree n , each interval is represented by a pair ( A ( x ) , M ( x ) ) , {\displaystyle (A(x),M(x)),} where A ( x ) is a polynomial of degree n and M ( x ) = p x + r q x + s {\displaystyle M(x)={\frac {px+r}{qx+s}}} is a Möbius transformation with integer coefficients. One has
and the interval represented by this data structure is the interval that has M ( ∞ ) = p q {\displaystyle M(\infty )={\frac {p}{q}}} and M ( 0 ) = r s {\displaystyle M(0)={\frac {r}{s}}} as end points. The Möbius transformation maps the roots of p in this interval to the roots of A in (0, +∞) .
The algorithm works with a list of intervals that, at the beginning, contains the two intervals ( A ( x ) = p ( x ) , M ( x ) = x ) {\displaystyle (A(x)=p(x),M(x)=x)} and ( A ( x ) = p ( − x ) , M ( x ) = − x ) , {\displaystyle (A(x)=p(-x),M(x)=-x),} corresponding to the partition of the reals into the positive and the negative ones (one may suppose that zero is not a root, as, if it were, it suffices to apply the algorithm to p ( x )/ x ). Then for each interval ( A ( x ), M ( x )) in the list, the algorithm remove it from the list; if the number of sign variations of the coefficients of A is zero, there is no root in the interval, and one passes to the next interval. If the number of sign variations is one, the interval defined by M ( 0 ) {\displaystyle M(0)} and M ( ∞ ) {\displaystyle M(\infty )} is an isolating interval. Otherwise, one chooses a positive real number b for dividing the interval (0, +∞) into (0, b) and (b, +∞) , and, for each subinterval, one composes M with a Möbius transformation that maps the interval onto (0, +∞) , for getting two new intervals to be added to the list. In pseudocode, this gives the following, where var( A ) denotes the number of sign variations of the coefficients of the polynomial A .
The different variants of the algorithm depend essentially on the choice of b . In Vincent's papers, and in Uspensky's book, one has always b = 1 , with the difference that Uspensky did not use Budan's theorem for avoiding further bisections of the interval associated to (0, b)
The drawback of always choosing b = 1 is that one has to do many successive changes of variable of the form x → 1 + x . These may be replaced by a single change of variable x → n + x , but, nevertheless, one has to do the intermediate changes of variables for applying Budan's theorem.
A way for improving the efficiency of the algorithm is to take for b a lower bound of the positive real roots, computed from the coefficients of the polynomial (see Properties of polynomial roots for such bounds). [ 8 ] [ 1 ]
The bisection method consists roughly of starting from an interval containing all real roots of a polynomial, and divides it recursively into two parts until getting eventually intervals that contain either zero or one root. The starting interval may be of the form (- B , B ) , where B is an upper bound on the absolute values of the roots, such as those that are given in Properties of polynomial roots § Bounds on (complex) polynomial roots . For technical reasons (simpler changes of variable, simpler complexity analysis , possibility of taking advantage of the binary analysis of computers), the algorithms are generally presented as starting with the interval [0, 1] . There is no loss of generality, as the changes of variables x = By and x = – By move respectively the positive and the negative roots in the interval [0, 1] . (The single changes variable x = (2 By – B ) may also be used.)
The method requires an algorithm for testing whether an interval has zero, one, or possibly several roots, and for warranting termination, this testing algorithm must exclude the possibility of getting infinitely many times the output "possibility of several roots". Sturm's theorem and Vincent's auxiliary theorem provide such convenient tests. As the use Descartes' rule of signs and Vincent's auxiliary theorem is much more computationally efficient than the use of Sturm's theorem, only the former is described in this section.
The bisection method based on Descartes' rules of signs and Vincent's auxiliary theorem has been introduced in 1976 by Akritas and Collins under the name of Modified Uspensky algorithm , [ 3 ] and has been referred to as the Uspensky algorithm , the Vincent–Akritas–Collins algorithm , or Descartes method , although Descartes, Vincent and Uspensky never described it.
The method works as follows. For searching the roots in some interval, one changes first the variable for mapping the interval onto [0, 1] giving a new polynomial q ( x ) . For searching the roots of q in [0, 1] , one maps the interval [0, 1] onto [0, +∞]) by the change of variable x → 1 x + 1 , {\displaystyle x\to {\frac {1}{x+1}},} giving a polynomial r ( x ) . Descartes' rule of signs applied to the polynomial r gives indications on the number of real roots of q in the interval [0, 1] , and thus on the number of roots of the initial polynomial in the interval that has been mapped on [0, 1] . If there is no sign variation in the sequence of the coefficients of r , then there is no real root in the considered intervals. If there is one sign variation, then one has an isolation interval. Otherwise, one splits the interval [0, 1] into [0, 1/2] and [1/2, 1] , one maps them onto [0, 1] by the changes of variable x = y /2 and x = ( y + 1)/2 . Vincent's auxiliary theorem insures the termination of this procedure.
Except for the initialization, all these changes of variable consists of the composition of at most two very simple changes of variable which are the scalings by two x → x /2 , the translation x → x + 1 , and the inversion x → 1/ x , the latter consisting simply of reverting the order of the coefficients of the polynomial. As most of the computing time is devoted to changes of variable, the method consisting of mapping every interval to [0, 1] is fundamental for insuring a good efficiency.
The following notation is used in the pseudocode that follows.
This procedure is essentially the one that has been described by Collins and Akritas. [ 3 ] The running time depends mainly on the number of intervals that have to be considered, and on the changes of variables. There are ways for improving the efficiency, which have been an active subject of research since the publication of the algorithm, and mainly since the beginning of the 21st century.
Various ways for improving Akritas–Collins bisection algorithm have been proposed. They include a method for avoiding storing a long list of polynomials without losing the simplicity of the changes of variables, [ 9 ] the use of approximate arithmetic ( floating point and interval arithmetic ) when it allows getting the right value for the number of sign variations, [ 9 ] the use of Newton's method when possible, [ 9 ] the use of fast polynomial arithmetic, [ 10 ] shortcuts for long chains of bisections in case of clusters of close roots, [ 10 ] bisections in unequal parts for limiting instability problems in polynomial evaluation. [ 10 ]
All these improvement lead to an algorithm for isolating all real roots of a polynomial with integer coefficients, which has the complexity (using soft O notation , Õ , for omitting logarithmic factors)
where n is the degree of the polynomial, k is the number of nonzero terms, t is the maximum of digits of the coefficients. [ 10 ]
The implementation of this algorithm appears to be more efficient than any other implemented method for computing the real roots of a polynomial, even in the case of polynomials having very close roots (the case which was previously the most difficult for the bisection method). [ 2 ] | https://en.wikipedia.org/wiki/Real-root_isolation |
Real-time Control System ( RCS ) is a reference model architecture , suitable for many software-intensive, real-time computing control problem domains. It defines the types of functions needed in a real-time intelligent control system , and how these functions relate to each other.
RCS is not a system design , nor is it a specification of how to implement specific systems . RCS prescribes a hierarchical control model based on a set of well-founded engineering principles to organize system complexity . All the control nodes at all levels share a generic node model. [ 1 ]
Also RCS provides a comprehensive methodology for designing, engineering, integrating, and testing control systems. Architects iteratively partition system tasks and information into finer, finite subsets that are controllable and efficient. RCS focuses on intelligent control that adapts to uncertain and unstructured operating environments. The key concerns are sensing, perception, knowledge, costs, learning, planning, and execution. [ 1 ]
A reference model architecture is a canonical form, not a system design specification. The RCS reference model architecture combines real-time motion planning and control with high level task planning, problem solving , world modeling , recursive state estimation, tactile and visual image processing , and acoustic signature analysis. In fact, the evolution of the RCS concept has been driven by an effort to include the best properties and capabilities of most, if not all, the intelligent control systems currently known in the literature, from subsumption to SOAR, from blackboards to object-oriented programming. [ 2 ]
RCS (real-time control system) is developed into an intelligent agent architecture designed to enable any level of intelligent behavior, up to and including human levels of performance. RCS was inspired by a theoretical model of the cerebellum, the portion of the brain responsible for fine motor coordination and control of conscious motions. It was originally designed for sensory-interactive goal-directed control of laboratory manipulators. Over three decades, it has evolved into a real-time control architecture for intelligent machine tools, factory automation systems, and intelligent autonomous vehicles. [ 3 ]
RCS applies to many problem domains including manufacturing examples and vehicle systems examples. Systems based on the RCS architecture have been designed and implemented to varying degrees for a wide variety of applications that include loading and unloading of parts and tools in machine tools, controlling machining workstations, performing robotic deburring and chamfering, and controlling space station telerobots, multiple autonomous undersea vehicles, unmanned land vehicles, coal mining automation systems, postal service mail handling systems, and submarine operational automation systems. [ 2 ]
RCS has evolved through a variety of versions over a number of years as understanding of the complexity and sophistication of intelligent behavior has increased. The first implementation was designed for sensory-interactive robotics by Barbera in the mid 1970s. [ 4 ]
In RCS-1, the emphasis was on combining commands with sensory feedback so as to compute the proper response to every combination of goals and states. The application was to control a robot arm with a structured light vision system in visual pursuit tasks. RCS-1 was heavily influenced by biological models such as the Marr-Albus model, [ 5 ] and the Cerebellar Model Arithmetic Computer (CMAC). [ 6 ] of the cerebellum . [ 2 ]
CMAC becomes a state machine when some of its outputs are fed directly back to the input, so RCS-1 was implemented as a set of state-machines arranged in a hierarchy of control levels. At each level, the input command effectively selects a behavior that is driven by feedback in stimulus-response fashion. CMAC thus became the reference model building block of RCS-1, as shown in the figure.
A hierarchy of these building blocks was used to implement a hierarchy of behaviors such as observed by Tinbergen [ 7 ] and others. RCS-1 is similar in many respects to Brooks ' subsumption architecture, [ 8 ] except that RCS selects behaviors before the fact through goals expressed in commands, rather than after the fact through subsumption. [ 2 ]
The next generation, RCS-2, was developed by Barbera, Fitzgerald, Kent, and others for manufacturing control in the NIST Automated Manufacturing Research Facility (AMRF) during the early 1980s. [ 9 ] [ 10 ] [ 11 ] The basic building block of RCS-2 is shown in the figure.
The H function remained a finite-state machine state-table executor. The new feature of RCS-2 was the inclusion of the G function consisting of a number of sensory processing algorithms including structured light and blob analysis algorithms. RCS-2 was used to define an eight level hierarchy consisting of Servo, Coordinate Transform, E-Move, Task, Workstation, Cell, Shop, and Facility levels of control.
Only the first six levels were actually built. Two of the AMRF workstations fully implemented five levels of RCS-2. The control system for the Army Field Material Handling Robot (FMR) [ 12 ] was also implemented in RCS-2, as was the Army TMAP semi-autonomous land vehicle project. [ 2 ]
RCS-3 was designed for the NBS/DARPA Multiple Autonomous Undersea Vehicle (MAUV) project [ 13 ] and was adapted for the NASA/NBS Standard Reference Model Telerobot Control System Architecture (NASREM) developed for the space station Flight Telerobotic Servicer [ 14 ] The basic building block of RCS-3 is shown in the figure.
The principal new features introduced in RCS-3 are the World Model and the operator interface. The inclusion of the World Model provides the basis for task planning and for model-based sensory processing. This led to refinement of the task decomposition (TD) modules so that each have a job assigner, and planner and executor for each of the subsystems assigned a job. This corresponds roughly to Saridis' [ 15 ] three level control hierarchy. [ 2 ]
RCS-4 is developed since the 1990s by the NIST Robot Systems Division. The basic building block is shown in the figure). The principal new feature in RCS-4 is the explicit representation of the Value Judgment (VJ) system. VJ modules provide to the RCS-4 control system the type of functions provided to the biological brain by the limbic system . The VJ modules contain processes that compute cost , benefit, and risk of planned actions, and that place value on objects , materials, territory, situations, events, and outcomes. Value state-variables define what goals are important and what objects or regions should be attended to, attacked, defended, assisted, or otherwise acted upon. Value judgments, or evaluation functions, are an essential part of any form of planning or learning. The application of value judgments to intelligent control systems has been addressed by George Pugh. [ 16 ] The structure and function of VJ modules are developed more completely developed in Albus (1991). [ 2 ] [ 17 ]
RCS-4 also uses the term behavior generation (BG) in place of the RCS-3 term task 5 decomposition (TD). The purpose of this change is to emphasize the degree of autonomous decision making . RCS-4 is designed to address highly autonomous applications in unstructured environments where high bandwidth communications are impossible, such as unmanned vehicles operating on the battlefield , deep undersea , or on distant planets . These applications require autonomous value judgments and sophisticated real-time perceptual capabilities. RCS-3 will continue to be used for less demanding applications, such as manufacturing , construction, or telerobotics for near-space, or shallow undersea operations, where environments are more structured and communication bandwidth to a human interface is less restricted. In these applications, value judgments are often represented implicitly in task planning processes, or in human operator input. [ 2 ]
In the figure, an example of the RCS methodology for designing a control system for autonomous onroad driving under everyday traffic conditions is summarized in six steps. [ 18 ]
The result of step 3 is that each organizational unit has for each input command a state-table of ordered production rules, each suitable for execution by an extended finite state automaton (FSA). The sequence of output subcommands required to accomplish the input command is generated by situations (i.e., branching conditions) that cause the FSA to transition from one output subcommand to the next. [ 18 ]
Based on the RCS Reference Model Architecture the NIST has developed a Real-time Control System Software Library. This is an archive of free C++, Java and Ada code, scripts, tools, makefiles, and documentation developed to aid programmers of software to be used in real-time control systems , especially those using the Reference Model Architecture for Intelligent Systems Design. [ 19 ] | https://en.wikipedia.org/wiki/Real-time_Control_System |
The Real-time Control System ( RCS ) is a software system developed by NIST based on the Real-time Control System Reference Model Architecture, that implements a generic Hierarchical control system . The RCS Software Library is an archive of free C++, Java and Ada code, scripts, tools, makefiles, and documentation developed to aid programmers of software to be used in real-time control systems (especially those using the Reference Model Architecture for Intelligent Systems Design). [ 1 ]
RCS has been used in automated manufacturing, robotics, and automated vehicle research at NIST. The software consists of a C++ library and GUI and configuration tools written in a variety of software languages. The Software Library is offering the following RCS tools: [ 1 ]
This article incorporates public domain material from the National Institute of Standards and Technology | https://en.wikipedia.org/wiki/Real-time_Control_System_Software |
Real-time Java is a catch-all term for a combination of technologies that enables programmers to write programs that meet the demands of real-time systems in the Java programming language .
Java's sophisticated memory management , native support for threading and concurrency, type safety , and relative simplicity have created a demand for its use in many domains. Its capabilities have been enhanced to support real-time computational needs:
The initial proposal [ 1 ] for an open standard for real-time Java was put forth by Kelvin Nilsen, then serving as a research faculty member at Iowa State University. A follow-on overview paper was published in the Communications of the ACM . [ 2 ] The overwhelmingly positive response to these early proposals resulted in a series of meetings hosted by the National Institute of Standards and Technology in an effort to establish an open standard for real-time Java. NIST was ultimately told that they were not the appropriate body to establish standards related to the Java language, as Java was trademarked, and the technologies were owned by Sun Microsystems. Therefore, NIST ended their efforts with publication of consensus requirements. [ 3 ] that could be considered by future standardization efforts to be hosted by Sun Microsystems.
When the Java Community was formed, the very first effort was the specification for real-time Java, JSR001. A number of implementations of the resulting Real-time specification for Java ( RTSJ ) have emerged, including a reference implementation from Timesys , IBM 's WebSphere Real Time, Sun Microsystems 's Java SE Real-Time Systems, [ 4 ] PTC Perc from PTC, Inc. , [ 5 ] or JamaicaVM from aicas.
The RTSJ addressed the critical issues by mandating a minimum specification for the threading model (and allowing other models to be plugged into the VM) and by providing for areas of memory that are not subject to garbage collection, along with threads that are not preemptable by the garbage collector. These areas are instead managed using region-based memory management . The latest specification, 2.0, supports direct device access and deterministic garbage collection as well.
The Real-Time Specification for Java (RTSJ) is a set of interfaces and behavioral refinements that enable real-time computer programming in the Java programming language . RTSJ 1.0 was developed as JSR 1 under the Java Community Process , which approved the new standard in November, 2001. RTSJ 2.0 is being developed under JSR 282. A draft version is available at a JCP page. [ 6 ] More information can be found from Aicas. [ 7 ] | https://en.wikipedia.org/wiki/Real-time_Java |
The Real-time Neutron Monitor Database (or NMDB) is a worldwide network of standardized neutron monitors, used to record variations of the primary cosmic rays . The measurements complement space-based cosmic ray measurements.
Unlike data from satellite experiments, neutron monitor data has never been available in high resolution from many stations in real-time. The data is often only available from the individual stations website, in varying formats, and not in real-time. To overcome this deficit, the European Commission is supporting the Real-time Neutron Monitor Database (NMDB) as an e-Infrastructures project in the Seventh Framework Programme in the Capacities section. Stations that do not have 1-minute resolution will be supported by the development of an affordable standard registration system that will submit the measurements to the database via the internet in real-time. This resolves the problem of different data formats and for the first time allows to use real-time cosmic ray measurements for space weather predictions ( Steigies , [ 1 ] Klein et al. [ 2 ] )
Besides creating a database and developing applications working with this data, a part of the project is dedicated to create a public outreach website to inform about cosmic rays and possible effects on humans, technological systems, and the environment ( Mavromichalaki et al. [ 3 ] ) | https://en.wikipedia.org/wiki/Real-time_Neutron_Monitor_Database |
Real-time communication ( RTC ) is a category of software protocols and communication hardware media that gives real-time guarantees, which is necessary to support real-time guarantees of real-time computing . [ 1 ] Real-time communication protocols are dependent not only on the validity and integrity of data transferred but also the timeliness of the transfer. Real-time communication systems are generally understood as one of two types: Hard Real-Time (HRT) and Soft Real-Time (SRT) . [ 2 ] The difference between a hard and soft real-time communication system is the consequences of incorrect operation. Safety-critical systems capable of causing catastrophic consequences upon a fault, such as aircraft fly-by-wire systems , are designated as hard real-time, whereas non-critical but ideally real-time systems, such as hotel reservation systems, are designated as soft real-time. [ 3 ] The designation of a real-time communication system as hard or soft has significant influence on its design.
Hard real-time communication systems are frequently electromechanically linked to a physical mechanism, often one that interfaces directly with people or property, which often contributes to or defines the potential danger of a fault. Due to their safety-critical nature, the communication protocols defined in a hard real-time system generally must be deterministic . [ 4 ] Hard real-time communication systems are particularly common in the transportation , industrial , and medical sectors. Common applications include control systems , automotive controllers , medical devices , and critical safety systems such as airbag firing computers .
Unlike hard real-time communication systems, soft real-time communication systems generally do not have the capacity to cause catastrophic harm upon a fault, which allows for non-deterministic, less rigorous network infrastructure . [ 6 ] This allows soft real-time communication systems to operate over consumer networks such as residential internet connections and cellular networks . A large amount of soft real-time systems are telecommunications products such as VoIP systems and certain video calling platforms such as Discord [ 7 ] and Google Meet . [ 8 ] Data transmitted over a soft real-time communication system is not stored in a centralized server, and peers are connected directly to one another rather than through a server, although intermediary connecting nodes between peers are allowed when a direct link cannot be established. [ 9 ] | https://en.wikipedia.org/wiki/Real-time_communication |
Timekeeping is relevant to many types of games , including video games , tabletop role-playing games , board games , and sports . The passage of time must be handled in a way that players find fair and easy to understand. In many games, this is done using real-time and/or turn-based timekeeping. In real-time games, time within the game passes continuously. However, in turn-based games, player turns represent a fixed duration within the game, regardless of how much time passes in the real world. Some games use combinations of real-time and turn-based timekeeping systems. Players debate the merits and flaws of these systems. There are also additional timekeeping methods, such as timelines and progress clocks.
In real-time games , time progresses continuously. This may occur at the same or different rates from the passage of time in the real world. For example, in Terraria , one day-night cycle of 24 hours in the game is equal to 24 minutes in the real world. [ 1 ]
In a multiplayer real-time game, players perform actions simultaneously as opposed to in sequential units or turns. In competitive games, players must consider that their opponents are working against them in real time and may act at any moment. This introduces additional challenges.
Many sports, such as soccer or basketball , are almost entirely simultaneous in nature, retaining a limited notion of turns in specific instances, such as the free kick in soccer and the free throw and shot clock in basketball. In the card games Nerts [ 2 ] and Ligretto , [ 3 ] players must compete to discard their cards as quickly as possible and do not take turns.
In turn-based games, game flow is partitioned into defined parts, called turns , moves, or plays. Each player is allowed a period of analysis (sometimes bounded, sometimes unbounded) before committing to a game action. [ 4 ]
Turns may represent periods of time, such as hours, days, or years. [ 4 ] [ 5 ] This is common in 4X video games like the Civilization series [ 6 ] and world-building tabletop role-playing games. For example, in Dialect , sets of turns represent eras in a society's development; [ 7 ] similarly, in The Quiet Year , each turn represents one week leading up to a community's destruction. [ 8 ] This is also common in both video games and tabletop games with dating sim elements. For example, in Persona 5 and Monster Prom , turns represent high school class periods, [ 9 ] [ 10 ] and in Visigoths vs. Mall Goths , each team's turn represents a specific hour at the mall. [ 11 ]
Turn-based games come in two main forms: simultaneous or sequential (also called player-alternated ). Diplomacy is an example of a simultaneous turn-based game. There are three types of player-alternated games: ranked, round-robin start, and random. The difference is the order in which players start a turn. In ranked player-alternated games, the first player is the same every time. In round-robin games, the first player selection policy is round-robin. Random player-alternated games randomly select the first player. Some games also decide the order of play using an initiative score based on players' attributes, positions within the game, or dice rolls. Dungeons & Dragons and Wizard101 are examples of this style. [ 12 ] [ 13 ]
The term turn-based gaming is also used for play-by-mail games and browser-based gaming websites that allow long-term gameplay of board games such as Go and chess .
Various adaptations of the real-time and turn-based systems have been implemented to address common or perceived shortcomings of these systems (though they often introduce new issues that did not exist before). [ 14 ] These include:
Timed turns are designed to prevent one player from using more time to complete turns than another. In chess , for instance, a pair of stop clocks may be used in order to place an upper limit on turn length.
In exchange chess , four players on two teams play on two boards with each team taking one white and one black side. A taken piece can be given to a teammate and placed on their board. A player can abuse this game mechanic by taking an opponent's piece, giving it to a teammate, then waiting unusually long to play a turn on their own board—thereby allowing the teammate to use the advantage for many future moves on their board. To avoid this, players are often limited to ten seconds per move—with their opponent being allowed to remove one of the player's pawns from the board for each additional ten seconds consumed. [ 15 ] [ 16 ]
The turn-based strategy game Utopia (1982) featured an early example of timed turns. [ 17 ] The early Ultima role-playing video games were strictly turn-based, but starting with Ultima III: Exodus (1983), if the player waited too long to issue a command, the game would issue a "pass" command automatically, thereby allowing enemies to take their turns while the player character did nothing.
Time compression is a feature commonly found in real-time games such as flight simulators . It allows the player to speed up the game time by some (usually adjustable) factor. This permits the player to shorten the subjective duration of long and relatively uneventful periods of gameplay.
Many browser-based MMORPGs allocate a number of turns that can be played within a certain period of time, called a tick . A tick can be any measurement of real time. Players are allocated a certain number of turns per tick, which are refreshed at the beginning of each new tick. Tick-based games differ from other turn-based games in that ticks always occur after the same amount of time has expired.
In some real-time games, game actions are timed according to a common interval that is longer than the duration of play in the real world. For instance, non-player characters might only begin actions at the beginning or end of a round . Some video games such as the Baldur's Gate series use a rounds system based on tabletop role-playing games such as Dungeons & Dragons.
The " Active Time Battle " (ATB) system was introduced by Hiroyuki Ito in Final Fantasy IV (1991). [ 18 ] ATB combines turn-based combat with a continuous flow of actions and variable wait times. [ 19 ] Enemies can attack or be attacked at any time. [ 20 ] The ATB system was further developed in Final Fantasy V (1992), which introducing a time gauge showing which character's turn is next. [ 21 ] The ATB system has since been used in VI (1994), VII (1997), VIII (1999), IX (2000), and X-2 (2003). Both Final Fantasy XII (2006) and XIII (2009) used heavily modified versions of the system. The ATB system was also used in Chrono Trigger (1995).
In simultaneously executed games (also called "phase-based", "We-Go" or "Turn-based WeGo"), turns are separated into two distinct phases: decision and execution . In the decision phase, each player simultaneously plans and determines their units' actions. In the execution phase, all players' chosen actions occur automatically and at the same time. One early example is the 1959 board game Diplomacy . Video game examples include Laser Squad Nemesis (2003), the Combat Mission series, Master of Orion series, Star Hammer: The Vanguard Prophecy (2015) and Battlestar Galactica Deadlock (2017).
Clock-based games tie all unit actions directly to the game clock. Turns begin and end depending on the duration specified for each action, resulting in a sequence of turns that is highly variable and has no set order. It is also possible for different players' actions to occur at the same time with respect to the game clock, as in real-time or simultaneously executed games. Examples of video games that use a clock-based system include Typhoon of Steel (1988) and MechForce (1991), both originally for the Amiga .
In some games, the sequence of turns depends on the initiative statistic of each unit, no matter which side the unit belongs to. Games of this type are still technically sequential, as only one unit can perform an action at a time, and the duration of actions is not tied to the game clock. Examples include the video games The Temple of Elemental Evil (2003) and Final Fantasy Tactics (1997).
Some games allow players to act outside of their normal turn by interrupting an opponent's turn and executing additional actions. The number and type of actions a player may take during an interrupt sequence is limited by the number of points remaining in the player's action point pool carried over from the previous turn. Examples include the X-COM series of video games, the board wargame Advanced Squad Leader (1985), and attacks of opportunity in Dungeons & Dragons . Newer editions of Dungeons & Dragons also allow a Ready -action to prepare an action to be executed during the enemy's turn. This is also implemented in some video games, such as Solasta: Crown of the Magister (2020).
The Silent Storm video game series includes an "Interrupt" statistic for each character, to determine the likelihood of out-of-turn action. In the video game M.A.X. (1996), defensive units may be set to fire out of turn instead of on their own turn. In the board game Tide of Iron , a special card interrupts an opponent's turn to perform an action. In the Mario & Luigi series, the player often has the opportunity to "counterattack" on the enemy's turn, causing damage and often halting the attack.
In some turn-based games, not all turns are alike. The board game Imperium Romanum II (1985), for instance, features a "Taxation and Mobilization" phase in every third turn (month), which does not occur in the other turns. In the video game King Arthur: The Role-Playing Wargame (2009), every fourth turn, the season turns to winter, the only time when buildings can be constructed. In the board game Napoleon (1974), every third player turn is a "night turn" when combat is not allowed.
Other turn-based games feature several phases dedicated to different types of activities within each turn. In the Battle Isle series of video games, players issue movement orders for all units in one phase, and attack orders in a later phase. In the board game Agricola (2007), turns are divided into three phases: "Upkeep", "Replenishing" and "Work." A fourth "Harvest" phase occurs every few turns.
Some games that are generally real-time use turn-based play during specific sequences. For example, the role-playing video games Fallout (1997), Silent Storm (2003) [ 22 ] and Baldur's Gate 3 (2023) are turn-based during the combat phase and real-time throughout the remainder of the game. This speeds up portions of the game where the careful timing of actions is not crucial to player success, such as exploration. [ 23 ] [ 24 ]
Other video games, such as the Total War series, X-COM (1994) and Jagged Alliance 2 (1999), combine a turn-based strategic layer with real-time tactical combat or vice versa. [ 25 ] [ 26 ]
The video games X-COM: Apocalypse (1997), Fallout Tactics (2001) Arcanum: Of Steamworks and Magick Obscura (2001), Pillars of Eternity II: Deadfire (2018), Pathfinder: Kingmaker (2018, added later per patch) and Pathfinder: Wrath of the Righteous (2021) offer the option of turn-based or real-time mode via a configuration setting. [ 27 ] [ 28 ]
In real-time games with an active pause system (also called "pausable real-time" or "real-time with pause"), players can pause the game and issue orders. When the game is un-paused, the orders automatically execute. This offers additional tactical options, such as letting players issue orders to multiple units at the same time. [ 29 ] [ 25 ]
The Baldur's Gate series popularized pausable real-time for mouse-driven party-based computer role-playing games , [ 30 ] although the mechanic was also present in earlier games such as in Knights of Xentar (1991), [ 31 ] [ 32 ] Darklands (1992), [ 29 ] Tales of Phantasia (1995), [ 33 ] Total Annihilation (1997) and Homeworld (1999). In Baldur's Gate , players may also let the artificial intelligence take control during combat and press the spacebar at any time to regain control of their characters. [ 29 ] Further, in Baldur's Gate , players are able to configure the game to automatically pause when certain conditions are met, such as at the end of a round or upon the death of a non-player character . A variation of active pause, called "Smart Pause Mode" or SPM, is a feature of Apeiron's Brigade E5: New Jagged Union (2006) and 7.62: High Calibre (2007). [ 34 ] [ 35 ]
The grand strategy games developed by Paradox Interactive exclusively use pausable real-time. [ 25 ] It was the originally intended mode of the Civilization series before the developers decided to switch to turn-based. [ 25 ] It has been present in the SimCity construction and management simulation series since SimCity (1989) and is also used in the Transport Tycoon and RollerCoaster Tycoon series.
In the single-character console RPGs Parasite Eve (1998) and Vagrant Story (2000), the player can pause the game to take aim with a weapon. [ 36 ] In Vagrant Story , this allows players to target specific body parts while the game is paused. A similar mechanic was later used in the real-time role-playing game Last Rebellion (2010). [ 37 ] Jagged Alliance 2 (1999) and Fallout (1997) allow players to target individual body parts during turn-based combat. The latter led to the creation of the V.A.T.S system in the real-time RPG Fallout 3 , where players could pause the game to target individual body parts. [ 38 ] Final Fantasy XII (2006) expanded on active pause combat with its "gambits" system, which allows players to collect and apply preferences to the artificial intelligence routines of partner characters, who then perform certain actions in response to certain conditions. A similar "tactics" system later appeared in Dragon Age: Origins (2009) [ 39 ] and Dragon Age II (2011). [ 40 ] Knights of Xentar (1991) [ 32 ] and Secret of Mana (1993) [ 41 ] also allow an adjustable artificial intelligence to take control during combat. [ 32 ] [ 41 ]
Some games use a timeline as part of a game mechanic that lets players establish or alter the order of events within the game world. For example, in the indie role-playing game Microscope , players invent a timeline together, then select different segments of the timeline to embellish through roleplaying. [ 42 ] In the card game Chrononauts (game) , everyone plays timeline cards to change the order of historical events, creating an alternate history . [ 43 ]
A progress clock is a tabletop role-playing gamemaster (GM) tool for keeping track of ongoing events that cannot be handled within a single turn, such as the player characters' continuous headway toward defeating a challenge, the gradual approach of an enemy, or a time-limited window of opportunity. The GM draws a segmented circle to represent a clock face, then fills in a segment whenever progress develops toward the outcome. Progress clocks are important in the heist film -inspired game Blades in the Dark and other games that adapt its Forged in the Dark system. [ 44 ] [ 45 ]
Debates occur between fans of real-time and turn-based video games based on the merits and flaws of each timekeeping style. [ 46 ] [ 47 ] [ 48 ] [ 49 ] [ 50 ]
Arguments made in favor of turn-based systems include:
Arguments made in favor of real-time systems include: | https://en.wikipedia.org/wiki/Real-time_game |
Real-time gross settlement ( RTGS ) systems are specialist funds transfer systems where the transfer of money or securities [ 1 ] takes place from one bank to any other bank on a "real-time" and on a " gross " basis to avoid settlement risk . Settlement in "real time" means a payment transaction is not subjected to any waiting period, with transactions being settled as soon as they are processed. "Gross settlement" means the transaction is settled on a one-to-one basis, without bundling or netting with any other transaction. "Settlement" means that once processed, payments are final and irrevocable.
As of 1985, three central banks implemented RTGS systems, while by the end of 2005, RTGS systems had been implemented by 90 central banks. [ 2 ]
The first system that had the attributes of an RTGS system was the US Fedwire system which was launched in 1970. This was based on a previous method of transferring funds electronically between US federal reserve banks via telegraph . The United Kingdom and France both independently developed RTGS type systems in 1984. The UK system was developed by the Bankers' Clearing House in February 1984 and was called CHAPS . The French system was called SAGITTAIRE. A number of other developed countries launched systems over the next few years. These systems were diverse in operation and technology, being country-specific as they were usually based upon previous processes and procedures used in each country.
In the 1990s international finance organizations emphasized the importance of large-value funds transfer systems which banks use to settle interbank transfers for their own account as well as for their customers as a key part of a country's financial market infrastructure . By 1997 a number of countries, inside as well as outside the Group of Ten , had introduced real-time gross settlement systems for large-value funds transfers. Nearly all G-10 countries had plans to have RTGS systems in operation in the course of 1997 and many other countries were also considering introducing such systems. [ 3 ]
RTGS systems are usually operated by a country's central bank as it is seen as critical infrastructure for a country's economy. Economists believe that an efficient national payment system reduces the cost of exchanging goods and services , and is indispensable to the functioning of the interbank, money, and capital markets. A weak payment system may severely drag on the stability and developmental capacity of a national economy; its failures can result in inefficient use of financial resources, inequitable risk-sharing among agents, actual losses for participants, and loss of confidence in the financial system and in the very use of money. [ 4 ]
RTGS system does not require any physical exchange of money; the central bank makes adjustments in the electronic accounts of Bank A and Bank B, reducing the balance in Bank A’s account by the amount in question and increasing the balance of Bank B’s account by the same amount. The RTGS system is suited for low-volume, high-value transactions. It lowers settlement risk, besides giving an accurate picture of an institution’s account at any point in time. The objective of RTGS systems by central banks throughout the world is to minimize risk in high-value electronic payment settlement systems. In an RTGS system, transactions are settled across accounts held at a central bank on a continuous gross basis. The settlement is immediate, final, and irrevocable. Credit risks due to settlement lags are eliminated. The best RTGS national payment systems cover up to 95% of high-value transactions within the national monetary market.
RTGS systems are an alternative to systems of settling transactions at the end of the day, also known as the net settlement system, such as the BACS system in the United Kingdom. In a net settlement system, all the inter-institution transactions during the day are accumulated, and at the end of the day, the central bank adjusts the accounts of the institutions by the net amounts of these transactions. [ 5 ]
The World Bank has been paying increasing attention to payment system development as a key component of the financial infrastructure of a country and has provided various forms of assistance to over 100 countries. Most of the RTGS systems in place are secure and have been designed around international standards and best practices. [ 6 ]
There are several reasons for central banks to adopt RTGS. First, a decision to adopt is influenced by competitive pressure from the global financial markets. Second, it is more beneficial to adopt an RTGS system for the central bank when this allows access to a broad system of other countries' RTGS systems. Third, it is very likely that the knowledge acquired through experiences with RTGS systems spills over to other central banks and helps them make their adoption decision. Fourth, central banks do not necessarily have to install and develop RTGS themselves. The possibility of sharing development with providers that have built RTGS systems in more than one country ( CGI of UK holding the IP, CMA Small System of Sweden, JV Perago of South Africa, SIA S.p.A. of Italy and Montran of USA) has presumably lowered the cost and hence made it feasible for many countries to adopt. [ 7 ]
Below is a listing of countries and their RTGS systems:
In 2010, the World Bank published a report on payment systems worldwide, which investigated these countries' usage of real-time gross settlement systems for large-value payments. [ 60 ] [ 61 ] | https://en.wikipedia.org/wiki/Real-time_gross_settlement |
Real-time kinematic positioning ( RTK ) is the application of surveying to correct for common errors in current satellite navigation (GNSS) systems. [ 1 ] It uses measurements of the phase of the signal's carrier wave in addition to the information content of the signal and relies on a single reference station or interpolated virtual station to provide real-time corrections, providing up to centimetre -level accuracy (see DGPS ). [ 2 ] With reference to GPS in particular, the system is commonly referred to as carrier-phase enhancement , or CPGPS . [ 3 ] It has applications in land surveying , hydrographic surveying , and in unmanned aerial vehicle navigation.
The distance between a satellite navigation receiver and a satellite can be calculated from the time it takes for a signal to travel from the satellite to the receiver. To calculate the delay, the receiver must align a pseudorandom binary sequence contained in the signal to an internally generated pseudorandom binary sequence. Since the satellite signal takes time to reach the receiver, the satellite's sequence is delayed in relation to the receiver's sequence. By increasingly delaying the receiver's sequence, the two sequences are eventually aligned.
The accuracy of the resulting range measurement is essentially a function of the ability of the receiver's electronics to accurately process signals from the satellite, and additional error sources such as non-mitigated ionospheric and tropospheric delays , multipath, satellite clock and ephemeris errors. [ 4 ]
RTK follows the same general concept, but uses the satellite signal's carrier wave as its signal, ignoring the information contained within. RTK uses a fixed base station and a rover to reduce the rover's position error. The base station transmits correction data to the rover.
As described in the previous section, the range to a satellite is essentially calculated by multiplying the carrier wavelength times the number of whole cycles between the satellite and the rover and adding the phase difference. Determining the number of cycles is non-trivial, since signals may be shifted in phase by one or more cycles. This results in an error equal to the error in the estimated number of cycles times the wavelength, which is 19 cm for the L1 signal. Solving this so-called integer ambiguity search problem results in centimeter precision. The error can be reduced with sophisticated statistical methods that compare the measurements from the C/A signals and by comparing the resulting ranges between multiple satellites.
The improvement possible using this technique is potentially very high if one continues to assume a 1% accuracy in locking. For instance, in the case of GPS, the coarse-acquisition (C/A) code, which is broadcast in the L1 signal, changes phase at 1.023 MHz, but the L1 carrier itself is 1575.42 MHz, which changes phase over a thousand times more often. A ±1% error in L1 carrier-phase measurement thus corresponds to a ±1.9 mm error in baseline estimation. [ 5 ]
In practice, RTK systems use a single base-station receiver and a number of mobile units. The base station re-broadcasts the phase of the carrier that it observes, and the mobile units compare their own phase measurements with the one received from the base station. There are several ways to transmit a correction signal from base station to mobile station. The most popular way to achieve real-time, low-cost signal transmission is to use a radio modem , typically in the UHF Band . In most countries, certain frequencies are allocated specifically for RTK purposes. Most land-survey equipment has a built-in UHF-band radio modem as a standard option. RTK provides accuracy enhancements up to about 20 km from the base station. [ 6 ]
This allows the units to calculate their relative position to within millimeters, although their absolute position is accurate only to the same accuracy as the computed position of the base station. For RTK with a single base station, accuracy of 8mm + 1ppm (parts per million / 1mm per km) horizontal and 15mm + 1ppm vertical relative to the base station can be achieved, depending on the device. [ 7 ] For example, with a base station 16 km (slightly less than 10 miles) away, relative horizontal error would be 8mm + 16mm = 24mm (slightly less than an inch).
Although these parameters limit the usefulness of the RTK technique for general navigation, the technique is perfectly suited to roles like surveying. In this case, the base station is located at a known surveyed location, often a benchmark , and the mobile units can then produce a highly accurate map by taking fixes relative to that point. RTK has also found uses in autodrive/autopilot systems, precision farming , machine control systems and similar roles.
Network RTK extend the use of RTK to a larger area containing a network of reference stations. [ 8 ] Operational reliability and accuracy depend on the density and capabilities of the reference-station network. With network RTK, accuracy of 8mm + 0.5ppm horizontal and 15mm + 0.5 ppm vertical relative to the nearest station can be achieved, depending on the device. [ 7 ] For example, with a base station 16 km (slightly less than 10 miles) away, relative horizontal error would be 8mm + 8mm = 16mm (roughly 5/8 of an inch).
A Continuously Operating Reference Station (CORS) network is a network of RTK base stations that broadcast corrections, usually over an Internet connection. Accuracy is increased in a CORS network, because more than one station helps ensure correct positioning and guards against a false initialization of a single base station. [ 9 ]
A Virtual Reference Network (VRN) can similarly enhance precision without using a base station, [ 10 ] using virtual reference stations (VRS), instead. The concept can help to satisfy this requirement using a network of reference stations. A typical CORS setup consists of a single reference station from which the raw data (or corrections) are sent to the rover receiver (i.e., the user). The user then forms the carrier phase differences (or corrects their raw data) and performs the data processing using the differential corrections.
In contrast, GNSS network architectures often make use of multiple reference stations. This approach allows a more precise modeling of distance-dependent systematic errors principally caused by ionospheric and tropospheric refractions, and satellite orbit errors. More specifically, a GNSS network decreases the dependence of the error budget on the distance of nearest antenna. | https://en.wikipedia.org/wiki/Real-time_kinematic_positioning |
Real-Time Path Planning is a term used in robotics that consists of motion planning methods that can adapt to real time changes in the environment. This includes everything from primitive algorithms that stop a robot when it approaches an obstacle to more complex algorithms that continuously takes in information from the surroundings and creates a plan to avoid obstacles. [ 1 ]
These methods are different from something like a Roomba robot vacuum as the Roomba may be able to adapt to dynamic obstacles but it does not have a set target. A better example would be Embark self-driving semi-trucks that have a set target location and can also adapt to changing environments.
The targets of path planning algorithms are not limited to locations alone. Path planning methods can also create plans for stationary robots to change their poses. An example of this can be seen in various robotic arms, where path planning allows the robotic system to change its pose without colliding with itself. [ 2 ]
As a subset of motion planning, it is an important part of robotics as it allows robots to find the optimal path to a target. This ability to find an optimal path also plays an important role in other fields such as video games and gene sequencing.
In order to create a path from a target point to a goal point there must be classifications about the various areas within the simulated environment . This allows a path to be created in a 2D or 3D space where the robot can avoid obstacles .
The work space is an environment that contains the robot and various obstacles. This environment can be either 2-dimensional or 3-dimensional. [ 3 ]
The configuration of a robot is determined by its current position and pose. The configuration space is the set of all configurations of the robot. By containing all the possible configurations of the robot, it also represents all transformations that can be applied to the robot. [ 3 ]
Within the configuration sets there are additional sets of configurations that are classified by the various algorithms.
The free space is the set of all configurations within the configuration space that does not collide with obstacles. [ 4 ]
The target space is the configuration that we want the robot to accomplish.
The obstacle space is the set of configurations within the configuration space where the robot is unable to move to.
The danger space is the set of configurations where the robot can move through but does not want to. Oftentimes robots will try to avoid these configurations unless they have no other valid path or are under a time restraint. For example, a robot would not want to move through a fire unless there were no other valid paths to the target space. [ 4 ]
Global path planning refers to methods that require prior knowledge of the robot's environment. Using this knowledge it creates a simulated environment where the methods can plan a path. [ 1 ] [ 5 ]
The rapidly exploring random tree method works by running through all possible translations from a specific configuration . By running through all possible series of translations a path is created for the robot to reach the target from the starting configuration. [ 6 ]
Local path planning refers to methods that take in information from the surroundings in order to generate a simulated field where a path can be found. This allows a path to be found in the real-time as well as adapt to dynamic obstacles. [ 1 ] [ 5 ]
The probabilistic roadmap method connects nearby configurations in order to determine a path that goes from the starting to target configuration. The method is split into two different parts: preprocessing phase and query phase. In the preprocessing phase, algorithms evaluate various motions to see if they are located in free space. Then in the query phase, the algorithms connects the starting and target configurations through a variety of paths. After creating the paths, it uses Dijkstra's shortest path query to find the optimal path. [ 7 ] [ 8 ]
The evolutionary artificial potential field method uses a mix of artificial repulsive and attractive forces in order to plan a path for the robot. The attractive forces originate from the target which leads the path to the target in the end. The repulsive forces come from the various obstacles the robot will come across. Using this mix of attractive and repulsive forces, algorithms can find the optimal path. [ 9 ]
The indicative route method uses a control path towards the target and an attraction point located at the target. Algorithms are often used to find the control path, which is oftentimes the path with the shortest minimum-clearance path. As the robot stays on the control path the attraction point on the target configuration leads the robot towards the target. [ 10 ]
The modified indicative routes and navigation method gives various weights to different paths the robot can take from its current position. For example, a rock would be given a high weight such as 50 while an open path would be given a lower weight such as 2. This creates a variety of weighted regions in the environment which allows the robot to decide on a path towards the target. [ 11 ]
For many robots the number of degrees of freedom is no greater than three. Humanoid robots on the other hand have a similar number of degrees of freedom to a human body which increases the complexity of path planning. For example, a single leg of a humanoid robot can have around 12 degrees of freedom. The increased complexity comes from the greater possibility of the robot colliding with itself. Real-time path planning is important for the motion of humanoid robots as it allows various parts of the robot to move at the same time while avoiding collisions with the other parts of the robot. [ 12 ]
For example, if we were to look at our own arms we can see that our hands can touch our shoulders. For a robotic arm this may pose a risk if the parts of the arms were to collide unintentionally with each other. This is why path planning algorithms are needed to prevent these accidental collisions.
Self-driving vehicles are a form of mobile robots that utilizes real-time path planning. Oftentimes a vehicle will first use global path planning to decide which roads to take to the target. When these vehicles are on the road they have to constantly adapt to the changing environment. This is where local path planning methods allow the vehicle to plan a safe and fast path to the target location. [ 13 ]
An example of this would be the Embark self-driving semi-trucks, which uses an array of sensors to take in information about their environment. The truck will have a predetermined target location and will use global path planning to have a path to the target. While the truck is on the road it will use its sensors alongside local path planning methods to navigate around obstacles to safely reach the target location. [ 14 ]
Oftentimes in video games there are a variety of non-player characters that are moving around the game which requires path planning. These characters must have paths planned for them as they need to know where to move to and how to move there.
For example, in the game Minecraft there are hostile mobs that track and follow the player in order to kill the player. This requires real-time path planning as the mob must avoid various obstacles while following the player. Even if the player were to add additional obstacles in the way of the mob, the mob would change its path to still reach the player. | https://en.wikipedia.org/wiki/Real-time_path_planning |
A real-time polymerase chain reaction ( real-time PCR , or qPCR when used quantitatively) is a laboratory technique of molecular biology based on the polymerase chain reaction (PCR). It monitors the amplification of a targeted DNA molecule during the PCR (i.e., in real time), not at its end, as in conventional PCR. Real-time PCR can be used quantitatively and semi-quantitatively (i.e., above/below a certain amount of DNA molecules).
Two common methods for the detection of PCR products in real-time PCR are (1) non-specific fluorescent dyes that intercalate with any double-stranded DNA and (2) sequence-specific DNA probes consisting of oligonucleotides that are labelled with a fluorescent reporter, which permits detection only after hybridization of the probe with its complementary sequence.
The Minimum Information for Publication of Quantitative Real-Time PCR Experiments ( MIQE ) guidelines propose that the abbreviation qPCR be used for quantitative real-time PCR and that RT-qPCR be used for reverse transcription–qPCR. [ 1 ] The acronym "RT-PCR" commonly denotes reverse transcription polymerase chain reaction and not real-time PCR, but not all authors adhere to this convention. [ 2 ]
Cells in all organisms regulate gene expression by turnover of gene transcripts (single stranded RNA ): The amount of an expressed gene in a cell can be measured by the number of copies of an RNA transcript of that gene present in a sample. In order to robustly detect and quantify gene expression from small amounts of RNA, amplification of the gene transcript is necessary. The polymerase chain reaction (PCR) is a common method for amplifying DNA; for RNA-based PCR the RNA sample is first reverse-transcribed to complementary DNA (cDNA) with reverse transcriptase .
In order to amplify small amounts of DNA, the same methodology is used as in conventional PCR using a DNA template, at least one pair of specific primers , deoxyribonucleotide triphosphates, a suitable buffer solution and a thermo-stable DNA polymerase . A substance marked with a fluorophore is added to this mixture in a thermal cycler that contains sensors for measuring the fluorescence of the fluorophore after it has been excited at the required wavelength allowing the generation rate to be measured for one or more specific products.
This allows the rate of generation of the amplified product to be measured at each PCR cycle. The data thus generated can be analysed by computer software to calculate relative gene expression (or mRNA copy number ) in several samples. Quantitative PCR can also be applied to the detection and quantification of DNA in samples to determine the presence and abundance of a particular DNA sequence in these samples. [ 3 ] This measurement is made after each amplification cycle, and this is the reason why this method is called real time PCR (that is, immediate or simultaneous PCR).
Quantitative PCR and DNA microarray are modern methodologies for studying gene expression . Older methods were used to measure mRNA abundance: differential display , RNase protection assay and northern blot . Northern blotting is often used to estimate the expression level of a gene by visualizing the abundance of its mRNA transcript in a sample. In this method, purified RNA is separated by agarose gel electrophoresis , transferred to a solid matrix (such as a nylon membrane), and probed with a specific DNA or RNA probe that is complementary to the gene of interest. Although this technique is still used to assess gene expression, it requires relatively large amounts of RNA and provides only qualitative or semi quantitative information of mRNA levels. [ 4 ] Estimation errors arising from variations in the quantification method can be the result of DNA integrity, enzyme efficiency and many other factors. For this reason a number of standardization systems (often called normalization methods ) have been developed. Some have been developed for quantifying total gene expression, but the most common are aimed at quantifying the specific gene being studied in relation to another gene called a normalizing gene, which is selected for its almost constant level of expression. These genes are often selected from housekeeping genes as their functions related to basic cellular survival normally imply constitutive gene expression . [ 5 ] [ 6 ] This enables researchers to report a ratio for the expression of the genes of interest divided by the expression of the selected normalizer, thereby allowing comparison of the former without actually knowing its absolute level of expression.
The most commonly used normalizing genes are those that code for the following molecules: tubulin , glyceraldehyde-3-phosphate dehydrogenase , albumin , cyclophilin , and ribosomal RNAs . [ 4 ]
Real-time PCR is carried out in a thermal cycler with the capacity to illuminate each sample with a beam of light of at least one specified wavelength and detect the fluorescence emitted by the excited fluorophore . The thermal cycler is also able to rapidly heat and chill samples, thereby taking advantage of the physicochemical properties of the nucleic acids and DNA polymerase .
The PCR process generally consists of a series of temperature changes that are repeated 25–50 times. These cycles normally consist of three stages: the first, at around 95 °C, allows the separation of the nucleic acid's double chain; the second, at a temperature of around 50–60 °C, allows the binding of the primers with the DNA template; [ 7 ] the third, at between 68 and 72 °C, facilitates the polymerization carried out by the DNA polymerase. Due to the small size of the fragments the last step is usually omitted in this type of PCR as the enzyme is able to replicate the DNA amplicon during the change between the alignment stage and the denaturing stage. In addition, in four-step PCR the fluorescence is measured during short temperature phases lasting only a few seconds in each cycle, with a temperature of, for example, 80 °C, in order to reduce the signal caused by the presence of primer dimers when a non-specific dye is used. [ 8 ] The temperatures and the timings used for each cycle depend on a wide variety of parameters, such as: the enzyme used to synthesize the DNA, the concentration of divalent ions and deoxyribonucleotide triphosphates (dNTPs) in the reaction and the bonding temperature of the primers. [ 9 ]
Real-time PCR technique can be classified by the chemistry used to detect the PCR product, specific or non-specific fluorochromes.
A DNA-binding dye binds to all double-stranded (ds) DNA in PCR, increasing the fluorescence quantum yield of the dye. An increase in DNA product during PCR therefore leads to an increase in fluorescence intensity measured at each cycle. However, dsDNA dyes such as SYBR Green will bind to all dsDNA PCR products, including nonspecific PCR products (such as primer dimer ). This can potentially interfere with, or prevent, accurate monitoring of the intended target sequence.
In real-time PCR with dsDNA dyes the reaction is prepared as usual, with the addition of fluorescent dsDNA dye. Then the reaction is run in a real-time PCR instrument , and after each cycle, the intensity of fluorescence is measured with a detector; the dye only fluoresces when bound to the dsDNA (i.e., the PCR product).
This method has the advantage of only needing a pair of primers to carry out the amplification, which keeps costs down; multiple target sequences can be monitored in a tube by using different types of dyes.
Fluorescent reporter probes detect only the DNA containing the sequence complementary to the probe; therefore, use of the reporter probe significantly increases specificity, and enables performing the technique even in the presence of other dsDNA. Using different-coloured labels, fluorescent probes can be used in multiplex assays for monitoring several target sequences in the same tube. The specificity of fluorescent reporter probes also prevents interference of measurements caused by primer dimers , which are undesirable potential by-products in PCR. However, fluorescent reporter probes do not prevent the inhibitory effect of the primer dimers, which may depress accumulation of the desired products in the reaction.
The method relies on a DNA-based probe with a fluorescent reporter at one end and a quencher of fluorescence at the opposite end of the probe. The close proximity of the reporter to the quencher prevents detection of its fluorescence; breakdown of the probe by the 5' to 3' exonuclease activity of the Taq polymerase breaks the reporter-quencher proximity and thus allows unquenched emission of fluorescence, which can be detected after excitation with a laser. An increase in the product targeted by the reporter probe at each PCR cycle therefore causes a proportional increase in fluorescence due to the breakdown of the probe and release of the reporter.
Real-time PCR permits the identification of specific, amplified DNA fragments using analysis of their melting temperature (also called T m value, from m elting t emperature ). The method used is usually PCR with double-stranded DNA-binding dyes as reporters and the dye used is usually SYBR Green. The DNA melting temperature is specific to the amplified fragment. The results of this technique are obtained by comparing the dissociation curves of the analysed DNA samples. [ 11 ]
Unlike conventional PCR, this method avoids the previous use of electrophoresis techniques to demonstrate the results of all the samples. This is because, despite being a kinetic technique, quantitative PCR is usually evaluated at a distinct end point. The technique therefore usually provides more rapid results and/or uses fewer reactants than electrophoresis. If subsequent electrophoresis is required it is only necessary to test those samples that real time PCR has shown to be doubtful and/or to ratify the results for samples that have tested positive for a specific determinant.
Unlike end point PCR (conventional PCR), real time PCR allows monitoring of the desired product at any point in the amplification process by measuring fluorescence (in real time frame, measurement is made of its level over a given threshold). A commonly employed method of DNA quantification by real-time PCR relies on plotting fluorescence against the number of cycles on a logarithmic scale . A threshold for detection of DNA-based fluorescence is set 3–5 times of the standard deviation of the signal noise above background. The number of cycles at which the fluorescence exceeds the threshold is called the threshold cycle (C t ) or, according to the MIQE guidelines, quantification cycle (C q ) . [ 1 ] Using this method, the greater the amount of starting mRNA, the lower the C q.
During the exponential amplification phase, the quantity of the target DNA template (amplicon) doubles every cycle. For example, a DNA sample whose C q precedes that of another sample by 3 cycles contained 2 3 = 8 times more template. However, the efficiency of amplification is often variable among primers and templates. Therefore, the efficiency of a primer-template combination is assessed in a titration experiment with serial dilutions of DNA template to create a standard curve of the change in (C q ) with each dilution. The slope of the linear regression is then used to determine the efficiency of amplification, which is 100% if a dilution of 1:2 results in a (C q ) difference of 1. The cycle threshold method makes several assumptions of reaction mechanism and has a reliance on data from low signal-to-noise regions of the amplification profile that can introduce substantial variance during the data analysis. [ 12 ]
To quantify gene expression, the (C q ) for an RNA or DNA from the gene of interest is subtracted from the (C q ) of RNA/DNA from a housekeeping gene in the same sample to normalize for variation in the amount and quality of RNA between different samples. This normalization procedure is commonly called the ΔC t -method [ 13 ] and permits comparison of expression of a gene of interest among different samples. However, for such comparison, expression of the normalizing reference gene needs to be very similar across all the samples. Choosing a reference gene fulfilling this criterion is therefore of high importance, and often challenging, because only very few genes show equal levels of expression across a range of different conditions or tissues. [ 14 ] [ 15 ] Although cycle threshold analysis is integrated with many commercial software systems, there are more accurate and reliable methods of analysing amplification profile data that should be considered in cases where reproducibility is a concern. [ 12 ]
Mechanism-based qPCR quantification methods have also been suggested, and have the advantage that they do not require a standard curve for quantification. Methods such as MAK2 [ 16 ] have been shown to have equal or better quantitative performance to standard curve methods. These mechanism-based methods use knowledge about the polymerase amplification process to generate estimates of the original sample concentration. An extension of this approach includes an accurate model of the entire PCR reaction profile, which allows for the use of high signal-to-noise data and the ability to validate data quality prior to analysis. [ 12 ]
According to research of Ruijter et al. [ 17 ] MAK2 assumes constant amplification efficiency during the PCR reaction. However, theoretical analysis of polymerase chain reaction, from which MAK2 was derived, has revealed that amplification efficiency is not constant throughout PCR. While MAK2 quantification provides reliable estimates of target DNA concentration in a sample under normal qPCR conditions, MAK2 does not reliably quantify target concentration for qPCR assays with competimeters.
There are numerous applications for quantitative polymerase chain reaction in the laboratory . It is commonly used for both diagnostic and basic research . Uses of the technique in industry include the quantification of microbial load in foods or on vegetable matter, the detection of GMOs ( genetically modified organisms ) and the quantification and genotyping of human viral pathogens.
Quantifying gene expression by traditional DNA detection methods is unreliable. Detection of mRNA on a northern blot or PCR products on a gel or Southern blot does not allow precise quantification. [ 18 ] For example, over the 20–40 cycles of a typical PCR, the amount of DNA product reaches a plateau that is not directly correlated with the amount of target DNA in the initial PCR. [ 19 ]
Real-time PCR can be used to quantify nucleic acids by two common methods: relative quantification and absolute quantification. [ 20 ] Absolute quantification gives the exact number of target DNA molecules by comparison with DNA standards using a calibration curve . It is therefore essential that the PCR of the sample and the standard have the same amplification efficiency . [ 21 ] Relative quantification is based on internal reference genes to determine fold-differences in expression of the target gene. The quantification is expressed as the change in expression levels of mRNA interpreted as complementary DNA (cDNA, generated by reverse transcription of mRNA). Relative quantification is easier to carry out as it does not require a calibration curve as the amount of the studied gene is compared to the amount of a control reference gene.
As the units used to express the results of relative quantification are unimportant the results can be compared across a number of different RTqPCR. The reason for using one or more housekeeping genes is to correct non-specific variation, such as the differences in the quantity and quality of RNA used, which can affect the efficiency of reverse transcription and therefore that of the whole PCR process. However, the most crucial aspect of the process is that the reference gene must be stable. [ 22 ]
The selection of these reference genes was traditionally carried out in molecular biology using qualitative or semi-quantitative studies such as the visual examination of RNA gels, northern blot densitometry or semi-quantitative PCR (PCR mimics). Now, in the genome era, it is possible to carry out a more detailed estimate for many organisms using transcriptomic technologies . [ 23 ] However, research has shown that amplification of the majority of reference genes used in quantifying the expression of mRNA varies according to experimental conditions. [ 24 ] [ 25 ] [ 26 ] It is therefore necessary to carry out an initial statistically sound methodological study in order to select the most suitable reference gene.
A number of statistical algorithms have been developed that can detect which gene or genes are most suitable for use under given conditions. Those like geNORM or BestKeeper can compare pairs or geometric means for a matrix of different reference genes and tissues . [ 4 ] [ 6 ]
Diagnostic qualitative PCR is applied to rapidly detect nucleic acids that are diagnostic of, for example, infectious diseases , [ 27 ] [ 28 ] cancer and genetic abnormalities. The introduction of qualitative PCR assays to the clinical microbiology laboratory has significantly improved the diagnosis of infectious diseases, [ 29 ] and is deployed as a tool to detect newly emerging diseases, such as new strains of flu and coronavirus , [ 30 ] in diagnostic tests . [ 31 ] [ 32 ]
Quantitative PCR is also used by microbiologists working in the fields of food safety, food spoilage and fermentation and for the microbial risk assessment of water quality (drinking and recreational waters) and in public health protection. [ 33 ]
qPCR may also be used to amplify taxonomic or functional markers of genes in DNA taken from environmental samples. [ 34 ] Markers are represented by genetic fragments of DNA or complementary DNA. [ 34 ] By amplifying a certain genetic element, one can quantify the amount of the element in the sample prior to amplification. [ 34 ] Using taxonomic markers (ribosomal genes) and qPCR can help determine the amount of microorganisms in a sample, and can identify different families, genera, or species based on the specificity of the marker. [ 34 ] Using functional markers (protein-coding genes) can show gene expression within a community, which may reveal information about the environment. [ 34 ]
The agricultural industry is constantly striving to produce plant propagules or seedlings that are free of pathogens in order to prevent economic losses and safeguard health. Systems have been developed that allow detection of small amounts of the DNA of Phytophthora ramorum , an oomycete that kills oaks and other species, mixed in with the DNA of the host plant. Discrimination between the DNA of the pathogen and the plant is based on the amplification of ITS sequences, spacers located in ribosomal RNA gene's coding area, which are characteristic for each taxon. [ 35 ] Field-based versions of this technique have also been developed for identifying the same pathogen. [ 36 ]
qPCR using reverse transcription (RT-qPCR) can be used to detect GMOs given its sensitivity and dynamic range in detecting DNA. Alternatives such as DNA or protein analysis are usually less sensitive. Specific primers are used that amplify not the transgene but the promoter , terminator or even intermediate sequences used during the process of engineering the vector. As the process of creating a transgenic plant normally leads to the insertion of more than one copy of the transgene its quantity is also commonly assessed. This is often carried out by relative quantification using a control gene from the treated species that is only present as a single copy. [ 37 ] [ 38 ]
Viruses can be present in humans due to direct infection or co-infections which makes diagnosis difficult using classical techniques and can result in an incorrect prognosis and treatment. The use of qPCR allows both the quantification and genotyping (characterization of the strain, carried out using melting curves) of a virus such as the hepatitis B virus . [ 39 ] The degree of infection, quantified as the copies of the viral genome per unit of the patient's tissue, is relevant in many cases; for example, the probability that the type 1 herpes simplex virus reactivates is related to the number of infected neurons in the ganglia . [ 40 ] This quantification is carried out either with reverse transcription or without it, as occurs if the virus becomes integrated in the human genome at any point in its cycle, such as happens in the case of HPV (human papillomavirus), where some of its variants are associated with the appearance of cervical cancer . [ 41 ] Real-time PCR has also brought the quantization of human cytomegalovirus (CMV) which is seen in patients who are immunosuppressed following solid organ or bone marrow transplantation. [ 42 ] | https://en.wikipedia.org/wiki/Real-time_polymerase_chain_reaction |
In information technology , real-time recovery (RTR) is the ability to recover a piece of IT infrastructure such as a server from an infrastructure failure or human-induced error in a time frame that has minimal impact on business operations. Real-time recovery focuses on the most appropriate technology for restores, thus reducing the Recovery Time Objective (RTO) to minutes, Recovery Point Objectives (RPO) to within 15 minutes ago, and minimizing Test Recovery Objectives (TRO), which is the ability to test and validate that backups have occurred correctly without impacting production systems. [ 1 ]
Real-Time Recovery is a new market segment in the backup , recovery and disaster recovery market that addresses the challenges companies that have historically faced with regards to protecting, and more importantly, recovering their data.
A real-time recovery solution must contain (at a minimum) the following attributes: The ability to restore a server in minutes to the same, totally different or to a virtual environment to within 5 minutes ago and not require the use of any additional agents, options or modules to accomplish this. It must be able to restore files in seconds (after all, the only reason anyone backups is to be able to restore). It must perform sector level backups, every 5 minutes and have the ability to self-heal a broken incremental chain of backups should part of the image set get corrupted or deleted. It must deliver improved recoverability of data files and databases. [ citation needed ]
Data Loss can be classified in three broad categories:
Data servers can be either physical hosts or run as guest servers within a virtualization platform, or a combination of both. It is very common for a customer environment to have a mixture of Virtual and Physical Servers. This is where attention to detail must be given to the approach of protecting the data on these servers at regular intervals. There are distinct advantages in selecting a technology that is virtual or physical independent. This would limit the number of technologies that organizations will have to get trained on, skilled up on, purchase, deploy, manage and maintain. In an ideal world, if you can reduce the complexity of managing multiple products to protect your physical and virtual infrastructure you will reap the rewards. A technology that gets installed at the operating system level ensures consistency in an environment that is either physical or virtual and eliminates API compatibility or Disk Volume Structure limitations (e.g. Raw Mapped Devices, VMFS).
Prior to selecting a real-time recovery strategy or solution, a disaster recovery planner will refer to their organization's business continuity plan for the key metrics of recovery point objective (RPO) and recovery time objective for various business processes (such as the process to run payroll, generate an order, e-mail, etc.). The metrics specified for the business processes must then be mapped to the underlying IT systems and infrastructure that support those processes.
Once the recovery time objective and recovery point objective metrics have been mapped to IT infrastructure, the DR planner can determine the most suitable recovery strategy for each system. The business ultimately sets the IT budget, and therefore the RTO and RPO metrics need to fit with the available budget. While the ideal is zero data loss and zero time loss, the cost associated with that level of protection historically have made high-availability solutions impractical and unaffordable. The costs of a Real-Time Recovery solution are far less than previous tape-based backup systems. | https://en.wikipedia.org/wiki/Real-time_recovery |
Real-time simulation refers to a computer model of a physical system that can execute at the same rate as actual "wall clock" time. In other words, the computer model runs at the same rate as the actual physical system. For example, if a tank takes 10 minutes to fill in the real world, it would take 10 minutes to fill in the simulation as well.
Real-time simulation occurs commonly in computer gaming , but also is important in the industrial market for operator training and off-line controller tuning. [ 1 ] Computer languages like LabVIEW , VisSim and Simulink allow quick creation of such real-time simulations and have connections to industrial displays and programmable logic controllers via OLE for process control or digital and analog I/O cards . Several real-time simulators are available on the market including xPC Target and RT-LAB for mechatronic systems, Simulink for power electronic simulation, and RTDS for power grid simulation.
In a real-time simulation, the simulation is performed in discrete time with a constant step (also known as fixed step) simulation as time moves forward in an equal duration of time. Other techniques having variable step are used for high frequency transients but are unsuitable for real time simulation. In a real time simulation, the time required to solve the internal state equations and functions representing the system must be less than the fixed step. If calculation time exceeds the time of the fixed step, an over run is said to have occurred and the simulation now lags behind the actual time. In simple words, real-time simulation must produce the internal variables and output within the same length of time as its physical counterpart would.
Configuring models to run in real-time enables one to use hardware-in-the-loop simulation to test controllers. It's possible to make design changes earlier in the development process, reducing costs and shortening the design cycle .
Real-time simulators are used extensively in many engineering fields. As a result, the inclusion of simulation applications in academic curricula can provide great value to the student. Statistical power grid protection tests, aircraft design and simulation, motor drive controller design methods and space robot integration are a few examples of real-time simulator technology applications. [ 2 ] | https://en.wikipedia.org/wiki/Real-time_simulation |
Real-time text ( RTT ) is text transmitted instantly as it is typed or created. Recipients can immediately read the message while it is being written, without waiting.
Real-time text is used for conversational text, in collaboration, and in live captioning. Technologies include TDD/TTY devices for the deaf, live captioning for TV, Text over IP (ToIP), some types of instant messaging , captioning for telephony / video teleconferencing , telecommunications relay services including ip-relay , transcription services including Remote CART , TypeWell, collaborative text editing , streaming text applications, next-generation 9-1-1 /1-1-2 [ 1 ] emergency service. Obsolete TDD/TTY devices are being replaced by more modern real-time text technologies, including Text over IP , ip-relay, and instant messaging.
While standard instant messaging is not real-time text (messages are sent deliberately when the writer is ready, not transmitted while they are being composed), a real-time text option is found in some instant messaging software, including AOL Instant Messenger 's "Real-Time IM" [ 2 ] feature. Real-time text is also possible over any XMPP compatible chat networks, including those used by Apple iChat , Cisco WebEx , and Google Talk , by using appropriate software that has a real-time text feature. When present in IM programs, the real-time text feature can be turned on/off, just like other chat features such as audio. Real-time text programs date at least to the 1970s, with the talk program on the DEC PDP-11 , which remains in use on Unix systems.
Beam Messenger, a mobile app offering real-time text messaging, was released in 2014. [ 3 ]
Certain real-time text applications have a feature that allows the real-time text to be "turned off", for temporary purposes. This allows the sender to pre-compose the message as a standard IM or text message before transmitting.
Real-time text is frequently used by the deaf , including IP-Relay services, TDD/TTY devices, and Text over IP . Real-time text allows the other person to read immediately, without waiting for the sender to finish composing his or her sentence/message. This allows conversational use of text, much like a hearing person can listen to someone speaking in real-time.
Captioned telephony is the streaming of real-time text captions in parallel with speech on a phone call. This is used by people who are hard of hearing to allow them to have the full benefit of listening as best they can, hearing all the intonation etc. in speech, yet have the captions for those words they cannot hear clearly enough. In the United States, captioned telephony is one of the free relay services that is available to anyone who is hard-of-hearing. Originally developed for use on the analog phone systems (where it requires a special phone) it is now available over IP using standard devices.
Collaborative real-time editing is the utilization of real-time text for shared editing, rather than for conversation. Split screen chat, where conversational text appears continuously, is also considered real-time text. Some examples that provide this as a service are Apache Wave and its fork SwellRT , [ 4 ] Etherpad , the editor Gobby, [ 5 ] and most notably Google Docs .
Real-time text is used in closed captioning and when captions are being streamed live continuously during live events. Transcription services including Communication Access Real-Time Translation and TypeWell frequently use real-time text, where text is streamed live to a remote display. This is used in court reporting , and is also used by deaf attendees at a conference. Also, real-time text provides an enhancement to text messaging on mobile phones, via real-time texting apps.
Real-time text protocols include Text over IP (ToIP) designed around ITU-T T.140 , [ 6 ] IETF RFC 4103, [ 7 ] RFC 5194, [ 8 ] and XMPP Extension Protocol XEP-0301. [ 9 ]
According to ITU-T Multimedia Recommendation F.703, [ 10 ] total conversation defines the simultaneous use of audio, video and real-time text. An instant messaging program that can enable all three features simultaneously would be compliant. Real time text is an important part of it.
Real-time text is also historically found in the old UNIX talk , BBS software such as Celerity BBS, and older versions of ICQ messaging software. | https://en.wikipedia.org/wiki/Real-time_text |
Real-time transcription is the general term for transcription by court reporters using real-time text technologies to deliver computer text screens within a few seconds of the words being spoken. Specialist software allows participants in court hearings or depositions to make notes in the text and highlight portions for future reference.
Real-time transcription is also used in the broadcasting environment where it is more commonly termed "captioning."
Real-time reporting is used in a variety of industries, including entertainment, television, the Internet, and law.
Specific careers include the following:
Before the advent of the stenotype machine, court reporters wrote official trial transcripts by hand using a shorthand system of stenoforms that could later be translated into readable English. It often took eight years of training to learn this manual form of writing at the necessary speed. Walter Heironimus was among the first stenographers to make use of the stenotype machine during his work in the U.S. District Court system in New Jersey in 1935. [ 2 ]
A "transcript crisis" arose during the later half of the twentieth century due to the increasing volume of lawsuits. There were not enough number of court reporters to match the increasing number of trials. Not only were court reporters unavailable to attend many court proceedings, court transcripts were constantly late and the qualities varied. Some believed it was due to the non-interchangeability between court reporters, and others believed it was simply due to a labor shortage. In the meantime, magnetic audiotape recording, or known as electronic recording (ER) began to threaten all reporters' job since it could record long-hour courtroom trials and replace a court reporter's position in the courtroom. As a result, machine translation (MT) intended to serve as a solution for preventing ER from potentially replacing reporters' jobs. However, MT relied heavily on human labors operating behind the system and many started to question if it should be the right way to end the "transcript crisis." Later in 1964, set up by CIA, the Automatic Language Processing Advisory Committee (ALPAC) was set to review whether MT was capable of solving this crisis. They concluded that MT had failed to do so. Then Patrick O'Neill, a skilled and experienced court reporter, stayed to work on the stenotype-translation project with CIA and developed the prototype CAT system. After adopting the CAT system in court-reporting community, CAT was brought into the television broadcasting system, aiming to provide captions for the deaf or hard-of-hearing communities. In 1983, Linda Miller developed a further use for the CAT system. She successfully translated a lecture live on the television screen and provided a transcript for students. This technique is known as Computer-Aided Real-time Translation, or CART . [ 2 ]
It is the court reporter's job to note down the exact words spoken by every participants during a court or deposition proceeding. Then court reporters will provide verbatim transcripts. The reason to have an official court transcript is that the real-time transcriptions allows attorneys and judges to have immediate access to the transcript. It also helps when there's a need to look up for information from the proceeding. Additionally, the deaf and the hard-of-hearing communities can also participate in the judicial process with the help of real-time transcriptions provided by court reporters. [ 3 ]
The required degree level for a court reporter to have is an Associate's degree or postsecondary certificate. [ 4 ]
In order to become a court reporter, more than 150 reporter training programs are provided at proprietary schools, community colleges , and four-year universities . After graduation, court reporters can choose to further pursue certifications to achieve a higher level of expertise and increase their marketability during a job search. [ 3 ] In most states, Certificates of Proficiency from the NCRA or from state agencies are now required certificates for court reporters to have in order to qualify for appointments. [ 5 ] The NCRA aims to set the national standard for the certification of court reporters, and since 1937 it has offered its certification program which is now accepted by 22 states instead of state licenses. [ 6 ]
Court reporter training programs include but not limited to: [ 7 ]
Other than official court reporters, who are assigned to and work for a particular court, other types of court reporters include free-lance reporter, who either works for a court reporting firm or self-employed. They are different from official court reporters in that they have the chances to work on a wider range of assignments and work on basis of hourly wage. Hearing reporters work at governmental agency hearings. Legislative reporters work in law-making bodies. [ 5 ] The demand for reporters is not limited in just the court settings. Reporters are also needed in conferences, meetings, conventions, investigations, [ 8 ] and a variety of industries with needs for employers with real-time data entry skills.
Transcription services are universally necessary, so it is not limited to the English language. A stenographer's ability to transcribe languages beyond only English is especially valuable as society as a whole becomes increasingly multilingual . Education in non-English transcription demands a comprehensive understanding of the given language. Phonetic differences between English and other languages are a particular challenge in carrying English transcription skills over into other languages. Stenography represents various sounds of a language in a formal system of shorthand, so differences within the sets of sounds that emerge in other languages require an alternative system of shorthand transcription. For example, the presence of many diphthongs and triphthongs in Spanish requires certain sounds to be distinguished that would not be present in transcribing English into shorthand. [ 9 ]
The usage of transcription in the context of linguistic discussions has been controversial. Typically, two kinds of linguistic records are considered to be scientifically relevant. First, linguistic records of general acoustic features, and secondly, records that only focuses on the distinctive phonemes of a language. While transcriptions are not entirely illegitimate, transcriptions without enough detailed commentary regarding any linguistic features, or transcriptions of poor quality resources, has a great chance of the content being misinterpreted. [ 10 ] Besides misinterpretation, transcribers could also bring in cultural biases and ignorance that reflect onto their transcription. [ 11 ] These instances may cause a disruption of reliability in the final real-time transcription, which could influence how the written utterance is seen as an evidence for a court-case.
Problems in the final resulting transcription can be caused by either the quality of the transcriber or the original source that is being transcribed. Transcribers can come from different levels of skill and training background. This makes the final transcription prone to poor quality, or if the transcription is being done by multiple people, lack of consistency in the content.
If the source of the transcription is a recording, the problem may root back to the quality of the recording device (mechanical failure, battery loss, etc.) or the clarity of the recording itself (background noise, poor placement of the recorder, etc.). [ 12 ]
The displaying of a dialect in transcription highlights a complication within transcription. The fundamental problem with this situation is that the transcribed product is not simply a spoken language in its written form, but a language that has been transcribed by someone other than the speaker, no matter the level of understanding the transcriber has for the spoken language. It is important to note that any transcription is an interpretation of the speech no matter how detailed it is, and will be selective in what it can include, leaves out and ultimately convey to the reader. [ 13 ] A way to supplement a transcription of dialectic speech is to provide phonetic information. However, without any knowledge on phonetic notation or a chart that serves as a key to the symbols used, the information can become irrelevant for use as a transcription. Dialects will be noted when it is well recognized, such as socially stereotyped dialects like doin' for doing .
Besides phonetic differences that may lead to misinterpretation, transcribers also have to consider the nuanced social and emotional meanings that are specific to the speaker at the time and or the culture surrounding the dialect.
The words in parentheses are considered misheard, but that can also be how the syntax works in the dialect. This example from J. Maxwell Atkinson and John Heritage (1984) shows the dilemma of doubt in accuracy of interpreting a dialect in the final transcript. [ 14 ] Court reporters also have the tendency to correct the speaker's grammar, which can also be the case if the speaker is speaking in a colloquial dialect. This can cause more doubt in the accuracy of the transcription, especially if the reporter is translating the dialect into the wrong equivalent of standard language. [ 12 ] | https://en.wikipedia.org/wiki/Real-time_transcription |
X → ℝ
In mathematics, a real-valued function is a function whose values are real numbers . In other words, it is a function that assigns a real number to each member of its domain .
Real-valued functions of a real variable (commonly called real functions ) and real-valued functions of several real variables are the main object of study of calculus and, more generally, real analysis . In particular, many function spaces consist of real-valued functions.
Let F ( X , R ) {\displaystyle {\mathcal {F}}(X,{\mathbb {R} })} be the set of all functions from a set X to real numbers R {\displaystyle \mathbb {R} } . Because R {\displaystyle \mathbb {R} } is a field , F ( X , R ) {\displaystyle {\mathcal {F}}(X,{\mathbb {R} })} may be turned into a vector space and a commutative algebra over the reals with the following operations:
These operations extend to partial functions from X to R , {\displaystyle \mathbb {R} ,} with the restriction that the partial functions f + g and f g are defined only if the domains of f and g have a nonempty intersection; in this case, their domain is the intersection of the domains of f and g .
Also, since R {\displaystyle \mathbb {R} } is an ordered set, there is a partial order
on F ( X , R ) , {\displaystyle {\mathcal {F}}(X,{\mathbb {R} }),} which makes F ( X , R ) {\displaystyle {\mathcal {F}}(X,{\mathbb {R} })} a partially ordered ring .
The σ-algebra of Borel sets is an important structure on real numbers. If X has its σ-algebra and a function f is such that the preimage f −1 ( B ) of any Borel set B belongs to that σ-algebra, then f is said to be measurable . Measurable functions also form a vector space and an algebra as explained above in § Algebraic structure .
Moreover, a set (family) of real-valued functions on X can actually define a σ-algebra on X generated by all preimages of all Borel sets (or of intervals only, it is not important). This is the way how σ-algebras arise in ( Kolmogorov's ) probability theory , where real-valued functions on the sample space Ω are real-valued random variables .
Real numbers form a topological space and a complete metric space . Continuous real-valued functions (which implies that X is a topological space) are important in theories of topological spaces and of metric spaces . The extreme value theorem states that for any real continuous function on a compact space its global maximum and minimum exist.
The concept of metric space itself is defined with a real-valued function of two variables, the metric , which is continuous. The space of continuous functions on a compact Hausdorff space has a particular importance. Convergent sequences also can be considered as real-valued continuous functions on a special topological space.
Continuous functions also form a vector space and an algebra as explained above in § Algebraic structure , and are a subclass of measurable functions because any topological space has the σ-algebra generated by open (or closed) sets.
Real numbers are used as the codomain to define smooth functions. A domain of a real smooth function can be the real coordinate space (which yields a real multivariable function ), a topological vector space , [ 1 ] an open subset of them, or a smooth manifold .
Spaces of smooth functions also are vector spaces and algebras as explained above in § Algebraic structure and are subspaces of the space of continuous functions .
A measure on a set is a non-negative real-valued functional on a σ-algebra of subsets. [ 2 ] L p spaces on sets with a measure are defined from aforementioned real-valued measurable functions , although they are actually quotient spaces . More precisely, whereas a function satisfying an appropriate summability condition defines an element of L p space, in the opposite direction for any f ∈ L p ( X ) and x ∈ X which is not an atom , the value f ( x ) is undefined . Though, real-valued L p spaces still have some of the structure described above in § Algebraic structure . Each of L p spaces is a vector space and have a partial order, and there exists a pointwise multiplication of "functions" which changes p , namely
For example, pointwise product of two L 2 functions belongs to L 1 .
Other contexts where real-valued functions and their special properties are used include monotonic functions (on ordered sets ), convex functions (on vector and affine spaces ), harmonic and subharmonic functions (on Riemannian manifolds ), analytic functions (usually of one or more real variables), algebraic functions (on real algebraic varieties ), and polynomials (of one or more real variables).
Weisstein, Eric W. "Real Function" . MathWorld . | https://en.wikipedia.org/wiki/Real-valued_function |
RealNames was a company founded in 1997 by Keith Teare . Its goal was to create a multilingual keyword-based naming system for the Internet that would translate keywords typed into the address bar of Microsoft's Internet Explorer web browser to Uniform Resource Identifiers , based on the existing Domain Name System , that would access the page registered by the owner of the RealNames keyword.
In effect, to users of Internet Explorer, RealNames became a domain registry which was capable of registering names that worked without needing to belong to a top-level domain such as ".com" or ".net". RealNames and its backers expected this to be a lucrative source of income, and it raised more than $130 million of funding.
RealNames depended on its partnership with Microsoft, which offered the RealNames service on Internet Explorer. RealNames shut down operations in 2002 following a decision by Microsoft to redirect the 1 billion page views per calendar quarter that RealNames was resolving from the browser address bar into the MSN search engine .
In 2014, Tucows purchased RealNames.com. The domain now hosts a customized e-mail service, made possible by its acquisition of Mailbank and its long list of surname domain names. [ 1 ]
This computing article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/RealNames |
The Real Time Information Group (also RTI ) is an organisation in the United Kingdom supporting the development of bus passenger information systems ; its 45 members include local authorities , bus operators, consultants and system suppliers together with representatives from the UK government . [ 1 ]
The main output of the group is guidelines, standards, case studies and best practice documents. [ 2 ] These documents are produced by RTIG on behalf of its members, usually with the assistance of specialist working groups.
In 2000, when real-time information (RTI) systems were beginning to be considered by UK local authorities to provide travellers with up-to-the-minute bus arrival and departure passenger information, it was realised that cross-boundary bus services made it imperative to coordinate projects around the UK. Technical and operational standards would therefore be required. A group of local authorities and bus operators began to meet regularly to discuss how to achieve this; and so RTIG was born.
Substantial government funding for projects around the UK, in particular from 2002 to 2004, provided an enormous boost to the development of RTI systems. The expanding and maturing market caused RTIG to reflect on its role, and in 2003 it determined to recreate itself as a subscription group - with the important step that the systems industry was to be a full and equal partner in its work. Equally importantly, it has maintained excellent links with central UK Government, from whom the Group continues to receive project funding for work of national scope and importance.
The National RTI Strategy, [ 3 ] ratified in March 2007, establishes a framework for how industry stakeholders and government need to work together to deliver benefit to passengers. RTIG's role has, as a consequence, been expanded to cover all aspects of technology in public transport, from systems to support disabled travellers through to safety and security systems.
In 2002 the group produced the first UK Annual RTI Survey, which surveyed the use of RTI technology by local authorities and passenger transport executives across England , as well as plans for the following two years. In 2004 the survey was extended to include Wales and in 2005 Scotland .
In order to reflect the widening deployment of bus-related technologies, the 2006 annual survey was re-branded as the ‘RTIG Passenger Transport Technology Survey’ and included questions on services for disabled travellers – partly in response to new obligations on bus operators under the Disability Discrimination Act 2005 . The 2007 survey continues to focus broadly on public transport and traffic management technology and has been expanded to include questions on bus CCTV and other security technologies.
The annual survey provides details on:
The annual survey has been discontinued with the last being carried out in 2012.
The majority of the documents, standards and guidelines produced by RTIG is done with the assistance of voluntary working groups. These working groups are made up of industry experts who lend their knowledge to particular projects. Examples of RTIG working groups include:
Working groups involve non-members where relevant; so, the Disability WG includes representatives from charities such a RNIB and Guide Dogs .
The RTIG library houses all of the documents produced by the group to date. These documents are held by RTIG electronically and distributed to members on request, or via the ‘members area’ of the RTIG website. The library catalogue is publicly available from the RTIG website [1] .
Publicly available documents in the Library include:
Members have access to a wider range of standards and guidelines, and to the outputs of RTIG workshops (see below).
The group also publishes a monthly newsletter [8] which provides both members and non-members with news on RTIG projects and events.
RTIG runs regular workshops , which are held at a different UK venue each time. Each workshop has a central theme and attract presentations from a wide variety of stakeholders. Workshops will include an update on ITS news, an update on RTIG projects and working group activities, and a set of presentations based around the workshop theme.
Previous workshop venues (and their respective themes) include [9] :
RTIG have assisted in the development of a number of standards, including the Service Interface for Real Time Information (SIRI). RTIG have also developed a number of best practice guidelines . | https://en.wikipedia.org/wiki/Real_Time_Information_Group |
Real World Records is a British record label specializing in world music . It was founded in 1989 by English musician Peter Gabriel and original members of WOMAD . [ 3 ] A majority of the works released on Real World Records feature music recorded at Real World Studios , in Box, Wiltshire , England.
The goal of its founding in 1989 was to give talented musicians from around the world access to state-of-the-art recording facilities and audiences beyond their geographic region. The musical relationships formed at WOMAD festivals were also intended to lead to new music recordings. As a result, the music label is known for bringing together musicians who share a common interest in music in general. New recording methods and new meeting places are created. [ 4 ]
In 1999, the label had sold over 3 million records worldwide and released 90 albums. [ 5 ] In 2015, it had reached the mark of over 200 albums. [ 3 ]
Many of the released recordings continue to be made at Real World Studios , also founded in 1989, whose facilities support the goals of Real World Records. [ 4 ]
In 2011, EMI Music Publishing renewed the distribution deal for the Real World catalogue outside of the United Kingdom, thereby also covering the United States for the first time. [ 6 ] | https://en.wikipedia.org/wiki/Real_World_Records |
In mathematics , a real closed ring ( RCR ) is a commutative ring A that is a subring of a product of real closed fields , which is closed under continuous semi-algebraic functions defined over the integers .
Since the rigorous definition of a real closed ring is of technical nature it is convenient to see a list of prominent examples first. The following rings are all real closed rings:
A real closed ring is a reduced, commutative unital ring A which has the following properties:
The link to the definition at the beginning of this article is given in the section on algebraic properties below.
Every commutative unital ring R has a so-called real closure rcl( R ) and this is unique up to a unique ring homomorphism over R . This means that rcl( R ) is a real closed ring and there is a (not necessarily injective ) ring homomorphism r : R → r c l ( R ) {\displaystyle r:R\to rcl(R)} such that for every ring homomorphism f : R → A {\displaystyle f:R\to A} to some other real closed ring A , there is a unique ring homomorphism g : r c l ( R ) → A {\displaystyle g:rcl(R)\to A} with f = g ∘ r {\displaystyle f=g\circ r} .
For example, the real closure of the polynomial ring R [ T 1 , . . . , T n ] {\displaystyle \mathbb {R} [T_{1},...,T_{n}]} is the ring of continuous semi-algebraic functions R n → R {\displaystyle \mathbb {R} ^{n}\to \mathbb {R} } .
An arbitrary ring R is semi-real (i.e. −1 is not a sum of squares in R ) if and only if the real closure of R is not the null ring.
The real closure of an ordered field is in general not the real closure of the underlying field. For example, the real closure of the ordered subfield Q ( 2 ) {\displaystyle \mathbb {Q} ({\sqrt {2}})} of R {\displaystyle \mathbb {R} } is the field R a l g {\displaystyle \mathbb {R} _{alg}} of real algebraic numbers , whereas the real closure of the field Q ( 2 ) {\displaystyle \mathbb {Q} ({\sqrt {2}})} is the ring R a l g × R a l g {\displaystyle \mathbb {R} _{alg}\times \mathbb {R} _{alg}} (corresponding to the two orders of Q ( 2 ) {\displaystyle \mathbb {Q} ({\sqrt {2}})} ). More generally the real closure of a field F is a certain subdirect product of the real closures of the ordered fields ( F , P ), where P runs through the orderings of F .
The class of real closed rings is first-order axiomatizable and undecidable . The class of all real closed valuation rings is decidable (by Cherlin-Dickmann) and the class of all real closed fields is decidable (by Tarski). After naming a definable radical relation, real closed rings have a model companion , namely von Neumann regular real closed rings.
There are many different characterizations of real closed fields . For example,
in terms of maximality (with respect to algebraic extensions): a real closed field is a maximally orderable field; or, a real closed field (together with its unique ordering) is a maximally ordered field. Another characterization says that the intermediate value theorem holds for all polynomials in one variable over the (ordered) field. In the case of commutative rings, all these properties can be (and are) analyzed in the literature. They all lead to different classes of rings which are unfortunately also called "real closed" (because a certain characterization of real closed fields has been extended to rings). None of them lead to the class of real closed rings and none of them allow a satisfactory notion of a closure operation. A central point in the definition of real closed rings is the globalisation of the notion of a real closed field to rings when these rings are represented as rings of functions on some space (typically, the real spectrum of the ring). | https://en.wikipedia.org/wiki/Real_closed_ring |
In mathematics , the real coordinate space or real coordinate n -space , of dimension n , denoted R n or R n {\displaystyle \mathbb {R} ^{n}} , is the set of all ordered n -tuples of real numbers , that is the set of all sequences of n real numbers, also known as coordinate vectors .
Special cases are called the real line R 1 , the real coordinate plane R 2 , and the real coordinate three-dimensional space R 3 .
With component-wise addition and scalar multiplication, it is a real vector space .
The coordinates over any basis of the elements of a real vector space form a real coordinate space of the same dimension as that of the vector space. Similarly, the Cartesian coordinates of the points of a Euclidean space of dimension n , E n ( Euclidean line , E ; Euclidean plane , E 2 ; Euclidean three-dimensional space , E 3 ) form a real coordinate space of dimension n .
These one to one correspondences between vectors, points and coordinate vectors explain the names of coordinate space and coordinate vector . It allows using geometric terms and methods for studying real coordinate spaces, and, conversely, to use methods of calculus in geometry. This approach of geometry was introduced by René Descartes in the 17th century. It is widely used, as it allows locating points in Euclidean spaces, and computing with them.
For any natural number n , the set R n consists of all n - tuples of real numbers ( R ). It is called the " n -dimensional real space" or the "real n -space".
An element of R n is thus a n -tuple, and is written ( x 1 , x 2 , … , x n ) {\displaystyle (x_{1},x_{2},\ldots ,x_{n})} where each x i is a real number. So, in multivariable calculus , the domain of a function of several real variables and the codomain of a real vector valued function are subsets of R n for some n .
The real n -space has several further properties, notably:
These properties and structures of R n make it fundamental in almost all areas of mathematics and their application domains, such as statistics , probability theory , and many parts of physics .
Any function f ( x 1 , x 2 , ..., x n ) of n real variables can be considered as a function on R n (that is, with R n as its domain ). The use of the real n -space, instead of several variables considered separately, can simplify notation and suggest reasonable definitions. Consider, for n = 2 , a function composition of the following form: F ( t ) = f ( g 1 ( t ) , g 2 ( t ) ) , {\displaystyle F(t)=f(g_{1}(t),g_{2}(t)),} where functions g 1 and g 2 are continuous . If
then F is not necessarily continuous. Continuity is a stronger condition: the continuity of f in the natural R 2 topology ( discussed below ), also called multivariable continuity , which is sufficient for continuity of the composition F .
The coordinate space R n forms an n -dimensional vector space over the field of real numbers with the addition of the structure of linearity , and is often still denoted R n . The operations on R n as a vector space are typically defined by x + y = ( x 1 + y 1 , x 2 + y 2 , … , x n + y n ) {\displaystyle \mathbf {x} +\mathbf {y} =(x_{1}+y_{1},x_{2}+y_{2},\ldots ,x_{n}+y_{n})} α x = ( α x 1 , α x 2 , … , α x n ) . {\displaystyle \alpha \mathbf {x} =(\alpha x_{1},\alpha x_{2},\ldots ,\alpha x_{n}).} The zero vector is given by 0 = ( 0 , 0 , … , 0 ) {\displaystyle \mathbf {0} =(0,0,\ldots ,0)} and the additive inverse of the vector x is given by − x = ( − x 1 , − x 2 , … , − x n ) . {\displaystyle -\mathbf {x} =(-x_{1},-x_{2},\ldots ,-x_{n}).}
This structure is important because any n -dimensional real vector space is isomorphic to the vector space R n .
In standard matrix notation, each element of R n is typically written as a column vector x = [ x 1 x 2 ⋮ x n ] {\displaystyle \mathbf {x} ={\begin{bmatrix}x_{1}\\x_{2}\\\vdots \\x_{n}\end{bmatrix}}} and sometimes as a row vector : x = [ x 1 x 2 ⋯ x n ] . {\displaystyle \mathbf {x} ={\begin{bmatrix}x_{1}&x_{2}&\cdots &x_{n}\end{bmatrix}}.}
The coordinate space R n may then be interpreted as the space of all n × 1 column vectors , or all 1 × n row vectors with the ordinary matrix operations of addition and scalar multiplication .
Linear transformations from R n to R m may then be written as m × n matrices which act on the elements of R n via left multiplication (when the elements of R n are column vectors) and on elements of R m via right multiplication (when they are row vectors). The formula for left multiplication, a special case of matrix multiplication , is: ( A x ) k = ∑ l = 1 n A k l x l {\displaystyle (A{\mathbf {x} })_{k}=\sum _{l=1}^{n}A_{kl}x_{l}}
Any linear transformation is a continuous function (see below ). Also, a matrix defines an open map from R n to R m if and only if the rank of the matrix equals to m .
The coordinate space R n comes with a standard basis: e 1 = ( 1 , 0 , … , 0 ) e 2 = ( 0 , 1 , … , 0 ) ⋮ e n = ( 0 , 0 , … , 1 ) {\displaystyle {\begin{aligned}\mathbf {e} _{1}&=(1,0,\ldots ,0)\\\mathbf {e} _{2}&=(0,1,\ldots ,0)\\&{}\;\;\vdots \\\mathbf {e} _{n}&=(0,0,\ldots ,1)\end{aligned}}}
To see that this is a basis, note that an arbitrary vector in R n can be written uniquely in the form x = ∑ i = 1 n x i e i . {\displaystyle \mathbf {x} =\sum _{i=1}^{n}x_{i}\mathbf {e} _{i}.}
The fact that real numbers , unlike many other fields , constitute an ordered field yields an orientation structure on R n . Any full-rank linear map of R n to itself either preserves or reverses orientation of the space depending on the sign of the determinant of its matrix. If one permutes coordinates (or, in other words, elements of the basis), the resulting orientation will depend on the parity of the permutation .
Diffeomorphisms of R n or domains in it , by their virtue to avoid zero Jacobian , are also classified to orientation-preserving and orientation-reversing. It has important consequences for the theory of differential forms , whose applications include electrodynamics .
Another manifestation of this structure is that the point reflection in R n has different properties depending on evenness of n . For even n it preserves orientation, while for odd n it is reversed (see also improper rotation ).
R n understood as an affine space is the same space, where R n as a vector space acts by translations . Conversely, a vector has to be understood as a " difference between two points", usually illustrated by a directed line segment connecting two points. The distinction says that there is no canonical choice of where the origin should go in an affine n -space, because it can be translated anywhere.
In a real vector space, such as R n , one can define a convex cone , which contains all non-negative linear combinations of its vectors. Corresponding concept in an affine space is a convex set , which allows only convex combinations (non-negative linear combinations that sum to 1).
In the language of universal algebra , a vector space is an algebra over the universal vector space R ∞ of finite sequences of coefficients, corresponding to finite sums of vectors, while an affine space is an algebra over the universal affine hyperplane in this space (of finite sequences summing to 1), a cone is an algebra over the universal orthant (of finite sequences of nonnegative numbers), and a convex set is an algebra over the universal simplex (of finite sequences of nonnegative numbers summing to 1). This geometrizes the axioms in terms of "sums with (possible) restrictions on the coordinates".
Another concept from convex analysis is a convex function from R n to real numbers, which is defined through an inequality between its value on a convex combination of points and sum of values in those points with the same coefficients.
The dot product x ⋅ y = ∑ i = 1 n x i y i = x 1 y 1 + x 2 y 2 + ⋯ + x n y n {\displaystyle \mathbf {x} \cdot \mathbf {y} =\sum _{i=1}^{n}x_{i}y_{i}=x_{1}y_{1}+x_{2}y_{2}+\cdots +x_{n}y_{n}} defines the norm | x | = √ x ⋅ x on the vector space R n . If every vector has its Euclidean norm , then for any pair of points the distance d ( x , y ) = ‖ x − y ‖ = ∑ i = 1 n ( x i − y i ) 2 {\displaystyle d(\mathbf {x} ,\mathbf {y} )=\|\mathbf {x} -\mathbf {y} \|={\sqrt {\sum _{i=1}^{n}(x_{i}-y_{i})^{2}}}} is defined, providing a metric space structure on R n in addition to its affine structure.
As for vector space structure, the dot product and Euclidean distance usually are assumed to exist in R n without special explanations. However, the real n -space and a Euclidean n -space are distinct objects, strictly speaking. Any Euclidean n -space has a coordinate system where the dot product and Euclidean distance have the form shown above, called Cartesian . But there are many Cartesian coordinate systems on a Euclidean space.
Conversely, the above formula for the Euclidean metric defines the standard Euclidean structure on R n , but it is not the only possible one. Actually, any positive-definite quadratic form q defines its own "distance" √ q ( x − y ) , but it is not very different from the Euclidean one in the sense that ∃ C 1 > 0 , ∃ C 2 > 0 , ∀ x , y ∈ R n : C 1 d ( x , y ) ≤ q ( x − y ) ≤ C 2 d ( x , y ) . {\displaystyle \exists C_{1}>0,\ \exists C_{2}>0,\ \forall \mathbf {x} ,\mathbf {y} \in \mathbb {R} ^{n}:C_{1}d(\mathbf {x} ,\mathbf {y} )\leq {\sqrt {q(\mathbf {x} -\mathbf {y} )}}\leq C_{2}d(\mathbf {x} ,\mathbf {y} ).} Such a change of the metric preserves some of its properties, for example the property of being a complete metric space .
This also implies that any full-rank linear transformation of R n , or its affine transformation , does not magnify distances more than by some fixed C 2 , and does not make distances smaller than 1 / C 1 times, a fixed finite number times smaller. [ clarification needed ]
The aforementioned equivalence of metric functions remains valid if √ q ( x − y ) is replaced with M ( x − y ) , where M is any convex positive homogeneous function of degree 1, i.e. a vector norm (see Minkowski distance for useful examples). Because of this fact that any "natural" metric on R n is not especially different from the Euclidean metric, R n is not always distinguished from a Euclidean n -space even in professional mathematical works.
Although the definition of a manifold does not require that its model space should be R n , this choice is the most common, and almost exclusive one in differential geometry .
On the other hand, Whitney embedding theorems state that any real differentiable m -dimensional manifold can be embedded into R 2 m .
Other structures considered on R n include the one of a pseudo-Euclidean space , symplectic structure (even n ), and contact structure (odd n ). All these structures, although can be defined in a coordinate-free manner, admit standard (and reasonably simple) forms in coordinates.
R n is also a real vector subspace of C n which is invariant to complex conjugation ; see also complexification .
There are three families of polytopes which have simple representations in R n spaces, for any n , and can be used to visualize any affine coordinate system in a real n -space. Vertices of a hypercube have coordinates ( x 1 , x 2 , ..., x n ) where each x k takes on one of only two values, typically 0 or 1. However, any two numbers can be chosen instead of 0 and 1, for example −1 and 1. An n -hypercube can be thought of as the Cartesian product of n identical intervals (such as the unit interval [0,1] ) on the real line. As an n -dimensional subset it can be described with a system of 2 n inequalities : 0 ≤ x 1 ≤ 1 ⋮ 0 ≤ x n ≤ 1 {\displaystyle {\begin{matrix}0\leq x_{1}\leq 1\\\vdots \\0\leq x_{n}\leq 1\end{matrix}}} for [0,1] , and | x 1 | ≤ 1 ⋮ | x n | ≤ 1 {\displaystyle {\begin{matrix}|x_{1}|\leq 1\\\vdots \\|x_{n}|\leq 1\end{matrix}}} for [−1,1] .
Each vertex of the cross-polytope has, for some k , the x k coordinate equal to ±1 and all other coordinates equal to 0 (such that it is the k th standard basis vector up to sign ). This is a dual polytope of hypercube. As an n -dimensional subset it can be described with a single inequality which uses the absolute value operation: ∑ k = 1 n | x k | ≤ 1 , {\displaystyle \sum _{k=1}^{n}|x_{k}|\leq 1\,,} but this can be expressed with a system of 2 n linear inequalities as well.
The third polytope with simply enumerable coordinates is the standard simplex , whose vertices are n standard basis vectors and the origin (0, 0, ..., 0) . As an n -dimensional subset it is described with a system of n + 1 linear inequalities: 0 ≤ x 1 ⋮ 0 ≤ x n ∑ k = 1 n x k ≤ 1 {\displaystyle {\begin{matrix}0\leq x_{1}\\\vdots \\0\leq x_{n}\\\sum \limits _{k=1}^{n}x_{k}\leq 1\end{matrix}}} Replacement of all "≤" with "<" gives interiors of these polytopes.
The topological structure of R n (called standard topology , Euclidean topology , or usual topology ) can be obtained not only from Cartesian product . It is also identical to the natural topology induced by Euclidean metric discussed above : a set is open in the Euclidean topology if and only if it contains an open ball around each of its points. Also, R n is a linear topological space (see continuity of linear maps above), and there is only one possible (non-trivial) topology compatible with its linear structure. As there are many open linear maps from R n to itself which are not isometries , there can be many Euclidean structures on R n which correspond to the same topology. Actually, it does not depend much even on the linear structure: there are many non-linear diffeomorphisms (and other homeomorphisms) of R n onto itself, or its parts such as a Euclidean open ball or the interior of a hypercube ).
R n has the topological dimension n .
An important result on the topology of R n , that is far from superficial, is Brouwer 's invariance of domain . Any subset of R n (with its subspace topology ) that is homeomorphic to another open subset of R n is itself open. An immediate consequence of this is that R m is not homeomorphic to R n if m ≠ n – an intuitively "obvious" result which is nonetheless difficult to prove.
Despite the difference in topological dimension, and contrary to a naïve perception, it is possible to map a lesser-dimensional [ clarification needed ] real space continuously and surjectively onto R n . A continuous (although not smooth) space-filling curve (an image of R 1 ) is possible. [ clarification needed ]
Cases of 0 ≤ n ≤ 1 do not offer anything new: R 1 is the real line , whereas R 0 (the space containing the empty column vector) is a singleton , understood as a zero vector space . However, it is useful to include these as trivial cases of theories that describe different n .
The case of ( x,y ) where x and y are real numbers has been developed as the Cartesian plane P . Further structure has been attached with Euclidean vectors representing directed line segments in P . The plane has also been developed as the field extension C {\displaystyle \mathbf {C} } by appending roots of X 2 + 1 = 0 to the real field R . {\displaystyle \mathbf {R} .} The root i acts on P as a quarter turn with counterclockwise orientation. This root generates the group { i , − 1 , − i , + 1 } ≡ Z / 4 Z {\displaystyle \{i,-1,-i,+1\}\equiv \mathbf {Z} /4\mathbf {Z} } . When ( x,y ) is written x + y i it is a complex number .
Another group action by Z / 2 Z {\displaystyle \mathbf {Z} /2\mathbf {Z} } , where the actor has been expressed as j, uses the line y = x for the involution of flipping the plane ( x,y ) ↦ ( y,x ), an exchange of coordinates. In this case points of P are written x + y j and called split-complex numbers . These numbers, with the coordinate-wise addition and multiplication according to jj =+1, form a ring that is not a field.
Another ring structure on P uses a nilpotent e to write x + y e for ( x,y ). The action of e on P reduces the plane to a line: It can be decomposed into the projection into the x-coordinate, then quarter-turning the result to the y-axis: e ( x + y e) = x e since e 2 = 0. A number x + y e is a dual number . The dual numbers form a ring, but, since e has no multiplicative inverse, it does not generate a group so the action is not a group action.
Excluding (0,0) from P makes [ x : y ] projective coordinates which describe the real projective line, a one-dimensional space. Since the origin is excluded, at least one of the ratios x / y and y / x exists. Then [ x : y ] = [ x / y : 1] or [ x : y ] = [1 : y / x ]. The projective line P 1 ( R ) is a topological manifold covered by two coordinate charts , [ z : 1] → z or [1 : z ] → z , which form an atlas . For points covered by both charts the transition function is multiplicative inversion on an open neighborhood of the point, which provides a homeomorphism as required in a manifold. One application of the real projective line is found in Cayley–Klein metric geometry.
R 4 can be imagined using the fact that 16 points ( x 1 , x 2 , x 3 , x 4 ) , where each x k is either 0 or 1, are vertices of a tesseract (pictured), the 4-hypercube (see above ).
The first major use of R 4 is a spacetime model: three spatial coordinates plus one temporal . This is usually associated with theory of relativity , although four dimensions were used for such models since Galilei . The choice of theory leads to different structure, though: in Galilean relativity the t coordinate is privileged, but in Einsteinian relativity it is not. Special relativity is set in Minkowski space . General relativity uses curved spaces, which may be thought of as R 4 with a curved metric for most practical purposes. None of these structures provide a (positive-definite) metric on R 4 .
Euclidean R 4 also attracts the attention of mathematicians, for example due to its relation to quaternions , a 4-dimensional real algebra themselves. See rotations in 4-dimensional Euclidean space for some information.
In differential geometry, n = 4 is the only case where R n admits a non-standard differential structure : see exotic R 4 .
One could define many norms on the vector space R n . Some common examples are
A really surprising and helpful result is that every norm defined on R n is equivalent . This means for two arbitrary norms ‖ ⋅ ‖ {\displaystyle \|\cdot \|} and ‖ ⋅ ‖ ′ {\displaystyle \|\cdot \|'} on R n you can always find positive real numbers α , β > 0 {\displaystyle \alpha ,\beta >0} , such that α ⋅ ‖ x ‖ ≤ ‖ x ‖ ′ ≤ β ⋅ ‖ x ‖ {\displaystyle \alpha \cdot \|\mathbf {x} \|\leq \|\mathbf {x} \|'\leq \beta \cdot \|\mathbf {x} \|} for all x ∈ R n {\displaystyle \mathbf {x} \in \mathbb {R} ^{n}} .
This defines an equivalence relation on the set of all norms on R n . With this result you can check that a sequence of vectors in R n converges with ‖ ⋅ ‖ {\displaystyle \|\cdot \|} if and only if it converges with ‖ ⋅ ‖ ′ {\displaystyle \|\cdot \|'} .
Here is a sketch of what a proof of this result may look like:
Because of the equivalence relation it is enough to show that every norm on R n is equivalent to the Euclidean norm ‖ ⋅ ‖ 2 {\displaystyle \|\cdot \|_{2}} . Let ‖ ⋅ ‖ {\displaystyle \|\cdot \|} be an arbitrary norm on R n . The proof is divided in two steps: | https://en.wikipedia.org/wiki/Real_coordinate_space |
A real data type is a data type used in a computer program to represent an approximation of a real number . Because the real numbers are not countable , computers cannot represent them exactly using a finite amount of information. Most often, a computer will use a rational approximation to a real number.
The most general data type for a rational number (a number that can be expressed as a fraction) stores the numerator and the denominator as integers . For example 1/3, which can be calculated to any desired precision. Rational number are used, for example, in Interpress from Xerox Corporation . [ 1 ]
A fixed-point data type uses the same, implied, denominator for all numbers. The denominator is usually a power of two . For example, in a hypothetical fixed-point system that uses the denominator 65,536 (2 16 ), the hexadecimal number 0x12345678 (0x1234.5678 with sixteen fractional bits to the right of the assumed radix point ) means 0x12345678/65536 or 305419896/65536, 4660 + the fractional value 22136/65536, or about 4660.33777. An integer is a fixed-point number with a fractional part of zero.
A floating-point data type is a compromise between the flexibility of a general rational number data type and the speed of fixed-point arithmetic. It uses some of the bits in the data type to specify an exponent for the denominator, today usually power of two although both ten and sixteen have been used. [ 2 ]
The decimal type is similar to fixed-point or floating-point data type, but with a denominator that is a power of 10 instead of a power of 2. | https://en.wikipedia.org/wiki/Real_data_type |
Real estate development , or property development , is a business process , encompassing activities that range from the renovation and re- lease of existing buildings to the purchase of raw land and the sale of developed land or parcels to others. Real estate developers are the people and companies who coordinate all of these activities, converting ideas from paper to real property . [ 1 ] Real estate development is different from construction or housebuilding , although many developers also manage the construction process or engage in housebuilding.
Developers buy land, finance real estate deals, build or have builders build projects, develop projects in joint ventures, and create, imagine, control, and orchestrate the process of development from beginning to end. [ 2 ] Developers usually take the greatest risk in the creation or renovation of real estate and receive the greatest rewards. Typically, developers purchase a tract of land, determine the marketing of the property, develop the building program and design, obtain the necessary public approval and financing, build the structures, and rent out, manage, and ultimately sell it. [ 1 ]
Sometimes property developers will only undertake part of the process. For example, some developers source a property and get the plans and permits approved before selling the property with the plans and permits to a builder at a premium price. Alternatively, a developer who is also a builder may purchase a property with the plans and permits in place so that they do not have the risk of failing to obtain planning approval and can start construction on the development immediately. The financial risks of real estate development and real estate investing differ due to leverage effects. [ 3 ]
Developers work with many different counterparts along each step of this process, including architects, city planners, engineers, surveyors, inspectors, contractors, lawyers, leasing agents, etc. In the Town and Country Planning context in the United Kingdom, 'development' is defined in the Town and Country Planning Act 1990 s55.
A development team can be put together in one of several ways. At one extreme, a large company might include many services, from architecture to engineering . At the other end of the spectrum, a development company might consist of one principal and a few staff who hire or contract with other companies and professionals for each service as needed.
Assembling a team of professionals to address the environmental, economic, private, physical and political issues inherent in a complex development project is critical. A developer's success depends on the ability to coordinate and lead the completion of a series of interrelated activities efficiently and at the appropriate time. [ 4 ]
Development process requires skills of many professionals: architects , landscape architects , civil engineers and site planners to address project design; market consultants to determine demand and a project's economics ; attorneys to handle agreements and government approvals ; environmental consultants and soils engineers to analyze a site's physical limitations and environmental impacts ; surveyors and title companies to provide legal descriptions of a property; and lenders to provide financing. The general contractor of the project hires subcontractors to put the architectural plans into action.
Purchasing unused land for a potential development is sometimes called speculative development .
Subdivision of land is the principal mechanism by which communities are developed. Technically, subdivision describes the legal and physical steps a developer must take to convert raw land into developed land. Subdivision is a vital part of a community's growth, determining its appearance, the mix of its land uses , and its infrastructure, including roads , drainage systems, water , sewerage , and public utilities .
Land development can pose the most risk, but can also be the most profitable technique as it is dependent on the public sector for approvals and infrastructure and because it involves a long investment period with no positive cash flow .
After subdivision is complete, the developer usually markets the land to a home builder or other end user, for such uses as a warehouse or shopping center . In any case, use of spatial intelligence tools mitigate the risk of these developers by modeling the population trends and demographic make-up of the sort of customers a home builder or retailer would like to have surrounding their new development. [ 5 ] | https://en.wikipedia.org/wiki/Real_estate_development |
Real options valuation , also often termed real options analysis , [ 1 ] ( ROV or ROA ) applies option valuation techniques to capital budgeting decisions. [ 2 ] A real option itself, is the right—but not the obligation—to undertake certain business initiatives, such as deferring, abandoning, expanding, staging, or contracting a capital investment project . [ 3 ] For example, real options valuation could examine the opportunity to invest in the expansion of a firm's factory and the alternative option to sell the factory. [ 4 ] Real options are most valuable when uncertainty is high; management has significant flexibility to change the course of the project in a favorable direction and is willing to exercise the options. [ 5 ]
Real options are generally distinguished from conventional financial options in that they are not typically traded as securities, and do not usually involve decisions on an underlying asset that is traded as a financial security. [ 6 ] A further distinction is that option holders here, i.e. management, can directly influence the value of the option's underlying project; whereas this is not a consideration regarding the underlying security of a financial option. Moreover, management cannot measure uncertainty in terms of volatility , and must instead rely on their perceptions of uncertainty. Unlike financial options, management must also create or discover real options, and such creation and discovery process comprises an entrepreneurial or business task.
Real options analysis, as a discipline, extends from its application in corporate finance , to decision making under uncertainty in general, adapting the techniques developed for financial options to "real-life" decisions. For example, R&D managers can use real options valuation to help them deal with various uncertainties in making decisions about the allocation of resources among R&D projects. [ 7 ] [ 8 ] [ 9 ] [ 10 ] Non-business examples might be evaluating the cost of cryptocurrency mining machines, [ 11 ] or the decision to join the work force, or rather, to forgo several years of income to attend graduate school . [ 12 ] It, thus, forces decision makers to be explicit about the assumptions underlying their projections, and for this reason ROV is increasingly employed as a tool in business strategy formulation. [ 13 ] [ 14 ] [ 15 ] This extension of real options to real-world projects often requires customized decision support systems , because otherwise the complex compound real options will become too intractable to handle. [ 16 ]
This simple example shows the relevance of the real option to delay investment and wait for further information. [ 17 ]
Consider a firm that has the option to invest in a new factory. It can invest this year or next year. The question is: when should the firm invest? If the firm invests this year, it has an income stream earlier. But, if it invests next year, the firm obtains further information about the state of the economy, which can prevent it from investing with losses. [ 17 ]
The firm knows its discounted cash flows if it invests this year: 5M. If it invests next year, the discounted cash flows are 6M with a 66.7% probability, and 3M with a 33.3% probability. Assuming a risk neutral rate of 10%, future discounted cash flows are, in present terms, 5.45M and 2.73M, respectively. The investment cost is 4M. If the firm invests next year, the present value of the investment cost is 3.63M. [ 17 ]
Following the net present value rule for investment, the firm should invest this year because the discounted cash flows (5M) are greater than the investment costs (4M) by 1M. Yet, if the firm waits for next year, it only invests if discounted cash flows do not decrease. If discounted cash flows decrease to 3M, then investment is no longer profitable. If, they grow to 6M, then the firm invests. This implies that the firm invests next year with a 66.7% probability and earns 5.45M - 3.63M if it does invest. Thus the value to invest next year is 1.21M. Given that the value to invest next year exceeds the value to invest this year, the firm should wait for further information to prevent losses. This simple example shows how the net present value may lead the firm to take unnecessary risk, which could be prevented by real options valuation. [ 17 ] Staged Investment Staged investments are quite often in the pharmaceutical, mineral, and oil industries. In this example, it is studied a staged investment abroad in which a firm decides whether to open one or two stores in a foreign country. [ 18 ]
The firm does not know how well its stores are accepted in a foreign country. If their stores have high demand, the discounted cash flows per store is 10M. If their stores have low demand, the discounted cash flows per store is 5M. Assuming that the probability of both events is 50%, the expected discounted cash flows per store is 7.5M. It is also known that if the store's demand is independent of the store: if one store has high demand, the other also has high demand. The risk neutral rate is 10%. The investment cost per store is 8M. [ 18 ]
Should the firm invest in one store, two stores, or not invest? The net present value suggests the firm should not invest: the net present value is -0.5M per store. But is it the best alternative? Following real options valuation, it is not: the firm has the real option to open one store this year, wait a year to know its demand, and invest in the new store next year if demand is high. [ 18 ]
By opening one store, the firm knows that the probability of high demand is 50%. The expected value today of the option of expanding next year is thus 50% * (10M - 8M) / (1 + 10%) = 0.91M. The value of opening one store this year is 7.5M - 8M = -0.5M. Thus the value of the real option to invest in one store, wait a year, and invest next year is 0.41M. Given this, the firm should opt by opening one store. This simple example shows that a negative net present value does not imply that the firm should not invest. [ 18 ]
The flexibility available to management – i.e. the actual "real options" – generically, will relate to project size, project timing, and the operation of the project once established. [ 19 ] In all cases, any (non-recoverable) upfront expenditure related to this flexibility is the option premium . Real options are also commonly applied to stock valuation - see Business valuation § Option pricing approaches - as well as to various other "Applications" referenced below .
Where the project's scope is uncertain, flexibility as to the size of the relevant facilities is valuable, and constitutes optionality. [ 20 ]
Where there is uncertainty as to when, and how, business or other conditions will eventuate, flexibility as to the timing of the relevant project(s) is valuable, and constitutes optionality.
Management may have flexibility relating to the product produced and/or the process used in manufacture . As in the preceding cases, this flexibility increases the value of the project, corresponding in turn, to the "premium" paid for the real option.
Given the above, it is clear that there is an analogy between real options and financial options , [ 21 ] and we would therefore expect options-based modelling and analysis to be applied here. At the same time, it is nevertheless important to understand why the more standard valuation techniques may not be applicable for ROV. [ 2 ]
ROV is often contrasted with more standard techniques of capital budgeting , such as discounted cash flow (DCF) analysis / net present value (NPV). [ 2 ] Under this "standard" NPV approach, future expected cash flows are present valued under the empirical probability measure at a discount rate that reflects the embedded risk in the project; see CAPM , APT , WACC . Here, only the expected cash flows are considered, and the "flexibility" to alter corporate strategy in view of actual market realizations is "ignored"; see below as well as Corporate finance § Valuing flexibility . The NPV framework (implicitly) assumes that management is "passive" with regard to their Capital Investment once committed. Some analysts account for this uncertainty by (i) adjusting the discount rate, e.g. by increasing the cost of capital , or (ii) adjusting the cash flows, e.g. using certainty equivalents , or (iii) applying (subjective) "haircuts" to the forecast numbers, or (iv) via probability-weighting these as in rNPV . [ 22 ] [ 23 ] [ 24 ] Even when employed, however, these latter methods do not normally properly account for changes in risk over the project's lifecycle and hence fail to appropriately adapt the risk adjustment. [ 25 ] [ 26 ]
By contrast, ROV assumes that management is "active" and can "continuously" respond to market changes. Real options consider "all" scenarios (or "states" ) and indicate the best corporate action in each of these contingent events . [ 27 ] Because management adapts to each negative outcome by decreasing its exposure and to positive scenarios by scaling up, the firm benefits from uncertainty in the underlying market, achieving a lower variability of profits than under the commitment/NPV stance. The contingent nature of future profits in real option models is captured by employing the techniques developed for financial options in the literature on contingent claims analysis . Here the approach, known as risk-neutral valuation, consists in adjusting the probability distribution for risk consideration , while discounting at the risk-free rate. This technique is also known as the "martingale" approach, and uses a risk-neutral measure . For technical considerations here, see below . For related discussion – and graphical representation – see Datar–Mathews method for real option valuation .
Given these different treatments, the real options value of a project is typically higher than the NPV – and the difference will be most marked in projects with major flexibility, contingency, and volatility. [ 28 ] As for financial options , a higher volatility of the underlying leads to a higher value. An application of real options valuation in the Philippine banking industry exhibited that increased levels of income volatility may adversely affect option values on the loan portfolio, when the presence of information asymmetry is considered. In this case, increased volatility may limit the value of an option. [ 29 ] Part of the criticism and subsequently slow adoption of real options valuation in practice and academia stems from the generally higher values for underlying assets these functions generate. However, studies have shown that these models are reliable estimators of underlying asset value, when input values are properly identified. [ 30 ]
Although there is much similarity between the modelling of real options and financial options , [ 21 ] [ 31 ] ROV is distinguished from the latter, in that it takes into account uncertainty about the future evolution of the parameters that determine the value of the project, coupled with management's ability to respond to the evolution of these parameters. [ 32 ] [ 33 ] It is the combined effect of these that makes ROV technically more challenging than its alternatives.
First, you must figure out the full range of possible values for the underlying asset. ... This involves estimating what the asset's value would be if it existed today and forecasting to see the full set of possible future values ... [These] calculations provide you with numbers for all the possible future values of the option at the various points where a decision is needed on whether to continue with the project. [ 31 ]
When valuing the real option, the analyst must therefore consider the inputs to the valuation, the valuation method employed, and whether any technical limitations may apply. Conceptually, valuing a real option looks at the premium between inflows and outlays for a particular project. Inputs to the value of a real option (time, discount rates, volatility, cash inflows and outflows) are each affected by the terms of business, and external environmental factors that a project exists in. Terms of business as information regarding ownership, data collection costs, and patents, are formed in relation to political, environmental, socio-cultural, technological, environmental and legal factors that affect an industry. Just as terms of business are affected by external environmental factors, these same circumstances affect the volatility of returns, as well as the discount rate (as firm or project specific risk). Furthermore, the external environmental influences that affect an industry affect projections on expected inflows and outlays. [ 34 ]
Given the similarity in valuation approach, the inputs required for modelling the real option correspond, generically, to those required for a financial option valuation. [ 21 ] [ 31 ] [ 32 ] [ 35 ] The specific application, though, is as follows:
The valuation methods usually employed, likewise, are adapted from techniques developed for valuing financial options . [ 37 ] [ 38 ] Note though that, in general, while most "real" problems allow for American style exercise at any point (many points) in the project's life and are impacted by multiple underlying variables, the standard methods are limited either with regard to dimensionality, to early exercise, or to both. In selecting a model, therefore, analysts must make a trade off between these considerations; see Option (finance) § Model implementation . The model must also be flexible enough to allow for the relevant decision rule to be coded appropriately at each decision point.
Various other methods, aimed mainly at practitioners , have been developed for real option valuation. [ 3 ] These typically use cash-flow scenarios for the projection of the future pay-off distribution, and are not based on restricting assumptions similar to those that underlie the closed form (or even numeric) solutions discussed. Recent additions include
the Datar–Mathews method (which can be understood as an extension of the net present value multi-scenario Monte Carlo model with an adjustment for risk aversion and economic decision-making), [ 44 ] [ 45 ] the fuzzy pay-off method , [ 46 ] and the simulation with optimized exercise thresholds method. [ 3 ]
By contrast, methods focusing on, for example, real option valuation in engineering design may be more sophisticated. [ 47 ] [ 48 ] These include analytics based on decision rules , [ 49 ] [ 50 ] which merge physical design considerations and management decisions through an intuitive "if-then-else" statement e.g., if demand is higher than a certain production capacity level, then expand existing capacity, else do nothing; this approach can be combined with advanced mathematical optimization methods like stochastic programming and robust optimisation to find the optimal design and decision rule variables. A more recent approach reformulates the real option problem as a data-driven Markov decision process , [ 51 ] [ 52 ] and uses advanced machine learning like deep reinforcement learning to evaluate a wide range of possible real option and design implementation strategies, well suited for complex systems and investment projects.
These help quantify the value of flexibility engineered early on in system designs and/or irreversible investment projects. The methods help rank order flexible design solutions relative to one another, and thus enable the best real option strategies to be exercised cost effectively during operations. These methods have been applied in many use cases in aerospace, defense, energy, transport, space, and water infrastructure design and planning. [ 53 ]
The relevance of Real options, even as a thought framework, may be limited due to market, organizational and / or technical considerations. [ 54 ] When the framework is employed, therefore, the analyst must first ensure that ROV is relevant to the project in question. These considerations are as follows.
As discussed above , the market and environment underlying the project must be one where "change is most evident", and the "source, trends and evolution" in product demand and supply, create the "flexibility, contingency, and volatility" [ 28 ] which result in optionality. Without this, the NPV framework would be more relevant.
Real options are "particularly important for businesses with a few key characteristics", [ 28 ] and may be less relevant otherwise. [ 33 ] In overview, it is important to consider the following in determining that the RO framework is applicable:
Limitations as to the use of these models arise due to the contrast between Real Options and financial options , for which these were originally developed. [ 55 ] The main difference is that the underlying is often not tradable – e.g. the factory owner cannot easily sell the factory upon which he has the option. Additionally, the real option itself may also not be tradeable – e.g. the factory owner cannot sell the right to extend his factory to another party, only he can make this decision (some real options, however, can be sold, e.g., ownership of a vacant lot of land is a real option to develop that land in the future). Even where a market exists – for the underlying or for the option – in most cases there is limited (or no) market liquidity . Finally, even if the firm can actively adapt to market changes, it remains to determine the right paradigm to discount future claims
The difficulties, are then:
These issues are addressed via several interrelated assumptions:
Whereas business managers have been making capital investment decisions for centuries, the term "real option" is relatively new, and was coined by Professor Stewart Myers of the MIT Sloan School of Management in 1977. In 1930, Irving Fisher wrote explicitly of the "options" available to a business owner ( The Theory of Interest , II.VIII ). The description of such opportunities as "real options", however, followed on the development of analytical techniques for financial options , such as Black–Scholes in 1973. As such, the term "real option" is closely tied to these option methods.
Real options are today an active field of academic research. Professor Lenos Trigeorgis has been a leading name for many years, publishing several influential books and academic articles. Other pioneering academics in the field include Professors Michael Brennan , Eduardo Schwartz , Avinash Dixit and Robert Pindyck (the latter two, authoring the pioneering text in the discipline). An academic conference on real options is organized yearly ( Annual International Conference on Real Options ).
Amongst others, the concept was "popularized" by Michael J. Mauboussin , then chief U.S. investment strategist for Credit Suisse First Boston . [ 28 ] He uses real options to explain the gap between how the stock market prices some businesses and the " intrinsic value " for those businesses. Trigeorgis also has broadened exposure to real options through layman articles in publications such as The Wall Street Journal . [ 27 ] This popularization is such that ROV is now a standard offering in postgraduate finance degrees , and often, even in MBA curricula at many Business Schools .
Recently, real options have been employed in business strategy , both for valuation purposes and as a conceptual framework . [ 13 ] [ 14 ] The idea of treating strategic investments as options was popularized by Timothy Luehrman [ 57 ] in two HBR articles: [ 21 ] "In financial terms, a business strategy is much more like a series of options, than a series of static cash flows". Investment opportunities are plotted in an "option space" with dimensions "volatility" & value-to-cost ("NPVq").
Luehrman also co-authored with William Teichner a Harvard Business School case study , Arundel Partners: The Sequel Project , in 1992, which may have been the first business school case study to teach ROV. [ 58 ] Reflecting the "mainstreaming" of ROV, Professor Robert C. Merton discussed the essential points of Arundel in his Nobel Prize Lecture in 1997. [ 59 ] Arundel involves a group of investors that is considering acquiring the sequel rights to a portfolio of yet-to-be released feature films. In particular, the investors must determine the value of the sequel rights before any of the first films are produced. Here, the investors face two main choices. They can produce an original movie and sequel at the same time or they can wait to decide on a sequel after the original film is released. The second approach, he states, provides the option not to make a sequel in the event the original movie is not successful. This real option has economic worth and can be valued monetarily using an option-pricing model. See Option (filmmaking) .
Standard texts:
Applications: | https://en.wikipedia.org/wiki/Real_options_valuation |
In geometry , a real point is a point in the complex projective plane with homogeneous coordinates ( x , y , z ) for which there exists a nonzero complex number λ such that λx , λy , and λz are all real numbers .
This definition can be widened to a complex projective space of arbitrary finite dimension as follows:
are the homogeneous coordinates of a real point if there exists a nonzero complex number λ such that the coordinates of
are all real.
A point which is not real is called an imaginary point . [ 1 ]
Geometries that are specializations of real projective geometry, such as Euclidean geometry , elliptic geometry or conformal geometry may be complexified , thus embedding the points of the geometry in a complex projective space, but retaining the identity of the original real space as special. Lines, planes etc. are expanded to the lines, etc. of the complex projective space. As with the inclusion of points at infinity and complexification of real polynomials, this allows some theorems to be stated more simply without exceptions and for a more regular algebraic analysis of the geometry.
Viewed in terms of homogeneous coordinates , a real vector space of homogeneous coordinates of the original geometry is complexified. A point of the original geometric space is defined by an equivalence class of homogeneous vectors of the form λu , where λ is an nonzero complex value and u is a real vector. A point of this form (and hence belongs to the original real space) is called a real point , whereas a point that has been added through the complexification and thus does not have this form is called an imaginary point .
A subspace of a projective space is real if it is spanned by real points.
Every imaginary point belongs to exactly one real line, the line through the point and its complex conjugate . [ 1 ]
This geometry-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Real_point |
In mathematics , real trees (also called R {\displaystyle \mathbb {R} } -trees ) are a class of metric spaces generalising simplicial trees . They arise naturally in many mathematical contexts, in particular geometric group theory and probability theory . They are also the simplest examples of Gromov hyperbolic spaces .
A metric space X {\displaystyle X} is a real tree if it is a geodesic space where every triangle is a tripod. That is, for every three points x , y , ρ ∈ X {\displaystyle x,y,\rho \in X} there exists a point c = x ∧ y {\displaystyle c=x\wedge y} such that the geodesic segments [ ρ , x ] , [ ρ , y ] {\displaystyle [\rho ,x],[\rho ,y]} intersect in the segment [ ρ , c ] {\displaystyle [\rho ,c]} and also c ∈ [ x , y ] {\displaystyle c\in [x,y]} . This definition is equivalent to X {\displaystyle X} being a "zero-hyperbolic space" in the sense of Gromov (all triangles are "zero-thin").
Real trees can also be characterised by a topological property. A metric space X {\displaystyle X} is a real tree if for any pair of points x , y ∈ X {\displaystyle x,y\in X} all topological embeddings σ {\displaystyle \sigma } of the segment [ 0 , 1 ] {\displaystyle [0,1]} into X {\displaystyle X} such that σ ( 0 ) = x , σ ( 1 ) = y {\displaystyle \sigma (0)=x,\,\sigma (1)=y} have the same image (which is then a geodesic segment from x {\displaystyle x} to y {\displaystyle y} ).
Here are equivalent characterizations of real trees which can be used as definitions:
1) (similar to trees as graphs) A real tree is a geodesic metric space which contains no subset homeomorphic to a circle. [ 1 ]
2) A real tree is a connected metric space ( X , d ) {\displaystyle (X,d)} which has the four points condition [ 2 ] (see figure):
3) A real tree is a connected 0-hyperbolic metric space [ 3 ] (see figure). Formally,
where ( x , y ) t {\displaystyle (x,y)_{t}} denotes the Gromov product of x {\displaystyle x} and y {\displaystyle y} with respect to t {\displaystyle t} , that is, 1 2 ( d ( x , t ) + d ( y , t ) − d ( x , y ) ) . {\displaystyle \textstyle {\frac {1}{2}}\left(d(x,t)+d(y,t)-d(x,y)\right).}
4) (similar to the characterization of plane trees by their contour process ). Consider a positive excursion of a function. In other words, let e {\displaystyle e} be a continuous real-valued function and [ a , b ] {\displaystyle [a,b]} an interval such that e ( a ) = e ( b ) = 0 {\displaystyle e(a)=e(b)=0} and e ( t ) > 0 {\displaystyle e(t)>0} for t ∈ ] a , b [ {\displaystyle t\in ]a,b[} .
For x , y ∈ [ a , b ] {\displaystyle x,y\in [a,b]} , x ≤ y {\displaystyle x\leq y} , define a pseudometric and an equivalence relation with:
Then, the quotient space ( [ a , b ] / ∼ e , d e ) {\displaystyle ([a,b]/\sim _{e}\,,\,d_{e})} is a real tree. [ 3 ] Intuitively, the local minima of the excursion e are the parents of the local maxima . Another visual way to construct the real tree from an excursion is to "put glue" under the curve of e , and "bend" this curve, identifying the glued points (see animation).
Real trees often appear, in various situations, as limits of more classical metric spaces.
A Brownian tree [ 4 ] is a random metric space whose value is a (non-simplicial) real tree almost surely. Brownian trees arise as limits of various random processes on finite trees. [ 5 ]
Any ultralimit of a sequence ( X i ) {\displaystyle (X_{i})} of δ i {\displaystyle \delta _{i}} - hyperbolic spaces with δ i → 0 {\displaystyle \delta _{i}\to 0} is a real tree. In particular, the asymptotic cone of any hyperbolic space is a real tree.
Let G {\displaystyle G} be a group . For a sequence of based G {\displaystyle G} -spaces ( X i , ∗ i , ρ i ) {\displaystyle (X_{i},*_{i},\rho _{i})} there is a notion of convergence to a based G {\displaystyle G} -space ( X ∞ , x ∞ , ρ ∞ ) {\displaystyle (X_{\infty },x_{\infty },\rho _{\infty })} due to M. Bestvina and F. Paulin. When the spaces are hyperbolic and the actions are unbounded the limit (if it exists) is a real tree. [ 6 ]
A simple example is obtained by taking G = π 1 ( S ) {\displaystyle G=\pi _{1}(S)} where S {\displaystyle S} is a compact surface, and X i {\displaystyle X_{i}} the universal cover of S {\displaystyle S} with the metric i ρ {\displaystyle i\rho } (where ρ {\displaystyle \rho } is a fixed hyperbolic metric on S {\displaystyle S} ).
This is useful to produce actions of hyperbolic groups on real trees. Such actions are analyzed using the so-called Rips machine . A case of particular interest is the study of degeneration of groups acting properly discontinuously on a real hyperbolic space (this predates Rips', Bestvina's and Paulin's work and is due to J. Morgan and P. Shalen [ 7 ] ).
If F {\displaystyle F} is a field with an ultrametric valuation then the Bruhat–Tits building of S L 2 ( F ) {\displaystyle \mathrm {SL} _{2}(F)} is a real tree. It is simplicial if and only if the valuations is discrete.
If Λ {\displaystyle \Lambda } is a totally ordered abelian group there is a natural notion of a distance with values in Λ {\displaystyle \Lambda } (classical metric spaces correspond to Λ = R {\displaystyle \Lambda =\mathbb {R} } ). There is a notion of Λ {\displaystyle \Lambda } -tree [ 8 ] which recovers simplicial trees when Λ = Z {\displaystyle \Lambda =\mathbb {Z} } and real trees when Λ = R {\displaystyle \Lambda =\mathbb {R} } . The structure of finitely presented groups acting freely on Λ {\displaystyle \Lambda } -trees was described. [ 9 ] In particular, such a group acts freely on some R n {\displaystyle \mathbb {R} ^{n}} -tree.
The axioms for a building can be generalized to give a definition of a real building. These arise for example as asymptotic cones of higher-rank symmetric spaces or as Bruhat-Tits buildings of higher-rank groups over valued fields. | https://en.wikipedia.org/wiki/Real_tree |
The distinction between real value and nominal value occurs in many fields. From a philosophical viewpoint, nominal value represents an accepted condition, which is a goal or an approximation, as opposed to the real value, which is always present.
In manufacturing, a nominal size or trade size is a size "in name only" used for identification. [ 1 ] The nominal size may not match any dimension of the product, but within the domain of that product the nominal size may correspond to a large number of highly standardized dimensions and tolerances .
Nominal sizes may be well-standardized across an industry, or may be proprietary to one manufacturer.
Applying the nominal size across domains requires understanding of the size systems in both areas; for example, someone wishing to select a drill bit to clear a " 1 ⁄ 4 -inch screw" may consult tables to show the proper drill bit size . Someone wishing to calculate the load capacity of a steel beam would have to consult tables to translate the nominal size of the beam into usable dimensions.
When considering the engineering tolerance between a shaft (or bolt) going through a hole in some other part (such as a nut), both the shaft (or bolt) have the same nominal size (also called the basic size ), [ 2 ] [ 3 ] [ 4 ] but all the holes are physically larger and all the shafts are physically smaller in order that any shaft (or bolt) of a given nominal size can fit into any hole of the same nominal size.
In measurement, a nominal value is often a value existing in name only; [ 5 ] it is assigned as a convenient designation rather than calculated by data analysis or following usual rounding methods. The use of nominal values can be based on de facto standards or some technical standards .
All real measurements have some variation depending on the accuracy and precision of the test method and the measurement uncertainty . The use of reported values often involves engineering tolerances .
One way to consider this is that the real value often has the characteristics of an irrational number . In real-world measuring situations, improving the measurement technique will eventually begin yielding unpredictable least significant digits. For example, a 1-inch long gauge block will measure to be exactly 1 inch long until the measuring techniques reach a certain degree of precision. As techniques improve beyond this threshold, it will become clear that 1 inch is not the real value of the gauge block length, but some other number approximates it.
In various subfields of engineering , a nominal value is one for which the "name" for the value is close to, but not the same as, the actual value. Some examples:
In the United Kingdom, pipe is available that is quoted in both metric size and imperial size. The metric size is larger than the imperial size. For example, both 1 ⁄ 2 inch and 15 millimetres (0.59 in) copper pipe is actually the same pipe which has a nominal internal diameter of 1 ⁄ 2 an inch and a nominal external diameter of 15 millimetres [ 6 ] (diameter is always internal in the imperial measurement system and always external in metric).
A machine is designed to operate at some particular condition, often stated on the device's nameplate. For example, a pump is designed to deliver its nominal pressure and flow while operating at its nominal speed and power. Actual operating conditions may vary.
Other cases involve diameter, speed, and volume.
Sometimes the word "nominal" is misused in engineering contexts as a synonym for "normal" or "expected"; for example, The rotor resistances on all the other operating wheels are nominal. [ 8 ] | https://en.wikipedia.org/wiki/Real_versus_nominal_value_(philosophy) |
Realgar ( / r i ˈ æ l ɡ ɑːr , - ɡ ər / ree- AL -gar, -gər ), also known as arsenic blende , ruby sulphur or ruby of arsenic , is an arsenic sulfide mineral with the chemical formula α - As 4 S 4 . It is a soft, sectile mineral occurring in monoclinic crystals, or in granular, compact, or powdery form, often in association with the related mineral, orpiment ( As 2 S 3 ). It is orange-red in color, melts at 320 °C, and burns with a bluish flame releasing fumes of arsenic and sulfur. Realgar is soft with a Mohs hardness of 1.5 to 2 and has a specific gravity of 3.5. Its streak is orange colored. It is trimorphous with pararealgar and bonazziite . [ 2 ]
Its name comes from the Arabic rahj al-ġār ( رهج الغار [rahdʒælɣaːr] listen ⓘ , "powder of the mine"), via Medieval Latin , and its earliest record in English is in the 1390s. [ 7 ] [ 8 ] [ 9 ]
Realgar is a minor ore of arsenic extracted in China, Peru, and the Philippines. [ 10 ]
Realgar was used by firework manufacturers to create the color white in fireworks prior to the availability of powdered metals such as aluminium , magnesium and titanium . It is still used in combination with potassium chlorate to make a contact explosive known as " red explosive " for some types of torpedoes and other novelty exploding fireworks branded as 'cracker balls', as well in the cores of some types of crackling stars. [ citation needed ]
Realgar is toxic. It was sometimes used to kill weeds , insects , and rodents , [ 11 ] even though more effective arsenic-based anti-pest agents are available such as cacodylic acid , (CH 3 ) 2 As(O)OH , an organoarsenic compound used as herbicide .
Realgar was commonly used in leather manufacturing to remove hair from animal pelts. Because it is a known carcinogen and an arsenic poison, and because substitutes are available, it is rarely used today for this purpose.
The ancient Greeks, who called realgar σανδαράκη ( sandarákē ), understood that it was poisonous. From this, realgar has also historically been known in English as sandarac .
Realgar was also used by Ancient Greek apothecaries to make a medicine known as "bull's blood". [ 12 ] The Greek physician Nicander described a death by "bull's blood", which matches the known effects of arsenic poisoning. [ 12 ] Bull's blood is the poison that is said to have been used by Themistocles and Midas for suicide. [ 12 ]
The Chinese name for realgar is 雄黃 ( Mandarin xiónghuáng ), literally 'masculine yellow', as opposed to orpiment which is 'feminine yellow'. [ 13 ]
Realgar was, along with orpiment , traded in the Roman Empire and was used as a red paint pigment . Early occurrences of realgar as a red paint pigment are known for works of art from China , India , Central Asia , and Egypt . It was used in Venetian fine-art painting during the Renaissance era, though rarely elsewhere in Europe, a use which died out by the 18th century. [ 14 ] It was also used as medicine. Other traditional uses include manufacturing lead shot , printing, and dyeing calico cloth. It was used to poison rats in medieval Spain and in 16th century England. [ 15 ]
Realgar most commonly occurs as a low-temperature hydrothermal vein mineral associated with other arsenic and antimony minerals. It also occurs as volcanic sublimations and in hot spring deposits. It occurs in association with orpiment , arsenolite , calcite and barite . [ 2 ]
It is found with lead , silver and gold ores in Hungary , Bohemia and Saxony . In the US it occurs notably in Mercur, Utah ; Manhattan, Nevada ; and in the geyser deposits of Yellowstone National Park . [ 5 ]
After a long period of exposure to light , realgar changes form to a yellow powder known as pararealgar (β- As 4 S 4 ). It was once thought that this powder was the yellow sulfide orpiment , but is a distinct chemical compound. [ 16 ] | https://en.wikipedia.org/wiki/Realgar |
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