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The molecular formula C5H12O3 (molar mass: 120.15 g/mol, exact mass: 120.0786 u) may refer to: 2-(2-Methoxyethoxy)ethanol Trimethylolethane (TME)
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The Paal–Knorr synthesis is a reaction used to synthesize substituted furans, pyrroles, or thiophenes from 1,4-diketones. It is a synthetically valuable method for obtaining substituted furans and pyrroles, which are common structural components of many natural products. It was initially reported independently by German chemists Carl Paal and Ludwig Knorr in 1884 as a method for the preparation of furans, and has been adapted for pyrroles and thiophenes. Although the Paal–Knorr synthesis has seen widespread use, the mechanism wasn't fully understood until it was elucidated by V. Amarnath et al. in the 1990s. The furan synthesis requires an acid catalyst: In the pyrrole synthesis a primary amine participates: and in that of thiophene for instance the compound phosphorus pentasulfide: == Mechanisms == === Furan synthesis === The acid catalyzed furan synthesis proceeds by protonation of one carbonyl which is attacked by the forming enol of the other carbonyl. Dehydration of the hemiacetal gives the resultant furan. The mechanism of the Paal–Knorr furan synthesis was elucidated in 1995 by V. Amarnath et al. Amarnath's work showed that the diastereomers of 3,4-disubstituted-2,5-hexane diones react at different rates. In the commonly accepted mechanism, these diones would go through a common enol intermediate, meaning that the meso and d,l-racemic isomers would cyclize at the same rate as they form from a common intermediate. The implication of different reaction is that cyclization needs to occur in a concerted step with enol formation. Thus the mechanism was proposed to occur via attack of the protonated carbonyl with the forming enol. Amarnath also found that the unreacted dione had not undergone conformational isomerization, which also indicated that an enol was not an intermediate. === Pyrrole synthesis === The mechanism for the synthesis of the pyrrole was investigated by V. Amarnath et al. in 1991. His work suggests
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that the protonated carbonyl is attacked by the amine to form the hemiaminal. The amine attacks the other carbonyl to form a 2,5-dihydroxytetrahydropyrrole derivative which undergoes dehydration to give the corresponding substituted pyrrole. The reaction is typically run under protic or Lewis acidic conditions, with a primary amine. Use of ammonium hydroxide or ammonium acetate (as reported by Paal) gives the N-unsubstituted pyrrole. === Thiophene synthesis === Thiophene synthesis is achieved via a mechanism very similar to the furan synthesis. The initial diketone is converted to a thioketone with a sulfurizing agent, which then undergoes the same mechanism as the furan synthesis. Most sulfurization agents are strong dehydrators and drive completion of the reaction. Early postulates toward the mechanism of the Paal-Knorr furan synthesis suggested that the thiophene was achieved by sulfurization of the furan product. Campaigne and Foye showed that treatment of isolated furans from the Paal-Knorr furan synthesis with phosphorus pentasulfide gave inconsistent results with the treatment of 1,4-dicarbonyls with phosphorus pentasulfide, which ruled out the sulfurization of a furan mechanism and suggests that the reaction proceeds via sulfurization of a dicarbonyl, producing a thioketone. == Scope == The Paal–Knorr reaction is quite versatile. In all syntheses almost all dicarbonyls can be converted to their corresponding heterocycle. R2 and R5 can be H, aryl or alkyl. R3 and R4 can be H, aryl, alkyl, or an ester. In the pyrrole synthesis (X = N), R1 can be H, aryl, alkyl, amino, or hydroxyl. A variety of conditions can be used to carry out these reactions, most of which are mild. The Paal–Knorr Furan synthesis is normally carried out under aqueous acidic conditions with protic acids such as aqueous sulfuric or hydrochloric acid, or anhydrous conditions with a Lewis acid or dehydrating agent. Common dehydrating agents include phosphorus pentoxide,
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anhydrides, or zinc chloride. The pyrrole synthesis requires a primary amine under similar conditions, or ammonia (or ammonia precursors) can be used. Synthesis of a thiophene requires a sulfurizing agent which is typically a sufficient dehydrator, such as phosphorus pentasulfide, Lawesson's reagent, or hydrogen sulfide. Traditionally, the Paal–Knorr reaction has been limited in scope by the availability of 1,4-diketones as synthetic precursors. Current chemical methods have greatly expanded the accessibility of these reagents, and variations of the Paal-Knorr now allow for different precursors to be used. The Paal–Knorr was also considered limited by harsh reaction conditions, such as prolonged heating in acid, which may degrade sensitive functionalities in many potential furan precursors. Current methods allow for milder conditions that can avoid heat altogether, including microwave catalyzed cyclizations. == Variations == Several 1,4-dicarbonyl surrogates can be used in place of a 1,4-dicarbonyl. While these substitutes have different structures from a 1,4-dicarbonyl, their reactions proceed via mechanisms very similar to that of the Paal-Knorr. === β,γ-Epoxy carbonyls === β,γ-Epoxy carbonyls have been known to cyclize to furans. This procedure can use the β-unsaturated carbonyls as starting materials, which can be epoxidized. The resulting epoxycarbonyl can be cyclized to a furan under acidic or basic conditions. === 2-Yn-1,4-diols === 2-Yn-1,4-diols systems have also been used to do Paal–Knorr chemistry. Using palladium, a 2-yn-1,4-diol can be isomerized to the corresponding 1,4-diketone in situ and then dehydrated to the corresponding furan using a dehydration agent. The significance of this variation is in the fact that it increases the scope of the Paal–Knorr by taking advantage of the wealth of acetylene chemistry that exists, specifically that for the generation of propargyl alcohols. === Acetals === Acetals have also proven useful starting materials for the Paal-Knorr. A ketone with an acetal 3 bonds away from it can
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be converted under exactly the same conditions as a 1,4-diketone to the corresponding heterocycle. === Microwave-assisted Paal–Knorr === Another variation has been the introduction of microwave radiation to enhance the Paal–Knorr. Traditional Paal–Knorr conditions involved prolonged heating of strong acids to drive dehydration which occurred over a period of several hours. Microwave-assisted Paal–Knorr reactions have been demonstrated to occur on time scales measured in minutes and in open flasks at room temperature. == Related reactions == The Knorr pyrrole synthesis, reported by Knorr in 1884 is the synthesis of a substituted pyrrole from an amino-ketone and a ketone. Also reported by Knorr is a synthesis of pyrazoles from 1,3-dicarbonyls and hydrazines, hydrazides, or semibicarbazides. This synthesis occurs via a condensation mechanism similar to the Paal-Knorr, however if a substituted hydrazine is used, it results in a mixture of regioisomers where the substituted heteroatom is either next to the R1 substituent or the R3 substituent. == Synthetic applications == In 2000, B. M. Trost et al. reported a formal synthesis of the antibiotic roseophilin. Trost's route to the macrocyclic core of roseophilin, like others, relied on a Paal–Knorr Pyrrole synthesis to obtain the fused pyrrole. Heating the 1,4-diketone with ammonium acetate in methanol with camphor sulfonic acid and 4 angstrom molecular sieves gave the pyrrole with no N-substitution. This pyrrole was found to be unstable, and as such was treated with trimethylsilyl ethoxy methoxy chloride (SEM-Cl) to protect the pyrrole prior to isolation. In 1982, H. Hart et al. reported a synthesis of a macrocycle containing fused furan rings using a Paal–Knorr furan synthesis. Refluxing para-toluene sulfonic acid in benzene was found to dehydrate the 1,4-diketones to their respective furans to achieve the challenging macrocyclic fused furans. == See also == Hantzsch pyrrole synthesis Knorr pyrrole synthesis Feist–Benary synthesis Volhard–Erdmann cyclization
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Hantzsch pyridine synthesis == References ==
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A sulfonyl nitrene is a chemical compound with generic formula RSO2N. Known sulfonyl nitrenes include methyl sulfonyl nitrene, trifluoromethyl sulfonyl nitrene, and tolyl sulfonyl nitrene. Also fluorosulfonyl nitrene FSO2N exists, but rearranges to FNSO2. Preparation of sulfonyl nitrenes can be accomplished by heating sulfonyl azides: RSO2N3 → RSO2N + N2 They are distinct from sulfinyl nitrenes which only have one oxygen attached to the sulfur atom. == References ==
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"title": "Sulfonyl nitrene"
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Many cutaneous neoplasms occur in the setting of systemic syndromes. == See also == == References == Bolognia, Jean L.; et al. (2007). Dermatology. St. Louis: Mosby. ISBN 1-4160-2999-0. James, William D.; et al. (2006). Andrews' Diseases of the Skin: Clinical Dermatology. Saunders Elsevier. ISBN 0-7216-2921-0. J Am Acad Dermatol. 1983 May;8(5):639-44. Pilomatricoma-like changes in the epidermal cysts of Gardner's syndrome. Cooper PH, Fechner RE.
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"page_id": 36962623,
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"title": "List of cutaneous neoplasms associated with systemic syndromes"
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In chemistry, a hypercycle is an abstract model of organization of self-replicating molecules connected in a cyclic, autocatalytic manner. It was introduced in an ordinary differential equation (ODE) form by the Nobel Prize in Chemistry winner Manfred Eigen in 1967 and subsequently further extended in collaboration with Peter Schuster. It was proposed as a solution to the error threshold problem encountered during modelling of replicative molecules that hypothetically existed on the primordial Earth (see: abiogenesis). As such, it explained how life on Earth could have begun using only relatively short genetic sequences, which in theory were too short to store all essential information. The hypercycle is a special case of the replicator equation. The most important properties of hypercycles are autocatalytic growth competition between cycles, once-for-ever selective behaviour, utilization of small selective advantage, rapid evolvability, increased information capacity, and selection against parasitic branches. == Central ideas == The hypercycle is a cycle of connected, self-replicating macromolecules. In the hypercycle, all molecules are linked such that each of them catalyses the creation of its successor, with the last molecule catalysing the first one. In such a manner, the cycle reinforces itself. Furthermore, each molecule is additionally a subject for self-replication. The resultant system is a new level of self-organization that incorporates both cooperation and selfishness. The coexistence of many genetically non-identical molecules makes it possible to maintain a high genetic diversity of the population. This can be a solution to the error threshold problem, which states that, in a system without ideal replication, an excess of mutation events would destroy the ability to carry information and prevent the creation of larger and fitter macromolecules. Moreover, it has been shown that hypercycles could originate naturally and that incorporating new molecules can extend them. Hypercycles are also subject to evolution and, as such,
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can undergo a selection process. As a result, not only does the system gain information, but its information content can be improved. From an evolutionary point of view, the hypercycle is an intermediate state of self-organization, but not the final solution. Over the years, the hypercycle theory has experienced many reformulations and methodological approaches. Among them, the most notable are applications of partial differential equations, cellular automata, and stochastic formulations of Eigen's problem. Despite many advantages that the concept of hypercycles presents, there were also some problems regarding the traditional model formulation using ODEs: a vulnerability to parasites and a limited size of stable hypercycles. In 2012, the first experimental proof for the emergence of a cooperative network among fragments of self-assembling ribozymes was published, demonstrating their advantages over self-replicating cycles. However, even though this experiment proves the existence of cooperation among the recombinase ribozyme subnetworks, this cooperative network does not form a hypercycle per se, so we still lack the experimental demonstration of hypercycles. == Model formulation == === Model evolution === 1971 (1971): Eigen introduces the hypercycle concept 1977 (1977): Eigen and Schuster extend the hypercycle concept, propose a hypercycle theory and introduce the concept of quasispecies 1982 (1982): Discovery of ribozyme catalytic properties 2001 (2001): Partial RNA polymerase ribozyme is designed via directed evolution 2012 (2012): Experimental demonstration that ribozymes can form collectively autocatalytic sets === Error threshold problem === When a model of replicating molecules was created, it was found that, for effective storage of information, macromolecules on prebiotic Earth could not exceed a certain threshold length. This problem is known as the error threshold problem. It arises because replication is an imperfect process, and during each replication event, there is a risk of incorporating errors into a new sequence, leading to the creation of a
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quasispecies. In a system that is deprived of high-fidelity replicases and error-correction mechanisms, mutations occur with a high probability. As a consequence, the information stored in a sequence can be lost due to the rapid accumulation of errors, a so-called error catastrophe. Moreover, it was shown that the genome size of any organism is roughly equal to the inverse of mutation rate per site per replication. Therefore, a high mutation rate imposes a serious limitation on the length of the genome. To overcome this problem, a more specialized replication machinery that is able to copy genetic information with higher fidelity is needed. Manfred Eigen suggested that proteins are necessary to accomplish this task. However, to encode a system as complex as a protein, longer nucleotide sequences are needed, which increases the probability of a mutation even more and requires even more complex replication machinery. John Maynard Smith and Eörs Szathmáry named this vicious circle Eigen's Paradox. According to current estimations, the maximum length of a replicated chain that can be correctly reproduced and maintained in enzyme-free systems is about 100 bases, which is assumed to be insufficient to encode replication machinery. This observation was the motivation for the formulation of the hypercycle theory. === Models === It was suggested that the problem with building and maintaining larger, more complex, and more accurately replicated molecules can be circumvented if several information carriers, each of them storing a small piece of information, are connected such that they only control their own concentration. Studies of the mathematical model describing replicating molecules revealed that to observe a cooperative behaviour among self-replicating molecules, they have to be connected by a positive feedback loop of catalytic actions. This kind of closed network consisting of self-replicating entities connected by a catalytic positive-feedback loop was named an elementary
|
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hypercycle. Such a concept, apart from an increased information capacity, has another advantage. Linking self-replication with mutual catalysis can produce nonlinear growth of the system. This, first, makes the system resistant to so-called parasitic branches. Parasitic branches are species coupled to a cycle that do not provide any advantage to the reproduction of a cycle, which, in turn, makes them useless and decreases the selective value of the system. Secondly, it reinforces the self-organization of molecules into the hypercycle, allowing the system to evolve without losing information, which solves the error threshold problem. Analysis of potential molecules that could form the first hypercycles in nature prompted the idea of coupling an information carrier function with enzymatic properties. At the time of the hypercycle theory formulation, enzymatic properties were attributed only to proteins, while nucleic acids were recognized only as carriers of information. This led to the formulation of a more complex model of a hypercycle with translation. The proposed model consists of a number of nucleotide sequences I (I stands for intermediate) and the same number of polypeptide chains E (E stands for enzyme). Sequences I have a limited chain length and carry the information necessary to build catalytic chains E. The sequence Ii provides the matrix to reproduce itself and a matrix to build the protein Ei. The protein Ei gives the catalytic support to build the next sequence in the cycle, Ii+1. The self-replicating sequences I form a cycle consisting of positive and negative strands that periodically reproduce themselves. Therefore, many cycles of the +/− nucleotide collectives are linked together by the second-order cycle of enzymatic properties of E, forming a catalytic hypercycle. Without the secondary loop provided by catalysis, I chains would compete and select against each other instead of cooperating. The reproduction is possible thanks to
|
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translation and polymerization functions encoded in I chains. In his principal work, Manfred Eigen stated that the E coded by the I chain can be a specific polymerase or an enhancer (or a silencer) of a more general polymerase acting in favour of formation of the successor of nucleotide chain I. Later, he indicated that a general polymerase leads to the death of the system. Moreover, the whole cycle must be closed, so that En must catalyse I1 formation for some integer n > 1. === Alternative concepts === During their research, Eigen and Schuster also considered types of protein and nucleotide coupling other than hypercycles. One such alternative was a model with one replicase that performed polymerase functionality and that was a translational product of one of the RNA matrices existing among the quasispecies. This RNA-dependent RNA polymerase catalysed the replication of sequences that had specific motifs recognized by this replicase. The other RNA matrices, or just one of their strands, provided translational products which had specific anticodons and were responsible for unique assignment and transportation of amino acids. Another concept devised by Eigen and Schuster was a model in which each RNA template's replication was catalysed by its own translational product; at the same time, this RNA template performed a transport function for one amino acid type. Existence of more than one such RNA template could make translation possible. Nevertheless, in both alternative concepts, the system will not survive due to the internal competition among its constituents. Even if none of the constituents of such a system is selectively favoured, which potentially allows coexistence of all of the coupled molecules, they are not able to coevolve and optimize their properties. In consequence, the system loses its internal stability and cannot live on. The reason for inability to survive
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is the lack of mutual control of constituent abundances. == Mathematical model == === Elementary hypercycle === The dynamics of the elementary hypercycle can be modelled using the following differential equation: x i ˙ = x i ( k i + ∑ j k i , j x j − 1 x ϕ ) {\displaystyle {\dot {x_{i}}}=x_{i}\left(k_{i}+\sum _{j}k_{i,j}x_{j}-{\frac {1}{x}}\phi \right)} where x = ∑ i x i , k i = f i − d i . {\displaystyle {\begin{aligned}x&=\sum _{i}x_{i},\\k_{i}&=f_{i}-d_{i}.\end{aligned}}} In the equation above, xi is the concentration of template Ii; x is the total concentration of all templates; ki is the excess production rate of template Ii, which is a difference between formation fi by self-replication of the template and its degradation di, usually by hydrolysis; ki,j is the production rate of template Ii catalysed by Ij; and φ is a dilution flux; which guarantees that the total concentration is constant. Production and degradation rates are expressed in numbers of molecules per time unit at unit concentration (xi = 1). Assuming that at high concentration x the term ki can be neglected, and, moreover, in the hypercycle, a template can be replicated only by itself and the previous member of the cycle, the equation can be simplified to: x i ˙ = x i ( k i , i − 1 x i − 1 − 1 x ϕ ) {\displaystyle {\dot {x_{i}}}=x_{i}\left(k_{i,i-1}x_{i-1}-{\frac {1}{x}}\phi \right)} where according to the cyclic properties, it can be assumed that k i , 0 = k i , n , x 0 = x n . {\displaystyle {\begin{aligned}k_{i,0}&=k_{i,n},\\x_{0}&=x_{n}.\end{aligned}}} === Hypercycle with translation === A hypercycle with translation consists of polynucleotides Ii (with concentration xi) and polypeptides Ei (with concentration yi). It is assumed that the kinetics of nucleotide synthesis follows a Michaelis–Menten-type reaction
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scheme in which the concentration of complexes cannot be neglected. During replication, molecules form complexes IiEi-1 (occurring with concentration zi). Thus, the total concentration of molecules (xi0 and yi0) will be the sum of free molecules and molecules involved in a complex: x i 0 = x i + z i , y i 0 = y i + z i + 1 . {\displaystyle {\begin{aligned}x_{i}^{0}&=x_{i}+z_{i},\\y_{i}^{0}&=y_{i}+z_{i+1}.\end{aligned}}} The dynamics of the hypercycle with translation can be described using a system of differential equations modelling the total number of molecules: x ˙ i 0 = f i z i − x i 0 c I ϕ x , y ˙ i 0 = k i x i − y i 0 c E ϕ y {\displaystyle {\begin{aligned}{\dot {x}}_{i}^{0}&=f_{i}z_{i}-{\frac {x_{i}^{0}}{c_{I}}}\phi _{x},\\{\dot {y}}_{i}^{0}&=k_{i}x_{i}-{\frac {y_{i}^{0}}{c_{E}}}\phi _{y}\end{aligned}}} where c I = ∑ i x i 0 , c E = ∑ i y i 0 . {\displaystyle {\begin{aligned}c_{I}&=\sum _{i}x_{i}^{0},\\c_{E}&=\sum _{i}y_{i}^{0}.\end{aligned}}} In the above equations, cE and cI are total concentrations of all polypeptides and all polynucleotides, φx and φy are dilution fluxes, ki is the production rate of polypeptide Ei translated from the polynucleotide Ii, and fi is the production rate of polynucleotide Ii synthesised by the complex IiEi-1 (through replication and polymerization). Coupling nucleic acids with proteins in such a model of hypercycle with translation demanded the proper model for the origin of translation code as a necessary condition for the origin of hypercycle organization. At the time of hypercycle theory formulation, two models for the origin of translation code were proposed by Crick and his collaborators. These were models stating that the first codons were constructed according to either an RRY or an RNY scheme, in which R stands for the purine base, Y for pyrimidine, and N for any base, with the latter
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assumed to be more reliable. Nowadays, it is assumed that the hypercycle model could be realized by utilization of ribozymes without the need for a hypercycle with translation, and there are many more theories about the origin of the genetic code. == Evolution == === Formation of the first hypercycles === Eigen made several assumptions about conditions that led to the formation of the first hypercycles. Some of them were the consequence of the lack of knowledge about ribozymes, which were discovered a few years after the introduction of the hypercycle concept and negated Eigen's assumptions in the strict sense. The primary of them was that the formation of hypercycles had required the availability of both types of chains: nucleic acids forming a quasispecies population and proteins with enzymatic functions. Nowadays, taking into account the knowledge about ribozymes, it may be possible that a hypercycle's members were selected from the quasispecies population and the enzymatic function was performed by RNA. According to the hypercycle theory, the first primitive polymerase emerged precisely from this population. As a consequence, the catalysed replication could exceed the uncatalysed reactions, and the system could grow faster. However, this rapid growth was a threat to the emerging system, as the whole system could lose control over the relative amount of the RNAs with enzymatic function. The system required more reliable control of its constituents—for example, by incorporating the coupling of essential RNAs into a positive feedback loop. Without this feedback loop, the replicating system would be lost. These positive feedback loops formed the first hypercycles. In the process described above, the fact that the first hypercycles originated from the quasispecies population (a population of similar sequences) created a significant advantage. One possibility of linking different chains I—which is relatively easy to achieve taking into account the
|
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quasispecies properties—is that the one chain I improves the synthesis of the similar chain I’. In this way, the existence of similar sequences I originating from the same quasispecies population promotes the creation of the linkage between molecules I and I’. === Evolutionary dynamics === After formation, a hypercycle reaches either an internal equilibrium or a state with oscillating concentrations of each type of chain I, but with the total concentration of all chains remaining constant. In this way, the system consisting of all chains can be expressed as a single, integrated entity. During the formation of hypercycles, several of them could be present in comparable concentrations, but very soon, a selection of the hypercycle with the highest fitness value will take place. Here, the fitness value expresses the adaptation of the hypercycle to the environment, and the selection based on it is very sharp. After one hypercycle wins the competition, it is very unlikely that another one could take its place, even if the new hypercycle would be more efficient than the winner. Usually, even large fluctuations in the numbers of internal species cannot weaken the hypercycle enough to destroy it. In the case of a hypercycle, we can speak of one-for-ever selection, which is responsible for the existence of a unique translation code and a particular chirality. The above-described idea of a hypercycle's robustness results from an exponential growth of its constituents caused by the catalytic support. However, Eörs Szathmáry and Irina Gladkih showed that an unconditional coexistence can be obtained even in the case of a non-enzymatic template replication that leads to a subexponential or a parabolic growth. This could be observed during the stages preceding a catalytic replication that are necessary for the formation of hypercycles. The coexistence of various non-enzymatically replicating sequences could help to
|
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maintain a sufficient diversity of RNA modules used later to build molecules with catalytic functions. From the mathematical point of view, it is possible to find conditions required for cooperation of several hypercycles. However, in reality, the cooperation of hypercycles would be extremely difficult, because it requires the existence of a complicated multi-step biochemical mechanism or an incorporation of more than two types of molecules. Both conditions seem very improbable; therefore, the existence of coupled hypercycles is assumed impossible in practice. Evolution of a hypercycle ensues from the creation of new components by the mutation of its internal species. Mutations can be incorporated into the hypercycle, enlarging it if, and only if, two requirements are satisfied. First, a new information carrier Inew created by the mutation must be better recognized by one of the hypercycle's members Ii than the chain Ii+1 that was previously recognized by it. Secondly, the new member Inew of the cycle has to better catalyse the formation of the polynucleotide Ii+1 that was previously catalysed by the product of its predecessor Ii. In theory, it is possible to incorporate into the hypercycle mutations that do not satisfy the second condition. They would form parasitic branches that use the system for their own replication but do not contribute to the system as a whole. However, it was noticed that such mutants do not pose a threat to the hypercycle, because other constituents of the hypercycle grow nonlinearly, which prevents the parasitic branches from growing. === Evolutionary dynamics: a mathematical model === According to the definition of a hypercycle, it is a nonlinear, dynamic system, and, in the simplest case, it can be assumed that it grows at a rate determined by a system of quadratic differential equations. Then, the competition between evolving hypercycles can be modelled using
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the differential equation: C l ˙ = q l C l 2 − C l ϕ C {\displaystyle {\dot {C_{l}}}=q_{l}C_{l}^{2}-C_{l}{\frac {\phi }{C}}} where C = ∑ l C l . {\displaystyle C=\sum _{l}C_{l}.} Here, Cl is the total concentration of all polynucleotide chains belonging to a hypercycle Hl, C is the total concentration of polynucleotide chains belonging to all hypercycles, ql is the rate of growth, and φ is a dilution flux that guarantees that the total concentration is constant. According to the above model, in the initial phase, when several hypercycles exist, the selection of the hypercycle with the largest ql value takes place. When one hypercycle wins the selection and dominates the population, it is very difficult to replace it, even with a hypercycle with a much higher growth rate q. == Compartmentalization and genome integration == Hypercycle theory proposed that hypercycles are not the final state of organization, and further development of more complicated systems is possible by enveloping the hypercycle in some kind of membrane. After evolution of compartments, a genome integration of the hypercycle can proceed by linking its members into a single chain, which forms a precursor of a genome. After that, the whole individualized and compartmentalized hypercycle can behave like a simple self-replicating entity. Compartmentalization provides some advantages for a system that has already established a linkage between units. Without compartments, genome integration would boost competition by limiting space and resources. Moreover, adaptive evolution requires the package of transmissible information for advantageous mutations in order not to aid less-efficient copies of the gene. The first advantage is that it maintains a high local concentration of molecules, which helps to locally increase the rate of synthesis. Secondly, it keeps the effect of mutations local, while at the same time affecting the whole compartment. This
|
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favours preservation of beneficial mutations, because it prevents them from spreading away. At the same time, harmful mutations cannot pollute the entire system if they are enclosed by the membrane. Instead, only the contaminated compartment is destroyed, without affecting other compartments. In that way, compartmentalization allows for selection for genotypic mutations. Thirdly, membranes protect against environmental factors because they constitute a barrier for high-weight molecules or UV irradiation. Finally, the membrane surface can work as a catalyst. Despite the above-mentioned advantages, there are also potential problems connected to compartmentalized hypercycles. These problems include difficulty in the transport of ingredients in and out, synchronizing the synthesis of new copies of the hypercycle constituents, and division of the growing compartment linked to a packing problem. In the initial works, the compartmentalization was stated as an evolutionary consequence of the hypercyclic organization. Carsten Bresch and coworkers raised an objection that hypercyclic organization is not necessary if compartments are taken into account. They proposed the so-called package model in which one type of a polymerase is sufficient and copies all polynucleotide chains that contain a special recognition motif. However, as pointed out by the authors, such packages are—contrary to hypercycles—vulnerable to deleterious mutations as well as a fluctuation abyss, resulting in packages that lack one of the essential RNA molecules. Eigen and colleagues argued that simple package of genes cannot solve the information integration problem and hypercycles cannot be simply replaced by compartments, but compartments may assist hypercycles. This problem, however, raised more objections, and Eörs Szathmáry and László Demeter reconsidered whether packing hypercycles into compartments is a necessary intermediate stage of the evolution. They invented a stochastic corrector model that assumed that replicative templates compete within compartments, and selective values of these compartments depend on the internal composition of templates. Numerical simulations showed
|
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that when stochastic effects are taken into account, compartmentalization is sufficient to integrate information dispersed in competitive replicators without the need for hypercycle organization. Moreover, it was shown that compartmentalized hypercycles are more sensitive to the input of deleterious mutations than a simple package of competing genes. Nevertheless, package models do not solve the error threshold problem that originally motivated the hypercycle. == Ribozymes == At the time of the hypercycle theory formulation, ribozymes were not known. After the breakthrough of discovering RNA's catalytic properties in 1982, it was realized that RNA had the ability to integrate protein and nucleotide-chain properties into one entity. Ribozymes potentially serving as templates and catalysers of replication can be considered components of quasispecies that can self-organize into a hypercycle without the need to invent a translation process. In 2001, a partial RNA polymerase ribozyme was designed via directed evolution. Nevertheless, it was able to catalyse only a polymerization of a chain having the size of about 14 nucleotides, even though it was 200 nucleotides long. The most up-to-date version of this polymerase was shown in 2013. While it has an ability to catalyse polymerization of longer sequences, even of its own length, it cannot replicate itself due to a lack of sequence generality and its inability to transverse secondary structures of long RNA templates. However, it was recently shown that those limitations could in principle be overcome by the assembly of active polymerase ribozymes from several short RNA strands. In 2014, a cross-chiral RNA polymerase ribozyme was demonstrated. It was hypothesized that it offers a new mode of recognition between an enzyme and substrates, which is based on the shape of the substrate, and allows avoiding the Watson-Crick pairing and, therefore, may provide greater sequence generality. Various other experiments have shown that, besides bearing
|
{
"page_id": 29491519,
"source": null,
"title": "Hypercycle (chemistry)"
}
|
polymerase properties, ribozymes could have developed other kinds of evolutionarily useful catalytic activity such as synthase, ligase, or aminoacylase activities. Ribozymal aminoacylators and ribozymes with the ability to form peptide bonds might have been crucial to inventing translation. An RNA ligase, in turn, could link various components of quasispecies into one chain, beginning the process of a genome integration. An RNA with a synthase or a synthetase activity could be critical for building compartments and providing building blocks for growing RNA and protein chains as well as other types of molecules. Many examples of this kind of ribozyme are currently known, including a peptidyl transferase ribozyme, a ligase, and a nucleotide synthetase. A transaminoacylator described in 2013 has five nucleotides, which is sufficient for a trans-amino acylation reaction and makes it the smallest ribozyme that has been discovered. It supports a peptidyl-RNA synthesis that could be a precursor for the contemporary process of linking amino acids to tRNA molecules. An RNA ligase's catalytic domain, consisting of 93 nucleotides, proved to be sufficient to catalyse a linking reaction between two RNA chains. Similarly, an acyltransferase ribozyme 82 nucleotides long was sufficient to perform an acyltransfer reaction. Altogether, the results concerning the RNA ligase's catalytic domain and the acyltransferase ribozyme are in agreement with the estimated upper limit of 100 nucleotides set by the error threshold problem. However, it was hypothesized that even if the putative first RNA-dependent RNA-polymerases are estimated to be longer—the smallest reported up-to-date RNA-dependent polymerase ribozyme is 165 nucleotides long—they did not have to arise in one step. It is more plausible that ligation of smaller RNA chains performed by the first RNA ligases resulted in a longer chain with the desired catalytically active polymerase domain. Forty years after the publication of Manfred Eigen's primary work dedicated to
|
{
"page_id": 29491519,
"source": null,
"title": "Hypercycle (chemistry)"
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|
hypercycles, Nilesh Vaidya and colleagues showed experimentally that ribozymes can form catalytic cycles and networks capable of expanding their sizes by incorporating new members. However, this is not a demonstration of a hypercycle in accordance with its definition, but an example of a collectively autocatalytic set. Earlier computer simulations showed that molecular networks can arise, evolve and be resistant to parasitic RNA branches. In their experiments, Vaidya et al. used an Azoarcus group I intron ribozyme that, when fragmented, has an ability to self-assemble by catalysing recombination reactions in an autocatalytic manner. They mutated the three-nucleotide-long sequences responsible for recognition of target sequences on the opposite end of the ribozyme (namely, Internal Guide Sequences or IGSs) as well as these target sequences. Some genotypes could introduce cooperation by recognizing target sequences of the other ribozymes, promoting their covalent binding, while other selfish genotypes were only able to self-assemble. In separation, the selfish subsystem grew faster than the cooperative one. After mixing selfish ribozymes with cooperative ones, the emergence of cooperative behaviour in a merged population was observed, outperforming the self-assembling subsystems. Moreover, the selfish ribozymes were integrated into the network of reactions, supporting its growth. These results were also explained analytically by the ODE model and its analysis. They differ substantially from results obtained in evolutionary dynamics. According to evolutionary dynamics theory, selfish molecules should dominate the system even if the growth rate of the selfish subsystem in isolation is lower than the growth rate of the cooperative system. Moreover, Vaidya et al. proved that, when fragmented into more pieces, ribozymes that are capable of self-assembly can not only still form catalytic cycles but, indeed, favour them. Results obtained from experiments by Vaidya et al. gave a glimpse on how inefficient prebiotic polymerases, capable of synthesizing only short oligomers, could
|
{
"page_id": 29491519,
"source": null,
"title": "Hypercycle (chemistry)"
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be sufficient at the pre-life stage to spark off life. This could happen because coupling the synthesis of short RNA fragments by the first ribozymal polymerases to a system capable of self-assembly not only enables building longer sequences but also allows exploiting the fitness space more efficiently with the use of the recombination process. Another experiment performed by Hannes Mutschler et al. showed that the RNA polymerase ribozyme, which they described, can be synthesized in situ from the ligation of four smaller fragments, akin to a recombination of Azoarcus ribozyme from four inactive oligonucleotide fragments described earlier. Apart from a substantial contribution of the above experiments to the research on the origin of life, they have not proven the existence of hypercycles experimentally. == Related problems and reformulations == The hypercycle concept has been continuously studied since its origin. Shortly after Eigen and Schuster published their main work regarding hypercycles, John Maynard Smith raised an objection that the catalytic support for the replication given to other molecules is altruistic. Therefore, it cannot be selected and maintained in a system. He also underlined hypercycle vulnerability to parasites, as they are favoured by selection. Later on, Josef Hofbauer and Karl Sigmund indicated that in reality, a hypercycle can maintain only fewer than five members. In agreement with Eigen and Schuster's principal analysis, they argued that systems with five or more species exhibit limited and unstable cyclic behaviour, because some species can die out due to stochastic events and break the positive feedback loop that sustains the hypercycle. The extinction of the hypercycle then follows. It was also emphasized that a hypercycle size of up to four is too small to maintain the amount of information sufficient to cross the information threshold. Several researchers proposed a solution to these problems by introducing space
|
{
"page_id": 29491519,
"source": null,
"title": "Hypercycle (chemistry)"
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into the initial model either explicitly or in the form of a spatial segregation within compartments. Bresch et al. proposed a package model as a solution for the parasite problem. Later on, Szathmáry and Demeter proposed a stochastic corrector machine model. Both compartmentalized systems proved to be robust against parasites. However, package models do not solve the error threshold problem that originally motivated the idea of the hypercycle. A few years later, Maarten Boerlijst and Paulien Hogeweg, and later Nobuto Takeuchi, studied the replicator equations with the use of partial differential equations and cellular automata models, methods that already proved to be successful in other applications. They demonstrated that spatial self-structuring of the system completely solves the problem of global extinction for large systems and, partially, the problem of parasites. The latter was also analysed by Robert May, who noticed that an emergent rotating spiral wave pattern, which was observed during computational simulations performed on cellular automata, proved to be stable and able to survive the invasion of parasites if they appear at some distance from the wave core. Unfortunately, in this case, rotation decelerates as the number of hypercycle members increases, meaning that selection tends toward decreasing the amount of information stored in the hypercycle. Moreover, there is also a problem with adding new information into the system. In order to be preserved, the new information has to appear near to the core of the spiral wave. However, this would make the system vulnerable to parasites, and, as a consequence, the hypercycle would not be stable. Therefore, stable spiral waves are characterized by once-for-ever selection, which creates the restrictions that, on the one hand, once the information is added to the system, it cannot be easily abandoned; and on the other hand, new information cannot be added. Another model
|
{
"page_id": 29491519,
"source": null,
"title": "Hypercycle (chemistry)"
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|
based on cellular automata, taking into account a simpler replicating network of continuously mutating parasites and their interactions with one replicase species, was proposed by Takeuchi and Hogeweg and exhibited an emergent travelling wave pattern. Surprisingly, travelling waves not only proved to be stable against moderately strong parasites, if the parasites' mutation rate is not too high, but the emergent pattern itself was generated as a result of interactions between parasites and replicase species. The same technique was used to model systems that include formation of complexes. Finally, hypercycle simulation extending to three dimensions showed the emergence of the three-dimensional analogue of a spiral wave, namely, the scroll wave. == Comparison with other theories of life == The hypercycle is just one of several current theories of life, including the chemoton of Tibor Gánti, the (M,R) systems of Robert Rosen, autopoiesis (or self-building) of Humberto Maturana and Francisco Varela, and the autocatalytic sets of Stuart Kauffman, similar to an earlier proposal by Freeman Dyson. All of these (including the hypercycle) found their original inspiration in Erwin Schrödinger's book What is Life? but at first they appear to have little in common with one another, largely because the authors did not communicate with one another, and none of them made any reference in their principal publications to any of the other theories. Nonetheless, there are more similarities than may be obvious at first sight, for example between Gánti and Rosen. Until recently there have been almost no attempts to compare the different theories and discuss them together. == Last Universal Common Ancestor (LUCA) == Some authors equate models of the origin of life with LUCA, the Last Universal Common Ancestor of all extant life. This is a serious error resulting from failure to recognize that L refers to the last common
|
{
"page_id": 29491519,
"source": null,
"title": "Hypercycle (chemistry)"
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|
ancestor, not to the first ancestor, which is much older: a large amount of evolution occurred before the appearance of LUCA. Gill and Forterre expressed the essential point as follows: LUCA should not be confused with the first cell, but was the product of a long period of evolution. Being the "last" means that LUCA was preceded by a long succession of older "ancestors." == References == This article was adapted from the following source under a CC BY 4.0 license (2016) (reviewer reports): Natalia Szostak; Szymon Wasik; Jacek Blazewicz (7 April 2016). "Hypercycle". PLOS Computational Biology. 12 (4): e1004853. doi:10.1371/JOURNAL.PCBI.1004853. ISSN 1553-734X. PMC 4824418. PMID 27054759. Wikidata Q34521204. == External links == J. Padgett's Hypercycle model implemented in repast
|
{
"page_id": 29491519,
"source": null,
"title": "Hypercycle (chemistry)"
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The molecular formula C6H4N4 (molar mass: 132.12 g/mol, exact mass: 132.0436 u) may refer to: Pteridine Tricyanoaminopropene (TRIAP)
|
{
"page_id": 23920960,
"source": null,
"title": "C6H4N4"
}
|
In molecular biology mir-23 microRNA is a short RNA molecule. MicroRNAs function to regulate the expression levels of other genes by several mechanisms. == See also == MicroRNA == References == == Further reading == == External links == Page for mir-23 microRNA precursor family at Rfam
|
{
"page_id": 36372803,
"source": null,
"title": "Mir-23 microRNA precursor family"
}
|
The molecular formula C3H7ClO2 (molar mass: 108.52 g/mol) may refer to: 2-MCPD 3-MCPD
|
{
"page_id": 23986501,
"source": null,
"title": "C3H7ClO2"
}
|
A lateral flow test (LFT), is an assay also known as a lateral flow immunochromatographic test (ICT), or rapid test. It is a simple device intended to detect the presence of a target substance in a liquid sample without the need for specialized and costly equipment. LFTs are widely used in medical diagnostics in the home, at the point of care, and in the laboratory. For instance, the home pregnancy test is an LFT that detects a specific hormone. These tests are simple and economical and generally show results in around five to thirty minutes. Many lab-based applications increase the sensitivity of simple LFTs by employing additional dedicated equipment. Because the target substance is often a biological antigen, many lateral flow tests are rapid antigen tests (RAT or ART). LFTs operate on the same principles of affinity chromatography as the enzyme-linked immunosorbent assays (ELISA). In essence, these tests run the liquid sample along the surface of a pad with reactive molecules that show a visual positive or negative result. The pads are based on a series of capillary beds, such as pieces of porous paper, microstructured polymer, or sintered polymer. Each of these pads has the capacity to transport fluid (e.g., urine, blood, saliva) spontaneously. The sample pad acts as a sponge and holds an excess of sample fluid. Once soaked, the fluid flows to the second conjugate pad in which the manufacturer has stored freeze dried bio-active particles called conjugates (see below) in a salt–sugar matrix. The conjugate pad contains all the reagents required for an optimized chemical reaction between the target molecule (e.g., an antigen) and its chemical partner (e.g., antibody) that has been immobilized on the particle's surface. This marks target particles as they pass through the pad and continue across to the test and control lines.
|
{
"page_id": 14352711,
"source": null,
"title": "Lateral flow test"
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The test line shows a signal, often a color as in pregnancy tests. The control line contains affinity ligands which show whether the sample has flowed through and the bio-molecules in the conjugate pad are active. After passing these reaction zones, the fluid enters the final porous material, the wick, that simply acts as a waste container. LFTs can operate as either competitive or sandwich assays. == History == LFTs derive from paper chromatography, which was developed in 1943 by Martin and Synge, and elaborated in 1944 by Consden, Gordon and Martin. There was an explosion of activity in this field after 1945. The ELISA technology was developed in 1971. A set of LFT patents, including the litigated US 6,485,982 described below, were filed by Armkel LLC starting in 1988. == Synopsis == === Colored particles === In principle, any colored particle can be used, but latex (blue color) or nanometer-sized particles of gold (red color) are most commonly used. The gold particles are red in color due to localized surface plasmon resonance. Fluorescent or magnetic labelled particles can also be used, but these require the use of an electronic reader to assess the test result. === Sandwich assays === Sandwich assays are generally used for larger analytes because they tend to have multiple binding sites. As the sample migrates through the assay it first encounters a conjugate, which is an antibody specific to the target analyte labelled with a visual tag, usually colloidal gold. The antibodies bind to the target analyte within the sample and migrate together until they reach the test line. The test line also contains immobilized antibodies specific to the target analyte, which bind to the migrated analyte bound conjugate molecules. The test line then presents a visual change due to the concentrated visual tag, hence
|
{
"page_id": 14352711,
"source": null,
"title": "Lateral flow test"
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confirming the presence of the target molecules. The majority of sandwich assays also have a control line which will appear whether or not the target analyte is present to ensure proper function of the lateral flow pad. The rapid, low-cost sandwich-based assay is commonly used for home pregnancy tests which detect human chorionic gonadotropin, hCG, in the urine of pregnant women. === Competitive assays === Competitive assays are generally used for smaller analytes since smaller analytes have fewer binding sites. The sample first encounters antibodies to the target analyte labelled with a visual tag (colored particles). The test line contains the target analyte fixed to the surface. When the target analyte is absent from the sample, unbound antibody will bind to these fixed analyte molecules, meaning that a visual marker will show. Conversely, when the target analyte is present in the sample, it binds to the antibodies to prevent them binding to the fixed analyte in the test line, and thus no visual marker shows. This differs from sandwich assays in that no band means the analyte is present. === Quantitative tests === Most LFTs are intended to operate on a purely qualitative basis. However, it is possible to measure the intensity of the test line to determine the quantity of analyte in the sample. Handheld diagnostic devices known as lateral flow readers are used by several companies to provide a fully quantitative assay result. By utilizing unique wavelengths of light for illumination in conjunction with either CMOS or CCD detection technology, a signal rich image can be produced of the actual test lines. Using image processing algorithms specifically designed for a particular test type and medium, line intensities can then be correlated with analyte concentrations. One such handheld lateral flow device platform is made by Detekt Biomedical L.L.C. Alternative
|
{
"page_id": 14352711,
"source": null,
"title": "Lateral flow test"
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|
non-optical techniques are also able to report quantitative assays results. One such example is a magnetic immunoassay (MIA) in the LFT form also allows for getting a quantified result. Reducing variations in the capillary pumping of the sample fluid is another approach to move from qualitative to quantitative results. Recent work has, for example, demonstrated capillary pumping with a constant flow rate independent from the liquid viscosity and surface energy. === Control line === Most tests will incorporate a second line which contains a further antibody (one which is not specific to the analyte) that binds some of the remaining colored particles which did not bind to the test line. This confirms that fluid has passed successfully from the sample-application pad, past the test line. By giving confirmation that the sample has had a chance to interact with the test line, this increases confidence that a visibly-unchanged test line can be interpreted as a negative result (or that a changed test line can be interpreted as a negative result in a competitive assay). === Blood plasma extraction === Because the intense red color of hemoglobin interferes with the readout of colorimetric or optical detection-based diagnostic tests, blood plasma separation is a common first step to increase diagnostic test accuracy. Plasma can be extracted from whole blood via integrated filters or via agglutination. === Speed and simplicity === Time to obtain the test result is a key driver for these products. Tests results can be available in as little as a few minutes. Generally there is a trade off between time and sensitivity: more sensitive tests may take longer to develop. The other key advantage of this format of test compared to other immunoassays is the simplicity of the test, by typically requiring little or no sample or reagent preparation. ==
|
{
"page_id": 14352711,
"source": null,
"title": "Lateral flow test"
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|
Patents == This is a highly competitive area and a number of people claim patents in the field, most notably Alere (formerly Inverness Medical Innovations, now owned by Abbott) who own patents originally filed by Unipath. The US 6,485,982 patent, that has been litigated, expired in 2019. A number of other companies also hold patents in this arena. A group of competitors are challenging the validity of the patents. The original patent is apparently from 1988. == Applications == Lateral flow assays have a wide array of applications and can test a variety of samples including urine, blood, saliva, sweat, serum, and other fluids. They are currently used by clinical laboratories, hospitals, physicians and veterinary clinics, food analysis labs and environmental testing facilities. Immediacy in obtaining results is normally the key factor in choosing this technique, although simplicity and lack of a need for formal equipment are also important factors. These features allow ICTs to be used a at-home test or in pharmacies. Because of their exceptional quality, rapid test are also used routinely in well-equippped laboratories when the demand for test is low. The broad applications of rapid test can be realized because of their simplicity accompanied by high quality analytical production. The sensitivity and specificity of these techniques tend to be comparable to those of other more complex methods, and on occasion significantly better. Other uses for lateral flow assays are food and environmental safety and veterinary medicine for chemicals such as diseases and toxins. LFTs are also commonly used for disease identification such as ebola, but the most common LFT are the home pregnancy and SARS-CoV-2 tests. === COVID-19 testing === Lateral flow assays have played a critical role in COVID-19 testing as they have the benefit of delivering a result in 15–30 minutes. The systematic evaluation
|
{
"page_id": 14352711,
"source": null,
"title": "Lateral flow test"
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|
of lateral flow assays during the COVID-19 pandemic was initiated at Oxford University as part of a UK collaboration with Public Health England. A study that started in June 2020 in the United Kingdom, FALCON-C19, confirmed the sensitivity of some lateral flow devices (LFDs) in this setting. Four out of 64 LFDs tested had desirable performance characteristics according to these early tests; the Innova SARS-CoV-2 Antigen Rapid Qualitative Test performed moderately in viral antigen detection/sensitivity with excellent specificity, although kit failure rates and the impact of training were potential issues. The Innova test's specificity is more widely publicised, but sensitivity in phase 4 trials was 50.1%. This describes a device for which one out of every two patients infected with COVID-19 and tested in real-world conditions would receive a false-negative result. After closure of schools in January 2021, biweekly LFTs were introduced in England for teachers, pupils, and households of pupils when schools re-opened on March 8, 2021 for asymptomatic testing. Biweekly LFT were made universally available to everyone in England on April 9, 2021. LFTs have been used for mass testing for COVID-19 globally and complement other public health measures for COVID-19. Some scientists outside government expressed serious misgivings in late 2020 about the use of Innova LFDs for screening for Covid. According to Jon Deeks, a professor of biostatistics at the University of Birmingham, England, the Innova test is "entirely unsuitable" for community testing: "as the test may miss up to half of cases, a negative test result indicates a reduced risk of Covid, but does not exclude Covid". Sensitivity of tests used in 2022 was around 70%. == See also == Luteinizing hormone § Predicting ovulation: LFT test for ovulation == References == == Further reading == Hassan, Muntaha M. Rapid Immunochrotographic Techniques. Ramadi, Al Anbar, Iraq:
|
{
"page_id": 14352711,
"source": null,
"title": "Lateral flow test"
}
|
University of Anbar. Didactic presentation (lab notes for students). Retrieved 12 January 2022. Porex Clinical Sciences (manufacturer) "Sample Collection & Transport | Sample Preparation | Sample Analysis".
|
{
"page_id": 14352711,
"source": null,
"title": "Lateral flow test"
}
|
Tryptic soy-serum-bacitracin-vancomycin (TSBV) is a type of agar plate medium used in microbiological testing to select for Aggregatibacter actinomycetemcomitans (A. a.). It was described by Jørgen Slots in 1982, who also discovered the role of A.a. in periodontitis. Per litre, TSBV contains: 40 g tryptic soy agar 1 g yeast extract 100 mL horse serum 75 mg bacitracin 5 mg vancomycin == References ==
|
{
"page_id": 26214730,
"source": null,
"title": "Tryptic soy-serum-bacitracin-vancomycin"
}
|
The Zoology Building is a facility owned by the University of Aberdeen. It is situated in Tillydrone. == History == During construction, the building collapsed on 1 November 1966. It had been expected to be completed by summer 1967. Eight people were trapped, of which five died. Clearing of the site started in February 1967, and was completed in April. The present building was constructed on the same plot as the previous building and is of a similar design. Plans were approved in September 1967. The present building opened in 1970. == Zoology Museum == The building contains the Zoology Museum. It holds various exhibits from the university's collections. Specimens range in age from the 1840s to the late 1970s. The only known egg from the Jerdon's courser was discovered in an uncatalogued drawer in the museum. The discovery was confirmed with DNA testing. The building was also featured in Tetris depicting a Soviet Russian government building. == References ==
|
{
"page_id": 30671185,
"source": null,
"title": "Zoology Building"
}
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A Markov logic network (MLN) is a probabilistic logic which applies the ideas of a Markov network to first-order logic, defining probability distributions on possible worlds on any given domain. == History == In 2002, Ben Taskar, Pieter Abbeel and Daphne Koller introduced relational Markov networks as templates to specify Markov networks abstractly and without reference to a specific domain. Work on Markov logic networks began in 2003 by Pedro Domingos and Matt Richardson. Markov logic networks is a popular formalism for statistical relational learning. == Syntax == A Markov logic network consists of a collection of formulas from first-order logic, to each of which is assigned a real number, the weight. The underlying idea is that an interpretation is more likely if it satisfies formulas with positive weights and less likely if it satisfies formulas with negative weights. For instance, the following Markov logic network codifies how smokers are more likely to be friends with other smokers, and how stress encourages smoking: 2.0 :: s m o k e s ( X ) ← s m o k e s ( Y ) ∧ i n f l u e n c e s ( X , Y ) 0.5 :: s m o k e s ( X ) ← s t r e s s ( X ) {\displaystyle {\begin{array}{lcl}2.0&::&\mathrm {smokes} (X)\leftarrow \mathrm {smokes} (Y)\land \mathrm {influences} (X,Y)\\0.5&::&\mathrm {smokes} (X)\leftarrow \mathrm {stress} (X)\end{array}}} == Semantics == Together with a given domain, a Markov logic network defines a probability distribution on the set of all interpretations of its predicates on the given domain. The underlying idea is that an interpretation is more likely if it satisfies formulas with positive weights and less likely if it satisfies formulas with negative weights. For any n {\displaystyle n} -ary predicate symbol
|
{
"page_id": 3670357,
"source": null,
"title": "Markov logic network"
}
|
R {\displaystyle R} that occurs in the Markov logic network and every n {\displaystyle n} -tuple a 1 , … , a n {\displaystyle a_{1},\dots ,a_{n}} of domain elements, R ( a 1 , … , a n ) {\displaystyle R(a_{1},\dots ,a_{n})} is a grounding of R {\displaystyle R} . An interpretation is given by allocating a Boolean truth value (true or false) to each grounding of an element. A true grounding of a formula φ {\displaystyle \varphi } in an interpretation with free variables x 1 , … , x n {\displaystyle x_{1},\dots ,x_{n}} is a variable assignment of x 1 , … , x n {\displaystyle x_{1},\dots ,x_{n}} that makes φ {\displaystyle \varphi } true in that interpretation. Then the probability of any given interpretation is directly proportional to exp ( ∑ j w j n j ) {\displaystyle \exp(\sum _{j}w_{j}n_{j})} , where w j {\displaystyle w_{j}} is the weight of the j {\displaystyle j} -th sentence of the Markov logic network and n j {\displaystyle n_{j}} is the number of its true groundings. This can also be seen as inducing a Markov network whose nodes are the groundings of the predicates occurring in the Markov logic network. The feature functions of this network are the groundings of the sentences occurring in the Markov logic network, with value e w {\displaystyle e^{w}} if the grounding is true and 1 otherwise (where again w {\displaystyle w} is the weight of the formula). == Inference == The probability distributions induced by Markov logic networks can be queried for the probability of a particular event, given by an atomic formula (marginal inference), possibly conditioned by another atomic formula. Marginal inference can be performed using standard Markov network inference techniques over the minimal subset of the relevant Markov network required for
|
{
"page_id": 3670357,
"source": null,
"title": "Markov logic network"
}
|
answering the query. Exact inference is known to be #P-complete in the size of the domain. In practice, the exact probability is often approximated. Techniques for approximate inference include Gibbs sampling, belief propagation, or approximation via pseudolikelihood. The class of Markov logic networks which use only two variables in any formula allows for polynomial time exact inference by reduction to weighted model counting. == See also == Markov random field Statistical relational learning Probabilistic logic network Probabilistic soft logic ProbLog == Resources == == External links == University of Washington Statistical Relational Learning group Alchemy 2.0: Markov logic networks in C++ pracmln: Markov logic networks in Python ProbCog: Markov logic networks in Python and Java that can use its own inference engine or Alchemy's markov thebeast: Markov logic networks in Java RockIt: Markov logic networks in Java (with web interface/REST API) Tuffy: A Learning and Inference Engine with strong RDBMs-based optimization for scalability Felix: A successor to Tuffy, with prebuilt submodules to speed up common subtasks Factorie: Scala based probabilistic inference language, with prebuilt submodules for natural language processing etc Figaro: Scala based MLN language LoMRF: Logical Markov Random Fields, an open-source implementation of Markov Logic Networks in Scala
|
{
"page_id": 3670357,
"source": null,
"title": "Markov logic network"
}
|
Lophelia reef (also known by its Wakashan name q̓áuc̓íwísuxv) is a coral reef that lies some 200 m underwater in Finlayson Channel in British Columbia, Canada. It is Canada's only known living coral reef, and the Pacific Ocean's northernmost known coral reef. It was discovered in the early 2020s after two local First Nations, the Kitasoo Xai'xais and the Heiltsuk, who "knew something was there," guided deepsea ecologist Cherisse Du Preez to the waters in which the coral ecosystem lives. Canada's Fisheries Department has closed the area over the coral reef to all commercial and recreational bottom-contact and mid-water trawl fisheries. This is, according to the Department, based on a significant scientific discovery at the small yet globally unique reef, which is highly susceptible to damage from fishing gear. The reef's site is now being assessed for the possibility of establishing there a Parks Canada National Marine Conservation Area. == References ==
|
{
"page_id": 76349782,
"source": null,
"title": "Lophelia reef"
}
|
Four Core Genotypes (FCG) mice are laboratory mice produced by genetic engineering that allow biomedical researchers to determine if a sex difference in phenotype is caused by effects of gonadal hormones or sex chromosome genes. The four genotypes include XX and XY mice with ovaries, and XX and XY mice with testes. The comparison of XX and XY mice with the same type of gonad reveals sex differences in phenotypes that are caused by sex chromosome genes. The comparison of mice with different gonads but the same sex chromosomes reveals sex differences in phenotypes that are caused by gonadal hormones. == Development == The FCG model was created by Paul Burgoyne and Robin Lovell-Badge at the National Institute for Medical Research, London (now Francis Crick Institute). The model involves deleting the testis-determining gene Sry from the Y chromosome, and inserting Sry onto chromosome 3. Therefore the sex chromosomes no longer determine the type of gonad, so that XX and XY mice can have the same type of gonad and gonadal hormones. == Significance == The FCG model has been used to discover that the XX and XY animals respond differently in models of human physiology and disease, including autoimmunity, metabolism, cardiovascular disease, cancer, Alzheimer’s disease, and neural and behavioral processes. These findings imply that some sex chromosome genes may protect from disease, rationalizing the search for therapies that enhance such protective factors. == References ==
|
{
"page_id": 74056025,
"source": null,
"title": "Four Core Genotypes mouse model"
}
|
Louis Sokoloff (October 14, 1921 – July 30, 2015) was an American neuroscientist. He is considered to be a pioneer in functional imaging of the brain. Louis Sokoloff was born in Philadelphia, Pennsylvania. He was a member of the National Academy of Sciences from 1980. In 1981, he received the Lasker-DeBakey Clinical Medical Research Award. In 1987, he received the Karl Spencer Lashley Award; "For his elucidation of the physiological and biochemical processes involved in the metabolism of the brain and the application of these discoveries to the measurement of functional activity within that organ". In 1988, Sokoloff, together with Seymour S. Kety received the NAS Award in the Neurosciences, "For developing techniques to measure brain blood flow and metabolism - valuable tools in the study of brain function that have major applications in clinical medicine." In 1996, he received the Ralph W. Gerard Prize in Neuroscience. He was elected to the American Philosophical Society in 2005. He died on July 30, 2015, in Washington, D.C. Many of his papers and biographical material are published as "The Sokoloff Papers" in Profiles in Science at the National Library of Medicine web site. (https://profiles.nlm.nih.gov/NL/) His wife, Betty, was an RN, served in WWII and earned a pilot's license. His son, Kenneth Sokoloff, was an economic historian. He also had a daughter, Ann. == References == == Further reading == The Louis Sokoloff Papers - Profiles in Science, National Library of Medicine Louis Sokoloff Papers (1923-2016) - National Library of Medicine finding aid
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{
"page_id": 42991961,
"source": null,
"title": "Louis Sokoloff"
}
|
In molecular biology mir-25 microRNA is a short RNA molecule. MicroRNAs function to regulate the expression levels of other genes by several mechanisms. mir-25 levels increase in human heart failure, and treatment with an anti-sense RNA molecule (antagomiR) was recently reported to halt disease progression and improves cardiac function in a mouse heart failure model. == See also == MicroRNA == References == == Further reading == == External links == Page for mir-25 microRNA precursor family at Rfam
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{
"page_id": 36372830,
"source": null,
"title": "Mir-25 microRNA precursor family"
}
|
The psychrometric constant γ {\displaystyle \gamma } relates the partial pressure of water in air to the air temperature. This lets one interpolate actual vapor pressure from paired dry and wet thermometer bulb temperature readings. γ = ( c p ) a i r ∗ P λ v ∗ M W r a t i o {\displaystyle \gamma ={\frac {\left(c_{p}\right)_{air}*P}{\lambda _{v}*MW_{ratio}}}} γ = {\displaystyle \gamma =} psychrometric constant [kPa °C−1], P = atmospheric pressure [kPa], λ v = {\displaystyle \lambda _{v}=} latent heat of water vaporization, 2.45 [MJ kg−1], c p = {\displaystyle c_{p}=} specific heat of air at constant pressure, [MJ kg−1 °C−1], M W r a t i o = {\displaystyle MW_{ratio}=} ratio molecular weight of water vapor/dry air = 0.622. Both λ v {\displaystyle \lambda _{v}} and M W r a t i o {\displaystyle MW_{ratio}} are constants. Since atmospheric pressure, P, depends upon altitude, so does γ {\displaystyle \gamma } . At higher altitude water evaporates and boils at lower temperature. Although ( c p ) H 2 O {\displaystyle \left(c_{p}\right)_{H_{2}O}} is constant, varied air composition results in varied ( c p ) a i r {\displaystyle \left(c_{p}\right)_{air}} . Thus on average, at a given location or altitude, the psychrometric constant is approximately constant. Still, it is worth remembering that weather impacts both atmospheric pressure and composition. == Vapor Pressure Estimation == Saturated vapor pressure, e s = e [ T d e w ] {\displaystyle e_{s}=e\left[T_{dew}\right]} Actual vapor pressure, e a = e s − γ ∗ ( T d r y − T w e t ) {\displaystyle e_{a}=e_{s}-\gamma *\left(T_{dry}-T_{wet}\right)} here e[T] is vapor pressure as a function of temperature, T. Tdew = the dewpoint temperature at which water condenses. Twet = the temperature of a wet thermometer bulb from which water can evaporate
|
{
"page_id": 13893984,
"source": null,
"title": "Psychrometric constant"
}
|
to air. Tdry = the temperature of a dry thermometer bulb in air. == References ==
|
{
"page_id": 13893984,
"source": null,
"title": "Psychrometric constant"
}
|
Electromagnetic or magnetic induction is the production of an electromotive force (emf) across an electrical conductor in a changing magnetic field. Michael Faraday is generally credited with the discovery of induction in 1831, and James Clerk Maxwell mathematically described it as Faraday's law of induction. Lenz's law describes the direction of the induced field. Faraday's law was later generalized to become the Maxwell–Faraday equation, one of the four Maxwell equations in his theory of electromagnetism. Electromagnetic induction has found many applications, including electrical components such as inductors and transformers, and devices such as electric motors and generators. == History == Electromagnetic induction was discovered by Michael Faraday, published in 1831. It was discovered independently by Joseph Henry in 1832. In Faraday's first experimental demonstration, on August 29, 1831, he wrapped two wires around opposite sides of an iron ring or "torus" (an arrangement similar to a modern toroidal transformer). Based on his understanding of electromagnets, he expected that, when current started to flow in one wire, a sort of wave would travel through the ring and cause some electrical effect on the opposite side. He plugged one wire into a galvanometer, and watched it as he connected the other wire to a battery. He saw a transient current, which he called a "wave of electricity", when he connected the wire to the battery and another when he disconnected it. This induction was due to the change in magnetic flux that occurred when the battery was connected and disconnected. Within two months, Faraday found several other manifestations of electromagnetic induction. For example, he saw transient currents when he quickly slid a bar magnet in and out of a coil of wires, and he generated a steady (DC) current by rotating a copper disk near the bar magnet with a sliding electrical
|
{
"page_id": 65888,
"source": null,
"title": "Electromagnetic induction"
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lead ("Faraday's disk"). Faraday explained electromagnetic induction using a concept he called lines of force. However, scientists at the time widely rejected his theoretical ideas, mainly because they were not formulated mathematically. An exception was James Clerk Maxwell, who used Faraday's ideas as the basis of his quantitative electromagnetic theory. In Maxwell's model, the time varying aspect of electromagnetic induction is expressed as a differential equation, which Oliver Heaviside referred to as Faraday's law even though it is slightly different from Faraday's original formulation and does not describe motional emf. Heaviside's version (see Maxwell–Faraday equation below) is the form recognized today in the group of equations known as Maxwell's equations. In 1834 Heinrich Lenz formulated the law named after him to describe the "flux through the circuit". Lenz's law gives the direction of the induced emf and current resulting from electromagnetic induction. == Theory == === Faraday's law of induction and Lenz's law === Faraday's law of induction makes use of the magnetic flux ΦB through a region of space enclosed by a wire loop. The magnetic flux is defined by a surface integral: Φ B = ∫ Σ B ⋅ d A , {\displaystyle \Phi _{\mathrm {B} }=\int _{\Sigma }\mathbf {B} \cdot d\mathbf {A} \,,} where dA is an element of the surface Σ enclosed by the wire loop, B is the magnetic field. The dot product B·dA corresponds to an infinitesimal amount of magnetic flux. In more visual terms, the magnetic flux through the wire loop is proportional to the number of magnetic field lines that pass through the loop. When the flux through the surface changes, Faraday's law of induction says that the wire loop acquires an electromotive force (emf). The most widespread version of this law states that the induced electromotive force in any closed circuit
|
{
"page_id": 65888,
"source": null,
"title": "Electromagnetic induction"
}
|
is equal to the rate of change of the magnetic flux enclosed by the circuit: E = − d Φ B d t , {\displaystyle {\mathcal {E}}=-{\frac {d\Phi _{\mathrm {B} }}{dt}}\,,} where E {\displaystyle {\mathcal {E}}} is the emf and ΦB is the magnetic flux. The direction of the electromotive force is given by Lenz's law which states that an induced current will flow in the direction that will oppose the change which produced it. This is due to the negative sign in the previous equation. To increase the generated emf, a common approach is to exploit flux linkage by creating a tightly wound coil of wire, composed of N identical turns, each with the same magnetic flux going through them. The resulting emf is then N times that of one single wire. E = − N d Φ B d t {\displaystyle {\mathcal {E}}=-N{\frac {d\Phi _{\mathrm {B} }}{dt}}} Generating an emf through a variation of the magnetic flux through the surface of a wire loop can be achieved in several ways: the magnetic field B changes (e.g. an alternating magnetic field, or moving a wire loop towards a bar magnet where the B field is stronger), the wire loop is deformed and the surface Σ changes, the orientation of the surface dA changes (e.g. spinning a wire loop into a fixed magnetic field), any combination of the above === Maxwell–Faraday equation === In general, the relation between the emf E {\displaystyle {\mathcal {E}}} in a wire loop encircling a surface Σ, and the electric field E in the wire is given by E = ∮ ∂ Σ E ⋅ d ℓ {\displaystyle {\mathcal {E}}=\oint _{\partial \Sigma }\mathbf {E} \cdot d{\boldsymbol {\ell }}} where dℓ is an element of contour of the surface Σ, combining this with the definition of
|
{
"page_id": 65888,
"source": null,
"title": "Electromagnetic induction"
}
|
flux Φ B = ∫ Σ B ⋅ d A , {\displaystyle \Phi _{\mathrm {B} }=\int _{\Sigma }\mathbf {B} \cdot d\mathbf {A} \,,} we can write the integral form of the Maxwell–Faraday equation ∮ ∂ Σ E ⋅ d ℓ = − d d t ∫ Σ B ⋅ d A {\displaystyle \oint _{\partial \Sigma }\mathbf {E} \cdot d{\boldsymbol {\ell }}=-{\frac {d}{dt}}{\int _{\Sigma }\mathbf {B} \cdot d\mathbf {A} }} It is one of the four Maxwell's equations, and therefore plays a fundamental role in the theory of classical electromagnetism. === Faraday's law and relativity === Faraday's law describes two different phenomena: the motional emf generated by a magnetic force on a moving wire (see Lorentz force), and the transformer emf that is generated by an electric force due to a changing magnetic field (due to the differential form of the Maxwell–Faraday equation). James Clerk Maxwell drew attention to the separate physical phenomena in 1861. This is believed to be a unique example in physics of where such a fundamental law is invoked to explain two such different phenomena. Albert Einstein noticed that the two situations both corresponded to a relative movement between a conductor and a magnet, and the outcome was unaffected by which one was moving. This was one of the principal paths that led him to develop special relativity. == Applications == The principles of electromagnetic induction are applied in many devices and systems, including: === Electrical generator === The emf generated by Faraday's law of induction due to relative movement of a circuit and a magnetic field is the phenomenon underlying electrical generators. When a permanent magnet is moved relative to a conductor, or vice versa, an electromotive force is created. If the wire is connected through an electrical load, current will flow, and thus electrical energy
|
{
"page_id": 65888,
"source": null,
"title": "Electromagnetic induction"
}
|
is generated, converting the mechanical energy of motion to electrical energy. For example, the drum generator is based upon the figure to the bottom-right. A different implementation of this idea is the Faraday's disc, shown in simplified form on the right. In the Faraday's disc example, the disc is rotated in a uniform magnetic field perpendicular to the disc, causing a current to flow in the radial arm due to the Lorentz force. Mechanical work is necessary to drive this current. When the generated current flows through the conducting rim, a magnetic field is generated by this current through Ampère's circuital law (labelled "induced B" in the figure). The rim thus becomes an electromagnet that resists rotation of the disc (an example of Lenz's law). On the far side of the figure, the return current flows from the rotating arm through the far side of the rim to the bottom brush. The B-field induced by this return current opposes the applied B-field, tending to decrease the flux through that side of the circuit, opposing the increase in flux due to rotation. On the near side of the figure, the return current flows from the rotating arm through the near side of the rim to the bottom brush. The induced B-field increases the flux on this side of the circuit, opposing the decrease in flux due to r the rotation. The energy required to keep the disc moving, despite this reactive force, is exactly equal to the electrical energy generated (plus energy wasted due to friction, Joule heating, and other inefficiencies). This behavior is common to all generators converting mechanical energy to electrical energy. === Electrical transformer === When the electric current in a loop of wire changes, the changing current creates a changing magnetic field. A second wire in reach
|
{
"page_id": 65888,
"source": null,
"title": "Electromagnetic induction"
}
|
of this magnetic field will experience this change in magnetic field as a change in its coupled magnetic flux, d Φ B d t {\displaystyle {\frac {d\Phi _{B}}{dt}}} . Therefore, an electromotive force is set up in the second loop called the induced emf or transformer emf. If the two ends of this loop are connected through an electrical load, current will flow. ==== Current clamp ==== A current clamp is a type of transformer with a split core which can be spread apart and clipped onto a wire or coil to either measure the current in it or, in reverse, to induce a voltage. Unlike conventional instruments the clamp does not make electrical contact with the conductor or require it to be disconnected during attachment of the clamp. === Magnetic flow meter === Faraday's law is used for measuring the flow of electrically conductive liquids and slurries. Such instruments are called magnetic flow meters. The induced voltage ε generated in the magnetic field B due to a conductive liquid moving at velocity v is thus given by: E = − B ℓ v , {\displaystyle {\mathcal {E}}=-B\ell v,} where ℓ is the distance between electrodes in the magnetic flow meter. == Eddy currents == Electrical conductors moving through a steady magnetic field, or stationary conductors within a changing magnetic field, will have circular currents induced within them by induction, called eddy currents. Eddy currents flow in closed loops in planes perpendicular to the magnetic field. They have useful applications in eddy current brakes and induction heating systems. However eddy currents induced in the metal magnetic cores of transformers and AC motors and generators are undesirable since they dissipate energy (called core losses) as heat in the resistance of the metal. Cores for these devices use a number of methods
|
{
"page_id": 65888,
"source": null,
"title": "Electromagnetic induction"
}
|
to reduce eddy currents: Cores of low frequency alternating current electromagnets and transformers, instead of being solid metal, are often made of stacks of metal sheets, called laminations, separated by nonconductive coatings. These thin plates reduce the undesirable parasitic eddy currents, as described below. Inductors and transformers used at higher frequencies often have magnetic cores made of nonconductive magnetic materials such as ferrite or iron powder held together with a resin binder. === Electromagnet laminations === Eddy currents occur when a solid metallic mass is rotated in a magnetic field, because the outer portion of the metal cuts more magnetic lines of force than the inner portion; hence the induced electromotive force is not uniform; this tends to cause electric currents between the points of greatest and least potential. Eddy currents consume a considerable amount of energy and often cause a harmful rise in temperature. Only five laminations or plates are shown in this example, so as to show the subdivision of the eddy currents. In practical use, the number of laminations or punchings ranges from 40 to 66 per inch (16 to 26 per centimetre), and brings the eddy current loss down to about one percent. While the plates can be separated by insulation, the voltage is so low that the natural rust/oxide coating of the plates is enough to prevent current flow across the laminations. This is a rotor approximately 20 mm in diameter from a DC motor used in a CD player. Note the laminations of the electromagnet pole pieces, used to limit parasitic inductive losses. === Parasitic induction within conductors === In this illustration, a solid copper bar conductor on a rotating armature is just passing under the tip of the pole piece N of the field magnet. Note the uneven distribution of the lines of
|
{
"page_id": 65888,
"source": null,
"title": "Electromagnetic induction"
}
|
force across the copper bar. The magnetic field is more concentrated and thus stronger on the left edge of the copper bar (a,b) while the field is weaker on the right edge (c,d). Since the two edges of the bar move with the same velocity, this difference in field strength across the bar creates whorls or current eddies within the copper bar. High current power-frequency devices, such as electric motors, generators and transformers, use multiple small conductors in parallel to break up the eddy flows that can form within large solid conductors. The same principle is applied to transformers used at higher than power frequency, for example, those used in switch-mode power supplies and the intermediate frequency coupling transformers of radio receivers. == See also == Alternator – Device converting mechanical into electrical energy Crosstalk – Signals in one channel affecting another Faraday paradox – Apparent paradox with Faraday's law of induction Fleming's right-hand rule – Mnemonic for the direction of induced current in a moving magnetic field Hall effect – Electromagnetic effect in physics Inductance Moving magnet and conductor problem == References == === Notes === === References === == Further reading == Maxwell, James Clerk (1881), A treatise on electricity and magnetism, Vol. II, Chapter III, §530, p. 178. Oxford, UK: Clarendon Press. ISBN 0-486-60637-6. == External links == Media related to Electromagnetic induction at Wikimedia Commons The Laws of Induction - The Feynman Lectures on Physics A free java simulation on motional EMF
|
{
"page_id": 65888,
"source": null,
"title": "Electromagnetic induction"
}
|
A subvariety (Latin: subvarietas) in botanical nomenclature is a taxonomic rank. They are rarely used to classify organisms. == Plant taxonomy == Subvariety is ranked: below that of variety (varietas) above that of form (forma). Subvariety is an infraspecific taxon. === Name === Its name consists of three parts: a genus name (genera) a specific epithet (species) an infraspecific epithet (subvariety) To indicate the subvariety rank, the abbreviation "subvar." is put before the infraspecific epithet. == References ==
|
{
"page_id": 393574,
"source": null,
"title": "Subvariety (botany)"
}
|
Kangina (Dari: کنگینه, lit. 'treasure', Dari pronunciation: [kʌn'ɡiːnɜ]) is the traditional Afghan technique of preserving fresh fruit, particularly grapes, in airtight discs (also called kangina) formed from mud and straw. The centuries-old technique is indigenous to Afghanistan's rural center and north, where remote communities that cannot import fresh fruit eat kangina-preserved fresh grapes throughout the winter, and merchants use kangina to safely store and transport grapes for sale at market. Grapes preserved using kangina in modern Afghanistan are typically of the thick-skinned Taifi or Kishmishi varieties, which are harvested later in the season and remain fresh in the mud vessels for up to six months. The method, a form of passive controlled-atmosphere storage, works by sealing fruit in the clay-rich mud, restricting flow of air, moisture and microbes, much as a plastic bag would. Discs are formed from two bowl-shaped pieces, which are sculpted from mud and straw, and baked in the sun before being filled with up to 1–2 kilograms (2.2–4.4 lb) of un-bruised fruit and sealed with more mud. They are kept dry and cool, away from direct sunlight. Gradual permeation of gas through the clay barrier allows oxygen to enter the container, keeping the grapes alive, while the elevated concentration of carbon dioxide inside the package inhibits the grapes' metabolism and prevents the growth of fungus. The grapes are prevented from drying out, and the mud absorbs liquid which would otherwise lead to bacterial and fungal growth. The practice of storing grapes in mud and straw has been recorded as far back as the 12th century: in his Book of Agriculture, Sevillan agronomist Ibn al-'Awwam noted layering grapes with straw in mud-sealed glass containers or "cowpat bowls" as an extant technique of preservation in Andalusia. Kangina are inexpensive, eco-friendly, and effective vessels for the preservation of fresh
|
{
"page_id": 75497831,
"source": null,
"title": "Kangina"
}
|
fruit. A 2023 study found kangina and polystyrene foam boxes to be the most effective vessels for preserving grapes. The containers are, however, heavy, unwieldy, and prone to absorbing moisture. == Notes == == References ==
|
{
"page_id": 75497831,
"source": null,
"title": "Kangina"
}
|
The L-ring of the bacterial flagellum is the ring in the lipid outer cell membrane through which the axial filament (rod, hook, and flagellum) passes. that l ring stands for lipopolysaccharide. == References ==
|
{
"page_id": 983400,
"source": null,
"title": "L ring"
}
|
Om Prakash Bhasin Award for Science and Technology is an Indian award, instituted in 1985 to recognize excellence in the areas of science and technology. The award, given individually or collectively to a group, is annual in cycle and carries a plaque, a citation and a cash prize of ₹ 100,000. The winners are invited to deliver the Om Prakash Bhasin Memorial Lecture at a venue decided by the award committee. == Profile == Om Prakash Bhasin Awards have been instituted by Shri Om Prakash Bhasin Foundation, a New Delhi-based charitable organization founded by Vinod Bhasin, along with her two sons, Shivy Bhasin and Hemant Kumar Bhasin, to honour the memory of her husband, Om Prakash Bhasin, a non resident Indian businessman. The corpus for the award of ₹ 5,100,000 was formed by Om Prakash Bhasin as a trust before his death. The awards, started in 1985, are given in five categories. The selection is through a notified procedure and is decided by a committee appointed for the purpose. The committee includes the Chairman of the foundation, two trustees representing the foundation, a member of the scientific community and a representative of the State Bank of India, the bankers to the foundation. The incumbent committee members are: Shivy Bhasin - Chairman Hemant Kumar Bhasin - Foundation trustee Vinod Prakash Sharma - Scientist trustee Samar Vikram Bhasin - Foundation trustee State Bank of India nominee == Categories == == Recipients == === Agriculture and Allied Sciences === Source: Shri Om Prakash Bhasin Foundation === Biotechnology === Source: Shri Om Prakash Bhasin Foundation |2020 || Asad Ullah Khan |} === Electronics and Information Technology === Source: Shri Om Prakash Bhasin Foundation === Engineering including Energy and Aerospace === Source: Shri Om Prakash Bhasin Foundation === Health and Medical Sciences === Source: Shri
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{
"page_id": 45023593,
"source": null,
"title": "Om Prakash Bhasin Award"
}
|
Om Prakash Bhasin Foundation == See also == List of general science and technology awards List of biology awards List of engineering awards List of medicine awards List of physics awards == References ==
|
{
"page_id": 45023593,
"source": null,
"title": "Om Prakash Bhasin Award"
}
|
Ecological classification or ecological typology is the classification of land or water into geographical units that represent variation in one or more ecological features. Traditional approaches focus on geology, topography, biogeography, soils, vegetation, climate conditions, living species, habitats, water resources, and sometimes also anthropic factors. Most approaches pursue the cartographical delineation or regionalisation of distinct areas for mapping and planning. == Approaches to classifications == Different approaches to ecological classifications have been developed in terrestrial, freshwater and marine disciplines. Traditionally these approaches have focused on biotic components (vegetation classification), abiotic components (environmental approaches) or implied ecological and evolutionary processes (biogeographical approaches). Ecosystem classifications are specific kinds of ecological classifications that consider all four elements of the definition of ecosystems: a biotic component, an abiotic complex, the interactions between and within them, and the physical space they occupy (ecotope). === Vegetation classification === Vegetation is often used to classify terrestrial ecological units. Vegetation classification can be based on vegetation structure and floristic composition. Classifications based entirely on vegetation structure overlap with land cover mapping categories. Many schemes of vegetation classification are in use by the land, resource and environmental management agencies of different national and state jurisdictions. The International Vegetation Classification (IVC or EcoVeg) has been recently proposed but has not been yet widely adopted. Vegetation classifications have limited use in aquatic systems, since only a handful of freshwater or marine habitats are dominated by plants (e.g. kelp forests or seagrass meadows). Also, some extreme terrestrial environments, like subterranean or cryogenic ecosystems, are not properly described in vegetation classifications. === Biogeographical approach === The disciplines of phytogeography and biogeography study the geographic distribution of plant communities and faunal communities. Common patterns of distribution of several taxonomic groups are generalised into bioregions, floristic provinces or zoogeographic regions. === Environmental approach === Climate
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{
"page_id": 196971,
"source": null,
"title": "Ecological classification"
}
|
classifications are used in terrestrial disciplines due to the major influence of climate on biological life in a region. The most popular classification scheme is probably the Köppen climate classification scheme. Similarly geological and soil properties can affect terrestrial vegetation. In marine disciplines, the stratification of water layers discriminate types based on the availability of light and nutrient, or changes in biogeochemical properties. === Ecosystem classifications === American geographer Robert Bailey defined a hierarchy of ecosystem units ranging from micro-ecosystems (individual homogeneous sites, in the order of 10 square kilometres (4 sq mi) in area), through meso-ecosystems (landscape mosaics, in the order of 1,000 square kilometres (400 sq mi)) to macro-ecosystems (ecoregions, in the order of 100,000 square kilometres (40,000 sq mi)).: Ch:2, p:25–28 Bailey outlined five different methods for identifying ecosystems: gestalt ("a whole that is not derived through considerable of its parts"), in which regions are recognized and boundaries drawn intuitively; a map overlay system where different layers like geology, landforms and soil types are overlain to identify ecosystems; multivariate clustering of site attributes; digital image processing of remotely sensed data grouping areas based on their appearance or other spectral properties; or by a "controlling factors method" where a subset of factors (like soils, climate, vegetation physiognomy or the distribution of plant or animal species) are selected from a large array of possible ones are used to delineate ecosystems.: Ch:3, p:29–40 In contrast with Bailey's methodology, Puerto Rico ecologist Ariel Lugo and coauthors identified ten characteristics of an effective classification system. For example that it be based on georeferenced, quantitative data; that it should minimize subjectivity and explicitly identify criteria and assumptions; that it should be structured around the factors that drive ecosystem processes; that it should reflect the hierarchical nature of ecosystems; that it should be flexible
|
{
"page_id": 196971,
"source": null,
"title": "Ecological classification"
}
|
enough to conform to the various scales at which ecosystem management operates. The International Union for The Conservation of Nature (IUCN) developed a global ecosystem typology that conforms to the definition of ecosystems as ecological units that comprise a biotic component, an abiotic complex, the interactions between and within them, and occupy a finite physical space or ecotope. This typology is based on six design principles: representation of ecological processes, representation of biota, conceptual consistency throughout the biosphere, scalable structure, spatially explicit units, parsimony and utility. This approach has led to a dual representation of ecosystem functionality and composition within a flexible hierarchical structure that can be built from a top-down approach (subdivision of upper units by function) and a bottom-up approach (representation of compositional variation within functional units). == See also == Land use Landscape ecology == References == == Bibliography == Gregorich, E. G., and et al. "Soil and Environmental Science Dictionary." Canadian ecological land classification system, pp 111 (2001). Canadian Society of Soil Science. CRC Press LLC. ISBN 0-8493-3115-3. Klijn, F., and H. A. Udo De Haes. 1994. "A hierarchical approach to ecosystems and its implications for ecological land classification." In: Landscape Ecology vol. 9 no. 2 pp 89–104 (1994). The Hague, SPB Academic Publishing bv. == External links == Example of ecological land classification in British Columbia (Canada) EcoSim Software Inc ELC eTool International Association for Vegetation Scientists (IAVS) – Vegetation Classification Methods
|
{
"page_id": 196971,
"source": null,
"title": "Ecological classification"
}
|
Comparative genomics is a branch of biological research that examines genome sequences across a spectrum of species, spanning from humans and mice to a diverse array of organisms from bacteria to chimpanzees. This large-scale holistic approach compares two or more genomes to discover the similarities and differences between the genomes and to study the biology of the individual genomes. Comparison of whole genome sequences provides a highly detailed view of how organisms are related to each other at the gene level. By comparing whole genome sequences, researchers gain insights into genetic relationships between organisms and study evolutionary changes. The major principle of comparative genomics is that common features of two organisms will often be encoded within the DNA that is evolutionarily conserved between them. Therefore, Comparative genomics provides a powerful tool for studying evolutionary changes among organisms, helping to identify genes that are conserved or common among species, as well as genes that give unique characteristics of each organism. Moreover, these studies can be performed at different levels of the genomes to obtain multiple perspectives about the organisms. The comparative genomic analysis begins with a simple comparison of the general features of genomes such as genome size, number of genes, and chromosome number. Table 1 presents data on several fully sequenced model organisms, and highlights some striking findings. For instance, while the tiny flowering plant Arabidopsis thaliana has a smaller genome than that of the fruit fly Drosophila melanogaster (157 million base pairs v. 165 million base pairs, respectively) it possesses nearly twice as many genes (25,000 v. 13,000). In fact, A. thaliana has approximately the same number of genes as humans (25,000). Thus, a very early lesson learned in the genomic era is that genome size does not correlate with evolutionary status, nor is the number of genes proportionate
|
{
"page_id": 917868,
"source": null,
"title": "Comparative genomics"
}
|
to genome size. In comparative genomics, synteny is the preserved order of genes on chromosomes of related species indicating their descent from a common ancestor. Synteny provides a framework in which the conservation of homologous genes and gene order is identified between genomes of different species. Synteny blocks are more formally defined as regions of chromosomes between genomes that share a common order of homologous genes derived from a common ancestor. Alternative names such as conserved synteny or collinearity have been used interchangeably. Comparisons of genome synteny between and within species have provided an opportunity to study evolutionary processes that lead to the diversity of chromosome number and structure in many lineages across the tree of life; early discoveries using such approaches include chromosomal conserved regions in nematodes and yeast, evolutionary history and phenotypic traits of extremely conserved Hox gene clusters across animals and MADS-box gene family in plants, and karyotype evolution in mammals and plants. Furthermore, comparing two genomes not only reveals conserved domains or synteny but also aids in detecting copy number variations, single nucleotide polymorphisms (SNPs), indels, and other genomic structural variations. Virtually started as soon as the whole genomes of two organisms became available (that is, the genomes of the bacteria Haemophilus influenzae and Mycoplasma genitalium) in 1995, comparative genomics is now a standard component of the analysis of every new genome sequence. With the explosion in the number of genome projects due to the advancements in DNA sequencing technologies, particularly the next-generation sequencing methods in late 2000s, this field has become more sophisticated, making it possible to deal with many genomes in a single study. Comparative genomics has revealed high levels of similarity between closely related organisms, such as humans and chimpanzees, and, more surprisingly, similarity between seemingly distantly related organisms, such as humans and
|
{
"page_id": 917868,
"source": null,
"title": "Comparative genomics"
}
|
the yeast Saccharomyces cerevisiae. It has also showed the extreme diversity of the gene composition in different evolutionary lineages. == History == See also: History of genomics Comparative genomics has a root in the comparison of virus genomes in the early 1980s. For example, small RNA viruses infecting animals (picornaviruses) and those infecting plants (cowpea mosaic virus) were compared and turned out to share significant sequence similarity and, in part, the order of their genes. In 1986, the first comparative genomic study at a larger scale was published, comparing the genomes of varicella-zoster virus and Epstein-Barr virus that contained more than 100 genes each. The first complete genome sequence of a cellular organism, that of Haemophilus influenzae Rd, was published in 1995. The second genome sequencing paper was of the small parasitic bacterium Mycoplasma genitalium published in the same year. Starting from this paper, reports on new genomes inevitably became comparative-genomic studies. Microbial genomes. The first high-resolution whole genome comparison system of microbial genomes of 10-15kbp was developed in 1998 by Art Delcher, Simon Kasif and Steven Salzberg and applied to the comparison of entire highly related microbial organisms with their collaborators at the Institute for Genomic Research (TIGR). The system is called MUMMER and was described in a publication in Nucleic Acids Research in 1999. The system helps researchers to identify large rearrangements, single base mutations, reversals, tandem repeat expansions and other polymorphisms. In bacteria, MUMMER enables the identification of polymorphisms that are responsible for virulence, pathogenicity, and anti-biotic resistance. The system was also applied to the Minimal Organism Project at TIGR and subsequently to many other comparative genomics projects. Eukaryote genomes. Saccharomyces cerevisiae, the baker's yeast, was the first eukaryote to have its complete genome sequence published in 1996. After the publication of the roundworm Caenorhabditis elegans genome
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in 1998 and together with the fruit fly Drosophila melanogaster genome in 2000, Gerald M. Rubin and his team published a paper titled "Comparative Genomics of the Eukaryotes", in which they compared the genomes of the eukaryotes D. melanogaster, C. elegans, and S. cerevisiae, as well as the prokaryote H. influenzae. At the same time, Bonnie Berger, Eric Lander, and their team published a paper on whole-genome comparison of human and mouse. With the publication of the large genomes of vertebrates in the 2000s, including human, the Japanese pufferfish Takifugu rubripes, and mouse, precomputed results of large genome comparisons have been released for downloading or for visualization in a genome browser. Instead of undertaking their own analyses, most biologists can access these large cross-species comparisons and avoid the impracticality caused by the size of the genomes. Next-generation sequencing methods, which were first introduced in 2007, have produced an enormous amount of genomic data and have allowed researchers to generate multiple (prokaryotic) draft genome sequences at once. These methods can also quickly uncover single-nucleotide polymorphisms, insertions and deletions by mapping unassembled reads against a well annotated reference genome, and thus provide a list of possible gene differences that may be the basis for any functional variation among strains. == Evolutionary principles == One character of biology is evolution, evolutionary theory is also the theoretical foundation of comparative genomics, and at the same time the results of comparative genomics unprecedentedly enriched and developed the theory of evolution. When two or more of the genome sequence are compared, one can deduce the evolutionary relationships of the sequences in a phylogenetic tree. Based on a variety of biological genome data and the study of vertical and horizontal evolution processes, one can understand vital parts of the gene structure and its regulatory function. Similarity of
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"page_id": 917868,
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related genomes is the basis of comparative genomics. If two creatures have a recent common ancestor, the differences between the two species genomes are evolved from the ancestors' genome. The closer the relationship between two organisms, the higher the similarities between their genomes. If there is close relationship between them, then their genome will display a linear behaviour (synteny), namely some or all of the genetic sequences are conserved. Thus, the genome sequences can be used to identify gene function, by analyzing their homology (sequence similarity) to genes of known function. Orthologous sequences are related sequences in different species: a gene exists in the original species, the species divided into two species, so genes in new species are orthologous to the sequence in the original species. Paralogous sequences are separated by gene cloning (gene duplication): if a particular gene in the genome is copied, then the copy of the two sequences is paralogous to the original gene. A pair of orthologous sequences is called orthologous pairs (orthologs), a pair of paralogous sequence is called collateral pairs (paralogs). Orthologous pairs usually have the same or similar function, which is not necessarily the case for collateral pairs. In collateral pairs, the sequences tend to evolve into having different functions. Comparative genomics exploits both similarities and differences in the proteins, RNA, and regulatory regions of different organisms to infer how selection has acted upon these elements. Those elements that are responsible for similarities between different species should be conserved through time (stabilizing selection), while those elements responsible for differences among species should be divergent (positive selection). Finally, those elements that are unimportant to the evolutionary success of the organism will be unconserved (selection is neutral). One of the important goals of the field is the identification of the mechanisms of eukaryotic genome evolution.
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"page_id": 917868,
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It is however often complicated by the multiplicity of events that have taken place throughout the history of individual lineages, leaving only distorted and superimposed traces in the genome of each living organism. For this reason comparative genomics studies of small model organisms (for example the model Caenorhabditis elegans and closely related Caenorhabditis briggsae) are of great importance to advance our understanding of general mechanisms of evolution. == Role of CNVs in evolution == Comparative genomics plays a crucial role in identifying copy number variations (CNVs) and understanding their significance in evolution. CNVs, which involve deletions or duplications of large segments of DNA, are recognized as a major source of genetic diversity, influencing gene structure, dosage, and regulation. While single nucleotide polymorphisms (SNPs) are more common, CNVs impact larger genomic regions and can have profound effects on phenotype and diversity. Recent studies suggest that CNVs constitute around 4.8–9.5% of the human genome and have a substantial functional and evolutionary impact. In mammals, CNVs contribute significantly to population diversity, influencing gene expression and various phenotypic traits. Comparative genomics analyses of human and chimpanzee genomes have revealed that CNVs may play a greater role in evolutionary change compared to single nucleotide changes. Research indicates that CNVs affect more nucleotides than individual base-pair changes, with about 2.7% of the genome affected by CNVs compared to 1.2% by SNPs. Moreover, while many CNVs are shared between humans and chimpanzees, a significant portion is unique to each species. Additionally, CNVs have been associated with genetic diseases in humans, highlighting their importance in human health. Despite this, many questions about CNVs remain unanswered, including their origin and contributions to evolutionary adaptation and disease. Ongoing research aims to address these questions using techniques like comparative genomic hybridization, which allows for a detailed examination of CNVs and their
|
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"page_id": 917868,
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"title": "Comparative genomics"
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significance. When investigators examined the raw sequence data of the human and chimpanzee. == Significance of comparative genomics == Comparative genomics holds profound significance across various fields, including medical research, basic biology, and biodiversity conservation. For instance, in medical research, predicting how genomic variants limited ability to predict which genomic variants lead to changes in organism-level phenotypes, such as increased disease risk in humans, remains challenging due to the immense size of the genome, comprising about three billion nucleotides. To tackle this challenge, comparative genomics offers a solution by pinpointing nucleotide positions that have remained unchanged over millions of years of evolution. These conserved regions indicate potential sites where genetic alterations could have detrimental effects on an organism's fitness, thus guiding the search for disease-causing variants. Moreover, comparative genomics holds promise in unraveling the mechanisms of gene evolution, environmental adaptations, gender-specific differences, and population variations across vertebrate lineages. Furthermore, comparative studies enable the identification of genomic signatures of selection—regions in the genome that have undergone preferential increase and fixation in populations due to their functional significance in specific processes. For instance, in animal genetics, indigenous cattle exhibit superior disease resistance and environmental adaptability but lower productivity compared to exotic breeds. Through comparative genomic analyses, significant genomic signatures responsible for these unique traits can be identified. Using insights from this signature, breeders can make informed decisions to enhance breeding strategies and promote breed development. == Methods == Computational approaches are necessary for genome comparisons, given the large amount of data encoded in genomes. Many tools are now publicly available, ranging from whole genome comparisons to gene expression analysis. This includes approaches from systems and control, information theory, string analysis and data mining. Computational approaches will remain critical for research and teaching, especially when information science and genome biology is taught in
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"page_id": 917868,
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conjunction. Comparative genomics starts with basic comparisons of genome size and gene density. For instance, genome size is important for coding capacity and possibly for regulatory reasons. High gene density facilitates genome annotation, analysis of environmental selection. By contrast, low gene density hampers the mapping of genetic disease as in the human genome. === Sequence alignment === Alignments are used to capture information about similar sequences such as ancestry, common evolutionary descent, or common structure and function. Alignments can be done for both nucleotide and protein sequences. Alignments consist of local or global pairwise alignments, and multiple sequence alignments. One way to find global alignments is to use a dynamic programming algorithm known as Needleman-Wunsch algorithmwhereas Smith–Waterman algorithm used to find local alignments. With the exponential growth of sequence databases and the emergence of longer sequences, there's a heightened interest in faster, approximate, or heuristic alignment procedures. Among these, the FASTA and BLAST algorithms are prominent for local pairwise alignment. Recent years have witnessed the development of programs tailored to aligning lengthy sequences, such as MUMmer (1999), BLASTZ (2003), and AVID (2003). While BLASTZ adopts a local approach, MUMmer and AVID are geared towards global alignment. To harness the benefits of both local and global alignment approaches, one effective strategy involves integrating them. Initially, a rapid variant of BLAST known as BLAT is employed to identify homologous "anchor" regions. These anchors are subsequently scrutinized to identify sets exhibiting conserved order and orientation. Such sets of anchors are then subjected to alignment using a global strategy. Additionally, ongoing efforts focus on optimizing existing algorithms to handle the vast amount of genome sequence data by enhancing their speed. Furthermore, MAVID stands out as another noteworthy pairwise alignment program specifically designed for aligning multiple genomes. Pairwise Comparison: The Pairwise comparison of genomic sequence
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"page_id": 917868,
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data is widely utilized in comparative gene prediction. Many studies in comparative functional genomics lean on pairwise comparisons, wherein traits of each gene are compared with traits of other genes across species. his method yields many more comparisons than unique observations, making each comparison dependent on others. Multiple comparisons: The comparison of multiple genomes is a natural extension of pairwise inter-specific comparisons. Such comparisons typically aim to identify conserved regions across two phylogenetic scales: 1. Deep comparisons, often referred to as phylogenetic footprinting reveal conservation across higher taxonomic units like vertebrates. 2. Shallow comparisons, recently termed Phylogenetic shadowing, probe conservation across a group of closely related species. === Whole-genome alignment === Whole-genome alignment (WGA) involves predicting evolutionary relationships at the nucleotide level between two or more genomes. It integrates elements of colinear sequence alignment and gene orthology prediction, presenting a greater challenge due to the vast size and intricate nature of whole genomes. Despite its complexity, numerous methods have emerged to tackle this problem because WGAs play a crucial role in various genome-wide analyses, such as phylogenetic inference, genome annotation, and function prediction. Thereby, SyRI (Synteny and Rearrangement Identifier) is one such method that utilizes whole genome alignment and it is designed to identify both structural and sequence differences between two whole-genome assemblies. By taking WGAs as input, SyRI initially scans for disparities in genome structures. Subsequently, it identifies local sequence variations within both rearranged and non-rearranged (syntenic) regions. === Phylogenetic reconstruction === Another computational method for comparative genomics is phylogenetic reconstruction. It is used to describe evolutionary relationships in terms of common ancestors. The relationships are usually represented in a tree called a phylogenetic tree. Similarly, coalescent theory is a retrospective model to trace alleles of a gene in a population to a single ancestral copy shared by members
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"page_id": 917868,
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of the population. This is also known as the most recent common ancestor. Analysis based on coalescence theory tries predicting the amount of time between the introduction of a mutation and a particular allele or gene distribution in a population. This time period is equal to how long ago the most recent common ancestor existed. The inheritance relationships are visualized in a form similar to a phylogenetic tree. Coalescence (or the gene genealogy) can be visualized using dendrograms. === Genome maps === An additional method in comparative genomics is genetic mapping. In genetic mapping, visualizing synteny is one way to see the preserved order of genes on chromosomes. It is usually used for chromosomes of related species, both of which result from a common ancestor. This and other methods can shed light on evolutionary history. A recent study used comparative genomics to reconstruct 16 ancestral karyotypes across the mammalian phylogeny. The computational reconstruction showed how chromosomes rearranged themselves during mammal evolution. It gave insight into conservation of select regions often associated with the control of developmental processes. In addition, it helped to provide an understanding of chromosome evolution and genetic diseases associated with DNA rearrangements. == Tools == Computational tools for analyzing sequences and complete genomes are developing quickly due to the availability of large amount of genomic data. At the same time, comparative analysis tools are progressed and improved. In the challenges about these analyses, it is very important to visualize the comparative results. Visualization of sequence conservation is a tough task of comparative sequence analysis. As we know, it is highly inefficient to examine the alignment of long genomic regions manually. Internet-based genome browsers provide many useful tools for investigating genomic sequences due to integrating all sequence-based biological information on genomic regions. When we extract large amount of
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"page_id": 917868,
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relevant biological data, they can be very easy to use and less time-consuming. UCSC Browser: This site contains the reference sequence and working draft assemblies for a large collection of genomes. Ensembl: The Ensembl project produces genome databases for vertebrates and other eukaryotic species, and makes this information freely available online. MapView: The Map Viewer provides a wide variety of genome mapping and sequencing data. VISTA is a comprehensive suite of programs and databases for comparative analysis of genomic sequences. It was built to visualize the results of comparative analysis based on DNA alignments. The presentation of comparative data generated by VISTA can easily suit both small and large scale of data. BlueJay Genome Browser: A stand-alone visualization tool for the multi-scale viewing of annotated genomes and other genomic elements. SyRI: SyRI stands for Synteny and Rearrangement Identifier and is a versatile tool for comparative genomics, offering functionalities for synteny analysis and visualization, aiding in the prediction of genomic differences between related genomes using whole-genome assemblies (WGA). Synmap2: Specifically designed for synteny mapping, Synmap2 efficiently compares genetic maps or assemblies, providing insights into genome evolution and rearrangements among related organisms. GSAlign: GSAlign facilitates accurate alignment of genomic sequences, particularly useful for large-scale comparative genomics studies, enabling researchers to identify similarities and differences across genomes. IGV (Integrative Genomics Viewer): A widely-used tool for visualizing and analyzing genomic data, IGV supports comparative genomics by enabling users to explore alignments, variants, and annotations across multiple genomes. Manta: Manta is a rapid structural variant caller, crucial for comparative genomics as it detects genomic rearrangements such as insertions, deletions, inversions, and duplications, aiding in understanding genetic variation among populations or species. CNVNatar: CNVNatar specializes in detecting copy number variations (CNVs), which are crucial in understanding genome evolution and population genetics, providing insights into genomic structural
|
{
"page_id": 917868,
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"title": "Comparative genomics"
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changes across different organisms. PIPMaker: PIPMaker facilitates the alignment and comparison of two genomic sequences, enabling the identification of conserved regions, duplications, and evolutionary breakpoints, aiding in comparative genomics analyses. GLASS (Genome-wide Location and Sequence Searcher): GLASS is a tool for identifying conserved regulatory elements across genomes, crucial for comparative genomics studies focusing on understanding gene regulation and evolution. PatternHunter: PatternHunter is a versatile tool for sequence analysis, offering functionalities for identifying conserved patterns, motifs, and repeats across genomic sequences, aiding in comparative genomics studies of gene families and regulatory elements. Mummer: Mummer is a suite of tools for whole-genome alignment and comparison, widely used in comparative genomics for identifying similarities, differences, and evolutionary events among genomes at various scales. An advantage of using online tools is that these websites are being developed and updated constantly. There are many new settings and content can be used online to improve efficiency. == Selected applications == === Agriculture === Agriculture is a field that reaps the benefits of comparative genomics. Identifying the loci of advantageous genes is a key step in breeding crops that are optimized for greater yield, cost-efficiency, quality, and disease resistance. For example, one genome wide association study conducted on 517 rice landraces revealed 80 loci associated with several categories of agronomic performance, such as grain weight, amylose content, and drought tolerance. Many of the loci were previously uncharacterized. Not only is this methodology powerful, it is also quick. Previous methods of identifying loci associated with agronomic performance required several generations of carefully monitored breeding of parent strains, a time-consuming effort that is unnecessary for comparative genomic studies. === Medicine === ==== Vaccine development ==== The medical field also benefits from the study of comparative genomics. In an approach known as reverse vaccinology, researchers can discover candidate antigens for
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"page_id": 917868,
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"title": "Comparative genomics"
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vaccine development by analyzing the genome of a pathogen or a family of pathogens. Applying a comparative genomics approach by analyzing the genomes of several related pathogens can lead to the development of vaccines that are multi-protective. A team of researchers employed such an approach to create a universal vaccine for Group B Streptococcus, a group of bacteria responsible for severe neonatal infection. Comparative genomics can also be used to generate specificity for vaccines against pathogens that are closely related to commensal microorganisms. For example, researchers used comparative genomic analysis of commensal and pathogenic strains of E. coli to identify pathogen-specific genes as a basis for finding antigens that result in immune response against pathogenic strains but not commensal ones. In May 2019, using the Global Genome Set, a team in the UK and Australia sequenced thousands of globally-collected isolates of Group A Streptococcus, providing potential targets for developing a vaccine against the pathogen, also known as S. pyogenes. Personalized Medicine Personalized Medicine, enabled by Comparative Genomics, represents a revolutionary approach in healthcare, tailoring medical treatment and disease prevention to the individual patient's genetic makeup. By analyzing genetic variations across populations and comparing them with an individual's genome, clinicians can identify specific genetic markers associated with disease susceptibility, drug metabolism, and treatment response. By identifying genetic variants associated with drug metabolism pathways, drug targets, and adverse reactions, personalized medicine can optimize medication selection, dosage, and treatment regimens for individual patients. This approach minimizes the risk of adverse drug reactions, enhances treatment efficacy, and improves patient outcomes. Cancer Cancer Genomics represents a cutting-edge field within oncology that leverages comparative genomics to revolutionize cancer diagnosis, treatment, and prevention strategies. Comparative genomics plays a crucial role in cancer research by identifying driver mutations, and providing comprehensive analyses of mutations, copy number alterations, structural
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"page_id": 917868,
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variants, gene expression, and DNA methylation profiles in large-scale studies across different cancer types. By analyzing the genomes of cancer cells and comparing them with healthy cells, researchers can uncover key genetic alterations driving tumorigenesis, tumor progression, and metastasis. This deep understanding of the genomic landscape of cancer has profound implications for precision oncology. Moreover, Comparative Genomics is instrumental in elucidating mechanisms of drug resistance—a major challenge in cancer treatment. ==== Mouse models in immunology ==== T cells (also known as a T lymphocytes or a thymocytes) are immune cells that grow from stem cells in the bone marrow. They assist to defend the body from infection and may aid in the fight against cancer. Because of their morphological, physiological, and genetic resemblance to humans, mice and rats have long been the preferred species for biomedical research animal models. Comparative Medicine Research is built on the ability to use information from one species to understand the same processes in another. We can get new insights into molecular pathways by comparing human and mouse T cells and their effects on the immune system utilizing comparative genomics. In order to comprehend its TCRs and their genes, Glusman conducted research on the sequencing of the human and mouse T cell receptor loci. TCR genes are well-known and serve as a significant resource for supporting functional genomics and understanding how genes and intergenic regions of the genome contribute to biological processes. T-cell immune receptors are important in seeing the world of pathogens in the cellular immune system. One of the reasons for sequencing the human and mouse TCR loci was to match the orthologous gene family sequences and discover conserved areas using comparative genomics. These, it was thought, would reflect two sorts of biological information: (1) exons and (2) regulatory sequences. In fact, the
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"page_id": 917868,
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majority of V, D, J, and C exons could be identified in this method. The variable regions are encoded by multiple unique DNA elements that are rearranged and connected during T cell (TCR) differentiation: variable (V), diversity (D), and joining (J) elements for the and polypeptides; and V and J elements for the and polypeptides.[Figure 1] However, several short noncoding conserved blocks of the genome had been shown. Both human and mouse motifs are largely clustered in the 200 bp [Figure 2], the known 3′ enhancers in the TCR/ were identified, and a conserved region of 100 bp in the mouse J intron was subsequently shown to have a regulatory function. Comparisons of the genomic sequences within each physical site or location of a specific gene on a chromosome (locs) and across species allow for research on other mechanisms and other regulatory signals. Some suggest new hypotheses about the evolution of TCRs, to be tested (and improved) by comparison to the TCR gene complement of other vertebrate species. A comparative genomic investigation of humans and mice will obviously allow for the discovery and annotation of many other genes, as well as identifying in other species for regulatory sequences. === Research === Comparative genomics also opens up new avenues in other areas of research. As DNA sequencing technology has become more accessible, the number of sequenced genomes has grown. With the increasing reservoir of available genomic data, the potency of comparative genomic inference has grown as well. A notable case of this increased potency is found in recent primate research. Comparative genomic methods have allowed researchers to gather information about genetic variation, differential gene expression, and evolutionary dynamics in primates that were indiscernible using previous data and methods. ==== Great Ape Genome Project ==== The Great Ape Genome Project used comparative
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"page_id": 917868,
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genomic methods to investigate genetic variation with reference to the six great ape species, finding healthy levels of variation in their gene pool despite shrinking population size. Another study showed that patterns of DNA methylation, which are a known regulation mechanism for gene expression, differ in the prefrontal cortex of humans versus chimps, and implicated this difference in the evolutionary divergence of the two species. == See also == Data mining Molecular evolution Comparative anatomy Homology Sequence mining Alignment-free sequence analysis == References == == Further reading == == External links == Genomes OnLine Database (GOLD) Genome News Network JCVI Comprehensive Microbial Resource Pathema: A Clade Specific Bioinformatics Resource Center CBS Genome Atlas Database The UCSC Genome Browser The U.S. National Human Genome Research Institute Ensembl The Ensembl Genome Browser Genolevures, comparative genomics of the Hemiascomycetous yeasts Phylogenetically Inferred Groups (PhIGs), a recently developed method incorporates phylogenetic signals in building gene clusters for use in comparative genomics. Metazome, a resource for the phylogenomic exploration and analysis of Metazoan gene families. IMG The Integrated Microbial Genomes system, for comparative genome analysis by the DOE-JGI. Dcode.org Dcode.org Comparative Genomics Center. SUPERFAMILY Protein annotations for all completely sequenced organisms Comparative Genomics Blastology and Open Source: Needs and Deeds Alignment-free comparative Genomics tool
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"page_id": 917868,
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Volume combustion synthesis (VCS) is method of chemical synthesis in which the reactants are heated uniformly in a controlled manner until a reaction ignites throughout the volume of the reaction chamber. The VCS mode is typically used for weakly exothermic reactions that require preheating prior to ignition. == References ==
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"page_id": 46268782,
"source": null,
"title": "Volume combustion synthesis"
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Tonk is a small carbonaceous chondrite meteorite that fell near Tonk, India in 1911. Despite its small size, it is often included in studies due to its compositional similarity to the early solar system. == Composition and classification == The meteorite consists of fragments that together weigh 7.7 g (0.27 oz) and fell near the city of Tonk in India near midday on 22 January 1911. It is one of five known meteorites belonging to the CI chondrite group. This group is remarkable for having an elemental distribution that has the strongest similarity to that of the solar nebula. Except for certain volatile elements, like carbon, hydrogen, oxygen, nitrogen and the noble gases, which are not present in the meteorite, the ratios of the elements are very similar. Notably though, the meteor is highly enriched in volatile mercury which is undetectable in the solar photosphere, and this is a major driver of the "mercury paradox" that mercury abundances in meteors do not follow its volatile nature and isotopic ratios based expected behaviour in the solar nebula. These features mean that it is often, despite its small size, included in meteorological studies. The meteorite contains dolomite, magnesite, magnetite, pentlandite and pyrrhotite. == Alternative names == The meteorite is also known as Chhabra and Jhalrapatan. == See also == Glossary of meteoritics == References ==
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{
"page_id": 63570288,
"source": null,
"title": "Tonk meteorite"
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The Food Processing Technology Building is a Georgia Institute of Technology and Georgia Tech Research Institute facility. It houses the Food Processing Technology Division of GTRI, which includes the Agricultural Technology Research Program (ATRP) and Georgia’s Traditional Industries Program for Food Processing. It opened on March 1, 2005, and was dedicated on May 19, 2005. == Facilities == The Food Processing Technology Building contains over 36,000 square feet of office and laboratory space, including a 4,370 square foot high-bay testing and fabrication space, a 16-by-24-foot climate-controlled experiment chamber, an indoor environmental pilot area, a full-service chemical wet laboratory, and a 48-seat auditorium. The building houses five research laboratories: an automation research laboratory, an electronics lab, a systems development and integration laboratory, an environmental laboratory, and an optics laboratory. The building's lower lobby area features an interactive exhibit about the role of technology in poultry and food processing. == References ==
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{
"page_id": 44302704,
"source": null,
"title": "Food Processing Technology Building"
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In physics, an elastic collision occurs between two physical objects in which the total kinetic energy of the two bodies remains the same. In an ideal, perfectly elastic collision, there is no net loss of kinetic energy into other forms such as heat, noise, or potential energy. During the collision of small objects, kinetic energy is first converted to potential energy associated with a repulsive or attractive force between the particles (when the particles move against this force, i.e. the angle between the force and the relative velocity is obtuse), then this potential energy is converted back to kinetic energy (when the particles move with this force, i.e. the angle between the force and the relative velocity is acute). Collisions of atoms are elastic, for example Rutherford backscattering. A useful special case of elastic collision is when the two bodies have equal mass, in which case they will simply exchange their momenta. The molecules—as distinct from atoms—of a gas or liquid rarely experience perfectly elastic collisions because kinetic energy is exchanged between the molecules’ translational motion and their internal degrees of freedom with each collision. At any instant, half the collisions are, to a varying extent, inelastic collisions (the pair possesses less kinetic energy in their translational motions after the collision than before), and half could be described as “super-elastic” (possessing more kinetic energy after the collision than before). Averaged across the entire sample, molecular collisions can be regarded as essentially elastic as long as Planck's law forbids energy from being carried away by black-body photons. In the case of macroscopic bodies, perfectly elastic collisions are an ideal never fully realized, but approximated by the interactions of objects such as billiard balls. When considering energies, possible rotational energy before and/or after a collision may also play a role. == Equations
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"page_id": 65907,
"source": null,
"title": "Elastic collision"
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== === One-dimensional Newtonian === In any collision without an external force, momentum is conserved; but in an elastic collision, kinetic energy is also conserved. Consider particles A and B with masses mA, mB, and velocities vA1, vB1 before collision, vA2, vB2 after collision. The conservation of momentum before and after the collision is expressed by: m A v A 1 + m B v B 1 = m A v A 2 + m B v B 2 . {\displaystyle m_{A}v_{A1}+m_{B}v_{B1}\ =\ m_{A}v_{A2}+m_{B}v_{B2}.} Likewise, the conservation of the total kinetic energy is expressed by: 1 2 m A v A 1 2 + 1 2 m B v B 1 2 = 1 2 m A v A 2 2 + 1 2 m B v B 2 2 . {\displaystyle {\tfrac {1}{2}}m_{A}v_{A1}^{2}+{\tfrac {1}{2}}m_{B}v_{B1}^{2}\ =\ {\tfrac {1}{2}}m_{A}v_{A2}^{2}+{\tfrac {1}{2}}m_{B}v_{B2}^{2}.} These equations may be solved directly to find v A 2 , v B 2 {\displaystyle v_{A2},v_{B2}} when v A 1 , v B 1 {\displaystyle v_{A1},v_{B1}} are known: v A 2 = m A − m B m A + m B v A 1 + 2 m B m A + m B v B 1 v B 2 = 2 m A m A + m B v A 1 + m B − m A m A + m B v B 1 . {\displaystyle {\begin{array}{ccc}v_{A2}&=&{\dfrac {m_{A}-m_{B}}{m_{A}+m_{B}}}v_{A1}+{\dfrac {2m_{B}}{m_{A}+m_{B}}}v_{B1}\\[.5em]v_{B2}&=&{\dfrac {2m_{A}}{m_{A}+m_{B}}}v_{A1}+{\dfrac {m_{B}-m_{A}}{m_{A}+m_{B}}}v_{B1}.\end{array}}} Alternatively the final velocity of a particle, v2 (vA2 or vB2) is expressed by: v 2 = ( 1 + e ) v C o M − e v 1 {\displaystyle v_{2}=(1+e)v_{CoM}-ev_{1}} Where: e is the coefficient of restitution. vCoM is the velocity of the center of mass of the system of two particles: v C o M = m A v A 1 + m B
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"page_id": 65907,
"source": null,
"title": "Elastic collision"
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v B 1 m A + m B {\displaystyle v_{CoM}={\dfrac {m_{A}v_{A1}+m_{B}v_{B1}}{m_{A}+m_{B}}}} v1 (vA1 or vB1) is the initial velocity of the particle. If both masses are the same, we have a trivial solution: v A 2 = v B 1 v B 2 = v A 1 . {\displaystyle {\begin{aligned}v_{A2}&=v_{B1}\\v_{B2}&=v_{A1}.\end{aligned}}} This simply corresponds to the bodies exchanging their initial velocities with each other. As can be expected, the solution is invariant under adding a constant to all velocities (Galilean relativity), which is like using a frame of reference with constant translational velocity. Indeed, to derive the equations, one may first change the frame of reference so that one of the known velocities is zero, determine the unknown velocities in the new frame of reference, and convert back to the original frame of reference. ==== Examples ==== Before collision Ball A: mass = 3 kg, velocity = 4 m/s Ball B: mass = 5 kg, velocity = 0 m/s After collision Ball A: velocity = −1 m/s Ball B: velocity = 3 m/s Another situation: The following illustrate the case of equal mass, m A = m B {\displaystyle m_{A}=m_{B}} . In the limiting case where m A {\displaystyle m_{A}} is much larger than m B {\displaystyle m_{B}} , such as a ping-pong paddle hitting a ping-pong ball or an SUV hitting a trash can, the heavier mass hardly changes velocity, while the lighter mass bounces off, reversing its velocity plus approximately twice that of the heavy one. In the case of a large v A 1 {\displaystyle v_{A1}} , the value of v A 2 {\displaystyle v_{A2}} is small if the masses are approximately the same: hitting a much lighter particle does not change the velocity much, hitting a much heavier particle causes the fast particle to bounce back with
|
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"page_id": 65907,
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"title": "Elastic collision"
}
|
high speed. This is why a neutron moderator (a medium which slows down fast neutrons, thereby turning them into thermal neutrons capable of sustaining a chain reaction) is a material full of atoms with light nuclei which do not easily absorb neutrons: the lightest nuclei have about the same mass as a neutron. ==== Derivation of solution ==== To derive the above equations for v A 2 , v B 2 , {\displaystyle v_{A2},v_{B2},} rearrange the kinetic energy and momentum equations: m A ( v A 2 2 − v A 1 2 ) = m B ( v B 1 2 − v B 2 2 ) m A ( v A 2 − v A 1 ) = m B ( v B 1 − v B 2 ) {\displaystyle {\begin{aligned}m_{A}(v_{A2}^{2}-v_{A1}^{2})&=m_{B}(v_{B1}^{2}-v_{B2}^{2})\\m_{A}(v_{A2}-v_{A1})&=m_{B}(v_{B1}-v_{B2})\end{aligned}}} Dividing each side of the top equation by each side of the bottom equation, and using a 2 − b 2 ( a − b ) = a + b , {\displaystyle {\tfrac {a^{2}-b^{2}}{(a-b)}}=a+b,} gives: v A 2 + v A 1 = v B 1 + v B 2 ⇒ v A 2 − v B 2 = v B 1 − v A 1 {\displaystyle v_{A2}+v_{A1}=v_{B1}+v_{B2}\quad \Rightarrow \quad v_{A2}-v_{B2}=v_{B1}-v_{A1}} That is, the relative velocity of one particle with respect to the other is reversed by the collision. Now the above formulas follow from solving a system of linear equations for v A 2 , v B 2 , {\displaystyle v_{A2},v_{B2},} regarding m A , m B , v A 1 , v B 1 {\displaystyle m_{A},m_{B},v_{A1},v_{B1}} as constants: { v A 2 − v B 2 = v B 1 − v A 1 m A v A 1 + m B v B 1 = m A v A 2 + m B v
|
{
"page_id": 65907,
"source": null,
"title": "Elastic collision"
}
|
B 2 . {\displaystyle \left\{{\begin{array}{rcrcc}v_{A2}&-&v_{B2}&=&v_{B1}-v_{A1}\\m_{A}v_{A1}&+&m_{B}v_{B1}&=&m_{A}v_{A2}+m_{B}v_{B2}.\end{array}}\right.} Once v A 2 {\displaystyle v_{A2}} is determined, v B 2 {\displaystyle v_{B2}} can be found by symmetry. ==== Center of mass frame ==== With respect to the center of mass, both velocities are reversed by the collision: a heavy particle moves slowly toward the center of mass, and bounces back with the same low speed, and a light particle moves fast toward the center of mass, and bounces back with the same high speed. The velocity of the center of mass does not change by the collision. To see this, consider the center of mass at time t {\displaystyle t} before collision and time t ′ {\displaystyle t'} after collision: x ¯ ( t ) = m A x A ( t ) + m B x B ( t ) m A + m B x ¯ ( t ′ ) = m A x A ( t ′ ) + m B x B ( t ′ ) m A + m B . {\displaystyle {\begin{aligned}{\bar {x}}(t)&={\frac {m_{A}x_{A}(t)+m_{B}x_{B}(t)}{m_{A}+m_{B}}}\\{\bar {x}}(t')&={\frac {m_{A}x_{A}(t')+m_{B}x_{B}(t')}{m_{A}+m_{B}}}.\end{aligned}}} Hence, the velocities of the center of mass before and after collision are: v x ¯ = m A v A 1 + m B v B 1 m A + m B v x ¯ ′ = m A v A 2 + m B v B 2 m A + m B . {\displaystyle {\begin{aligned}v_{\bar {x}}&={\frac {m_{A}v_{A1}+m_{B}v_{B1}}{m_{A}+m_{B}}}\\v_{\bar {x}}'&={\frac {m_{A}v_{A2}+m_{B}v_{B2}}{m_{A}+m_{B}}}.\end{aligned}}} The numerators of v x ¯ {\displaystyle v_{\bar {x}}} and v x ¯ ′ {\displaystyle v_{\bar {x}}'} are the total momenta before and after collision. Since momentum is conserved, we have v x ¯ = v x ¯ ′ . {\displaystyle v_{\bar {x}}=v_{\bar {x}}'\,.} === One-dimensional relativistic === According to special relativity, p = m v 1 − v 2 c
|
{
"page_id": 65907,
"source": null,
"title": "Elastic collision"
}
|
2 {\displaystyle p={\frac {mv}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}} where p denotes momentum of any particle with mass, v denotes velocity, and c is the speed of light. In the center of momentum frame where the total momentum equals zero, p 1 = − p 2 p 1 2 = p 2 2 E = m 1 2 c 4 + p 1 2 c 2 + m 2 2 c 4 + p 2 2 c 2 = E p 1 = ± E 4 − 2 E 2 m 1 2 c 4 − 2 E 2 m 2 2 c 4 + m 1 4 c 8 − 2 m 1 2 m 2 2 c 8 + m 2 4 c 8 2 c E u 1 = − v 1 . {\displaystyle {\begin{aligned}p_{1}&=-p_{2}\\p_{1}^{2}&=p_{2}^{2}\\E&={\sqrt {m_{1}^{2}c^{4}+p_{1}^{2}c^{2}}}+{\sqrt {m_{2}^{2}c^{4}+p_{2}^{2}c^{2}}}=E\\p_{1}&=\pm {\frac {\sqrt {E^{4}-2E^{2}m_{1}^{2}c^{4}-2E^{2}m_{2}^{2}c^{4}+m_{1}^{4}c^{8}-2m_{1}^{2}m_{2}^{2}c^{8}+m_{2}^{4}c^{8}}}{2cE}}\\u_{1}&=-v_{1}.\end{aligned}}} Here m 1 , m 2 {\displaystyle m_{1},m_{2}} represent the rest masses of the two colliding bodies, u 1 , u 2 {\displaystyle u_{1},u_{2}} represent their velocities before collision, v 1 , v 2 {\displaystyle v_{1},v_{2}} their velocities after collision, p 1 , p 2 {\displaystyle p_{1},p_{2}} their momenta, c {\displaystyle c} is the speed of light in vacuum, and E {\displaystyle E} denotes the total energy, the sum of rest masses and kinetic energies of the two bodies. Since the total energy and momentum of the system are conserved and their rest masses do not change, it is shown that the momentum of the colliding body is decided by the rest masses of the colliding bodies, total energy and the total momentum. Relative to the center of momentum frame, the momentum of each colliding body does not change magnitude after collision, but reverses its direction of movement. Comparing with classical mechanics, which gives accurate results dealing with macroscopic objects
|
{
"page_id": 65907,
"source": null,
"title": "Elastic collision"
}
|
moving much slower than the speed of light, total momentum of the two colliding bodies is frame-dependent. In the center of momentum frame, according to classical mechanics, m 1 u 1 + m 2 u 2 = m 1 v 1 + m 2 v 2 = 0 m 1 u 1 2 + m 2 u 2 2 = m 1 v 1 2 + m 2 v 2 2 ( m 2 u 2 ) 2 2 m 1 + ( m 2 u 2 ) 2 2 m 2 = ( m 2 v 2 ) 2 2 m 1 + ( m 2 v 2 ) 2 2 m 2 ( m 1 + m 2 ) ( m 2 u 2 ) 2 = ( m 1 + m 2 ) ( m 2 v 2 ) 2 u 2 = − v 2 ( m 1 u 1 ) 2 2 m 1 + ( m 1 u 1 ) 2 2 m 2 = ( m 1 v 1 ) 2 2 m 1 + ( m 1 v 1 ) 2 2 m 2 ( m 1 + m 2 ) ( m 1 u 1 ) 2 = ( m 1 + m 2 ) ( m 1 v 1 ) 2 u 1 = − v 1 . {\displaystyle {\begin{aligned}m_{1}u_{1}+m_{2}u_{2}&=m_{1}v_{1}+m_{2}v_{2}=0\\m_{1}u_{1}^{2}+m_{2}u_{2}^{2}&=m_{1}v_{1}^{2}+m_{2}v_{2}^{2}\\{\frac {(m_{2}u_{2})^{2}}{2m_{1}}}+{\frac {(m_{2}u_{2})^{2}}{2m_{2}}}&={\frac {(m_{2}v_{2})^{2}}{2m_{1}}}+{\frac {(m_{2}v_{2})^{2}}{2m_{2}}}\\(m_{1}+m_{2})(m_{2}u_{2})^{2}&=(m_{1}+m_{2})(m_{2}v_{2})^{2}\\u_{2}&=-v_{2}\\{\frac {(m_{1}u_{1})^{2}}{2m_{1}}}+{\frac {(m_{1}u_{1})^{2}}{2m_{2}}}&={\frac {(m_{1}v_{1})^{2}}{2m_{1}}}+{\frac {(m_{1}v_{1})^{2}}{2m_{2}}}\\(m_{1}+m_{2})(m_{1}u_{1})^{2}&=(m_{1}+m_{2})(m_{1}v_{1})^{2}\\u_{1}&=-v_{1}\,.\end{aligned}}} This agrees with the relativistic calculation u 1 = − v 1 , {\displaystyle u_{1}=-v_{1},} despite other differences. One of the postulates in Special Relativity states that the laws of physics, such as conservation of momentum, should be invariant in all inertial frames of reference. In a general inertial frame where the total momentum could be arbitrary, m 1 u 1 1
|
{
"page_id": 65907,
"source": null,
"title": "Elastic collision"
}
|
− u 1 2 / c 2 + m 2 u 2 1 − u 2 2 / c 2 = m 1 v 1 1 − v 1 2 / c 2 + m 2 v 2 1 − v 2 2 / c 2 = p T m 1 c 2 1 − u 1 2 / c 2 + m 2 c 2 1 − u 2 2 / c 2 = m 1 c 2 1 − v 1 2 / c 2 + m 2 c 2 1 − v 2 2 / c 2 = E {\displaystyle {\begin{aligned}{\frac {m_{1}\;u_{1}}{\sqrt {1-u_{1}^{2}/c^{2}}}}+{\frac {m_{2}\;u_{2}}{\sqrt {1-u_{2}^{2}/c^{2}}}}&={\frac {m_{1}\;v_{1}}{\sqrt {1-v_{1}^{2}/c^{2}}}}+{\frac {m_{2}\;v_{2}}{\sqrt {1-v_{2}^{2}/c^{2}}}}=p_{T}\\{\frac {m_{1}c^{2}}{\sqrt {1-u_{1}^{2}/c^{2}}}}+{\frac {m_{2}c^{2}}{\sqrt {1-u_{2}^{2}/c^{2}}}}&={\frac {m_{1}c^{2}}{\sqrt {1-v_{1}^{2}/c^{2}}}}+{\frac {m_{2}c^{2}}{\sqrt {1-v_{2}^{2}/c^{2}}}}=E\end{aligned}}} We can look at the two moving bodies as one system of which the total momentum is p T , {\displaystyle p_{T},} the total energy is E {\displaystyle E} and its velocity v c {\displaystyle v_{c}} is the velocity of its center of mass. Relative to the center of momentum frame the total momentum equals zero. It can be shown that v c {\displaystyle v_{c}} is given by: v c = p T c 2 E {\displaystyle v_{c}={\frac {p_{T}c^{2}}{E}}} Now the velocities before the collision in the center of momentum frame u 1 ′ {\displaystyle u_{1}'} and u 2 ′ {\displaystyle u_{2}'} are: u 1 ′ = u 1 − v c 1 − u 1 v c c 2 u 2 ′ = u 2 − v c 1 − u 2 v c c 2 v 1 ′ = − u 1 ′ v 2 ′ = − u 2 ′ v 1 = v 1 ′ + v c 1 + v 1 ′ v c c 2 v 2 = v 2 ′ + v c
|
{
"page_id": 65907,
"source": null,
"title": "Elastic collision"
}
|
1 + v 2 ′ v c c 2 {\displaystyle {\begin{aligned}u_{1}'&={\frac {u_{1}-v_{c}}{1-{\frac {u_{1}v_{c}}{c^{2}}}}}\\u_{2}'&={\frac {u_{2}-v_{c}}{1-{\frac {u_{2}v_{c}}{c^{2}}}}}\\v_{1}'&=-u_{1}'\\v_{2}'&=-u_{2}'\\v_{1}&={\frac {v_{1}'+v_{c}}{1+{\frac {v_{1}'v_{c}}{c^{2}}}}}\\v_{2}&={\frac {v_{2}'+v_{c}}{1+{\frac {v_{2}'v_{c}}{c^{2}}}}}\end{aligned}}} When u 1 ≪ c {\displaystyle u_{1}\ll c} and u 2 ≪ c , {\displaystyle u_{2}\ll c\,,} p T ≈ m 1 u 1 + m 2 u 2 v c ≈ m 1 u 1 + m 2 u 2 m 1 + m 2 u 1 ′ ≈ u 1 − v c ≈ m 1 u 1 + m 2 u 1 − m 1 u 1 − m 2 u 2 m 1 + m 2 = m 2 ( u 1 − u 2 ) m 1 + m 2 u 2 ′ ≈ m 1 ( u 2 − u 1 ) m 1 + m 2 v 1 ′ ≈ m 2 ( u 2 − u 1 ) m 1 + m 2 v 2 ′ ≈ m 1 ( u 1 − u 2 ) m 1 + m 2 v 1 ≈ v 1 ′ + v c ≈ m 2 u 2 − m 2 u 1 + m 1 u 1 + m 2 u 2 m 1 + m 2 = u 1 ( m 1 − m 2 ) + 2 m 2 u 2 m 1 + m 2 v 2 ≈ u 2 ( m 2 − m 1 ) + 2 m 1 u 1 m 1 + m 2 {\displaystyle {\begin{aligned}p_{T}&\approx m_{1}u_{1}+m_{2}u_{2}\\v_{c}&\approx {\frac {m_{1}u_{1}+m_{2}u_{2}}{m_{1}+m_{2}}}\\u_{1}'&\approx u_{1}-v_{c}\approx {\frac {m_{1}u_{1}+m_{2}u_{1}-m_{1}u_{1}-m_{2}u_{2}}{m_{1}+m_{2}}}={\frac {m_{2}(u_{1}-u_{2})}{m_{1}+m_{2}}}\\u_{2}'&\approx {\frac {m_{1}(u_{2}-u_{1})}{m_{1}+m_{2}}}\\v_{1}'&\approx {\frac {m_{2}(u_{2}-u_{1})}{m_{1}+m_{2}}}\\v_{2}'&\approx {\frac {m_{1}(u_{1}-u_{2})}{m_{1}+m_{2}}}\\v_{1}&\approx v_{1}'+v_{c}\approx {\frac {m_{2}u_{2}-m_{2}u_{1}+m_{1}u_{1}+m_{2}u_{2}}{m_{1}+m_{2}}}={\frac {u_{1}(m_{1}-m_{2})+2m_{2}u_{2}}{m_{1}+m_{2}}}\\v_{2}&\approx {\frac {u_{2}(m_{2}-m_{1})+2m_{1}u_{1}}{m_{1}+m_{2}}}\end{aligned}}} Therefore, the classical calculation holds true when the speed of both colliding bodies is much lower than the speed of light (~300,000 kilometres per second). === Relativistic derivation using hyperbolic functions === Using
|
{
"page_id": 65907,
"source": null,
"title": "Elastic collision"
}
|
the so-called parameter of velocity s {\displaystyle s} (usually called the rapidity), v c = tanh ( s ) , {\displaystyle {\frac {v}{c}}=\tanh(s),} we get 1 − v 2 c 2 = sech ( s ) . {\displaystyle {\sqrt {1-{\frac {v^{2}}{c^{2}}}}}=\operatorname {sech} (s).} Relativistic energy and momentum are expressed as follows: E = m c 2 1 − v 2 c 2 = m c 2 cosh ( s ) p = m v 1 − v 2 c 2 = m c sinh ( s ) {\displaystyle {\begin{aligned}E&={\frac {mc^{2}}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}=mc^{2}\cosh(s)\\p&={\frac {mv}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}=mc\sinh(s)\end{aligned}}} Equations sum of energy and momentum colliding masses m 1 {\displaystyle m_{1}} and m 2 , {\displaystyle m_{2},} (velocities v 1 , v 2 , u 1 , u 2 {\displaystyle v_{1},v_{2},u_{1},u_{2}} correspond to the velocity parameters s 1 , s 2 , s 3 , s 4 {\displaystyle s_{1},s_{2},s_{3},s_{4}} ), after dividing by adequate power c {\displaystyle c} are as follows: m 1 cosh ( s 1 ) + m 2 cosh ( s 2 ) = m 1 cosh ( s 3 ) + m 2 cosh ( s 4 ) m 1 sinh ( s 1 ) + m 2 sinh ( s 2 ) = m 1 sinh ( s 3 ) + m 2 sinh ( s 4 ) {\displaystyle {\begin{aligned}m_{1}\cosh(s_{1})+m_{2}\cosh(s_{2})&=m_{1}\cosh(s_{3})+m_{2}\cosh(s_{4})\\m_{1}\sinh(s_{1})+m_{2}\sinh(s_{2})&=m_{1}\sinh(s_{3})+m_{2}\sinh(s_{4})\end{aligned}}} and dependent equation, the sum of above equations: m 1 e s 1 + m 2 e s 2 = m 1 e s 3 + m 2 e s 4 {\displaystyle m_{1}e^{s_{1}}+m_{2}e^{s_{2}}=m_{1}e^{s_{3}}+m_{2}e^{s_{4}}} subtract squares both sides equations "momentum" from "energy" and use the identity cosh 2 ( s ) − sinh 2 ( s ) = 1 , {\textstyle \cosh ^{2}(s)-\sinh ^{2}(s)=1,} after simplifying
|
{
"page_id": 65907,
"source": null,
"title": "Elastic collision"
}
|
we get: 2 m 1 m 2 ( cosh ( s 1 ) cosh ( s 2 ) − sinh ( s 2 ) sinh ( s 1 ) ) = 2 m 1 m 2 ( cosh ( s 3 ) cosh ( s 4 ) − sinh ( s 4 ) sinh ( s 3 ) ) {\displaystyle 2m_{1}m_{2}(\cosh(s_{1})\cosh(s_{2})-\sinh(s_{2})\sinh(s_{1}))=2m_{1}m_{2}(\cosh(s_{3})\cosh(s_{4})-\sinh(s_{4})\sinh(s_{3}))} for non-zero mass, using the hyperbolic trigonometric identity cosh ( a − b ) = cosh ( a ) cosh ( b ) − sinh ( b ) sinh ( a ) , {\textstyle \cosh(a-b)=\cosh(a)\cosh(b)-\sinh(b)\sinh(a),} we get: cosh ( s 1 − s 2 ) = cosh ( s 3 − s 4 ) {\displaystyle \cosh(s_{1}-s_{2})=\cosh(s_{3}-s_{4})} as functions cosh ( s ) {\displaystyle \cosh(s)} is even we get two solutions: s 1 − s 2 = s 3 − s 4 s 1 − s 2 = − s 3 + s 4 {\displaystyle {\begin{aligned}s_{1}-s_{2}&=s_{3}-s_{4}\\s_{1}-s_{2}&=-s_{3}+s_{4}\end{aligned}}} from the last equation, leading to a non-trivial solution, we solve s 2 {\displaystyle s_{2}} and substitute into the dependent equation, we obtain e s 1 {\displaystyle e^{s_{1}}} and then e s 2 , {\displaystyle e^{s_{2}},} we have: e s 1 = e s 4 m 1 e s 3 + m 2 e s 4 m 1 e s 4 + m 2 e s 3 e s 2 = e s 3 m 1 e s 3 + m 2 e s 4 m 1 e s 4 + m 2 e s 3 {\displaystyle {\begin{aligned}e^{s_{1}}&=e^{s_{4}}{\frac {m_{1}e^{s_{3}}+m_{2}e^{s_{4}}}{m_{1}e^{s_{4}}+m_{2}e^{s_{3}}}}\\e^{s_{2}}&=e^{s_{3}}{\frac {m_{1}e^{s_{3}}+m_{2}e^{s_{4}}}{m_{1}e^{s_{4}}+m_{2}e^{s_{3}}}}\end{aligned}}} It is a solution to the problem, but expressed by the parameters of velocity. Return substitution to get the solution for velocities is: v 1 / c =
|
{
"page_id": 65907,
"source": null,
"title": "Elastic collision"
}
|
tanh ( s 1 ) = e s 1 − e − s 1 e s 1 + e − s 1 v 2 / c = tanh ( s 2 ) = e s 2 − e − s 2 e s 2 + e − s 2 {\displaystyle {\begin{aligned}v_{1}/c&=\tanh(s_{1})={\frac {e^{s_{1}}-e^{-s_{1}}}{e^{s_{1}}+e^{-s_{1}}}}\\v_{2}/c&=\tanh(s_{2})={\frac {e^{s_{2}}-e^{-s_{2}}}{e^{s_{2}}+e^{-s_{2}}}}\end{aligned}}} Substitute the previous solutions and replace: e s 3 = c + u 1 c − u 1 {\displaystyle e^{s_{3}}={\sqrt {\frac {c+u_{1}}{c-u_{1}}}}} and e s 4 = c + u 2 c − u 2 , {\displaystyle e^{s_{4}}={\sqrt {\frac {c+u_{2}}{c-u_{2}}}},} after long transformation, with substituting: Z = ( 1 − u 1 2 / c 2 ) ( 1 − u 2 2 / c 2 ) {\textstyle Z={\sqrt {\left(1-u_{1}^{2}/c^{2}\right)\left(1-u_{2}^{2}/c^{2}\right)}}} we get: v 1 = 2 m 1 m 2 c 2 u 2 Z + 2 m 2 2 c 2 u 2 − ( m 1 2 + m 2 2 ) u 1 u 2 2 + ( m 1 2 − m 2 2 ) c 2 u 1 2 m 1 m 2 c 2 Z − 2 m 2 2 u 1 u 2 − ( m 1 2 − m 2 2 ) u 2 2 + ( m 1 2 + m 2 2 ) c 2 v 2 = 2 m 1 m 2 c 2 u 1 Z + 2 m 1 2 c 2 u 1 − ( m 1 2 + m 2 2 ) u 1 2 u 2 + ( m 2 2 − m 1 2 ) c 2 u 2 2 m 1 m 2 c 2 Z − 2 m 1 2 u 1 u 2 − ( m 2 2 − m 1 2 ) u 1
|
{
"page_id": 65907,
"source": null,
"title": "Elastic collision"
}
|
2 + ( m 1 2 + m 2 2 ) c 2 . {\displaystyle {\begin{aligned}v_{1}&={\frac {2m_{1}m_{2}c^{2}u_{2}Z+2m_{2}^{2}c^{2}u_{2}-(m_{1}^{2}+m_{2}^{2})u_{1}u_{2}^{2}+(m_{1}^{2}-m_{2}^{2})c^{2}u_{1}}{2m_{1}m_{2}c^{2}Z-2m_{2}^{2}u_{1}u_{2}-(m_{1}^{2}-m_{2}^{2})u_{2}^{2}+(m_{1}^{2}+m_{2}^{2})c^{2}}}\\v_{2}&={\frac {2m_{1}m_{2}c^{2}u_{1}Z+2m_{1}^{2}c^{2}u_{1}-(m_{1}^{2}+m_{2}^{2})u_{1}^{2}u_{2}+(m_{2}^{2}-m_{1}^{2})c^{2}u_{2}}{2m_{1}m_{2}c^{2}Z-2m_{1}^{2}u_{1}u_{2}-(m_{2}^{2}-m_{1}^{2})u_{1}^{2}+(m_{1}^{2}+m_{2}^{2})c^{2}}}\,.\end{aligned}}} == Two-dimensional == For the case of two non-spinning colliding bodies in two dimensions, the motion of the bodies is determined by the three conservation laws of momentum, kinetic energy and angular momentum. The overall velocity of each body must be split into two perpendicular velocities: one tangent to the common normal surfaces of the colliding bodies at the point of contact, the other along the line of collision. Since the collision only imparts force along the line of collision, the velocities that are tangent to the point of collision do not change. The velocities along the line of collision can then be used in the same equations as a one-dimensional collision. The final velocities can then be calculated from the two new component velocities and will depend on the point of collision. Studies of two-dimensional collisions are conducted for many bodies in the framework of a two-dimensional gas. In a center of momentum frame at any time the velocities of the two bodies are in opposite directions, with magnitudes inversely proportional to the masses. In an elastic collision these magnitudes do not change. The directions may change depending on the shapes of the bodies and the point of impact. For example, in the case of spheres the angle depends on the distance between the (parallel) paths of the centers of the two bodies. Any non-zero change of direction is possible: if this distance is zero the velocities are reversed in the collision; if it is close to the sum of the radii of the spheres the two bodies are only slightly deflected. Assuming that the second particle is at rest before the collision, the angles of deflection of the two particles,
|
{
"page_id": 65907,
"source": null,
"title": "Elastic collision"
}
|
θ 1 {\displaystyle \theta _{1}} and θ 2 {\displaystyle \theta _{2}} , are related to the angle of deflection θ {\displaystyle \theta } in the system of the center of mass by tan θ 1 = m 2 sin θ m 1 + m 2 cos θ , θ 2 = π − θ 2 . {\displaystyle \tan \theta _{1}={\frac {m_{2}\sin \theta }{m_{1}+m_{2}\cos \theta }},\qquad \theta _{2}={\frac {{\pi }-{\theta }}{2}}.} The magnitudes of the velocities of the particles after the collision are: v 1 ′ = v 1 m 1 2 + m 2 2 + 2 m 1 m 2 cos θ m 1 + m 2 v 2 ′ = v 1 2 m 1 m 1 + m 2 sin θ 2 . {\displaystyle {\begin{aligned}v'_{1}&=v_{1}{\frac {\sqrt {m_{1}^{2}+m_{2}^{2}+2m_{1}m_{2}\cos \theta }}{m_{1}+m_{2}}}\\v'_{2}&=v_{1}{\frac {2m_{1}}{m_{1}+m_{2}}}\sin {\frac {\theta }{2}}.\end{aligned}}} === Two-dimensional collision with two moving objects === The final x and y velocities components of the first ball can be calculated as: v 1 x ′ = v 1 cos ( θ 1 − φ ) ( m 1 − m 2 ) + 2 m 2 v 2 cos ( θ 2 − φ ) m 1 + m 2 cos ( φ ) + v 1 sin ( θ 1 − φ ) cos ( φ + π 2 ) v 1 y ′ = v 1 cos ( θ 1 − φ ) ( m 1 − m 2 ) + 2 m 2 v 2 cos ( θ 2 − φ ) m 1 + m 2 sin ( φ ) + v 1 sin ( θ 1 − φ ) sin ( φ + π 2 ) , {\displaystyle {\begin{aligned}v'_{1x}&={\frac {v_{1}\cos(\theta _{1}-\varphi )(m_{1}-m_{2})+2m_{2}v_{2}\cos(\theta
|
{
"page_id": 65907,
"source": null,
"title": "Elastic collision"
}
|
_{2}-\varphi )}{m_{1}+m_{2}}}\cos(\varphi )+v_{1}\sin(\theta _{1}-\varphi )\cos(\varphi +{\tfrac {\pi }{2}})\\[0.8em]v'_{1y}&={\frac {v_{1}\cos(\theta _{1}-\varphi )(m_{1}-m_{2})+2m_{2}v_{2}\cos(\theta _{2}-\varphi )}{m_{1}+m_{2}}}\sin(\varphi )+v_{1}\sin(\theta _{1}-\varphi )\sin(\varphi +{\tfrac {\pi }{2}}),\end{aligned}}} where v1 and v2 are the scalar sizes of the two original speeds of the objects, m1 and m2 are their masses, θ1 and θ2 are their movement angles, that is, v 1 x = v 1 cos θ 1 , v 1 y = v 1 sin θ 1 {\displaystyle v_{1x}=v_{1}\cos \theta _{1},\;v_{1y}=v_{1}\sin \theta _{1}} (meaning moving directly down to the right is either a −45° angle, or a 315° angle), and lowercase phi (φ) is the contact angle. (To get the x and y velocities of the second ball, one needs to swap all the '1' subscripts with '2' subscripts.) This equation is derived from the fact that the interaction between the two bodies is easily calculated along the contact angle, meaning the velocities of the objects can be calculated in one dimension by rotating the x and y axis to be parallel with the contact angle of the objects, and then rotated back to the original orientation to get the true x and y components of the velocities. In an angle-free representation, the changed velocities are computed using the centers x1 and x2 at the time of contact as where the angle brackets indicate the inner product (or dot product) of two vectors. === Other conserved quantities === In the particular case of particles having equal masses, it can be verified by direct computation from the result above that the scalar product of the velocities before and after the collision are the same, that is ⟨ v 1 ′ , v 2 ′ ⟩ = ⟨ v 1 , v 2 ⟩ . {\displaystyle \langle \mathbf {v} '_{1},\mathbf {v} '_{2}\rangle =\langle \mathbf {v} _{1},\mathbf {v} _{2}\rangle
|
{
"page_id": 65907,
"source": null,
"title": "Elastic collision"
}
|
.} Although this product is not an additive invariant in the same way that momentum and kinetic energy are for elastic collisions, it seems that preservation of this quantity can nonetheless be used to derive higher-order conservation laws. === Derivation of two dimensional solution === The impulse J {\displaystyle \mathbf {J} } during the collision for each particle is: Conservation of Momentum implies J ≡ J 1 = − J 2 {\displaystyle \mathbf {J} \equiv \mathbf {J_{1}} =-\mathbf {J_{2}} } . Since the force during collision is perpendicular to both particles' surfaces at the contact point, the impulse is along the line parallel to x 1 − x 2 ≡ Δ x {\displaystyle \mathbf {x} _{1}-\mathbf {x} _{2}\equiv \Delta \mathbf {x} } , the relative vector between the particles' center at collision time: J = λ n ^ , {\displaystyle \mathbf {J} =\lambda \,\mathbf {\hat {n}} ,} for some λ {\displaystyle \lambda } to be determined and n ^ ≡ Δ x ‖ Δ x ‖ {\displaystyle \mathbf {\hat {n}} \equiv {\frac {\Delta \mathbf {x} }{\|\Delta \mathbf {x} \|}}} Then from (2): From above equations, conservation of kinetic energy now requires: λ 2 m 1 + m 2 m 1 m 2 + 2 λ ⟨ n ^ , Δ v ⟩ = 0 , {\displaystyle \lambda ^{2}{\frac {m_{1}+m_{2}}{m_{1}m_{2}}}+2\lambda \,\langle \mathbf {\hat {n}} ,\Delta \mathbf {v} \rangle =0,\quad } with Δ v ≡ v 1 − v 2 . {\displaystyle \quad \Delta \mathbf {v} \equiv \mathbf {v} _{1}-\mathbf {v} _{2}.} The both solutions of this equation are λ = 0 {\displaystyle \lambda =0} and λ = − 2 m 1 m 2 m 1 + m 2 ⟨ n ^ , Δ v ⟩ {\displaystyle \lambda =-2{\frac {m_{1}m_{2}}{m_{1}+m_{2}}}\langle \mathbf {\hat {n}} ,\Delta \mathbf {v} \rangle } , where λ =
|
{
"page_id": 65907,
"source": null,
"title": "Elastic collision"
}
|
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