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Monod Equation
The Monod equation is a mathematical model for the growth of microorganisms. It is named for Jacques Monod (1910 – 1976, a French biochemist, Nobel Prize in Physiology or Medicine in 1965), who proposed using an equation of this form to relate microbial growth rates in an aqueous environment to the concentration of a limiting nutrient. The Monod equation has the same form as the Michaelis–Menten equation, but differs in that it is empirical while the latter is based on theoretical considerations. The Monod equation is commonly used in environmental engineering. For example, it is used in the activated sludge model for sewage treatment. Equation The empirical Monod equation is: : \mu = \mu_\max where: * ''μ'' is the growth rate of a considered microorganism * ''μ''max is the maximum growth rate of this microorganism * 'S''is the concentration of the limiting substrate ''S'' for growth * ''K''''s'' is the "half-velocity constant"—the value of 'S''when ''μ''/''Π... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science). The use of mathematical models to solve problems in business or military operations is a large part of the field of operations research. Mathematical models are also used in music, linguistics, and philosophy (for example, intensively in analytic philosophy). A model may help to explain a system and to study the effects of different components, and to make predictions about behavior. Elements of a mathematical model Mathematical models can take many forms, including dynamical systems, statisti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hanes–Woolf Plot
In biochemistry, a Hanes–Woolf plot, Hanes plot, or plot of a/v against a, is a graphical representation of enzyme kinetics in which the ratio of the initial substrate concentration a to the reaction velocity v is plotted against a. It is based on the rearrangement of the Michaelis–Menten equation shown below: : = + where K_\mathrm is the Michaelis constant and V is the limiting rate. J B S Haldane stated, reiterating what he and K. G. Stern had written in their book, that this rearrangement was due to Barnet Woolf. However, it was just one of three transformations introduced by Woolf, who did not use it as the basis of a plot. There is therefore no strong reason for attaching his name to it. It was first published by C. S. Hanes, though he did not use it as plot either. Hanes said that the use of linear regression to determine kinetic parameters from this type of linear transformation is flawed, because it generates the best fit between observed and calculated ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Enzyme Kinetics
Enzyme kinetics is the study of the rates of enzyme-catalysed chemical reactions. In enzyme kinetics, the reaction rate is measured and the effects of varying the conditions of the reaction are investigated. Studying an enzyme's kinetics in this way can reveal the catalytic mechanism of this enzyme, its role in metabolism, how its activity is controlled, and how a drug or a modifier ( inhibitor or activator) might affect the rate. An enzyme (E) is typically a protein molecule that promotes a reaction of another molecule, its substrate (S). This binds to the active site of the enzyme to produce an enzyme-substrate complex ES, and is transformed into an enzyme-product complex EP and from there to product P, via a transition state ES*. The series of steps is known as the mechanism: : E + S ⇄ ES ⇄ ES* ⇄ EP ⇄ E + P This example assumes the simplest case of a reaction with one substrate and one product. Such cases exist: for example, a mutase such as phosphoglucomutase ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Environmental Engineering
Environmental engineering is a professional engineering discipline that encompasses broad scientific topics like chemistry, biology, ecology, geology, hydraulics, hydrology, microbiology, and mathematics to create solutions that will protect and also improve the health of living organisms and improve the quality of the environment. Environmental engineering is a sub-discipline of civil engineering and chemical engineering. While on the part of civil engineering, the Environmental Engineering is focused mainly on Sanitary Engineering. Environmental engineering is the application of scientific and engineering principles to improve and maintain the environment to: * protect human health, *protect nature's beneficial ecosystems, *and improve environmental-related enhancement of the quality of human life. Environmental engineers devise solutions for wastewater management, water and air pollution control, recycling, waste disposal, and public health. They design municipal water supply ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chemical Kinetics
Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is to be contrasted with chemical thermodynamics, which deals with the direction in which a reaction occurs but in itself tells nothing about its rate. Chemical kinetics includes investigations of how experimental conditions influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition states, as well as the construction of mathematical models that also can describe the characteristics of a chemical reaction. History In 1864, Peter Waage and Cato Guldberg pioneered the development of chemical kinetics by formulating the law of mass action, which states that the speed of a chemical reaction is proportional to the quantity of the reacting substances.C.M. Guldberg and P. Waage,"Studies Concerning Affinity" ''Forhandlinger i Videnskabs-Selskabet i Christiania'' (1864), 35P. W ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Catalysis
Catalysis () is the process of increasing the rate of a chemical reaction by adding a substance known as a catalyst (). Catalysts are not consumed in the reaction and remain unchanged after it. If the reaction is rapid and the catalyst recycles quickly, very small amounts of catalyst often suffice; mixing, surface area, and temperature are important factors in reaction rate. Catalysts generally react with one or more reactants to form intermediates that subsequently give the final reaction product, in the process of regenerating the catalyst. Catalysis may be classified as either homogeneous, whose components are dispersed in the same phase (usually gaseous or liquid) as the reactant, or heterogeneous, whose components are not in the same phase. Enzymes and other biocatalysts are often considered as a third category. Catalysis is ubiquitous in chemical industry of all kinds. Estimates are that 90% of all commercially produced chemical products involve catalysts at some s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Von Bertalanffy Function
The von Bertalanffy growth function (VBGF), or von Bertalanffy curve, is a type of growth curve for a time series and is named after Ludwig von Bertalanffy. It is a special case of the generalised logistic function. The growth curve is used to model mean length from age in animals. The function is commonly applied in ecology to model fish growth and in paleontology to model sclerochronological parameters of shell growth. The model can be written as the following: : L(a)= L_\infty(1-\exp(-k(a-t_0))) where a is age, k is the growth coefficient, t_0 is the theoretical age when size is zero, and L_\infty is asymptotic size. It is the solution of the following linear differential equation: : \frac = k (L_ - L ) Seasonally-adjusted von Bertalanffy The seasonally-adjusted von Bertalanffy is an extension of this function that accounts for organism growth that occurs seasonally. It was created by I. F. Somers in 1988. See also * Gompertz function * Monod equation The Monod equa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Victor Henry
Victor Henry (; 17 August 1850 in Colmar, Alsace6 February 1907 in Sceaux) was a French philologist, specializing in Indian languages. Biography Having held appointments at the University of Douai and the University of Lille, Henry was appointed professor of Sanskrit and comparative grammar at the University of Paris. A prolific and versatile writer, he is probably best known by the English translations of his ''Précis de Grammaire comparée de l'anglais et de l'allemand'' and ''Précis de Grammaire comparée du Grec et du Latin''. Important works by him on India and Indian languages are: * ''Manuel pour étudier le Sanscrit védique'' (with Abel Bergaigne, 1890) * ''Éléments de Sanscrit classique'' (1902) * ''Précis de grammaire Pâlie'' (1904) * ''Les Littératures de l'Inde: sanscrit, Pâli, Prâcrit'' (1904) * ''La Magie dans l'Inde antique'' (1904) * ''Le Parsisme'' (1905) * ''L'Agniá¹£á¹oma'' (1906; with Willem Caland) Native American languages (such as Siglit, Que ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gompertz Function
The Gompertz curve or Gompertz function is a type of mathematical model for a time series, named after Benjamin Gompertz (1779–1865). It is a sigmoid function which describes growth as being slowest at the start and end of a given time period. The right-side or future value asymptote of the function is approached much more gradually by the curve than the left-side or lower valued asymptote. This is in contrast to the simple logistic function in which both asymptotes are approached by the curve symmetrically. It is a special case of the generalised logistic function. The function was originally designed to describe human mortality, but since has been modified to be applied in biology, with regard to detailing populations. History Benjamin Gompertz (1779–1865) was an actuary in London who was privately educated. He was elected a fellow of the Royal Society in 1819. The function was first presented in his June 16, 1825 paper at the bottom of page 518. The Gompertz function r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Langmuir Adsorption Model
The Langmuir adsorption model explains adsorption by assuming an adsorbate behaves as an ideal gas at isothermal conditions. According to the model, adsorption and desorption are reversible processes. This model even explains the effect of pressure i.e at these conditions the adsorbate's partial pressure, p_A, is related to the volume of it, , adsorbed onto a solid adsorbent. The adsorbent, as indicated in the figure, is assumed to be an ideal solid surface composed of a series of distinct sites capable of binding the adsorbate. The adsorbate binding is treated as a chemical reaction between the adsorbate gaseous molecule A_\text and an empty sorption site, . This reaction yields an adsorbed species A_\text with an associated equilibrium constant K_\text: : A_ + S A_ From these basic hypotheses the mathematical formulation of the Langmuir adsorption isotherm can be derived in various independent and complementary ways: by the kinetics, the thermodynamics, and the statistical me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archibald Hill
Archibald Vivian Hill (26 September 1886 – 3 June 1977), known as A. V. Hill, was a British physiologist, one of the founders of the diverse disciplines of biophysics and operations research. He shared the 1922 Nobel Prize in Physiology or Medicine for his elucidation of the production of heat and mechanical work in muscles. Biography Born in Bristol, he was educated at Blundell's School and graduated from Trinity College, Cambridge as third wrangler in the mathematics tripos before turning to physiology. While still an undergraduate at Trinity College, he derived in 1909 what came to be known as the Langmuir equation. This is closely related to Michaelis-Menten kinetics. In this paper, Hill's first publication, he derived both the equilibrium form of the Langmuir equation, and also the exponential approach to equilibrium. The paper, written under the supervision of John Newport Langley, is a landmark in the history of receptor theory, because the context for the derivatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hill Equation (biochemistry)
In biochemistry and pharmacology, the Hill equation refers to two closely related equations that reflect the binding of ligands to macromolecules, as a function of the ligand concentration. A ligand is "a substance that forms a complex with a biomolecule to serve a biological purpose" ( ligand definition), and a macromolecule is a very large molecule, such as a protein, with a complex structure of components ( macromolecule definition). Protein-ligand binding typically changes the structure of the target protein, thereby changing its function in a cell. The distinction between the two Hill equations is whether they measure ''occupancy'' or ''response''. The Hill–Langmuir equation reflects the occupancy of macromolecules: the fraction that is saturated or bound by the ligand.For clarity, this article will use the International Union of Basic and Clinical Pharmacology convention of distinguishing between the Hill-Langmuir equation (for receptor saturation) and Hill equation (for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
