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Autocatalytic Endogenous Reflective Architecture
In chemistry, a chemical reaction is said to be autocatalytic if one of the reaction products is also a catalyst for the same reaction. Many forms of autocatalysis are recognized.Steinfeld J.I., Francisco J.S. and Hase W.L. ''Chemical Kinetics and Dynamics'' (2nd ed., Prentice-Hall 1999) pp. 151–2 A ''set'' of chemical reactions can be said to be "collectively autocatalytic" if a number of those reactions produce, as reaction products, catalysts for enough of the other reactions that the entire set of chemical reactions is self-sustaining given an input of energy and food molecules (see autocatalytic set). Examples Acid-catalyzed hydrolysis of esters produces carboxylic acids that also catalyze the same reaction. Indeed, the observation of an accelerating hydrolysis of gamma valerolactone to gamma-hydroxyvaleric acid led to the introduction of the concept of autocatalysis in 1890. The oxidation of hydrocarbons by air or oxygen is the basis of autoxidation. Like many radical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chemistry
Chemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies the chemical elements that make up matter and chemical compound, compounds made of atoms, molecules and ions: their composition, structure, properties, behavior and the changes they undergo during chemical reaction, reactions with other chemical substance, substances. Chemistry also addresses the nature of chemical bonds in chemical compounds. In the scope of its subject, chemistry occupies an intermediate position between physics and biology. It is sometimes called the central science because it provides a foundation for understanding both Basic research, basic and Applied science, applied scientific disciplines at a fundamental level. For example, chemistry explains aspects of plant growth (botany), the formation of igneous rocks (geology), how atmospheric ozone is formed and how environmental pollutants are degraded (ecology), the prop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crystal Growth
Crystal growth is a major stage of a crystallization, crystallization process, and consists of the addition of new atoms, ions, or polymer strings into the characteristic arrangement of the crystalline lattice. The growth typically follows an initial stage of either homogeneous or heterogeneous (surface catalyzed) nucleation, unless a "seed" crystal, purposely added to start the growth, was already present. The action of crystal growth yields a crystalline solid whose atoms or molecules are close packed, with fixed positions in space relative to each other. The crystalline states of matter, state of matter is characterized by a distinct structural rigidity and very high resistance to Plastic deformation in solids, deformation (i.e. changes of shape and/or volume). Most crystalline solids have high values both of Young's modulus and of the shear modulus of elasticity (physics), elasticity. This contrasts with most liquids or fluids, which have a low shear modulus, and typically exh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alcohol (chemistry)
In chemistry, an alcohol (), is a type of organic compound that carries at least one hydroxyl () functional group bound to a Saturated and unsaturated compounds, saturated carbon atom. Alcohols range from the simple, like methanol and ethanol, to complex, like sugar alcohols and cholesterol. The presence of an OH group strongly modifies the properties of Hydrocarbon, hydrocarbons, conferring Hydrophile, hydrophilic (water-loving) properties. The OH group provides a site at which many reactions can occur. History The flammable nature of the exhalations of wine was already known to ancient natural philosophers such as Aristotle (384–322 BCE), Theophrastus (–287 BCE), and Pliny the Elder (23/24–79 CE). However, this did not immediately lead to the isolation of alcohol, even despite the development of more advanced distillation techniques in second- and third-century Roman Egypt. An important recognition, first found in one of the writings attributed to Jabir ibn Hayyan, JÄ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carboxylic Acid
In organic chemistry, a carboxylic acid is an organic acid that contains a carboxyl group () attached to an Substituent, R-group. The general formula of a carboxylic acid is often written as or , sometimes as with R referring to an organyl group (e.g., alkyl, alkenyl, aryl), or hydrogen, or other groups. Carboxylic acids occur widely. Important examples include the amino acids and fatty acids. Deprotonation of a carboxylic acid gives a carboxylate anion. Examples and nomenclature Carboxylic acids are commonly identified by their trivial names. They often have the suffix ''-ic acid''. IUPAC-recommended names also exist; in this system, carboxylic acids have an ''-oic acid'' suffix. For example, butyric acid () is butanoic acid by IUPAC guidelines. For nomenclature of complex molecules containing a carboxylic acid, the carboxyl can be considered position one of the parent chain even if there are other substituents, such as 3-chloropropanoic acid. Alternately, it can be named ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ester
In chemistry, an ester is a compound derived from an acid (either organic or inorganic) in which the hydrogen atom (H) of at least one acidic hydroxyl group () of that acid is replaced by an organyl group (R). These compounds contain a distinctive functional group. Analogues derived from oxygen replaced by other chalcogens belong to the ester category as well. According to some authors, organyl derivatives of acidic hydrogen of other acids are esters as well (e.g. amides), but not according to the IUPAC. Glycerides are fatty acid esters of glycerol; they are important in biology, being one of the main classes of lipids and comprising the bulk of animal fats and vegetable oils. Lactones are cyclic carboxylic esters; naturally occurring lactones are mainly 5- and 6-membered ring lactones. Lactones contribute to the aroma of fruits, butter, cheese, vegetables like celery and other foods. Esters can be formed from oxoacids (e.g. esters of acetic acid, carbonic acid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Induction Period
An induction period in chemical kinetics is an initial slow stage of a chemical reaction; after the induction period, the reaction accelerates. Ignoring induction periods can lead to runaway reactions. In some catalytic reactions, a pre-catalyst needs to undergo a transformation to form the active catalyst, before the catalyst can take effect. Time is required for this transformation, hence the induction period. For example, with Wilkinson's catalyst, one triphenylphosphine ligand must dissociate to give the coordinatively unsaturated 14-electron species which can participate in the catalytic cycle: : Similarly, for an autocatalytic reaction, where one of the reaction products catalyzes the reaction itself, the rate of reaction is low initially until sufficient products have formed to catalyze the reaction. Reactions generally accelerate when heat is applied. Where a reaction is exothermic, the rate of the reaction may initially be low. As the reaction proceeds, heat is gen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logistic Function
A logistic function or logistic curve is a common S-shaped curve ( sigmoid curve) with the equation f(x) = \frac where The logistic function has domain the real numbers, the limit as x \to -\infty is 0, and the limit as x \to +\infty is L. The exponential function with negated argument (e^ ) is used to define the standard logistic function, depicted at right, where L=1, k=1, x_0=0, which has the equation f(x) = \frac and is sometimes simply called the sigmoid. It is also sometimes called the expit, being the inverse function of the logit. The logistic function finds applications in a range of fields, including biology (especially ecology), biomathematics, chemistry, demography, economics, geoscience, mathematical psychology, probability, sociology, political science, linguistics, statistics, and artificial neural networks. There are various generalizations, depending on the field. History The logistic function was introduced in a series of three papers by Pier ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sigmoid Function
A sigmoid function is any mathematical function whose graph of a function, graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the logistic function, which is defined by the formula :\sigma(x) = \frac = \frac = 1 - \sigma(-x). Other sigmoid functions are given in the #Examples, Examples section. In some fields, most notably in the context of artificial neural networks, the term "sigmoid function" is used as a synonym for "logistic function". Special cases of the sigmoid function include the Gompertz curve (used in modeling systems that saturate at large values of ''x'') and the ogee curve (used in the spillway of some dams). Sigmoid functions have domain of all real numbers, with return (response) value commonly monotonically increasing but could be decreasing. Sigmoid functions most often show a return value (''y'' axis) in the range 0 to 1. Another commonly used range is from −1 to 1. A wide variety of sigmoid functions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ralph Pearson
Ralph Gottfrid Pearson (January 12, 1919 – October 12, 2022) was an American physical inorganic chemist best known for the development of the concept of hard and soft acids and bases (HSAB). He received his Ph.D. in physical chemistry in 1943 from Northwestern University, and taught chemistry at Northwestern faculty from 1946 until 1976, when he moved to University of California at Santa Barbara (UCSB). He retired in 1989 but remained active in research in theoretical inorganic chemistry until his death. In 1958 Pearson and Fred Basolo, his colleague at Northwestern wrote the influential monograph "Mechanisms of Inorganic Reactions", which integrated concepts from ligand field theory and physical organic chemistry and signaled a shift from descriptive coordination chemistry to a more quantitative science. With another Northwestern colleague, Arthur Atwater Frost, Pearson wrote in 1961 another classic text, ''Kinetics and Mechanism: A Study of Homogeneous Chemical Reactions'' ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Macroscopic
The macroscopic scale is the length scale on which objects or phenomena are large enough to be visible with the naked eye, without magnifying optical instruments. It is the opposite of microscopic. Overview When applied to physical phenomena and bodies, the macroscopic scale describes things as a person can directly perceive them, without the aid of magnifying devices. This is in contrast to observations ( microscopy) or theories ( microphysics, statistical physics) of objects of geometric lengths smaller than perhaps some hundreds of micrometres. A macroscopic view of a ball is just that: a ball. A microscopic view could reveal a thick round skin seemingly composed entirely of puckered cracks and fissures (as viewed through a microscope) or, further down in scale, a collection of molecules in a roughly spherical shape (as viewed through an electron microscope). An example of a physical theory that takes a deliberately macroscopic viewpoint is thermodynamics. An exampl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Equation
In mathematics, a quadratic equation () is an equation that can be rearranged in standard form as ax^2 + bx + c = 0\,, where the variable (mathematics), variable represents an unknown number, and , , and represent known numbers, where . (If and then the equation is linear equation, linear, not quadratic.) The numbers , , and are the ''coefficients'' of the equation and may be distinguished by respectively calling them, the ''quadratic coefficient'', the ''linear coefficient'' and the ''constant coefficient'' or ''free term''. The values of that satisfy the equation are called ''solution (mathematics), solutions'' of the equation, and ''zero of a function, roots'' or ''zero of a function, zeros'' of the quadratic function on its left-hand side. A quadratic equation has at most two solutions. If there is only one solution, one says that it is a double root. If all the coefficients are real numbers, there are either two real solutions, or a single real double root, or two comple ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear System
In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists since most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems. Typically, the behavior of a nonlinear system is described in mathematics by a nonlinear system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a lin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
