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Brusselator
The Brusselator is a theoretical model for a type of autocatalytic reaction. The Brusselator model was proposed by Ilya Prigogine and his collaborators at the Université Libre de Bruxelles. It is a portmanteau of Brussels and oscillator. It is characterized by the reactions : A \rightarrow X : 2X + Y \rightarrow 3X : B + X \rightarrow Y + D : X \rightarrow E Under conditions where A and B are in vast excess and can thus be modeled at constant concentration, the rate equations become :\left\ = \left\ + \left\^2 \left\ - \left\ \left\ - \left\ \, :\left\ = \left\ \left\ - \left\^2 \left\ \, where, for convenience, the rate constants have been set to 1. The Brusselator has a fixed point at :\left\ = A \, :\left\ = \,. The fixed point becomes unstable when : B>1+A^2 \, leading to an oscillation of the system. Unlike the Lotka–Volterra equation, the oscillations of the Brusselator do not depend on the amount of reactant present initially. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brusselator Oscillations HQ Render
The Brusselator is a theoretical model for a type of autocatalytic reaction. The Brusselator model was proposed by Ilya Prigogine and his collaborators at the Université Libre de Bruxelles. It is a portmanteau of Brussels and oscillator. It is characterized by the reactions : A \rightarrow X : 2X + Y \rightarrow 3X : B + X \rightarrow Y + D : X \rightarrow E Under conditions where A and B are in vast excess and can thus be modeled at constant concentration, the rate equations become :\left\ = \left\ + \left\^2 \left\ - \left\ \left\ - \left\ \, :\left\ = \left\ \left\ - \left\^2 \left\ \, where, for convenience, the rate constants have been set to 1. The Brusselator has a fixed point at :\left\ = A \, :\left\ = \,. The fixed point becomes unstable when : B>1+A^2 \, leading to an oscillation of the system. Unlike the Lotka–Volterra equation, the oscillations of the Brusselator do not depend on the amount of reactant present initial ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brusselator Space
The Brusselator is a theoretical model for a type of autocatalytic reaction. The Brusselator model was proposed by Ilya Prigogine and his collaborators at the Université Libre de Bruxelles. It is a portmanteau of Brussels and oscillator. It is characterized by the reactions : A \rightarrow X : 2X + Y \rightarrow 3X : B + X \rightarrow Y + D : X \rightarrow E Under conditions where A and B are in vast excess and can thus be modeled at constant concentration, the rate equations become :\left\ = \left\ + \left\^2 \left\ - \left\ \left\ - \left\ \, :\left\ = \left\ \left\ - \left\^2 \left\ \, where, for convenience, the rate constants have been set to 1. The Brusselator has a fixed point at :\left\ = A \, :\left\ = \,. The fixed point becomes unstable when : B>1+A^2 \, leading to an oscillation of the system. Unlike the Lotka–Volterra equation, the oscillations of the Brusselator do not depend on the amount of reactant present initial ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Autocatalytic Reaction
A single chemical reaction is said to be autocatalytic if one of the reaction products is also a catalyst for the same or a coupled reaction.Steinfeld J.I., Francisco J.S. and Hase W.L. ''Chemical Kinetics and Dynamics'' (2nd ed., Prentice-Hall 1999) p.151-2 Such a reaction is called an autocatalytic reaction. 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). Chemical reactions A chemical reaction of two reactants and two products can be written as : \alpha A + \beta B \rightleftharpoons \sigma S + \tau T where the Greek letters are stoichiometric coefficients and the capital Latin letters represent chemical species. The chemical reaction proceeds in both the forward and reverse direction. This equation is easily g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oregonator
The Oregonator is a theoretical model for a type of autocatalytic reaction. The Oregonator is the simplest realistic model of the chemical dynamics of the oscillatory Belousov–Zhabotinsky reaction. It was created by Richard Field and Richard M. Noyes at the University of Oregon. It is a portmanteau of Oregon and oscillator. Earlier, the Brusselator model was proposed by Ilya Prigogine and his collaborators at the Université libre de Bruxelles, Free University of Brussels as a portmanteau of Brussels and oscillator. The Oregonator is a reduced model of the FKN mechanism (developed by Richard Field, Endre Kőrös, and Richard M. Noyes) which still involved 11 reactions and 12 species (21 intermediate species and 18 elementary steps). The Oregonator is characterized by the reactions : \begin \text \quad & A+Y \longrightarrow X+P \\[5pt] \text \quad & X+Y \longrightarrow 2P \\[5pt] \text \quad & A+X \longrightarrow 2X+2Z \\[5pt] \text \quad & 2X \longrightarrow A+P \\[5pt] \text ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Belousov–Zhabotinsky Reaction
A Belousov–Zhabotinsky reaction, or BZ reaction, is one of a class of reactions that serve as a classical example of non-equilibrium thermodynamics, resulting in the establishment of a nonlinear chemical oscillator. The only common element in these oscillators is the inclusion of bromine and an acid. The reactions are important to theoretical chemistry in that they show that chemical reactions do not have to be dominated by equilibrium thermodynamic behavior. These reactions are far from equilibrium and remain so for a significant length of time and evolve chaotically. In this sense, they provide an interesting chemical model of nonequilibrium biological phenomena; as such, mathematical models and simulations of the BZ reactions themselves are of theoretical interest, showing phenomenon as noise-induced order. An essential aspect of the BZ reaction is its so called "excitability"; under the influence of stimuli, patterns develop in what would otherwise be a perfectly quies ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ilya Prigogine
Viscount Ilya Romanovich Prigogine (; russian: Илья́ Рома́нович Приго́жин; 28 May 2003) was a physical chemist and Nobel laureate noted for his work on dissipative structures, complex systems, and irreversibility. Biography Prigogine was born in Moscow a few months before the Russian Revolution of 1917, into a Jewish family. His father, Ruvim Abramovich Prigogine, was a chemical engineer at the Imperial Moscow Technical School; his mother, Yulia Vikhman, was a pianist. Because the family was critical of the new Soviet system, they left Russia in 1921. They first went to Germany and in 1929, to Belgium, where Prigogine received Belgian nationality in 1949. His brother Alexandre (1913–1991) became an ornithologist. Prigogine studied chemistry at the Free University of Brussels, where in 1950, he became professor. In 1959, he was appointed director of the International Solvay Institute in Brussels, Belgium. In that year, he also started teaching at the U ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chaotic Maps
Chaotic was originally a Danish trading card game. It expanded to an online game in America which then became a television program based on the game. The program was able to be seen on 4Kids TV (Fox affiliates, nationwide), Jetix, The CW4Kids, Cartoon Network and Disney XD. It was brought over to the United States from Denmark by Bryan C. Gannon and Chaotic USA Entertainment Group, and produced by Chaotic USA Entertainment Group, 4Kids Productions and Bardel Entertainment. The trading card game came out 6 September 2006 in the U.S. and Canada. Each card comes with a unique code which the owner can upload onto the Chaotic website. This allows the owner to trade and play online using their own card collection. The game was well known to be the only game with a TV show, an online game, and a TCG that were all integrated. However, the online game is currently closed. History Chaotic started out as a trading card game known as "Grolls and Gorks" and an idea for a cartoon se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-equilibrium Thermodynamics
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with physical systems that are not in thermodynamic equilibrium but can be described in terms of macroscopic quantities (non-equilibrium state variables) that represent an extrapolation of the variables used to specify the system in thermodynamic equilibrium. Non-equilibrium thermodynamics is concerned with transport processes and with the rates of chemical reactions. Almost all systems found in nature are not in thermodynamic equilibrium, for they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems and to chemical reactions. Some systems and processes are, however, in a useful sense, near enough to thermodynamic equilibrium to allow description with useful accuracy by currently known non-equilibrium thermodynamics. Nevertheless, many natural systems and processes will always remain far beyond the scope o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clock Reaction
A chemical clock (or clock reaction) is a complex mixture of reacting chemical compounds in which the onset of an observable property (discoloration or coloration) occurs after a predictable induction time due to the presence of clock species at a detectable amount. In cases where one of the reagents has a visible color, crossing a concentration threshold can lead to an abrupt color change after a reproducible time lapse. Types Clock reactions may be classified into three or four types: Substrate-depletive clock reaction The simplest clock reaction featuring two reactions: :A → C (rate k1) :B + C → products (rate k2, fast) When substrate (B) is present, the clock species (C) is quickly consumed in the second reaction. Only when substrate B is all used up or depleted, species C can build up in amount causing the color to change. An example for this clock reaction is the sulfite/iodate reaction or iodine clock reaction, also known as Landolt's reaction. Sometimes, a c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
