Brusselator - dissipative structures

I. Prigogine (Brussels) non-equilibrium thermodynamics, particularly the theory of dissipative structures. 

Jan. 25,1917, Moscow, Russia - May 28, 2003, Brussels, Belgium) Ilya Prigogine studied chemistry and physics at the Universite Libre de Bruxelles, where he completed his PhD in 1941, and became a professor in 1947. He joined the Brussels -> thermodynamics school founded by Theophile De Donder (1873-1957) and Jean Timmermans (1882-1971). He received the Nobel Prize in Chemistry in 1977 for his contributions to nonequilibrium thermodynamics, particularly the theory of dissipative structure. His work established a thermodynamic basis of -> transport phenomena in electrolyte solutions and -> electrochemical oscillations. 

Catastrophes occurring in these models in the presence of diffusion will be examined next. We shall investigate wave phenomena in the Fisher-Kolmogorov model and in the Oregonator as well as dissipative structures in the Brusselator. The studies of systems of reactions with diffusion, both experimental and theoretical, have not led yet to the formulation of a complete theory. Consequently, only fundamental results concerning the phenomena of a loss of stability type in these models will be presented. 

At present, we will examine the problem of the stability of the spatially homogeneous stationary solution, x = a, y = b/a, of the Brusselator in terms of the possibile loss of stability of this state and the generation of dissipative structures. Introducing into (6.154) the substitutions... 

While Belousov was describing his e)q)eriments into oscillatory chemical reactions, Ilya Prigogine in Brussels was developing theoretical models of nonequilibrium thermodynamics and ended with the notion of "structure dissipative" for which he was awarded the 1977 Nobel Prize in Chemistry. The concept of "Dissipative Structure" is ejq)licitly mentioned in the Nobel quotation "The 1977 Nobel Prize in Chemistry has been awarded to Professor Ilya Prigogine, Brussels, for his contributions to non-equilibrium thermodynamics, particularly the theory of dissipative structures". In the first half of the 1950s, Glansdorff and Balescu defined with Prigogine the thermodynamic criteria necessary for oscillatory behavior in dissipative systems [7]. Nicohs and Lefever then applied these to models of autocatalytic reactions [8]. 

Symmetry-Breaking Instabilities The Trimolecular Reaction. The "Brusselator" or trimolecular reaction is the simplest model which exhibits instabilities that may be symmetry-breaking in space and/or time. Although it does not represent an actual chemical reaction, it is nevertheless the best-studied and most widely known theoretical model for chemical instability phenomena. Historically it is the model on which the study of dissipative structures was begun by members of the Brussels. School of Thermodynamics (hence its popular name) a decade ago (44, 45, 46, 47). 

New Photochemical Reactions Leading to Spatial Dissipative Structures. Gimenez, M. Micheau, J.C. (Lab Chim.-Phys. II, Univ. Libre Bruxelles, B-1050 Brussels, Belg.). Naturwissenschaften 1983, 70 (2), 90-2 (Eng.). Spatial dissipative structures were formed during visible or UV light irradn. of shallow layer solns. of photochromic (reversible) or chromogenic (irreversible) compds. The origin of the structures was independent of the mechanisms involved in the chem. reaction. 

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