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MATHEMATICAL MODELS IN CHEMICAL PHYSICS AND COMBUSTION THEORY

A brief review of mathematical models in chemical physics is given. More attention is devoted to the theory of chain reactions. This theory was created by N.N. Semenoff. Chain theory is theoretical foundation of modern models. Being extremely significant in the field of chemistry, chain processes are investigated by experimental methods as well as by mathematical models. The results of calculations are given in terms of parameters of the model: temperature, form of vessel (plane, cylindrical or spherical) etc. Different questions are discussed: link between energy and kinetics of reaction, a length of chains, development of chains in time, paths of chain breaking a breaking of chains in volume and on a surface. The modified Chester–Chisnell–Whitham (CCW) model has been examined to account for reactive mixtures and to describe detonation wave propagation, diffraction, and reflection. This model makes it possible to investigate the behavior of detonation propagation and reflection near and at the Chapman–Jouguet (CJ) point. Model of the temporal evolution of a reduced combustion chemical system with an artificial neural network and a model for calculating heat release in premixed turbulent flames are briefly discussed.