The application of theory of probability to the modelling of chemical kinetics systems

Abstract

We consider a model of chemical kinetics for which the derivation of equations does not rely on the law of mass action, but is rather based on such principles as the joint probability and the geometric probability. For this model a generalisation is constructed for the case of reaction-diffusion systems in heterogeneous medium with respect to the convective and diffusive transfer of heat. The construction of this generalisation is carried out by an alternative methodology which is based fully on a systems of ordinary differential equations, without a transition to the partial derivatives. The description of this new method is a bit similar to the finite volume method, except that it uses statistical simplifying positions and geometric probability to describe the diffusion processes. Such approach allows us to greatly simplify the numerical implementation of the resulting model, as well as to simplify the quantitative analysis of it with dynamical systems theory. Moreover, the efficiency of the parallel implementation of the numerical method is increased for the resulting model. In addition, we will consider an application of this model for the description of some example reaction with quasi-periodic regime, as well as consider an algorithm for the transition from standard models with dimensional kinetic constants to its formalism.