Coagulation of particles in a stochastic medium (Q2714009)

In the framework of Smoluchowski's model, the coagulation process in a stochastic medium is studied. It is assumed that the system consists of random sources and sinks of particles. The aim of the article is to give qualitative and quantitative predictions of the influence of stochastic fluctuations on dynamics of the process under consideration. The random sources and sinks are described by the Markov dichotomous process. The authors derive the exact kinetic equation for a countable concentration of particles and find a steady-state solution to the equation which describes the abating of the correlations of noise. It is shown that the frequency of switching a source or a sink of particles is a parameter of the system, and different values of this parameter represent different scenarios of the stationary average equation. A particular attention is paid to investigate the phase transitions in the system of coagulation particles which are produced by the so-called \(D\)-noise.