On probability simulation of one particle interaction process

The article analyzes and quantitatively simulates the dynamic process of a random subsequent approach of particles to a system of cells. When two particles enter the cell, the particles annihilate with the release of a certain amount of energy. The selection of cell for the approaching particle is random. If an empty cell is occupied, the particle is in this cell until the next particle approach. We have considered various correlations of the number of particles and cells, analyzed the limiting cases. It is proposed a model for chemiluminescense processes, during which light energy is released due to a chemical reaction. We have used the methods of classical probability theory with the construction of trees of the events under investigation. The presented model is simplified, but allows further generalization for more accurate accounting of ongoing processes. In addition, the problem has a link to a model of simple flows with applications in counter theory.