Jumps and Coalescence in the Continuum: a Numerical Study

TL;DR

This paper numerically investigates the dynamics of an infinite system of particles that jump and coalesce, revealing unique behaviors, stationary states, and the roles of these processes in the system's evolution.

Contribution

It provides a numerical analysis of a kinetic equation derived from microscopic particle dynamics, highlighting new insights into jump and coalescence effects.

Findings

Identification of interesting dynamical peculiarities

Clarification of the roles of jumps and coalescence

Discovery and analysis of possible stationary states

Abstract

The dynamics is studied of an infinite continuum system of jumping and coalescing point particles. In the course of jumps, the particles repel each other whereas their coalescence is free. As the equation of motion we take a kinetic equation, derived by a scaling procedure from the microscopic Fokker-Planck equation corresponding to this kind of motion. The result of the paper is the numerical study (by the Runge-Kutta method) of the solutions of the kinetic equation revealing a number of interesting peculiarities of the dynamics and clarifying the particular role of the jumps and the coalescence in the system's evolution. Possible nontrivial stationary states are also found and analyzed.