On the growth of a particle coalescing in a Poisson distribution of obstacles

Abstract

In this paper we consider the coalescence dynamics of a tagged particle moving in a random distribution of particles with volumes independently distributed according to a probability distribution (CTP model). We provide a rigorous derivation of a kinetic equation for the probability density for the size and position of the tagged particle in the kinetic limit where the volume fraction $\varphi$ filled by the background of particles tends to zero. Moreover, we prove that the particle system, i.e. CTP model, is well posed for a small but positive volume fraction with probability one as long as the the distribution of the particle sizes is compactly supported.

57 pages, 2 figures

References in corpus (4)

• A diffusion limit for a test particle in a random distribution of scatterers
• Derivation of the Fick's Law for the Lorentz Model in a low density regime
• Derivation of the linear Landau equation and linear Boltzmann equation from the Lorentz model with magnetic field
• Diffusive limit for the random Lorentz gas

Cited by in corpus (2)

• Kinetic description of a Rayleigh Gas with annihilation
• A Kac model for kinetic annihilation