Mass-Transport Models with Multiple-Chipping Processes

TL;DR

This paper investigates mass-transport models involving multiple-chipping processes, deriving steady-state distributions through mean-field theory and confirming accuracy with Monte Carlo simulations, revealing the models' analytical tractability.

Contribution

It introduces and analyzes mass-transport models with multiple-chipping processes, providing exact mean-field solutions and validating them with simulations.

Findings

Mean-field solutions match Monte Carlo results precisely.

Models exhibit exact solvability through mean-field theory.

Steady-state distributions are explicitly obtained.

Abstract

We study mass-transport models with multiple-chipping processes. The rates of these processes are dependent on the chip size and mass of the fragmenting site. In this context, we consider k-chip moves (where k = 1, 2, 3, ....); and combinations of 1-chip, 2-chip and 3-chip moves. The corresponding mean-field (MF) equations are solved to obtain the steady-state probability distributions, P (m) vs. m. We also undertake Monte Carlo (MC) simulations of these models. The MC results are in excellent agreement with the corresponding MF results, demonstrating that MF theory is exact for these models.