Aggregate formation in a system of coagulating and fragmenting particles with mass-dependent diffusion rates

TL;DR

This paper investigates how mass-dependent diffusion rates affect aggregation and fragmentation dynamics, revealing the suppression of phase transitions and characterizing finite-size effects through analytical and numerical methods.

Contribution

It introduces a mass-dependent diffusion rate into coagulation models, showing how it prevents phase transitions and analyzing finite-size scaling and probability distributions.

Findings

Phase transition is suppressed for all alpha > 0 at finite densities.

Finite systems exhibit large aggregates indicative of the transition.

Mean field results agree with one-dimensional simulations.

Abstract

The effect of introducing a mass dependent diffusion rate ~ m^{-alpha} in a model of coagulation with single-particle break up is studied both analytically and numerically. The model with alpha=0 is known to undergo a nonequilibrium phase transition as the mass density in the system is varied from a phase with an exponential distribution of mass to a phase with a power-law distribution of masses in addition to a single infinite aggregate. This transition is shown to be curbed, at finite densities, for all alpha > 0 in any dimension. However, a signature of this transition is seen in finite systems in the form of a large aggregate and the finite size scaling implications of this are characterized. The exponents characterizing the steady state probability that a randomly chosen site has mass m are calculated using scaling arguments. The full probability distribution is obtained within a mean field approximation and found to compare well with the results from numerical simulations in one dimension.