Aggregation with constant kernel under stochastic resetting

TL;DR

This paper studies a stochastic resetting mechanism in binary aggregation with a constant kernel, deriving an exact solution for the non-equilibrium steady state and identifying optimal resetting rates for aggregate densities.

Contribution

It introduces a stochastic resetting model into aggregation processes and provides an exact analytical solution for the resulting steady state.

Findings

Steady state densities depend on the resetting rate and aggregate size.

Optimal resetting rate maximizes the density of a given aggregate size.

Exact solution of the master equation for the model.

Abstract

The model of binary aggregation with constant kernel is subjected to stochastic resetting: aggregates of any size explode into monomers at independent stochastic times. These resetting times are Poisson distributed, and the rate of the process is called the resetting rate. The master equation yields a Bernoulli-type equation in the generating function of the concentration of aggregates of any size, which can be solved exactly. This resetting prescription leads to a non-equilibrium steady state for the densities of aggregates, which is a function of the size of the aggregate, rescaled by a function of the resetting rate. The steady-state density of aggregates of a given size is maximised if the resetting rate is set to the quotient of the aggregation rate by the size of the aggregate (minus one).