Stochastic resetting in aggregation with sum kernel

Abstract

Stochastic resetting, specifically that which follows the Poisson time distribution, has been observed to introduce non-trivial steady states and optimization of such states in the constant-kernel aggregation model. In this paper, we extend the study of Poissonian resetting to sum-kernel aggregation. We examine the maximum cluster concentrations reached and the time it is attained as functions of resetting rate. We also demonstrate that in the long-time limit, cluster concentrations can be optimized, with higher-mass clusters having optimal resetting rates approaching a nonzero value, unlike that of the constant-kernel case. Furthermore, we identify dynamical phase transitions in the formation of higher-mass clusters and describe resetting regimes, which are features unique to the sum kernel.