Stochastic gel-shatter cycles in coalescence-fragmentation models

TL;DR

This paper introduces gel-shatter cycles as a new stochastic phenomenon in coalescence-fragmentation models, characterized by cyclic coalescence and abrupt shattering, supported by simulations and scaling analysis.

Contribution

It reveals the existence of gel-shatter cycles in stochastic coalescence-fragmentation models and provides a scaling framework to understand their regimes.

Findings

Identification of gel-shatter cycles in simulations

Characterization of the cyclicity regime using an order parameter

Development of a scaling argument for the regimes

Abstract

We describe a new phenomenon in models of coalescence and fragmentation, that of gel-shatter cycles. These are dynamical, unforced, stochastic cycles in which slow, approximately deterministic coalescence up to and beyond gelation is followed by abrupt random shattering. We describe their appearance in simulations of stochastic models with multiplicative kernels for coalescence and spontaneous fragmentation into monomers (`shattering'). The regime in which such cycles occur is characterized by a cyclicity order parameter, and we provide a simple scaling argument which describes both this regime and those which border it.