Direct simulation Monte Carlo for new regimes in aggregation-fragmentation kinetics

TL;DR

This paper extends and tests Direct Simulation Monte Carlo methods for aggregation-fragmentation kinetics, including collisional fragmentation, validating their accuracy and stability in oscillating regimes.

Contribution

It introduces extended stochastic methods for aggregation with shattering and compares them with deterministic approaches, confirming oscillation stability.

Findings

Validated stochastic methods against deterministic models

Confirmed existence of stable oscillations in aggregation-fragmentation systems

Demonstrated robustness of oscillations to noise

Abstract

We revisit two basic Direct Simulation Monte Carlo Methods to model aggregation kinetics and extend them for aggregation processes with collisional fragmentation (shattering). We test the performance and accuracy of the extended methods and compare their performance with efficient deterministic finite-difference method applied to the same model. We validate the stochastic methods on the test problems and apply them to verify the existence of oscillating regimes in the aggregation-fragmentation kinetics recently detected in deterministic simulations. We confirm the emergence of steady oscillations of densities in such systems and prove the stability of the oscillations with respect to fluctuations and noise.