Effective Mean Field Approach to Kinetic Monte Carlo Simulations in Limit Cycle Dynamics with Reactive and Diffusive Rewiring

TL;DR

This paper introduces effective reactive parameters to improve mean field models for 2D lattice limit cycle dynamics, accounting for reactive and diffusive rewiring, and highlights the limitations of the approach with diffusion.

Contribution

The study develops an effective mean field approach that incorporates spatial support effects and reactive rewiring, enhancing the accuracy of kinetic models for complex reactive systems.

Findings

Effective parameters recover MF steady states on 2D lattices.

Reactive rewiring is well-captured by the effective parameters.

Diffusive coupling breaks the predictive power of the effective MF model.

Abstract

The dynamics of complex reactive schemes is known to deviate from the Mean Field (MF) theory when restricted on low dimensional spatial supports. This failure has been attributed to the limited number of species-neighbours which are available for interactions. In the current study, we introduce effective reactive parameters, which depend on the type of the spatial support and which allow for an effective MF description. As working example the Lattice Limit Cycle dynamics is used, restricted on a 2D square lattice with nearest neighbour interactions. We show that the MF steady state results are recovered when the kinetic rates are replaced with their effective values. The same conclusion holds when reactive stochastic rewiring is introduced in the system via long distance reactive coupling. Instead, when the stochastic coupling becomes diffusive the effective parameters no longer predict the steady state. This is attributed to the diffusion process which is an additional factor introduced into the dynamics and is not accounted for, in the kinetic MF scheme.