Efficient kinetic Monte Carlo method for reaction-diffusion processes with spatially varying annihilation rates

TL;DR

This paper introduces an efficient Monte Carlo algorithm for simulating reaction-diffusion processes with spatially varying rates, avoiding small hops by propagating particles in large steps, and accurately handling unknown diffusion propagators.

Contribution

The paper develops a novel Monte Carlo method that efficiently simulates reaction-diffusion with spatially varying rates without requiring analytical propagators.

Findings

Algorithm accurately reproduces reaction-diffusion dynamics.

Demonstrates improved efficiency over traditional small-hop methods.

Validated with an illustrative numerical example.

Abstract

We present an efficient Monte Carlo method to simulate reaction-diffusion processes with spatially varying particle annihilation or transformation rates as it occurs for instance in the context of motor-driven intracellular transport. Like Green's function reaction dynamics and first-passage time methods, our algorithm avoids small diffusive hops by propagating sufficiently distant particles in large hops to the boundaries of protective domains. Since for spatially varying annihilation or transformation rates the single particle diffusion propagator is not known analytically, we present an algorithm that generates efficiently either particle displacements or annihilations with the correct statistics, as we prove rigorously. The numerical efficiency of the algorithm is demonstrated with an illustrative example.