Reaction-diffusion with stochastic decay rates

TL;DR

This paper develops a model linking microscopic disorder in reaction-diffusion systems to macroscopic anomalous transport behaviors, revealing power-law decay and subdiffusion due to non-Markovian effects.

Contribution

It introduces a framework connecting microscopic fluctuations in decay rates and transition times to mesoscopic reaction-diffusion equations, explaining anomalous transport phenomena.

Findings

Power-law decay of survival probability

Spatially heterogeneous decay leading to subdiffusion

Non-Markovian effects couple transport and reaction properties

Abstract

Understanding anomalous transport and reaction kinetics due to microscopic physical and chemical disorder is a long-standing goal in many fields including geophysics, biology, and engineering. We consider reaction-diffusion characterized by fluctuations in both transitions times and decay rates. We introduce and analyze a model framework that explicitly connects microscopic fluctuations with the mescoscopic description. For broad distributions of transport and reaction time scales we compute the particle density and derive the equations governing its evolution, finding power-law decay of the survival probability, and spatially heterogeneous decay that leads to subdiffusion and an asymptotically stationary surviving-particle density. These anomalies are clearly attributable to non-Markovian effects that couple transport and chemical properties in both reaction and diffusion terms.