Small-scale properties of a stochastic cubic-autocatalytic reaction-diffusion model

TL;DR

This paper analyzes the small-scale behavior of a stochastic cubic-autocatalytic reaction-diffusion model using renormalization, revealing how environmental noise influences structure growth at small scales.

Contribution

It introduces a renormalization approach to handle noise-induced divergences in the CARD model and explores the impact of colored noise on system behavior.

Findings

Decay rate and coupling depend on noise exponent.

Power law noise can either promote or inhibit small-scale structure growth.

Renormalization techniques reveal scale-dependent effects of environmental fluctuations.

Abstract

We investigate the small-scale properties of a stochastic cubic-autocatalytic reaction-diffusion (CARD) model using renormalization techniques. We renormalize noise-induced ultraviolet divergences and obtain beta functions for the decay rate and coupling at one-loop. Assuming colored (power law) noise, our results show that the behavior of both decay rate and coupling with scale depends crucially on the noise exponent. Interpreting the CARD model as a proxy for a (very simple) living system, our results suggest that power law correlations in environmental fluctuations can both decrease or increase the growth of structures at smaller scales.