Composite Molecules and Decoupling in Reaction Diffusion Models

TL;DR

This paper demonstrates that the Gray-Scott reaction-diffusion model can be derived as an effective large-scale theory from a more fundamental model that includes a composite molecule, showing consistent pattern formation at late times.

Contribution

It introduces a derivation of the Gray-Scott model from a fundamental theory involving a composite molecule, linking microscopic interactions to macroscopic pattern formation.

Findings

Late time dynamics match Gray-Scott patterns

Composite molecule inclusion reproduces known patterns

Parameter choices align fundamental and effective theories

Abstract

The Gray-Scott model can be thought of as an effective theory at large spatiotemporal scales coming from a more fundamental theory valid at shorter spatiotemporal scales. The more fundamental theory includes a composite molecule which is trilinear in the molecules of the Gray-Scott model as was shown in the recent derivation of the Gray-Scott model from the master equation. Here we show that at a classical level, ignoring the fluctuations describable in a Langevin description, the late time dynamics of the more fundamental theory leads to the same pattern formation as found in the Gray-Scott model with suitable choices of the parameters describing the diffusion of the composite molecule.