Refined Simulations of the Reaction Front for Diffusion-Limited Two-Species Annihilation in One Dimension

TL;DR

This paper presents detailed simulations of a one-dimensional diffusion-limited A+B reaction, demonstrating dynamic scaling of reaction profiles and lengthscales, and discussing multiscaling phenomena in the context of reaction front behavior.

Contribution

It provides refined simulation data showing all lengthscales scale as t^{1/4} and discusses the implications for multiscaling in diffusion-limited reactions.

Findings

Reaction rate profile exhibits dynamic scaling.

All lengthscales behave as t^{1/4} as time increases.

Evidence and discussion of multiscaling phenomena.

Abstract

Extensive simulations are performed of the diffusion-limited reaction A$+$B$\to 0$ in one dimension, with initially separated reagents. The reaction rate profile, and the probability distributions of the separation and midpoint of the nearest-neighbour pair of A and B particles, are all shown to exhibit dynamic scaling, independently of the presence of fluctuations in the initial state and of an exclusion principle in the model. The data is consistent with all lengthscales behaving as $t^{1/4}$ as $t\to\infty$. Evidence of multiscaling, found by other authors, is discussed in the light of these findings.