Radial Evolution in a Reaction-Diffusion Model

TL;DR

This paper studies an off-lattice diffusion-reaction model with radial symmetry, revealing that the fluctuating interface belongs to the circular KPZ universality class through extensive numerical simulations.

Contribution

It introduces a radial off-lattice diffusion-reaction model and demonstrates its front fluctuations belong to the circular KPZ universality class.

Findings

The fluctuating front is circular and grows over time.

The interface fluctuations follow the KPZ universality class.

Numerical simulations confirm the universality class assignment.

Abstract

In this work, we investigate an off-lattice version of the diffusion-reaction model, $A + A \leftrightarrow A$. We consider extensive numerical simulation of the radial system obtained from a single seed. Observed fluctuations in such an evolving system are characterized by a circular region occupied by particles growing over an empty one. We show that the fluctuating front separating the two regions belongs to the circular subclass of the Kardar-Parisi-Zhang universality class.