# The asymptotic speed of reaction fronts in active reaction-diffusion systems

## TL;DR

This paper investigates how active diffusion influences the asymptotic speed of reaction fronts in reaction-diffusion systems, revealing dimension-dependent effects on wavefront propagation speed.

## Contribution

It extends reaction-diffusion models to include active diffusion, analyzing the impact on wavefront speed in different spatial dimensions.

## Key findings

- Active processes have smaller speeds than passive ones in 1D.
- In higher dimensions, active processes can have larger speeds.
- Wavefront speed depends on the interplay between activity and spatial dimension.

## Abstract

We study various combinations of active diffusion with branching, as an extension of standard reaction-diffusion processes. We concentrate on the selection of the asymptotic wavefront speed for thermal run-and-tumble and for thermal active Brownian processes in general spatial dimensions. Comparing 1D active branching processes with a passive counterpart (which has the same effective diffusion constant and reproduction rate), we find that the active process has a smaller propagation speed. In higher dimensions, a similar comparison yields the opposite conclusion.