Radially Locked Sun-Ray Patterns in Autocatalytic Reaction-Diffusion-Advection Systems

Abstract

Traveling fronts ubiquitous in physics, chemistry, and biology are prone to transverse cellular deformations due to diffusive or convective instabilities. Here we show both theoretically and experimentally that new patterns can be obtained if the destabilization is triggered around a front locked radially by advection. Specifically, angularly shifting sun-ray-like patterns can develop around radially advected autocatalytic fronts due to a diffusive instability developing when the autocatalyst X and the reactant Y diffuse at different rates. The properties of these shining-star structures can be controlled by tuning the flow rate $Q$ and the ratio of diffusion coefficients $\hat{I}´$ as evidenced by linear stability analysis, nonlinear simulations, and experiments on the chlorite-tetrathionate reaction.