Pattern Propagation Driven by Surface Curvature

TL;DR

This paper demonstrates that static Turing patterns on flat surfaces can propagate on curved surfaces due to surface geometry, revealing a new mechanism influenced by surface curvature in reaction-diffusion systems.

Contribution

It introduces the novel finding that surface curvature can induce propagation of static patterns, supported by numerical and theoretical analysis of reaction-diffusion systems on curved surfaces.

Findings

Pattern propagation is driven by surface curvature.

Symmetries of surface and pattern influence propagation.

Provides a new mechanism for pattern dynamics on curved surfaces.

Abstract

Pattern dynamics on curved surfaces are found everywhere in nature. The geometry of surfaces have been shown to influence dynamics and play a functional role, yet a comprehensive understanding is still elusive. Here, we report for the first time that a static Turing pattern on a flat surface can propagate on a curved surface, as opposed to previous studies, where the pattern is presupposed to be static irrespective of the surface geometry. To understand such significant changes on curved surfaces, we investigate reaction-diffusion systems on axisymmetric curved surfaces. Numerical and theoretical analyses reveal that both the symmetries of the surface and pattern participate in the initiation of pattern propagation. This study provides a novel and generic mechanism of pattern propagation that is caused by surface curvature, as well as insights into the general role of surface geometry.