Pattern Propagation Driven by Surface Curvature

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.

arXiv commentAccepted by PRL (https://journals.aps.org/prl/accepted/9e070Yd7Ce41e478502d7524db41ca3ec89bef83d)

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Cited by in corpus (9)

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• Physical interactions promote Turing patterns
• Effective quantum dynamics in curved thin-layer system with inhomogeneous confinement
• Nonequilibrium Membrane Dynamics Induced by Active Protein Interactions and Chemical Reactions: A Review
• Geometric thermodynamics of reaction-diffusion systems: Thermodynamic trade-off relations and optimal transport for pattern formation
• Oscillatory and chaotic pattern dynamics driven by surface curvature
• Weakly nonlinear analysis of Turing pattern dynamics on curved surfaces
• Turing patterns on polymerized membranes: a coarse-grained lattice modelling with internal degree of freedom for polymer direction
• Spot solutions to a neural field equation on oblate spheroids