Pinning of diffusional patterns by non-uniform curvature

Frank, John R; Guven, Jemal; Kardar, Mehran; Shackleton, Henry

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Pinning of diffusional patterns by non-uniform curvature

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Author(s)

Frank, John R

•

Guven, Jemal

•

Kardar, Mehran

•

Shackleton, Henry

Journal

EPL (Europhysics Letters)

Publisher

IOP Publishing

Version

Author's final manuscript

Abstract

© 2019 EPLA. Diffusion-driven patterns appear on curved surfaces in many settings, initiated by unstable modes of an underlying Laplacian operator. On a flat surface or perfect sphere, the patterns are degenerate, reflecting translational/rotational symmetry. Deformations, e.g., by a bulge or indentation, break symmetry and can pin a pattern. We adapt methods of conformal mapping and perturbation theory to examine how curvature inhomogeneities select and pin patterns, and confirm the results numerically. The theory provides an analogy to quantum mechanics in a geometry-dependent potential and yields intuitive implications for cell membranes, tissues, thin films, and noise-induced quasipatterns.

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Creative Commons Attribution-Noncommercial-Share Alike

http://creativecommons.org/licenses/by-nc-sa/4.0/

Persistent DSpace Link

https://hdl.handle.net/1721.1/132518

DOI of Published Version

10.1209/0295-5075/127/48001