Volume 127, Number 4, August 2019
|Number of page(s)||5|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||09 September 2019|
Pinning of diffusional patterns by non-uniform curvature
1 Department of Physics, Massachusetts Institute of Technology - Cambridge, MA 02138, USA
2 Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México - Apdo. Postal 70-543, 04510 México, DF, Mexico
3 Department of Physics, Harvard University - Cambridge, MA 02138, USA
Received: 5 June 2019
Accepted: 10 August 2019
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.
PACS: 82.40.Ck – Pattern formation in reactions with diffusion, flow and heat transfer / 89.75.Kd – Patterns / 02.40.Ky – Riemannian geometries
© EPLA, 2019
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