Pinning of diffusional patterns by non-uniform curvature

@article{Frank2019PinningOD,
  title={Pinning of diffusional patterns by non-uniform curvature},
  author={John R. Frank and J. Guven and Mehran Kardar and Henry Shackleton},
  journal={EPL (Europhysics Letters)},
  year={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… 

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