Pinning of Diffusional Patterns by Non-Uniform Curvature
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866912574859116544 |
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| author | Frank, John R. Guven, Jemal Kardar, Mehran Shackleton, Leyna |
| author_facet | Frank, John R. Guven, Jemal Kardar, Mehran Shackleton, Leyna |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1901_09900 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Pinning of Diffusional Patterns by Non-Uniform Curvature Frank, John R. Guven, Jemal Kardar, Mehran Shackleton, Leyna Soft Condensed Matter 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. |
| title | Pinning of Diffusional Patterns by Non-Uniform Curvature |
| topic | Soft Condensed Matter |
| url | https://arxiv.org/abs/1901.09900 |