Buckling and wrinkling from geometric and energetic viewpoints

Sergei Nechaev; Kirill Polovnikov

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arXiv · 1511.07862

Buckling and wrinkling from geometric and energetic viewpoints

Sergei Nechaev·Kirill Polovnikov

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Abstract

We discuss shape profiles emerging in inhomogeneous growth of squeezed tissues. Two approaches are used simultaneously: i) conformal embedding of two-dimensional domain with hyperbolic metrics into the plane, and ii) a pure energetic consideration based on the minimization of the total energy functional. In the latter case the non-uniformly pre-stressed plate, which models the inhomogeneous two-dimensional growth, is analyzed in linear regime under small stochastic perturbations. It is explicitly demonstrated that both approaches give consistent results for buckling profiles and reveal self-similar behavior. We speculate that fractal-like organization of growing squeezed structure has a far-reaching impact on understanding cell proliferation in various biological tissues.

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Sergei Nechaev, Kirill Polovnikov. 2015-11-24. Buckling and wrinkling from geometric and energetic viewpoints. https://arxiv.org/abs/1511.07862

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