2015/11/24 by Sergei Nechaev, Nechaev, Sergei, Kirill Polovnikov +1
Biochemistry, Genetics and Molecular Biology · Engineering · #Advanced Materials and Mechanics #Cellular Mechanics and Interactions #FOS: Physical sciences #Soft Condensed Matter (cond-mat.soft)
paper · pdf · doi:10.48550/arxiv.1511.07862
openalex publication_date 2015/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.