%0 Journal Article
%T Elasticity and Glocality: Initiation of Embryonic Inversion in ${\it Volvox}$
%A Pierre A. Haas
%A Raymond E. Goldstein
%J Quantitative Biology
%D 2015
%I arXiv
%X Elastic objects across a wide range of scales deform under local changes of their intrinsic properties, yet the shapes are ${\it glocal}$, set by a complicated balance between local properties and global geometric constraints. Here, we explore this interplay during the inversion process of the green alga ${\it Volvox}$, whose embryos must turn themselves inside out to complete their development. This process has recently been shown [S. H\"ohn ${\it et~al}.$, ${\it Phys. Rev. Lett.}$ $\textbf{114}$, 178101 (2015)] to be well described by the deformations of an elastic shell under local variations of its intrinsic curvatures and stretches, although the detailed mechanics of the process have remained unclear. Through a combination of asymptotic analysis and numerical studies of the bifurcation behavior, we illustrate how appropriate local deformations can overcome global constraints to initiate inversion.
%U http://arxiv.org/abs/1507.01439v1