Equilibrium and growth shapes of fiber-covered surfaces
AbstractCo-authors: Thi-Hanh Nguyen (CNRS, Ecole Polytechnique), Vincent Fleury (CNRS, Ecole Polytechnique), Hervé Henry (CNRS, Ecole Polytechnique)
Branched growth patterns are generally formed by an interplay between instabilities that favor branching and stabilizing effects that result from the microscopic structure of matter. We consider nematic surfaces (that is, surfaces that are covered by fibers which remain tangential to the surface) and investigate the consequences of an anisotropic bending rigidity (surfaces are easier to bend in the direction normal to the fibers than along it) on equilibrium and growth shapes. We formulate a continuum model that allows us to determine the organization of the fibers and the geometric shape of a simply connected domain which correspond to a minimum of the total (free) energy. The coupling with a simple diffusive growth mechanisms leads to growth shapes that could not have been obtained with a simple crystalline material. Possible connections with the growth of biological structures will be discussed.