title: From geometric optics to plants: the eikonal equation for buckling.
abstract: Optimal buckling of a tissue, e.g. a plant leaf, growing by means of exponential division of its peripheral cells, is considered in the framework of a conformal approach. It is shown that the boundary profile of a tissue is described by the 2D eikonal equation, which provides the geometric optic approximation for the wavefront propagating in a medium with an inhomogeneous refraction coefficient. A variety of optimal surfaces embedded in 3D is controlled by spatial dependence of the refraction coefficient which, in turn, is dictated by the local growth protocol.
authors.affiliation: J.-V. Poncelet Laboratory, CNRS, UMI 2615, 119002 Moscow, Russia. sergei.nechaev@gmail.com and P.N. Lebedev Physical Institute, RAS, 119991 Moscow, Russia.
authors.forename: Sergei
authors.initials: S
authors.lastname: Nechaev
authors.affiliation: Physics Department, Moscow State University, 119992 Moscow, Russia and The Skolkovo Institute for Science and Technology, 143005 Skolkovo, Russia.
authors.forename: Kirill
authors.identifier: http://orcid.org/0000-0001-9903-9623
authors.initials: K
authors.lastname: Polovnikov
mesh_terms: D001696:Biomechanical Phenomena; D055595:Mechanical Phenomena; D008954:Models, Biological; D055620:Optical Phenomena; D059828:Plant Cells / Q000378:metabolism; D063245:Plant Development