Issue 7, 2017

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.

Graphical abstract: From geometric optics to plants: the eikonal equation for buckling

Article information

Article type
Paper
Submitted
28 Oct 2016
Accepted
05 Jan 2017
First published
05 Jan 2017

Soft Matter, 2017,13, 1420-1429

From geometric optics to plants: the eikonal equation for buckling

S. Nechaev and K. Polovnikov, Soft Matter, 2017, 13, 1420 DOI: 10.1039/C6SM02438F

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