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Updated: Mar 8, 2026

Ultrasonic Fatigue Testing in the Tension-Compression Mode
Published on: March 7, 2018
From geometric optics to plants: the eikonal equation for buckling
Sergei Nechaev1, Kirill Polovnikov2
1J.-V. Poncelet Laboratory, CNRS, UMI 2615, 119002 Moscow, Russia. sergei.nechaev@gmail.com and P.N. Lebedev Physical Institute, RAS, 119991 Moscow, Russia.
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.
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