"Spontaneous wrinkling in free sheets and the Geometry of wavy leaves and flowers"
Dr. Eran Sharon
The Racah Institute of Physics, The Hebrew University of Jerusalem
I present an experimental study of the buckling cascades that are formed along the edge of a torn plastic sheet.
The edge is composed of an organized cascade with up to six generations of waves. The waves are similar in shape
but differ greatly in scale, leading to the formation of a fractal edge as an equilibrium configuration. We show
that the tearing process prescribes a hyperbolic metric near the edge of the sheet. This metric should be
satisfied in order to reduce the stretching energy. We suggest, however that no smooth surfaces exist in a
3D Euclidean space with the prescribed metric. The free sheet, thus, undergoes a "geometrically driven"
wrinkling instability. Our data support this picture, showing that the scaling of wavelengths in the cascades
depends explicitly on the sheet thickness.
Similar geometrical features (similar metrics) could result from very simple growth mechanisms. We, thus,
suggest that some of the complex shapes of leaves and flowers might result from this buckling instability.
The complexity, in this case, results from elasticity and not from complex growth processes, as commonly
accepted. Finally, I will present results from experiments in plants and environmentally responsive gels.
Host:
Dr. Ron Lifshitz, x5145
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