WFU Physics Colloquium
TITLE: “Why is Lettuce So Wrinkly?”
SPEAKER: Professor John Gemmer
Assistant Professor, Department of Mathematics and Statistics
Wake Forest University
TIME: Wed. Feb. 21, 2018, at 4:00 PM
PLACE: George P. Williams, Jr. Lecture Hall, (Olin 101)
There will be a reception with refreshments at 3:30 PM in the lounge. All interested persons are cordially invited to attend.
Many patterns in nature and industry arise from the system minimizing an appropriate energy. Examples range from the periodic rippling in hanging drapes to the six-fold symmetries observed in snowflakes. Torn plastic sheets and growing leaves provide striking examples of pattern forming systems which can transition from single wavelength geometries (hosta leaves) to complex fractal like shapes (lettuce). These fractal-like patterns seem to have many length scales – the same amount of extra detail can be seen when looking closer (“statistical self-similarity”). It is a mystery how such complex patterns could arise from energy minimization alone.
In this talk, I will address this puzzle by showing that such patterns naturally arise from the sheet adopting a hyperbolic non-Euclidean geometry. However, there are many different hyperbolic geometries that the growing leaf could select. I will show, using techniques from nonlinear elasticity, analysis, differential geometry and numerical optimization, that the fractal-like patterns are indeed the natural minimizers for the system.