Cornell University

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CAM Colloquium: John Gemmer (Wake Forest University) - Why does lettuce look like a fractal?

Friday, October 30, 2020 at 3:30pm

Virtual Event

Abstract:
Many patterns in Nature and industry arise from the system minimizing an appropriate energy. Torn plastic sheets and growing leaves provide striking examples of pattern forming systems which can transition from single wavelength geometries (leaves) to complex fractal like shapes (lettuce). These fractal like patterns seem to have many length scales, i.e. 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 analysis, differential geometry and numerical optimization that the fractal like patterns are indeed the natural minimizers for the system. I will also discuss the implications of our work to developing shape changing soft matter which can be implemented in soft machines.

Bio:
John Gemmer is an assistant professor in the Department of Mathematics and Statistics at Wake Forest University where he has been a faculty member since 2016 and a Sterge Faculty Fellow since 2019. In the 2019-2020 academic year John was on sabbatical and held visiting research positions at University of North Carolina Chapel Hill and the University of Chicago. He was a NSF-RTG postdoctoral fellow at Brown University from 2013-2016, a long term visitor at the Kavli Institute for Theoretical Physics, and he completed his Ph.D. at the University of Arizona and his undergraduate studies at Millersville University of Pennsylvania. His interests lie in the areas of calculus of variations, dynamical systems, and stochastic differential equations. He has collaborated actively with researchers in several other areas of applied mathematics, physics, and biology on problems in continuum mechanics, optics, neuroscience, and climate dynamics. 

Zoom Link Access:
This talk will be given via Zoom, and the link is emailed to the CAM Seminar listserv the week of the talk. If you are not on the listserv, please contact Erika Fowler-Decatur to request the link. 

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Event Type

Colloquium

Departments

Center for Applied Mathematics

Tags

center for applied math, calmath

Contact E-Mail

ef48@cornell.edu

Contact Name

Erika Fowler-Decatur

Speaker

John Gemmer

Speaker Affiliation

Department of Mathematics and Statistics, Wake Forest University

Dept. Web Site

cam.cornell.edu

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