[Amath-seminars] Boeing Lecture by Robert Kohn

Bahman Angoshtari bahmang at uw.edu
Thu Oct 17 15:14:28 PDT 2019


Hello everyone,

Our next Boeing Colloquium will be delivered by Professor Robert Kohn (NYU
Courant).

When: Thursday October 24th - 4:00pm
Where: Smith Hall 205

There will be a reception in the Lewis hall lounge after the talk.

Please find below the title and abstract of the lecture.

====================
Title:
The Mathematics of Wrinkles and Folds

Abstract:
The wrinkling and folding of thin elastic sheets is very familiar: our
skin wrinkles; a crumpled sheet of paper has folds; and a flat sheet
stretched over a round surface must wrinkle or fold.

What kind of mathematics is relevant? The stable configurations of a sheet
are local minima of a variational problem involving its elastic energy --
which consists of a nonconvex membrane energy (favoring isometry) plus a
small coefficient times bending energy (penalizing curvature). The bending
term is a singular perturbation; its small coefficient is the sheet
thickness squared. The patterns and defects seen in thin sheets arise from
energy minimization -- but not in the same way that minimal surfaces arise
from area minimization. Rather, the analysis of wrinkles and folds
involves the asymptotic character of minimizers as the sheet thickness
tends to zero.

What kind of methods are useful? It has been fruitful to focus on the
energy scaling law, in other words the dependence of the minimum energy
upon the thickness of the sheet. Optimizing within an ansatz gives an
upper bound. A key mathematical challenge is to obtain ansatz-free lower
bounds. When the lower and upper bounds are close to agreement they
demonstrate the adequacy of the ansatz, and the underlying arguments help
to explain why certain configurations are preferred.

A current frontier is the study of wrinkling due to geometric
incompatibility. Such wrinkling occurs, for example, when a flat sheet is
wrapped around a sphere or a curved shell is flattened by placing it on
water. My talk will include some problems of this type, including dramatic
recent progress by Ian Tobasco on wrinkling driven by geometric
incompatibility in a regime involving "asymptotic isometry."

https://amath.washington.edu/calendar?trumbaEmbed=view%3Devent%26eventid%3D133511164
====================

Best,
Bahman
--
Bahman Angoshtari

Research Associate
University of Washington, Department of Applied Mathematics
+1 (206) 543-4065
http://faculty.washington.edu/bahmang/
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