[Amath-seminars] Boeing Lecture by Robert Kohn
bahmang at uw.edu
Wed Oct 23 12:31:58 PDT 2019
This is a final reminder for the Boeing Colloquium by Professor Robert Kohn
tomorrow. Please see my earlier email below for the details.
University of Washington, Department of Applied Mathematics
+1 (206) 543-4065
On Thu, Oct 17, 2019 at 3:14 PM Bahman Angoshtari <bahmang at uw.edu> wrote:
> Hello everyone,
> Our next Boeing Colloquium will be delivered by Professor Robert Kohn (NYU
> 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.
> The Mathematics of Wrinkles and Folds
> 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."
> Bahman Angoshtari
> Research Associate
> University of Washington, Department of Applied Mathematics
> +1 (206) 543-4065
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