[Amath-seminars] Boeing Lecture by Robert Kohn

Bahman Angoshtari bahmang at uw.edu
Wed Oct 23 12:31:58 PDT 2019


Dear All,

This is a final reminder for the Boeing Colloquium by Professor Robert Kohn
tomorrow. Please see my earlier email below for the details.

Best,
Bahman

--
Bahman Angoshtari

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


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

> 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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