Campuses:

Elastic

Thursday, February 25, 2016 - 11:00am - 12:00pm
Scott Hansen (Iowa State University)
The standard 2-dimensional cochlea model consists of a one-dimensional elastic structure which models the basilar membrane (BM) surrounded by an incompressible 2-dimensional fluid within the cochlear cavity. First we describe an idealized model in which the basilar membrane is modeled as an
Wednesday, February 25, 2015 - 2:00pm - 2:50pm
Nathan (Nati) Srebro (Technion-Israel Institute of Technology)
I will first present the k-support norm, which is the tightest convex
relaxation of sparsity combined with an ell-2 penalty. In
particular, the k-support norm is strictly tighter then relaxing
sparsity to L1 as in the elastic net, and allows us to study the
looseness of the elastic net relaxation. I will also discuss
tightness of convex relaxations to the rank, establishing that the
max-norm is tighter then the trace-norm, though possibly not the
tightest.
Monday, July 22, 2013 - 11:00am - 11:50am
Marta Lewicka (University of Pittsburgh)
This course will be concerned with the analysis of thin elastic films which exhibit residual stress at free equilibria. Examples of such structures include, in particular, growing tissues such as leaves, flowers or marine invertebrates, as well as specifically engineered gels. There, it is conjectured that the growth process results in the formation of non-Euclidean target metrics, leading to complicated morphogenesis of the tissue which attains an orientation-preserving configuration closest possible to an isometric immersion of the metric.
Monday, July 21, 2008 - 2:30pm - 2:40pm
Efi Efrati (Hebrew University)
Thin elastic sheets are very common in both natural and
man-made structures. The configurations these structures assume in space are
often very complex and may contain many length scales, even in the case of
unconstrained thin sheets. We will show that in some cases, a simple intrinsic
geometry leads to complex three-dimensional configurations, and discuss the
mechanism shaping thin elastic sheets through the prescription of an intrinsic metric.

Current reduced (two-dimensional) elastic theories devised to describe thin
Thursday, July 24, 2008 - 2:45pm - 2:55pm
Sergio Rica (Centre National de la Recherche Scientifique (CNRS))
I will talk about a work in collaboration with G.
During and C. Josserand on the long-time evolution
of waves of a thin elastic plate in the limit of small
deformation so that modes of oscillations interact weakly. According to the
theory of weak turbulence (successfully applied in the past to plasma, optics,
and hydrodynamic waves), this nonlinear wave system evolves at
long times with a slow transfer of energy from one mode to
another. We derived a kinetic equation for the spectral transfer in terms of
Thursday, July 24, 2008 - 2:30pm - 2:40pm
Laurent Boué (École Normale Supérieure)
Low dimensional elastic manifolds (such as rods 1D or sheets
2D) have been drawing a lot of attention lately. When confined into
environments smaller than their size at rest, elastic objects sustain
large deformations involving many fascinating mechanisms such as energy
condensation from large length-scales to small singular structures,
topological self-avoidance, complex energetical landscapes... One only
needs to crumple a piece of paper to observe the extreme complexity of
Thursday, July 24, 2008 - 2:00pm - 2:10pm
Arshad Kudrolli (Clark University)
We will discuss the packing and folding of a confined beaded
chain vibrated in a flat circular container as a function of chain
length, and compare with random walk models from polymer physics. Time
permitting, we will briefly discuss crumpling and folding structures
obtained with paper and elastic sheets obtained with a laser-aided
topography technique. We have shown that the ridge length distribution
is consistent with a hierarchical model for ridge breaking during crumpling.
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