Applied Mathematics Seminar
Spring 2021
Most seminars are Fridays at 2:30p.m. in Warren Weaver Hall Rm 1302.
Fall 2020 Semester seminars will be held on Zoom
Questions or comments? Please email: Leif Ristroph
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Upcoming Events

Friday, October 22, 20212:30PM, Warren Weaver Hall 1302
Courant Instructor Day
Synopsis:

Friday, October 29, 20212:30PM, Warren Weaver Hall 1302
TBA
Jane Wang, Cornell UniversitySynopsis:

Friday, November 5, 20212:30PM, Warren Weaver Hall 1314
TBA
Niall Mangan, Northwestern UniversitySynopsis:
Notes:
Zoom + In person projection

Friday, November 12, 20212:30PM, Warren Weaver Hall 1302
TBA
Aref Hashemi Amrei, Courant InstituteSynopsis:

Friday, November 19, 202111AM, Warren Weaver Hall 1302
TBA
Corentin Herbert, Ecole Normale Superieure de LyonSynopsis:
Notes:
Zoom + In person projection

Friday, December 3, 20212:30PM, Warren Weaver Hall 1302
TBA
Eric Falcon, Ecole Normale Superieure de ParisSynopsis:

Friday, December 10, 202112:45PM, Warren Weaver Hall 1314
TBA
Robert Dudley, BerkeleySynopsis:
Past Events

Friday, October 15, 20212:30PM, Warren Weaver Hall 1302
Untangling in time: designing time varying applied fields to reveal interior structure
Graeme Milton, University of UtahSynopsis:
In two phase materials, each phase having a nonlocal response in time, we were surprised to discover that for appropriate driving fields the response somehow untangles at specific times, allowing one to directly infer useful information about the geometry of the material, such as the volume fractions of the phases. This rests on the existence of approximate, measure independent, linear relations between the values that Markov functions take at a given set of possibly complex points, not belonging to the interval [1,1] where the measure is supported. The problem is reduced to simply one of polynomial approximation of a given function on the interval [1,1]. In the context of the motivating problem, the analysis also yields bounds on the response at any particular time for any driving field, and allows one to estimate the response at a given frequency using an appropriately designed driving field that effectively is turned on only for a fixed interval of time. The approximation extends directly to Markovtype functions with a positive semidefinite operator valued measure, and this has applications to determining the shape of an inclusion in a body from boundary flux measurements at a specific time, when the timedependent boundary potentials are suitably tailored. This is joint work with Ornella Mattei and Mihai Putinar.

Friday, October 1, 20212:30PM, Warren Weaver Hall 1314
Surface gravity waves enhance the settling and dispersion of finitesize particles
Michelle DiBenedetto, University of WashingtonSynopsis:
Surface gravity waves transport mass through a process referred to as Stokes drift. Finitesized particles of arbitrary shape exhibit additional Stokes driftlike phenomena. In this talk, I explore the effects of particle inertia and shape on particle behavior in waves. I demonstrate both an angular analogue of Stokes drift for nonspherical particles and a vertical Stokes drift for settling particles. Experimental observations are compared with these analytical results, and these behaviors are discussed in the context of microplastic transport in the ocean.
Notes:
Zoom + In person projection

Friday, September 24, 20212:30PM, Warren Weaver Hall 1302
Singular measures and information capacity of turbulent cascades
Gregory Falkovich, Weizmann InstituteSynopsis:
How weak is the weak turbulence? We analyze turbulence of weakly
interacting waves using the tools of information theory. It offers a
unique perspective for comparing thermal equilibrium and turbulence. The
mutual information between resonant modes in a finite box is shown to be
stationary and small in thermal equilibrium, yet to grow with time in
weak turbulence. We trace this growth to the concentration of
probability on the resonance surfaces, which can go all the way to a
singular measure. The surprising conclusion is that no matter how small
is the nonlinearity and how close to Gaussian is the statistics of any
single amplitude, a stationary phasespace measure is far from Gaussian,
as manifested by a large relative entropy. At the end I shall describe a
new class of the socalled Fibonacci models that describe resonantly
interacting waves and allow turbulence close to thermal equilibrium.
(0.1103/PhysRevLett.125.104501) 
Friday, September 17, 20212:30PM, Warren Weaver Hall 1302
Could convection in porous media explain the geysers of Enceladus?
Samuel Boury, CIMSSynopsis:
Motivated by Enceladus cryovolcanism and possible shear heating along
its south pole fractures, we perform a theoretical and numerical study
of boundarylayer convection along a vertical heated wall in a bounded
ideal mushy region. By focusing on this simple model, we demonstrate the
existence of four regions with different regimes and scalings that are
studied asymptotically, showing a good agreement between the theory and
the numerical simulations. Close to the heated wall, the convection in
the mushy layer is similar to a rising buoyant plume abruptly stopped at
the top, leading to increased pressure and temperature in the upper
region, that could be the ignition of Enceladus' geysers.