If you want to receive e-mail announcements of talks please contact
Dionisios Margetis (dio@math.umd.edu).
| August 30
|
NO SEMINAR
|
|
|
|
September 6
|
NO SEMINAR
|
|
|
|
September 13
|
SEMINAR CANCELLED FOR THIS DATE
|
|
|
|
September 20
|
Blowup, periodicity, and parametric instability for shells
Stuart Antman
Department of Mathematics & IPST -- UMCP
|
|
Abstract:
This lecture treats the qualitative behavior of radial motions of
nonlinearly
viscoelastic cylindrical and spherical shells under
time-dependent pressures on their faces. The behavior of
solutions depends critically upon the material properties.
There are marked differences in the responses of
cylindrical and spherical shells.
|
September 27, 3:30-4:30pm
JOINT PDE/N. WIENER CENTER SEMINAR:
|
Boundary value problems for higher-order elliptic operators
Irina Mitrea
Department of Mathematics -- University of Virginia
|
|
Abstract:
In this talk I will discuss the multiple layer potential approach
for the treatment of
boundary value problems associated with higher-order, constant
coefficient,
elliptic differential operators on smooth and Lipschitz domains.
This study
falls within the scope of the program outlined by A.P. Calder\'on
in his 1978
ICM plenary address in which he advocates the use of layer
potentials
"for much more general elliptic systems [than the Laplacian]".
|
|
October 4
|
Coarsening of discrete, ill-posed diffusion equations
John Greer
National Geospatial-Intelligence Agency (NGA)
|
|
Abstract:
We prove a weak upper bound on the coarsening rate of the
discrete-in-space version of an ill-posed, nonlinear diffusion
equation. The continuum version of the equation violates parabolicity
and lacks a complete well-posedness theory. In particular, numerical
simulations indicate very sensitive dependence on initial data.
Nevertheless, models based on its discrete-in-space version, which we
study, are widely used in a number of applications, including
population dynamics (chemotactic movement of bacteria), granular flow
(formation of shear bands), and computer vision (image denoising and
segmentation). Our bounds have implications for all three
applications. This is joint work with Selim Esedoglu (U. of Michigan
Mathematics).
|
|
October 11
|
Uniform L^p-stability problem for the Boltzmann equation
Seung-Yeal Ha
Department of Mathematical Sciences
-- Seoul National University
|
|
Abstract:
The Boltzmann equation governs the dynamics of a
dilute gas.
In this talk, I will address the L^p-stability problem of the
Boltzmann
equation near vacuum and a global Maxwellian. In a
close-to-vacuum regime,
I will explain the nonlinear functional approach motivated by
Glimm's
theory in hyperbolic conservation laws. This functional
approach yields
the uniform L^1-stability
estimate. In contrast, in a
close-to-global
maxwellian regime, I will present the L^2-stability theory
which
establishes the uniform L^2-stability of several classical
solutions.
|
|
October 18
|
Strong trace for scalar conservation laws
Young-sam Kwon
CSCAMM & Department of Mathematics - UMCP
|
|
Abstract:
In this talk we consider bounded weak solutions u of scalar
conservation laws, not necessarily of class BV, defined in a
subset, Omega, of (R^+) x R. We define a strong notion of
trace at the boundary of Omega reached by L^1 convergence for a
large class of functionals of u, G(u). Those functionals G
depend on the flux function of the conservation law and on the
boundary of Omega. The result holds for general flux function and
general subset.
|
|
October 25
|
Impurity and quaternions in nonrelativistic scattering from a quantum
memory
Manoussos Grillakis
Department of Mathematics -- UMCP
|
|
Abstract:
Models in quantum computing rely on transformations of the states
of quantum memory. We study a model proposed by T. T. Wu in which the
memory is changed via scattering of an incoming particle. Pure
states corresponding to single frequency particles scatter into
pure states, but a superposition of pure states scatter into an
impure state. Following the analysis of impurity by Margetis and Myers,
we offer an alternative analysis based on null hyperbolic quaternions
as the manifestation of pure states. This work is in collaboration
with D. Margetis.
|
|
November 1
|
Drift diffusion equations with fractional diffusion and the
quasi-geostrophic equation
Alexis Vasseur
Department of Mathematics -- University of Texas at Austin
|
|
Abstract:
Motivated by the critical dissipative quasi-geostrophic
equation, we prove that drift-diffusion equations with L2 initial data
and minimal assumptions on the drift are locally Holder continuous.
As an application we show that solutions of the quasi-
geostrophic equation with initial L2 data and critical diffusion are
locally smooth for any space dimension. This problem was proposed by
previous authors as a toy problem for the global regularity of solutions
to 3D Navier-Stokes equations.
|
|
November 8
|
Critical thresholds in Eulerian dynamics
Eitan Tadmor
Department of Mathematics, CSCAMM & IPST -- UMCP
|
|
Abtract:
We are concerned with the questions of global regularity vs.
finite time breakdown in Eulerian dynamics, driven by different models of
the nonlinear forcing. To address these questions, we propose the notion
Critical Threshold (CT), where a conditional finite time breakdown depends
on whether the initial configuration crosses an intrinsic, O(1) critical
threshold. Our approach is based on spectral dynamics, tracing the
eigenvalues of velocity gradient which determine the boundaries of CT
surfaces in configuration space.
We demonstrate the CT phenomena with several prototype models. We begin with
the n-dimensional restricted Euler equations, obtaining a surprising
4-dimensional global existence for a large set of sub-critical initial
data. A second example consists of the corresponding n-dimensional
restricted Euler-Poisson equations. Here we identify a set of [n/2]
spectral invariants which lead to a remarkable characterization of
two-dimensional sub-critical initial configurations with global smooth
solutions. Finally, we show how the CT phenomenon associated with rotation
prevents finite-time breakdown, which, in turn, yields a long-time
regularity regime in the shallow-water equations. Our study reveals the
critical dependence of the two-dimensional CT phenomenon on the initial
spectral gap.
|
November 15
JOINT PDE AND NUMERICAL ANALYSIS SEMINAR
|
Near optimal recovery of arbitrary signals from uncomplete measurements
Albert Cohen
Laboratoire Jacques-Louis Lions, Universite Pierre et Marie Curie, Paris
|
|
Abstract:
Compressed sensing is a recent concept in signal and image processing where one seeks to minimize the number of measurements to be taken from signals or images while still retaining the information necessary to approximate them well. The ideas have their origins in certain abstract results from functional analysis and approximation theory but were recently brought into the forefront by the work of Candes-Romberg-Tao, and Donoho who constructed concrete algorithms and showed their promise in application. There remain several fundamental questions on both the theoretical and practical side of compressed sensing. This talk is primarily concerned about one of these issues revolving around just how well compressed sensing can approximate a given signal from a given budget of fixed linear measurements, as compared to adaptive linear measurements. More precisely, we consider discrete N-dimensional signals x with N>>1, allocate n<
|
|
November 22
|
THANKSGIVING HOLIDAY - NO SEMINAR
|
|
Abstract:
|
|
November 29
|
OPEN
|
|
Abstract:
|
|
December 6
|
Towards a Model of a Sensory Feedback Loop in the
Locomotion CPG of the Lamprey
Kathleen Hoffman
Department of Mathematics -- University of Maryland, Baltimore County
|
|
Abstract:
Swimming in the lamprey is generated by neural circuits called central
pattern generators (CPGs) that signal a muscle contraction or
extension. A wave of muscular activation occurs down the body of the
lamprey, propelling it through the water. The CPGs can be modeled by a
chain of coupled nonlinear neural oscillators. In this talk,
I will focus on two different models of the CPG: connectionist
models and phase models. I will discuss a `random' coupling
strategy for connecting the oscillators, which limits to
the analogous deterministic connections. I will further discuss
the role of proprioceptive sensor, called edge cells in locomotion,
and describe some of the biological experiments and mathematical
challenges in understanding this closed loop system.
|
December 13
SPECIAL TIME: 4-5PM
|
Non-Gaussian distributions in physics, materials science and mathematics: a universal paradigm
Alberto Pimpinelli
Universite Blaise Pascal V Clermont-Ferrand I, France
|
|
Abstract:
Gaussian, or normal distributions pop up in very many descriptions of natural
phenomena, mainly as a consequence of the Central Limit Theorem. However, more
and more situations are known in which non-Gaussian distributions appear to be
the rule. These include the distribution of spacings of energy levels of atomic
nuclei, as well as the spacing distributions of energy levels of quantum
chaotic Hamiltonians, the distribution of domain sizes in 1D Potts and Ising
models, the distribution of step spacings on crystal surfaces at equilibrium,
the spacings between parked cars and the intervals between arrival of buses in
Cuernavaca, Mexico, the distribution of capture zone areas in atomic and
molecular deposition on surfaces, and the distribution of the spacings between
zeros of the Riemann zeta function.
The latter are considered the consequence of the ubiquity and universality of
the description that Random Matrix Theory (RMT) gives of fluctuating
quantities. However, the relation with RMT is often far from obvious.
After describing several examples among those listed above, I will discuss how a
simple argument based on a simple stochastic differential equation may help
understanding why such distributions are so common, and what is their relation
with RMT.
|
Special accomodations for individuals with disabilities can be made
by calling in advance (301) 405-5048. It would be appreciated if we are
notified at least one week in advance.
