If you want to receive e-mail announcements of talks please contact
Dionisios Margetis (dio@math.umd.edu).
| January 25
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Some sharp integral inequalities and conformally
invariant integral equations
Fengbo Hang,
Department of Mathematics -- Princeton University
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Abstract:
It is usually interesting to identify the best
constant and extremal functions for classical analytical
inequalities. Lieb studied these issues for the
Hardy-Littlewood-Sobolev inequalities and the special case when
the inequality is conformally invariant is particularly well
understood. I will discuss some recent progresses on the
regularity and symmetry property for the associated
Euler-Lagrange system and applications of the approach to some
sharp integral inequalities for harmonic functions and a
conformally invariant integral equation motivated from
Carleman's proof of the isoperimetric inequality in dimension
two.
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Wednesday, January 31, 2:00PM
Rm Math 3206 -- JOINT CSCAMM/PDE Seminar
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Leray-type regularizations of the Burgers and the
isentropic Euler equations
Razvan Fetecau,
Department of Mathematics -- Simon Fraser University
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Abstract:
We start from the Burgers equation v_t + vv_x = 0 and investigate
a smoothing mechanism that replaces the convective velocity v in the nonlinear
term by a smoother velocity field u. This type of regularization was first proposed in
1934 by Leray, who applied it in the context of the incompressible Navier-Stokes equations.
We show strong analytical and numerical indication that the Leray smoothing procedure
yields a valid regularization of the Burgers equation.
We also study the stability of the front traveling waves. The front stability
results show that the regularized equation mirrors the physics of rarefaction and
shock waves in the Burgers equation.
Finally, we apply the Leray regularization to the isentropic Euler equations and
use the
weakly nonlinear geometrical optics (WNGO) asymptotic theory to analyze the
resulting system. As it turns out, the Leray procedure regularizes the Euler
equations only in special cases. We further investigate these cases using
Riemann invariants techniques.
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February 1
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NO SEMINAR
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February 8
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Analysis of a
reaction-diffusion
system: Global solutions and steady states
Huiqiang Jiang,
Department of Mathematics -- University of Minnesota
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Abstract:
We consider the Gierer-Meinhardt system in a
bounded smooth domain which is used to model pattern formation
in morphogenesis. The system is of reaction-diffusion form with
nonlinear terms of the form u^p/v^q and u^r/v^s. We will
discuss past achievement on this system and present new results
on existence of global solutions as well as existence and
nonexistence of nontrivial steady states.
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February 15
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RESERVED FOR FEBRUARY FOURIER TALKS (N. Wiener Center)
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Abstract:
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February 22
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Geometric and Mechanistic Models for Phyllotactic Patterns on Plants
Patrick Shipman,
Department of Mathematics -- UMCP
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Abstract:
Starting with biomechanical and biochemical models, we will try to
understand how various tiling patterns (of ridges, hexagons or diamonds)
develop at plant apices and how these patterns relate to Voronoi diagrams.
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March 1
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The problem of stability for black hole spacetimes in general relativity
Mihalis Dafermos
Department of Pure Mathematics and Mathematical Statistics -- University of Cambridge
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Abstract:
The notion of black hole plays a central role in general relativity.
Nonetheless, the most basic mathematical questions about black holes
remain unanswered, in particular, the question of their stability with
respect to perturbation of initial data. In this talk, I will discuss how
this problem is mathematically formulated, emphasizing its relation to
decay properties for solutions of wave equations. I will then discuss
recent progress on various related problems.
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March 8
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Artificial compressibility method for the incompressible
Navier-Stokes equations in 3-D
Donatella Donatelli,
Department of Pure and Applied Mathematics -- University of L'Aquila, Italy
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Abstract:
We study a
hyperbolic approximation of the Leray solution
of the
3D
Navier Stokes equation. In particular we describe a
hyperbolic version of the so called artificial compressibility
method investigated by J.L.Lions, Temam. This approximation is
motivated by numerical analysis applications where,
in order to overcome the difficulty related to the divergence
free condition, an artificial compressibilty is introduced.
We will recover compactness by the use of dispersive estimates
of Strichartz type.
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March 15
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A multiscale model for suspensions of rod--like molecules
Christiane Helzel, Institute for Applied Mathematics -- University of Bonn,
Germany
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Abstract:
We study the Doi model for suspensions of rod--like molecules.
This model couples a microscopic Fokker--Planck type equation
(the Smoluchowski equation) to the macroscopic Stokes equation.
The Smoluchowski equation describes the evolution of the distribution of the
rod orientation; it comes as a drift--diffusion equation on the sphere at
every point in physical space. The macroscopic flow model is coupled to the
microscopic description of rod orientations via an elastic stress. The drift
term in the microscopic Smoluchowski equation depends on the macroscopic
velocity gradient of the flow. Besides the interaction of the rod--like
molecules with the flow an interaction between molecules is modeled.
The coupled flow problem shows interesting phenomena (in particular the
spurt phenomenon) which will be discussed using appropriate numerical
methods.
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March 22
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SPRING BREAK -- NO SEMINAR
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Abstract:
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March 29
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NO SEMINAR
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Abstract:
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April 5
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NO SEMINAR
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Abtract
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April 12
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NO SEMINAR
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Abstract:
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April 19
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NO SEMINAR
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Abstract:
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SPECIAL PDE/APPLIED MATH SEMINAR
Friday, April 20, 11am - Rm Math 3206
(Note different day and time)
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The thermodynamic closure approximation of kinetic theories
for complex fluids
Pingwen Zhang,
School of Mathematical Sciences,
Peking University
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Abstract:
PDF FILE HERE
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| April 26
|
Scattering from a surface undergoing random motion
Jeffery Cooper
Department of Mathematics -- UMCP
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Abstract:
A problem of sonar scattering consists of studying the reflection
of an acoustic pulse, emitted by an underwater source, from the
underside of the surface. The surface is modeled as a stationary
stochastic process. The nature of the pulse requires a
treatment of the problem entirely in the time domain. We analyse the
far-field of the reflected signal to discover properties of the
spectral density of the stochastic process that models the
surface.
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JOINT PDE/CSCAMM SEMINAR:
Tuesday, May 1, 11am - Rm Math 3206
(Note different day and time)
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Nonlinear Schroedinger equations : semi-classics and blow up :
numerical studies
Norbert Mauser,
Wolfgang Pauli Institute,
University of Vienna
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Abstract:
We present recent numerical methods and simulations of time dependent
NLS with nonlinearities of the local type ("cubic NLS") or/and of the
nonlocal type ("Hartree/Poisson equation") and of Davey Stewartson
equations.
Particular interest is laid on simulations of "blow up" of the critical (=
2-d cubic)
NLS (*), depending on parameters of the data / equation, where a conjecture
on monotonicity of the blow up time (Fibich) is shown not to hold.
Also we show the Schroedinger-Poisson-X-alpha model, where we
investigate properties of semi-classical asymptotics.
We briefly present the equations, analysis and the numerical methods
(time split spectral scheme and relaxation scheme implemented on a
fixed grid on a parallel machine, thus allowing for 3-d simulations
with up to 1000 points in each direction) and instructive simulation
results.
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May 3
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Applications of Compressive Sampling to Error Correction
Emmanuel Candes,
Applied and Computational Mathematics - California Institute of Technology
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Abstract:
``Compressed Sensing'' or ``Compressive Sampling'' (CS) is a new
sampling or sensing theory which goes somewhat against the
conventional wisdom in signal acquisition. This theory allows the
faithful recovery of signals and images from what appear to be highly
incomplete sets of data, i.e. from far fewer data bits than
traditional methods use. It is believed that this phenomenon may have
significant implications. For instance, CS may come to underlie
procedures for sensing and compressing data simultaneously and much
faster. In this talk, we will present the basic tenets of this new
sampling theory and introduce applications in the area of error
correction.
Consider a stylized communications problem where one wishes to
transmit a real-valued signal x, a block of n pieces of information,
to a remote receiver. We ask whether it is possible to transmit this
information reliably when a fraction of the transmitted message is
corrupted by arbitrary (malicious) gross errors, and when in addition,
all the entries of the message might be contaminated by smaller errors
(e.g. quantization errors). We show that if one encodes the information
as Ax where A is a suitable m by n matrix, there are a couple of
decoding schemes which allow the recovery of the block of n pieces
of information x with nearly the same accuracy as if no gross errors
occur upon transmission (or equivalently as if one has
an oracle supplying perfect information about the sites and amplitudes
of the gross errors). In the special case where there are only gross
errors, the decoded vector is provably exact. The key point is that
both decoding strategies are very concrete and only involve solving
simple convex optimization programs, either a linear program or a
second-order cone program. Numerical simulations show that the
encoder/decoder pair performs remarkably well.
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May 10
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NO SEMINAR
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Abstract:
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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.
