If you want to receive e-mail announcements of talks please contact
Antoine Mellet (mellet@math.umd.edu).
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September 3
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NO SEMINAR
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Abstract:
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September 10
JOINT PDE/DYNAMICAL
SYSTEMS SEMINAR
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Shuddering motions of a pendulum.
Stuart S. Antman
Department of Mathematics -- UMCP
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Abstract:
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September 17
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Localization and shear bands in high strain-rate plasticity
Thanos Tzavaras
Department of Mathematics -- UMCP
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Abstract:
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September 24
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CSCAMM Workshop -- NO SEMINAR
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October 1
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The many solutions of morphology and morphogenesis problems
Xiaofeng Ren
George Washington University
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Abstract:
Pattern formation problems arise in many physical and
biological systems as orderly outcomes of self-organization principles.
Examples include animal coats, skin pigmentation, and morphological
phases in a block copolymer. Recent advances in singular perturbation
theory and asymptotic analysis have made it possible to study these
problems rigorously. In this talk I will discuss a central theme in the
construction of various patterns as solutions to some well known PDE and
geometric problems: how a single piece of structure built on the entire
space can be used as an Ansatz to produce a near periodic pattern on a
bounded domain. We start with the simple disc and show how the spot
pattern in morphogenesis and the cylindrical phase in diblock copolymers
can be mathematically explained. More complex are the ring structure and
the oval structure which can also be used to construct solutions on
bounded domains. Finally we will discuss the newly discovered smoke-ring
structure and the toroidal tube structure in space.
The results presented in this lecture come from my joint works with
Kang, Kolokolnikov, and Wei.
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October 8
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Mathematical modeling of animal displacements and derivation of macroscopic models
Sebastien Motsch
CSCAMM -- UMCP
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Abstract: The modeling of animals displacements can occur at two different scales. One may either
describes the trajectories of each individual using the so-called individual based models (at a
microscopic scale), or we can describe the dynamics of the all group with macroscopic quan-
tities (density, flux...). In this talk, we will see how we can connect these two
descriptions for different models used in biology.
In a first part, we introduce a new model for fish displacement called Persistent
Turning Walker (PTW) based on experimental data. The originality of the PTW model mainly
relies in the use of curvature to describe individual displacement. We give two methods to
derive a diffusion equation from this model, a method using tools from functional analysis
and a second method using probabilistic tools.
In a second part, we study the so-called Vicsek model which is a very popular individual based
model describing alignment between congeners. We have derived for the first time a
macroscopic model from this model (a non-conservative hyperbolic system with a geometric
constraint). The numerical simulations of the macroscopic model obtained will confirm the
relevance of the macroscopic model to describe the microscopic dynamics of the Vicsek
model at large scales.
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October 15
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Recent global results for the relativistic Boltzmann equation
Robert Strain
University of Pennsylvania
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Abstract:
We will discuss several recent results regarding the relativistic Boltzmann equation. The talk will start with an overview of relativistic Kinetic theory for non-specialists.
New results to be discussed include the previously open problem of stability of the Maxwellian equilibrium for the relativistic Boltzmann equation with soft interactions. The soft potentials are important for particles moving at relativistic speeds. We can also prove for the first time the global validity of the Newtonian Limit in the near Vacuum regime.
Additionally we can establish the rigorous connection between the Boltzmann equation and Relativistic Euler via a Hilbert Expansion, this is joint work with Jared Speck.
Furthermore, we consider the relativistic Boltzmann equation coupled with it's internally generated electric and magnetic forces. Despite its importance, no global in time solutions have been established so far for this Lorentz invariant model. We prove existence of the first global in time classical solutions. This project is joint work with Yan Guo.
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October 22
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Singular diffusion equations with nonuniform driving force
Yoshi Giga
University of Tokyo
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Abstract:
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October 29
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Free surface problems in fluid dynamics
David Ambrose
Drexel University
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Abstract:
Fluid flows in the presence of free surfaces occur in a great many
situations in nature; examples include waves on the ocean and the flow of
groundwater. In this talk, I will discuss my contributions to the
understanding of the systems of nonlinear partial differential equations
which model such phenomena. The most important step in these results is
making a suitable formulation of the problem. Influenced by the
computational work of Hou, Lowengrub, and Shelley, we formulate the
problems in natural, geometric variables. I will discuss my proofs (most
of which are joint with Nader Masmoudi) of existence of solutions to the
initial value problems for vortex sheets and water waves. I will also
discuss computational results, including work with Jon Wilkening on the
computation of special solutions, especially time-periodic interfacial
flows.
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November 5
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Jump discontinuities of compressible viscous flows
grazing a non-convex corner
Jae Ryong Kweon
POSTECH (Pohang University of Science and Technology)
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Abstract:
In this talk I will talk about that the compressible viscous steady state Navier Stokes system
can have solutions with a discontinuous density. Specifically, we give a boundary value problem
for system, establish the local well-posedness of the problem, and show that the density
component of the solution has a jump discontinuity across a curve inside the domain of the problem.
In earlier works, we have found solutions for which first derivatives of the density
are discontinuous. This is the first example of a stationary flow for which the density itself is discontinuous.
The decay formula suggests that density jumps may be noticeable in a high speed flow occurring in a very viscous,
very compressible fluid. This is a joint work with B. Kellogg.
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November 12
APPLIED MATH COLLOQUIUM
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Mathematical challenges in the modelling of biological invasions
Mark Lewis
University of Alberta
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Abstract: Biological invaders are introduced locally, and then spread spatially into new environments, often impacting ecosystems. Models for invasions track the front of an expanding wave of population density. The underlying equations are often systems of parabolic partial differential equations and related integral formulations.
I will structure this talk around three challenges in the analysis of biological invasions where mathematical theory has provided new insight:
(i) Reid's paradox of rapid plant migration. How were trees were able
to migrate very quickly behind retreating ice sheets after the last ice age?
(ii) Multispecies competition paradox. Why do classical mathematical
methods, based on linearization, fail to predict the rate of competitive
spread of one species into another?
(iii) Reid's paradox in multispecies communities. Pollen data indicates that secondary species can spread very quickly into regions already occupied by a close competitor. How can this spread occur so quickly?
Each of these challenges will be addressed using mathematical analysis to provide insight regarding the behaviour of the biological models. I will finish by suggesting some new mathematical challenges where biological invasion theory and mathematical models meet.
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Monday November 16 at 3-4pm
Special RIT/PDE/NA seminar
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A Seamless Multiscale Method and Its Application to Complex Fluids
Weiqing Ren
Courant Institute of Mathematical Sciences
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Abstract:
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Wednesday November 18 at 4:30- 5:30 p.m.
Special PDE seminar
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Reaction and Diffusion in Fluid Flow
Andrej Zlatos
University of Chicago
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Abstract: Reaction-diffusion equations are parabolic partial differential equations used in the modeling of phenomena such as propagation of species in an environment or spreading of flames in combustible media. Their general solutions exhibit two basic behaviors, extinction (quenching) and spreading. In this talk we will review recent progress in our understanding of how the motion of the underlying medium, modelled by a fluid flow, affects both the occurence of quenching and the speed of spreading of reaction. The problem turns out to have fruitful connections to questions about mixing effixiency of flows and homogenization of advection-diffusion operators.
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November 26
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THANKSGIVING HOLIDAY -- NO SEMINAR
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December 3
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Hyperbolic conservation laws on manifolds: theory and numerics
Phillippe LeFloch
Universite Pierre et Marie Curie (Paris VI) and CNRS
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Abstract:
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December 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.
