Many physical problems, particularly in chemical and biological
systems, involve processes that occur on widely varying time
scales. The resulting model is a system that has a singular
perturbation character. Such problems have motivated the development
of much mathematical theory, including classical asymptotic
theory and a geometric theory based on invariant manifolds.
The phenomena that appear in singular-perturbation problems
are subtle, often involving expansions in terms of quantities
that are exponentially small in terms of a small parameter in
the problem. The singular structure of these equations can also
pose formidable numerical challenges. The goal of this workshop
was to explore the connection between the asymptotic and geometric
theories, with a particular emphasis on exponentially small
phenomena, and to bring researchers developing these methods
together with people working on applications in biology, chemistry
and mechanics.
Click on the titles to find abstracts and/or
links to presentation materials
| MONDAY, OCTOBER
27 |
W. Miller, R. Gulliver,
C. Jones |
Welcome and Orientation |
David McLaughlin,
Courant Institute, NYU |
Chaotic
and Homoclinic Behavior in PDE's |
Nigel Goldenfeld,
University of Illinois |
Renormalization
Group Approach to Global Asymptotic Analysis |
Amadeu Delshams,
Univ. Politécnica de Catalunya |
Homoclinic
orbits to invariant tori in Hamiltonian Systems |
Richard Haberman,
Southern Methodist Univ. |
Slow
passage through a homoclinic orbit with subharmonic resonances |
Alexandra Milik,
Techn. Univ. of Vienna |
The Geometry
of Mixed-mode Oscillations in a Chemical Oscillator |
| TUESDAY, OCTOBER
28 |
Konstantin Mischaikow,
Georgia Institute of Technology |
A topological approach to fast-slow dynamics |
Michael J. Davis,
Argonne National Laboratory |
Some Multiple-Time-Scale
Problems in Chemical Dynamics, Molecular Spectroscopy, &
Kinetic Modeling |
Linda Petzold,
University of California-Santa Barbara |
Model
Reduction for Nonlinear Dynamical Systems from Chemical
Kinetics |
Michael Ward,
University of British Columbia |
Dynamic Metastability
for Reaction-Diffusion Equations |
Xiao-Biao Lin,
North Carolina State University |
Method of
singular characteristics for Hamilton-Jacobi equations that
develop shock structures |
Mohammed Ziane,
Stanford University |
A mathematical formulation of the Goldenfeld renormalization
group method |
Jiangzhong Su,
Univ. of Texas at Arlington |
Delay of bifurcation
phenomena and their analysis |
| WEDNESDAY,
OCTOBER 29 |
Anatoly Neishtadt,
Space Research Institute, Moscow |
On stability
loss delay f or dynamical bifurcations |
Robert A. Gardner,
University of Massachusetts |
Stability
Analysis of Singular Patterns for the 1-D Gray-Scott Model |
David Terman,
Ohio State University |
Multiple
Time Scales in Networks of Neural Oscillators |
Tasso Kaper,
Boston University |
Exchange lemmas: an overveiew and some new applications |
| THURSDAY,
OCTOBER 30 |
Chongchun Zeng,
Courant Institute, NYU |
Invariant
Manifolds and Invariant Foliations for Semiflows in Banach
Space |
Yulij Ilyashenko,
Cornell University/ Moscow State & Indep. Universities |
Embedding
theorems for maps and normal forms for the slow-fast systems |
George Haller,
Brown University |
Homoclinic
jumping in evolution equations |
Robert Roussarie,
University of Bourgogne |
Multiple Canard Cycles in Van Der Pol-like Equations |
Pavol Brunovsky,
Cornenius University |
Ck inclination theorems for singularly
perturbed problems |
Peter Szmolyan,
Technische Universität Wein |
Extending Geometric Singular Perturbation Theory to Non-hyperbolic
Points |
| Discussion Session |
Panel: Marc Diener, Freddy Dumortier, Paul Fife, Chris
Jones, David McLaughlin |
| FRIDAY, OCTOBER
31 |
Petar Kokotovic,
University of California-Santa Barbara |
Singular
Perturbations and Multiple Time Scales in Control System
Modeling and Design |
Dennis Perchak,
Kodak |
This talk is joint with the IMA Seminar on Industrial
Problems:
Stokesian Dynamics
Simulation of Interacting Solid Particles
|
