Large Scale Dynamical Systems

September 29 - October 03, 1997

Emerging Applications of Dynamical Systems

Content

Overview

Organizers:

Donald Aronson	University of Minnesota, Twin Cities
Herbert Keller	California Institute of Technology
Edriss Titi	University of California
Laurette Tuckerman	NONE

The numerical study of low-dimensional dynamics in large-scale sets of ODEs and discretizations of PDEs necessitates the development of special-purpose algorithms for simulation, stability and bifurcation analysis. This workshop addressed development and application of special iterative methods for large-scale systems that exploit local stability properties of the linearized system. It also considered global model reduction schemes for PDEs such as approximate inertial manifolds and lattice dynamics. Applications of special interest included selected problems arising in fluid flow and nucleation in alloys.

Schedule

Monday, September 29, 1997

9:15 am - 9:30 am	Welcome and Orientation Robert Gulliver, Willard Miller Jr., Laurette Tuckerman (NONE)	Keller 3-180
9:30 am - 10:30 am	Nonlinear Model Reduction for Feedback Control Yannis Kevrekidis (Princeton University)	Keller 3-180
10:30 am - 11:00 am	Coffee Break	Keller 3-176
11:00 am - 12:00 pm	Postprocessing the Galerkin Method: a Novel Approach to Approximate Inertial Manifolds Edriss Titi (University of California)	Keller 3-180
12:00 pm - 2:00 pm	Lunch
2:00 pm - 3:00 pm	Applications of Rosa's Sequence of Approximate Inertial Manifolds Michael Jolly (Indiana University)	Keller 3-180

Tuesday, September 30, 1997

9:15 am - 9:30 am	Coffee	Keller 3-176
9:30 am - 10:30 am	Creating Jovian-Like Zonal Flows by Reverse-Energy Cascades Philip Marcus (University of California, Berkeley)	Keller 3-180
10:30 am - 11:00 am	Coffee Break	Keller 3-176
11:00 am - 12:00 pm	The Formation of Structures in Wall-Bounded Shear Flows Katie Coughlin (University of Montreal)	Keller 3-180
12:00 pm - 2:00 pm	Lunch
2:00 pm - 3:00 pm	Influence of Constraint on Routes to Chaotic Natural Convection in Hele-Shaw Slot, Loop, and Annulus Paul Steen (Cornell University)	Keller 3-180

Wednesday, October 01, 1997

9:15 am - 9:30 am	Coffee	Keller 3-176
9:30 am - 10:30 am	Bifurcations in Kolmogorov Flows via DAE and RPM Herbert Keller (California Institute of Technology)	Keller 3-180
10:30 am - 11:00 am	Coffee Break	Keller 3-176
11:00 am - 12:00 pm	Newton-Picard methods for the bifurcation analysis of partial differential equations and delay differential equations Dirk Roose (Katholieke Universiteit Leuven)	Keller 3-180
12:00 pm - 2:00 pm	Lunch
2:00 pm - 3:00 pm	Bifurcation analysis for time steppers Laurette Tuckerman (NONE)	Keller 3-180
3:00 pm - 4:00 pm	Chaos in Traveling Waves of Lattice Models of Unbounded Media Yakov Pesin	Keller 3-180

Thursday, October 02, 1997

9:15 am - 9:30 am	Coffee	Keller 3-180
9:30 am - 10:30 am	Statistical Properties of Computations for Large Coupled Systems of Oscillators Andrew Stuart (Stanford University)	Keller 3-180
10:30 am - 11:00 am	Coffee Break	Keller 3-176
11:00 am - 12:00 pm	The Complex Ginzburg-Landau Equation as a Pertubation of the Nonlinear Schrödinger Equation: A Melnikov Approach Charles Levermore (University of Arizona)	Keller 3-180
12:00 pm - 2:00 pm	Lunch	Keller 3-180
2:00 pm - 3:00 pm	Two PDE Dynamical Systems with Bifurcations Rudiger Seydel (Universität Ulm)	Keller 3-180

Friday, October 03, 1997

9:15 am - 9:30 am	Coffee	Keller 3-180
9:30 am - 10:30 am	Pattern Formation in Early Development of Dictyostelium discoideum Hans Othmer (The University of Utah)	Keller 3-180
10:30 am - 11:00 am	Coffee Break	Keller 3-176
11:00 am - 12:00 pm	Path-following Techniques for Large Dynamical Systems Jeroen Molemaker (Institute for Marine and Atmospheric Research Utrecht)	Keller 3-180
12:00 pm - 2:00 pm	Lunch
2:00 pm - 3:00 pm	Variants of Krylov Projection Methods for Eigenvalue Problems Yousef Saad (University of Minnesota, Twin Cities)	Keller 3-180

Participants

Name	Department	Affiliation
Alain Bergeon	UFR MIG Dpt. Mecanique	Université de Toulouse III (Paul Sabatier)
Klaus Boehmer	Department of Mathematics	Philipps-Universität Marburg
Katie Coughlin		University of Montreal
Martin Golubitsky	Department of Mathematics	University of Houston
Willy Govaerts	Department of Applied Mathematics and Computer Science	University of Ghent (UG)
Ronald Henderson	Department of Aeronautics and Applied Mathematics	California Institute of Technology
Daniel Henry	Lab. de Mecanique des Fluides et d'Acoustique	École Centrale de Lyon
Kathleen Hoffman	Institute for Mathematics and its Applications	University of Minnesota, Twin Cities
Michael Jolly	Department of Mathematics	Indiana University
Herbert Keller	Center for Research on Parallel Computation	California Institute of Technology
Yohannes Ketema	Department of Aerospace Engineering and Mechanics	University of Minnesota, Twin Cities
Yannis Kevrekidis	Department of Chemicial Engineering	Princeton University
Igor Kukavica	Department of Mathematics	University of Chicago
William Langford		The Fields Institute
Charles Levermore	Department of Mathematics	University of Arizona
Milton Lopes	Department of Mathematics	Indiana University
Juan Lopez	Department of Mathematics	The Pennsylvania State University
Philip Marcus	Department of Mechanical Engineering	University of California, Berkeley
Zhen Mei		Philipps-Universität Marburg
Brian Meloon	Department of Mathematics	Cornell University
Paul Milewski	Department of Mathematics	University of Wisconsin, Madison
Jeroen Molemaker		Institute for Marine and Atmospheric Research Utrecht
Hans Othmer		The University of Utah
Peter Perry	Department of Mathematics	University of Kentucky
Keith Promislow		Simon Fraser University
Douglas Riley	Department of Mathematics	University of Kentucky
Dirk Roose	Department of Computer Science	Katholieke Universiteit Leuven
Yousef Saad	Department of Computer Science	University of Minnesota, Twin Cities
Kenneth Saldanha	Department of Mathematics	University of Chicago
Arnd Scheel	Institut für Mathematik	Freie Universität Berlin
Rudiger Seydel	Abteilung fur Numerik	Universität Ulm
Jie Shen	Department of Mathematics	The Pennsylvania State University
Bart Sijnave	Department of Applied Mathematics and Computer Science	University of Gent
Michael Smiley	Department of Mathematics	Iowa State University
Paul Steen	Department of Chemicial Engineering	Cornell University
Andrew Stuart		Stanford University
Edriss Titi	Department of Mathematics	University of California
Laurette Tuckerman		NONE