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Fall 1999
IMA Minisymposium:
Mathematical and Computational Strategies for Simplifying Complex Kinetics
October 14-15, 1999


John D. Buckmaster
University of Illinois-Urbana Champaign
Talbot Laboratory

In most practical combustion systems, the number of reactions and reactants is very large. It is a serious challenge to construct 2D steady solutions for relatively simple gases such as methane/air. If one is interested in engine chemistry, rocket propellant chemistry; or unsteady 2D or steady 3D problems for simple gases, the chemistry is limiting. Rational simplification of the chemistry, or 'reduced chemistry' is one approach to the problem. So called 'steady state approximations for active radicals', and other such approximations, are made. This can be effective, but there are computational difficulties that arise from the mathematical descriptions that arise. A new strategy is to calculate low dimensional manifolds in reactant space on which the system moves after initial brief transients. This concept arises in a natural way when one looks at the extraordinary variations in time scales of the various reactions. However, there appear to be serious difficulties for spatially dependent problems, which is what flame researchers are interested in. One problem appears to be that the manifold is different at different points.

The minisymposium will bring together combustion researchers who have been wrestling with these issues, and mathematicians (asymptoticists, dynamical systems experts, etc.) to assess the present situation, and if there are avenues to be explored, whether there are difficulties that can be expressed in mathematical terms, and so might have mathematical answers.


All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
Thursday Friday

8:30 am Coffee and Registration Reception Room EE/CS 3-176
9:10 am Willard Miller, Fred Dulles,
and John D. Buckmaster
Welcome and Introduction
9:30 am Sau-Hai Lam
Princeton University
The Role of Computational Singular Perturbation (CSP) in Chemical Kinetics

Material for the talk

10:00 am Dimitris Goussis
Institute of Chemical Engineering &
High Temperature Chemical Processes
Development of Manifolds in Reaction-Diffusion Systems: Construction of Reduced Kinetic Mechanisms

Material for the Talk

10:30 am Break Reception Room EE/CS 3-176
11:00 am Christopher K.R.T. Jones
Brown University
Geometric Singular Perturbation Theory

Material for the talk

1:30 pm Michael Frenklach
University of California-Berkeley
Solution Mapping for Numerically Efficient Implementation of Chemical Kinetics

Material for the Talk

2:15 pm Tilmann Blasenbrey
Universitaet Stuttgart
Some New Aspects of Efficient Calculation and Implementation of ILDM
3:15 pm Break Reception Room EE/CS 3-176
4:30 pm Linda R. Petzold
University of California-Santa Barbara
Model Reduction for Chemical Kinetics: An Optimization Approach
4:30-5:00 pm Tasso Kaper
Boston University
Singular Perturbation Theory for Reaction-diffusion PDEs
9:15 am Coffee Reception Room EE/CS 3-176
9:30 am Peter Lindstedt
Imperial College
Time Scale Separation and Scalar Space Requirements of Complex Chemical Systems
10:15 am John C. Hewson
Sandia National Laboratory
Applications of Systematically Reduced Mechanisms to Combustion Research
10:45 am Break Reception Room EE/CS 3-176
11:15 am Discussion with Working Lunch
1:30 pm Samuel Paolucci
University of Notre Dame
The Relationship between Finite-dimensional Manifolds of Reduced Kinetics and Infinite-dimensional Manifolds of Reacting Flows
2:00 pm Nelson Butuk
Prairie View A & M University
New Approach of Computing the Intrinsic Low Dimensional Manifold Reaction Space Via Complex Variables

Material for the Talk

2:30 pm Discussion

Thursday Friday


as of 10/13/99

Fall 1999 IMA Worksh
Name Department Affiliation
Ioannis Androulakis Corporate Reseach Science Labs Exxon Research and Engineering Company
Tilmann Blasenbrey Institut fuer Technische Verbrennung ITV Universitaet Stuttgart
J.D. Buckmaster Aeronautical Engineering University of Illinois at Urbana Champaign
Nelson Butuk   Prairie View A& M University
Fred Dulles   Institute for Mathematics and its Applications
Michael Frenklach Mechanical Engineering University of California-Berkeley
Sean C. Garrick Mechanical Engineering University of Minnesota
Dimitris Goussis   Inst. of Chem. Eng. & High Temp. Chem. Processes
John C. Hewson Combustion Research Facility, MS 9051 Sandia National Laboratory
Darryl Holm   Los Alamos Laboratory
James Hyman   Los Alamos Laboratory
Christopher K.R.T. Jones Applied Mathematics Brown University
Tasso Kaper Mathematics Boston University
Yannis Kevrekidis Chemical Engineering Princeton University
Sau-Hai Lam   Princeton University
Peter Lindstedt Mechanical Engineering Imperial College
Moshe Matalon Eng. Sci & Appl. Math Northwestern University
James McDonough Mechanical Engineering University of Kentucky
Paul Merz   Chevron Reserach & Technology Company
Willard Miller   Institute for Mathematics and its Applications
Samuel Paolucci Aeospace & Mechanical Engineering University of Notre Dame
Linda Petzold Mechanical & Environmental Engineering University of California-Santa Barbara
Stephen Pope Mechanical & Aerospace Eng. Cornell University
Fadil Santosa MCIM IMA & Minnesota Center for Industrial Math
Akeel Abbas Shah Mathematics UMIST
Sandeep Singh Aerospace & Mechanical Engineering University of Notre Dame
Mitchell Smooke Mechanical Engineering Yale University
Cynthia Spade Engineering Sciences & Appld. Math. Northwestern University
Song-Moon Suh Mechanical Engineering University of Minnesota
Edriss Titi Mathematics University of California - Irvine
Dion G. Vlachos Chemical Engineering University of Massachusetts

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