• Professor Suzanne Lenhart - University of Tennessee at Knoxville and Oak Ridge National Lab
Can you park your car with Lie brackets?
Applications of Optimal Control to Various Population Models


Biography:

Suzanne Lenhart received her PhD in mathematics from the University of Kentucky in 1981 in the area of partial differential equations.  She is currently a full professor at the University of Tennessee. Her current research interests include applications of optimal control of differential equations .... (continued)
 
Professor Linda Petzold - University of California at Santa Barbara
Computational Science and Engineering: A Case Study
Biography:
Dr. Linda R. Petzold is currently Professor in the Departments of Computer Science, and Mechanical and Environmental Engineering, and Director of the Computational Science and Engineering Program, at University of California Santa Barbara.  She received her Ph.D ..... (continued)

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Abstracts

Abstract:
Computational science and engineering (CSE) is a rapidly growing multidisciplinary area with connections to mathematics, computer science, physical science and engineering.  CSE focuses on the integration of problem-specific knowledge with mathematics and computer science techniques for the development of problem-solving methodologies and tools which will be the building blocks for the solution of scientific and engineering problems of ever-increasing complexity.

In this lecture we describe our efforts towards building such a problem-solving environment, for the dynamic optimization of physical, chemical and biological processes.  We will outline some of the mathematical, computational and computer science challenges and describe our results for an application from spacecraft trajectory design.
 
 
 

CAN YOU PARK YOUR CAR WITH LIE BRACKETS?
Professor Suzanne Lenhart - University of Tennessee at Knoxville and Oak Ridge National Lab
Friday, March 16, 2001, 7:00 - 8:00, Room E104 of Moench Hall.

Abstract:
This talk will introduce the idea of controllability for a certain type of ordinary differential equation.  The idea of Lie brackets can give conditions to guarantee controllability.  Parallel parking works because of the non-commutativity of the operations involved; Lie brackets measure this non-commutativity.

APPLICATIONS OF OPTIMAL CONTROL TO VARIOUS POPULATION MODELS
Professor Suzanne Lenhart - University of Tennessee at Knoxville
Saturday, March 17, 2001,  9:30-10:30 Room E104 of Moench Hall.

Abstract:
An introduction to the basic ideas of optimal control of ordinary differential equations will be given.  The differences between optimal control of ordinary differential equations and optimal control of partial differential equations will be briefly explained.  An ordinary differential system for an immunology model for AIDS and control of chemotherapy will be used to illustrate the techniques.  Bioreactors can be used to transform contaminants into less hazardous substances through bacteria metabolism.  An example model for a gas phase bioreactor has a parabolic partial differential equation coupled with an ordinary differential equation.