NSF/CBMS Regional Conference in the Mathematical Sciences, Using Spectral Data to Solve Inverse Problems, December 14-18, 2001

The University Of Texas Rio Grande Valley, Edinburg TX

Investigators

Abstract

An NSF/CBMS Regional Conference on Using Spectral Data to Solve Inverse Problems will be held at the University of Texas - Pan American. The dates for the conference are December 14-18, 2001. Professor Joyce McLaughlin, the Ford Foundation Professor of Mathematics at Rensselaer Polytechnic Institute, will provide ten lectures as the conference Principal Lecturer. The lectures will provide a self-contained and comprehensive exposition on the use of spectral data to solve inverse problems. In these problems, indirect measurements are used to determine material properties of objects. For the set of problems to be presented, the data consists of natural frequencies and selected mode shape measurements. These lectures will present the newest methods for solving these problems, and give both mathematical and experimental insight into how the data depends on the material properties to be recovered. The main thrust for these lectures is for two-dimensional problems, with a brief introduction and insight given for one-dimensional problems. Demonstration experiments will be included to exhibit the response of vibrating systems at natural frequencies, to show the change in the response as material properties change, and to show geometric properties of selected mode shape data. A select number of additional lectures will be provided by applied mathematicians and scientists addressing related inverse problems, in some cases where spectral data is utilized in other contexts.