DMS-9523292 Bruno The mathematical investigations associated with this proposal relate to the classical theory of Partial Differential Equations and its applications to the study of the physical properties of materials and media; they constitute a natural continuation of my research of the last five years. By using methods of homogenization, integral equations, spectral analysis and regularity together with computational techniques I intend mathematical techniques will be developed to study and predict the physical properties of composite materials, shape memory materials and plasmas, as well as the scattering of electromagnetic radiation by general obstacles. In the area of electromagnetism some computational methods are introduced recently to new areas, including remote sensing of obstacles as well as the mathematically related problem of detection of damaged biological tissue (perhaps cancer) by means of electromagnetic scattering. In its previous applications these methods were highly successful; These methods will be used to deal with shape memory alloys. These materials can be used in a variety of applications (including generation of electricity from low temperature sources, medical devices, etc.) by exploiting their ability to recover their shape, after they have been deformed, by means of appropriate changes in their temperature.
