Mathematiical Sciences: Mathematical Study of Nonlinear Materials

点击翻译按钮获取中文摘要

9314082 Xu The 1994 Arkansas Spring Lectures in Mathematics will be held in the Center for Continuing Education on the Square in downtown Fayetteville, Arkansas from March 31 to April 2. The principal lecturer will be Professor David Kinderlehrer of Carnegie Mellon University. In addition, talks will be given by a number of other scholars studying mathematical systems which, it is believed, will be useful in the study of nonlinear materials. One of the foci of considerable research in both the sciences and mathematics is how local or micro behavior affects global or macro behavior. In general, it is often very difficult to predict the properties of a large structure when only the properties of its constituent parts are known. This general problem presents itself in fields as diverse as economics and solid state physics. Professor Kinderlehrer will be lecturing on mathematics that addresses the response of materials to changes in its environment. In general, one knows the properties of the individual atoms that make up a material and one knows the ways in which they can fit together. This knowledge can be used to predict, for instance, the structure of crystals and the magnetic properties of iron. However, when a material is subjected to changes in its environment, for example changes in temperature. pressure, or electromagnetic fields, the atoms begin to realign themselves in sometimes surprising ways. The phenomenon has already lent itself to the development of many useful applications such as shape-memory alloys and liquid crystals. However the mathematical questions that are posed by an attempt to obtain a detailed understanding of this phenomenon are deep and require the development of new mathematical machinery. Recent, progress has been made with some averaging methods which enable one to cope with the rapidly spatially varying systems involved. Professor Kinderlehrer's lectures will be on the application of these averaging met hods which promise a more unified theory and treatment of the subject. The other invited speakers for the conference have been selected because of their knowledge of and contributions to this and related material in order to achieve a rich and productive interaction between researchers currently active in this area. ***