Mathematiical Sciences: Mathematical Study of Nonlinear Materials

1994年阿肯色州春季数学讲座将于3月31日至4月2日在阿肯色州费耶特维尔市中心广场上的继续教育中心举行。首席讲师将是卡内基梅隆大学的大卫·金德莱勒教授。此外，一些其他研究数学系统的学者也将进行讲座，相信这些数学系统将对非线性材料的研究有用。局部或微观行为如何影响全局或宏观行为，是科学和数学领域研究的热点之一。一般来说，当只知道一个大结构的组成部分的性质时，通常很难预测它的性质。这个普遍的问题出现在经济学和固体物理学等不同的领域。Kinderlehrer教授将讲授有关材料对环境变化的反应的数学。一般来说，我们知道构成物质的单个原子的性质，也知道它们如何组合在一起。这些知识可以用来预测，例如，晶体的结构和铁的磁性。然而，当材料受到环境变化的影响时，例如温度变化。压力，或电磁场，原子开始以有时令人惊讶的方式重新排列。这一现象已经使许多有用的应用得以发展，如形状记忆合金和液晶。然而，试图获得对这一现象的详细理解所提出的数学问题是深刻的，需要发展新的数学机制。最近，一些平均方法取得了进展，使人们能够处理所涉及的快速空间变化的系统。Kinderlehrer教授的讲座将是关于这些平均方法的应用，这些方法保证了对这个问题的更统一的理论和处理。会议的其他受邀演讲者之所以被选中，是因为他们对这方面和相关材料的知识和贡献，以便在目前活跃在这一领域的研究人员之间实现丰富和富有成效的互动。* * *

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. ***