Mathematiical Sciences: Mathematical Study of Nonlinear Materials

小行星9314082 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的广场继续教育中心举行。 主讲人将是卡内基梅隆大学的大卫金德勒教授。 此外，一些研究数学系统的其他学者也将发表演讲，相信这将有助于非线性材料的研究。 在科学和数学中，相当多的研究焦点之一是局部或微观行为如何影响全局或宏观行为。 一般来说，当只知道一个大型结构的组成部分的性质时，往往很难预测它的性质。 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教授将讲授数学，解决材料对其环境变化的反应。 一般来说，人们知道组成材料的单个原子的性质，也知道它们可以组合在一起的方式。 这些知识可以用来预测，例如，晶体的结构和铁的磁性。 然而，当材料经受其环境的变化时，例如温度的变化。压力，或电磁场，原子开始以有时令人惊讶的方式重新排列。 这一现象已经有助于许多有用应用的发展，如形状记忆合金和液晶。 然而，数学问题所提出的试图获得详细了解这一现象是深刻的，需要发展新的数学机器。 最近，取得了进展，一些平均方法，使人们能够科普迅速空间变化的系统。 Kinderlehrer教授的讲座将是关于这些平均方法的应用，这些方法有望使该主题的理论和治疗更加统一。 会议邀请的其他发言者之所以被选中，是因为他们对这一材料和相关材料的了解和贡献，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. ***