Mathematiical Sciences: Mathematical Study of Nonlinear Materials

数学科学：非线性材料的数学研究

• 批准号: 9314082
• 负责人: Xiangsheng Xu
• 金额: $ 0.8万
• 依托单位: University of Arkansas
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-03-01 至 1994-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9314082&HistoricalAwards=false
• 关键词: Mathematiical; Sciences; Mathematical; Study; Nonlinear

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. ***

9314082徐一九九四年阿肯色州春季数学讲座将於三月三十一日至四月二日在阿肯色州费耶特维尔市中心广场的持续教育中心举行，首席讲师将由卡内基梅隆大学的金德勒教授担任。此外，其他一些研究数学系统的学者将发表演讲，相信这将对非线性材料的研究有用。科学和数学领域大量研究的焦点之一是局部或微观行为如何影响全球或宏观行为。一般来说，当只知道一个大型结构的组成部分的性质时，预测它的性质通常是非常困难的。这个普遍的问题出现在经济学和固态物理等不同的领域。Kinderlehrer教授将讲授数学，阐述材料对环境变化的反应。一般来说，人们知道组成材料的各个原子的性质，也知道它们可以组合在一起的方式。例如，这种知识可以用来预测晶体的结构和铁的磁性。然而，当一种材料受到其环境变化的影响时，例如温度变化。在压力或电磁场的作用下，原子开始以有时令人惊讶的方式重新排列。这一现象已被用于形状记忆合金和液晶等许多有用应用的开发。然而，试图详细了解这一现象所提出的数学问题是深刻的，需要开发新的数学机制。最近，一些平均方法取得了进展，这些方法使人们能够处理所涉及的快速空间变化的系统。Kinderlehrer教授的讲座将介绍这些平均法的应用，这些方法承诺对这一问题有一个更统一的理论和处理方法。会议的其他受邀发言者之所以被选中，是因为他们了解这一材料和相关材料并对其作出了贡献，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。***