Conference: Homogenization and Materials Science

为纪念德国慕尼黑联邦国防军已故教授乌尔里希·霍农，将于2000年9月15日至17日在俄亥俄州阿克伦大学举行一次名为“均质化与材料科学”的国际会议。这次跨学科会议的目的是将材料科学相互作用领域的研究人员聚集在一起。特别是关于均匀化理论和方法的最新科学和工业发展。均匀化是解决周期性和随机微结构非均匀材料的静态(有效性质)和动态(波传播，输运方程)问题的强有力的数学工具。这包括对复合材料、形状记忆材料、相变材料和聚合物复合材料的机械和介电性能的预测。这些问题的解决为设计具有现代技术需求所要求的特定性能的新材料提供了指导。会议将讨论这些问题的建模和计算两个方面。这次会议将汇聚来自欧洲和美国的顶尖科学家，他们致力于材料科学中的均匀化问题和应用。现代电子和机械设备在设计时要求材料具有特定的性质。例如，汽车工业需要重量轻但强度很大的材料。这样的物质不一定是自然产生的。因此，这些材料必须从现有资源中进行工程设计。一种方法是形成一种复合材料。合成材料是由其他材料混合而成的。复合材料设计的基本问题是(1)应使用什么材料来形成复合材料，(2)每种材料应在复合材料中使用多少，以及(3)材料应如何组合以形成复合材料？在后一种情况下，组合材料的几何图案(想想胶合板)起着重要的作用。材料科学家和工程师试图回答上述问题，同时牢记合成复合材料所需的特定性能。实践经验和试错方法是获得答案的常见手段。在过去的二十年里，应用数学界开发了许多新的工具来帮助回答这些问题。这些工具属于所谓的均质化理论的范畴。举办这次会议的一个原因是为了突出这些新工具的使用。拟议中的会议的第二个目的是突出材料设计中出现的新的均质化问题的制定和解决。例如，可能进一步受益于均质化工具的一个领域是聚合物基复合材料。因此，这次会议应该有助于回答两个问题：(1)基于现代技术当前需要的均匀化理论的未来方向是什么(简而言之，应该解决哪些问题)，以及(2)利用新发展的数学工具来解决这些问题的最佳方式是什么，以加强材料设计中均匀化方法的使用？这些问题将通过发言者发言和小组讨论来回答，小组讨论将总结这一主题的现状和未来趋势。

An International Conference, "Homogenization and Materials Science", inhonor of the late Professor Ulrich Hornung of Bundeswehr University Munich,Germany, will take place at the University of Akron, Akron, Ohio, duringSeptember 15 - 17, 2000. The purpose of this interdisciplinary conferenceis to bring together researchers from interacting areas of MaterialsScience. In particular special focus will be paid to the latest scientificand industrial developments concerning homogenization theory and methods.Homogenization is a powerful mathematical tool for solving, both static (effectiveproperties) and dynamic (wave propagation, transport equations) problems ininhomogeneous materials with periodic and random microstructure. Thisincludes prediction of mechanical and dielectrical properties ofcomposites, shape memory materials, materials undergoing phasetransitions, and polymeric composites. Solutions of these problems provideguidance in the design of new materials possessing the specific properties required by modern technological needs. The conference shall address both modeling and computational aspects of these problems. This conference will bringtogether the leading scientists from Europe and the U.S. who are working onhomogenization problems and applications in materials science.Modern electronic and mechanical devices require materials with specificproperties in their design. For example, the automotive industry seekslightweight yet very strong materials. Such materials do not necessarilyoccur naturally. Hence, these materials must be engineered from existingresources. One approach is to form a composite material. A compositematerial is made from a blend of other materials. Fundamental questions inthe design of composites are (1) what materials should be used to form thecomposite, (2) how much of each material should be used in the composite,and (3) how should the materials be combined to form the composite? In thelatter case the geometric patterns of the combined materials (think ofplywood) play an important role. Materials scientists and engineers try toanswer the above keeping in mind the specific properties required from theresulting composite. Practical experience and trial and error approachesare common means of obtaining answers. Within the past two decades manynew tools have been developed by the applied mathematics community to helpanswer these questions. These tools fall under the heading of what iscalled homogenization theory. One reason for holding this conference willbe to highlight the use of these new tools. A second purpose of theproposed conference will be to highlight the formulation and solution ofnew homogenization problems arising in materials design. For example, onearea that may further benefit from the utilization of homogenization toolsis polymer-based composites. Hence, the conference should help answer twoquestions: (1) what should be the future directions in homogenizationtheory based upon the current needs of modern technology (in short, whichproblems should be solved), and (2) what is the best way of utilizing newlydeveloped mathematical tools to solve these problems in order to enhancethe use of homogenization methods in materials design? These questionswill be answered through both speaker presentations and a panel discussion,which will summarize the current state of the subject and future trends.