Microscopic properties and physical behavior of materials and media.

材料和介质的微观特性和物理行为。

• 批准号: 0408040
• 负责人: Oscar Bruno
• 金额: --
• 依托单位: California Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-08-01 至 2007-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0408040&HistoricalAwards=false
• 关键词: Microscopic; properties; physical; behavior; materials

Proposal: DMS-0408040PI: Oscar P. BrunoInstitution: CaltechTitle: Microscopic properties and physical behavior of materials and mediaABSTRACTThe investigator and his colleagues will consider two distinct research areas: 1) Estimation of the overall (homogenized) behavior of inhomogeneous materials containing microscopic misfits, and, 2) Direct and inverse scattering by inhomogeneous media. As is well known, fine scale material interactions (including microscopic strains, stresses, thermal and plastic fields, etc.) play crucial roles in determining the overall behavior of materials. While such microscopic interactions are well understood in many cases, certain fundamental issues in this context have remained elusive from both theoretical and experimental standpoints, and have still not been fully resolved. The proposed efforts in these regards will seek to produce an improved theoretical understanding as well significantly more general rigorous solvers than previously available for problems involving three-dimensional fields of misfits in anisotropic and nonlinear materials. Such solvers should allow significant improvements in our capability to investigate problems such as polycrystalline plasticity and magneto-rheology of elastomers. Problems of direct and inverse scattering of electromagnetic and acoustic waves by inhomogeneous media will also be investigated as part of this research effort. The work proposed here will build upon recent contributions by the investigator and his colleagues on fast high-order integral-equation solvers for penetrable and surface scattering problems. These solvers can deal with complex scattering problems with unprecedented accuracy and efficiency; the proposed work will deal with special emphasis on recently developed O(1) algorithms - which can resolve problems of arbitrarily high frequency (which would usually require increasingly large discretization densities as frequencies increase) with a prescribed accuracy and within a fixed computational time-independent of frequency.The proposed work impacts upon a variety of areas of societal interest, including the medical field (optical coherence tomography), automotive (magneto-rheological elastomers), materials design (actuators, strength of materials), military (radars); communications (aircraft- and spacecraft-mounted antennas, wireless communications); critical dimension metrology (optical monitoring of silicon wafers); modeling of electromagnetic induction in next-generation processors; etc. As previous work by this PI, on the other hand, the present effort will result in training of students at both, graduate and undergraduate levels, as well as postdoctoral associates. In particular, over the last five years, fifteen different research efforts have been directed by this PI, each one for a period of ten summer weeks and each one centered around one undergraduate student. The undergraduate students included seven American citizens, three women, two black males, two Hispanic, and two students from a local community college. These activities have been highly rewarding for all involved, including the graduate students and postdocs that collaborated with the undergraduate students and this PI, as well as some of the industrial and lab researchers who proposed specific engineering applications. As a result of this work, some of the participating graduate students and postdocs discovered a talent for teaching and advising in mathematics. Most of the participating undergraduate students went on to graduate schools or four-year colleges, as appropriate, and have sought to pursue work on mathematically related fields. The efforts to integrate undergraduate students in research projects will continue as part of the proposed work.The award is funded jointly by the Applied Mathematics and Computational Mathematics programs of the Division of Mathematical Sciences.

提案：DMS-0408040 PI：Oscar P. Bruno机构：Caltech标题：材料和介质的微观特性和物理行为摘要研究者和他的同事将考虑两个不同的研究领域：1）包含微观失配的非均匀材料的整体（均匀化）行为的估计，以及，2）非均匀介质的直接和逆散射。 众所周知，精细尺度材料相互作用（包括微观应变、应力、热和塑性场等）在决定材料的整体性能方面起着关键作用。 虽然这种微观相互作用在许多情况下都很好地理解，但从理论和实验的角度来看，这方面的某些基本问题仍然难以理解，并且仍然没有得到充分解决。 在这些方面提出的努力将寻求产生一个更好的理论理解，以及显着更一般的严格的求解器比以前提供的问题，涉及三维领域的各向异性和非线性材料的失配。 这样的解决方案，应允许显着改善我们的能力，调查问题，如多晶塑性和磁流变弹性体。 作为这项研究工作的一部分，还将研究非均匀介质对电磁波和声波的直接和反向散射问题。 这里提出的工作将建立在最近的贡献，调查员和他的同事对快速高阶积分方程求解器的穿透和表面散射问题。 这些求解器可以处理复杂的散射问题，具有前所未有的精度和效率;所提出的工作将特别强调最近开发的O（1）算法--它可以解决任意高频率的问题（这通常需要随着频率增加而增加的大离散密度），具有规定的精度并且在固定的计算时间内，独立的频率。拟议的工作影响到社会利益的各种领域，包括医学领域（光学相干断层扫描），汽车（磁流变弹性体），材料设计（执行器，材料强度），军事（雷达）;通信（航空器和航天器天线，无线通信）.临界尺寸计量学（硅晶片的光学监测）;下一代处理器中电磁感应的建模等。另一方面，作为本PI以前的工作，目前的努力将导致对研究生和本科生以及博士后的培训。特别是，在过去的五年里，十五个不同的研究工作已经由这个PI，每一个为期十个夏季周，每一个围绕一个本科生。这些本科生包括7名美国公民、3名女性、2名黑人男性、2名西班牙裔和2名当地社区学院的学生。 这些活动对所有参与者来说都是非常有益的，包括与本科生和PI合作的研究生和博士后，以及提出具体工程应用的一些工业和实验室研究人员。由于这项工作，一些参与的研究生和博士后发现了在数学教学和咨询方面的天赋。 大多数参与的本科生继续研究生院或四年制大学，并寻求在数学相关领域的工作。将本科生融入研究项目的努力将继续作为拟议工作的一部分。该奖项由数学科学部的应用数学和计算数学项目共同资助。