Microscopic Process and Macroscopic Behavior of Material: Modeling, Simulation, and Analysis

亲爱的彭博士，附件是我的提案摘要的普通文件，格式是按要求的。如果你认为需要进一步修改，请告诉我。最好的问候，李博- DMS-0072958.主要研究者：Bo Li，马里兰州大学帕克分校。提案标题： 材料的微观过程和宏观行为： 建模、仿真和分析提案摘要本项目涉及材料的各种微观过程和宏观行为的建模、仿真和分析，这些过程和行为通常涉及相变、多组分和多尺度以及移动界面。它们包括马氏体薄膜的外延生长、弹性应力下固体的微观结构演化和马氏体微观结构的宏观性质。本文作者将首先继续和扩展他在DARPA/NSF VIP项目中开展的工作，以开发和改进薄膜外延生长的连续模型。特别是，他将仔细研究边缘扩散和扭结对流以及堆叠对称性和各向异性对薄膜形态和生长比例律的影响。然后，他将开发混合数值技术，将有限元方法和多重网格算法结合到水平集公式中，以模拟应力微结构的三维演变。最后，他将扩展他以前的研究，进一步研究复杂的马氏体微观结构，重点是施加应力对其形成，演变和稳定性的影响。创新，智能和高质量材料的设计，如在这个项目中将要研究的那些材料，对现代技术的进步至关重要。这种设计的成功极大地要求对基本物理过程和材料行为的基本原理和基本机制有深刻的理解。因此，本研究的目标是系统地发展合理的科学概念和新颖的研究技术来实现这样的理解。这一目标的实现将为实验工作者提供有关可控物理数据的详细信息，使开发新的和改进的材料成为可能，这些材料应用于许多现代技术和工业，从通信到航空航天到医学。另一方面，由于其科学完整性的性质，该项目将自然地促进和促进涉及材料科学，物理学，应用数学，和高性能计算。-

Dear Dr. Pang, Attached is the plain file of an abstract of my proposal in the requestedformat. Please let me know if you think that further revision is needed. Best regards,Bo Li--------------------------------------------------------------------------------Proposal number: DMS-0072958. Principal investigator: Bo Li, Univ. of Maryland, College Park. Title of proposal: Microscopic Process and Macroscopic Behavior of Material: Modeling, Simulation, and AnalysisProposal AbstractThis project concerns the modeling, simulation, and analysis of a varietyof microscopic processes and macroscopic behaviors of materials that incommon involve phase transitions, multiple components and multiple scales,and moving interfaces. They include the epitaxial growth of semiconductorthin films, microstructural evolution of elastically stressed solids, andmacroscopic properties of martensitic microstructures. The proposer willfirst continue and extend his work initiated during his participation ina DARPA/NSF VIP project to develop and improve continuum models for theepitaxial growth of thin films. In particular, he will carefully examine theeffect of edge diffusion and kink convection as well as that of crystallineasymmetry and anisotropy to the thin film morphology and growth scaling laws.He will then develop hybrid numerical techniques that incorporate finiteelement methods and multigrid algorithms into level set formulations tosimulate the three-dimensional evolution of stressed microstructures. Hewill finally expand his previous research to further investigate complexmartensitic microstructures with an emphasis on the effect of applied stressto their formation, evolution, and stability.The design of innovative, intelligent, and high quality materials such asthose to be studied in this project is essential to the advance of moderntechnologies. The success in such design demands greatly a deep understandingof the fundamental principles and basic mechanisms of the underlying physicalprocesses and material behaviors. It is therefore the goal of this researchto systematically develop rational scientific concepts and novel researchtechniques to accomplish such an understanding. The fulfillment of such agoal will potentially provide experimentalists with detailed information oncontrollable physical data, making possible the development of new and improvedmaterials for applications in many modern technologies and industrials rangingfrom communication to aerospace to medicine. Highlighted by its nature ofscientific integrity, on the other hand, this project will naturally fosterand promote an interdisciplinary research that involves materials science,physics, applied mathematics, and high-performance computing.--------------------------------------------------------------------------------