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

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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.--------------------------------------------------------------------------------