CAREER: Thermodynamic and kinetic approaches for epitaxial material systems

MargetisDMS-0847587 调查员专注于研究和教育目标在数学与材料科学和物理学的十字路口。这项研究将晶体界面现象的宏观原理与微观过程联系起来。 原子线缺陷的物理机制用离散的“粒子”方案来描述。 然而，介观和宏观后果最好通过连续模型来理解。 模型之间的联系是由动力学理论，偏微分方程和随机分析。 教育部分包括培养一名研究生，开发应用数学创新课程，开展数学知识宣传和推广活动，撰写一本关于积分方程的书，以及组织工作组研讨会。 该项目涉及纳米技术和材料建模的基本问题。 研究者使用应用数学的工具来系统地研究纳米结构如何在技术上重要的材料表面衰变。 这项工作的动机是迫切需要设计越来越小，更快，但更可靠的设备。 拟议的工作推进的能力，模型和预测的理论方法可靠性的设备，为下一代的应用程序在微电子和信息技术。 该项目整合了研究和教育：应用数学的跨学科概念被塑造成教学工具，面向不同领域的学生和科学专家。 该职业奖由MPS数学科学部和MPS材料研究部支持。

MargetisDMS-0847587 The investigator focuses on research and education goals atthe crossroads of mathematics with materials science and physics. This research links macroscopic principles for crystalinterfacial phenomena to microscale processes. The physicalmechanisms are described by discrete "particle" schemes foratomic line defects. However, mesoscopic and macroscopicconsequences are best understood via continuous models. Linkagesbetween models are sought by kinetic theory, partial differentialequations, and stochastic analysis. The education part includesthe training of a graduate student, development of innovativecourses in applied mathematics, activities for mathematicsawareness and outreach, authorship of a book on integralequations, and organization of working group seminars. The project addresses fundamental issues in nanotechnologyand materials modeling. The investigator uses tools of appliedmathematics to study systematically how nano-structures decay onsurfaces of technologically important materials. This work ismotivated by the pressing need to design increasingly smaller andfaster, yet more reliable, devices. The proposed work advancesthe ability to model and predict by theoretical methods thereliability of devices for the next generation of applications inmicroelectronics and information technology. The projectintegrates research and education: Interdisciplinary concepts ofapplied mathematics are shaped into instruction tools that reachout to students and science experts in diverse areas. This Careeraward is supported by the MPS Division of Mathematical Sciencesand by the MPS Division of Materials Research.