CAREER: Thermodynamic and kinetic approaches for epitaxial material systems

Margetis DMS-0847587研究人员专注于数学与材料科学和物理的十字路口的研究和教育目标。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。物理机制用原子线缺陷的离散“粒子”方案来描述。然而，通过连续模型最好地理解了中观和宏观后果。模型之间的联系通过运动学理论、偏微分方程组和随机分析来寻找。教育部分包括培养研究生，开发应用数学的创新课程，开展提高数学意识和推广数学的活动，编写一本关于积分方程式的书，以及组织工作组研讨会。该项目解决了纳米技术和材料建模方面的基本问题。研究人员利用应用数学的工具，系统地研究纳米结构如何在具有重要技术价值的材料表面衰变。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。这项拟议的工作提高了用理论方法模拟和预测器件在下一代微电子和信息技术应用中的可靠性的能力。该项目将研究和教育融为一体：应用数学的跨学科概念被塑造成教学工具，供不同领域的学生和科学专家使用。该Career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.