Collaborative Research: Focused Research Group: Analysis and Simulation of Magnetic Devices

纳米级的磁性设备具有关键的技术重要性。这个项目将通过一个协调的建模、分析、模拟和实验程序来促进我们对它们的性质的理解。要解决的问题包括：(A)开发用于模拟磁性材料和器件的改进的数值方法；(B)探索微磁“能量图景”和噪声在热激活开关中的作用；(C)研究特定的纳米尺度效应，如构型各向异性和几何约束墙。数学有很多贡献，也有很多收获。对适当极限的研究导致了具有挑战性的分析问题，这些问题的解决将有助于揭示基本物理学。对噪声和开关的分析导致了对能量图景的研究和随机偏微分方程物理上相关的例子。与实验室实验相结合的建模将加深我们对相关现象的理解。这一重点研究小组的活动将从一个由数学家、物理学家和计算科学家组成的多学科小组中汲取专业知识。该项目包括与IBM的合作以及对博士后科学家和研究生的培训。磁存储设备是现代计算的基础。它们的建模、模拟、分析和设计引发了物理和数学的基本问题，其中许多问题仍未得到解答。随着器件尺寸的减小，相关科学发生了变化：缺陷、空间无序和热涨落在纳米尺度的体系中变得至关重要。数学有很多贡献，也有很多收获。对适当极限的研究导致了具有挑战性的分析问题，这些问题的解决将有助于揭示基本物理学。噪声和开关的分析将从数学分析、数值模拟和实验研究三个方面进行。与实验室实验相结合的建模将加深我们对相关现象的理解。这一重点研究小组的活动将从一个由数学家、物理学家和计算科学家组成的多学科小组中汲取专业知识。该项目包括与IBM的合作以及对博士后科学家和研究生的培训。

Nanoscale magnetic devices are of critical technological importance. This project will advance our understanding of their properties through a coordinated program of modeling, analysis, simulation and experiment. Topics to be addressed include (a) development of improved numerical methods for the simulation of magnetic materials and devices; (b) exploration of the micromagnetic "energy landscape" and the role of noise in thermally activated switching; and (c) investigation of specific nanoscale effects such as configurational anisotropy and geometrically constrained walls. Mathematics has much to contribute and much to gain. The study of appropriate limits leads to challenging problems of analysis whose solution will shed light on the essential physics. The analysis of noise and switching leads to the study of the energy landscape and to physically relevant examples of stochastic partial differential equations. Modeling coordinated with laboratory experiments will refine our understanding of the relevant phenomena. This Focused Research Group activity will draw expertise from a multidisciplinary group of mathematicians, physicists and computational scientists. The project includes a collaboration with IBM and training of postdoctoral scientists and graduate students. Magnetic storage devices lie at the foundation of modern computing. Their modeling, simulation, analysis and design raise fundamental questions of physics and mathematics, many still unanswered. As device size decreases, the relevant science changes: defects, spatial disorder and thermal fluctuations become crucial in the nanoscale regime. Mathematics has much to contribute and much to gain. The study of appropriate limits leads to challenging problems of analysis whose solution will shed light on the essential physics. The analysis of noise and switching will be studied in a three-pronged approach: by mathematical analysis, numerical modeling and experimental investigation. Modeling coordinated with laboratory experiments will refine our understanding of the relevant phenomena. This Focused Research Group activity will draw expertise from a multidisciplinary group of mathematicians, physicists and computational scientists. The project includes a collaboration with IBM and training of postdoctoral scientists and graduate students.