Fronts, Fluctuations and Growth

提案：DMS-0244419PI: Charles DoeringInstitution: University of Michigan标题：锋面、波动和生长摘要这项跨学科研究汇集了密歇根大学数学系、物理系和化学工程系的研究人员，研究材料科学和化学中出现的锋面传播和模式形成问题。该项目的中心目标是从理论上和数学上阐明涨落、噪声和无序在非平衡系统（如化学反应和薄膜生长）界面动力学中的作用。该项目结合了理论凝聚态和统计物理，动力学蒙特卡罗和数值模拟，以及数学建模和分析，以研究科学和技术兴趣系统中随机和非线性效应的相互作用。关于这项活动的智力价值，该项目的研究成果将导致有效的数学描述和高效的计算方案的发展，以解决材料科学和纳米技术中小规模物理和化学过程中日益重要的问题。就该活动的广泛影响而言，它还有一个重要的高级培训方面：与该项目相关的研究生研究助理将在主要研究员的指导下进行原创性博士论文研究。

Proposal: DMS-0244419PI: Charles DoeringInstitution: University of MichiganTitle: Fronts, Fluctuations, and GrowthABSTRACTThis interdisciplinary investigation brings together researchers from the University of Michigan's Departments of Mathematics, Physics and Chemical Engineering to study questions of front propagation and pattern formation arising in materials science and chemistry. The central goal of the project is to elucidate, theoretically and mathematically, the roles of fluctuations, noise and disorder on the dynamics of interfaces in nonequilibrium systems such as chemical reactions and thin film growth. This project combines theoretical condensed matter and statistical physics, Kinetic Monte Carlo and numerical simulations, and mathematical modeling and analysis to investigate the interplay of stochastic and nonlinear effects in systems of scientific and technological interest.With regard to the intellectual merit of this activity, research results from this project will lead to the development of effective mathematical descriptions and efficient computational schemes for problems of increasing importance for small-scale physical and chemical processes in materials science and nanotechnology. With regard to the broader impacts of this activity, it also has a significant advanced training aspect: a graduate student research assistant associated with this project will carry out original PhD thesis research under the guidance of the principal investigators.