Fronts, Fluctuations and Growth

提议：DMS-0244419PI：Charles DoeringInstitution：密歇根大学标题：前沿、波动和增长这项跨学科调查汇集了密歇根大学数学、物理和化学工程系的研究人员，研究材料科学和化学中出现的前沿传播和图案形成问题。该项目的中心目标是从理论和数学上阐明涨落、噪声和无序对化学反应和薄膜生长等非平衡系统界面动力学的作用。这个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来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。考虑到这一活动的智力优势，这个项目的研究成果将导致为材料科学和纳米技术中日益重要的小范围物理化学过程中日益重要的问题开发有效的数学描述和高效的计算方案。关于这项活动的更广泛影响，它还有一个重要的高级培训方面：与该项目相关的一名研究生研究助理将在首席调查人员的指导下开展原创博士论文研究。

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.