Fronts, Fluctuations and Growth

提案：DMS-0244419 PI：查尔斯Doering机构：密歇根大学标题：前沿，波动和增长摘要这一跨学科的研究汇集了来自密歇根大学数学系，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前沿传播和图案形成问题。 该项目的中心目标是从理论上和数学上阐明波动、噪声和无序对非平衡系统（如化学反应和薄膜生长）中界面动力学的作用。 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，以研究具有科学和技术意义的系统中随机和非线性效应的相互作用。该项目的研究成果将导致发展有效的数学描述和有效的计算方案的问题对于材料科学和纳米技术中的小规模物理和化学过程越来越重要。 关于这一活动的广泛影响，它也有一个重要的高级培训方面：与该项目有关的研究生研究助理将在主要研究者的指导下进行原创博士论文研究。

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.