FRG: Fluctuation Effects in Near-Continuum Descriptions of Discrete Dynamical Systems in Physics, Chemistry and Biology

FRG：物理、化学和生物学中离散动力系统近连续描述中的涨落效应

• 批准号: 0553487
• 负责人: Charles Doering
• 金额: $ 101.72万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2010-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0553487&HistoricalAwards=false
• 关键词: FRG; Fluctuation; Effects; Near; Continuum

Abstract This Focused Research Group brings together researchers from the University of Michigan's Departments of Mathematics, Physics and Chemical Engineering to address important problems of modeling, simulation and analysis for dynamical processes where underlying discreteness plays a non-negligible role in large scale descriptions via deterministic continuum systems (generally systems of ordinary and partial differential equations). This Focused Research Group combines the investigators' expertise in theory, modeling, analysis and scientific computation to study a suite of problems from materials physics, chemical kinetics and the life sciences to elucidate the fundamental scientific issues and develop appropriate quantitative tools to analyze them. The specific problems to be studied are: (1) Mesoscopic mathematical models of wound healing with cell proliferation and migration, and including the biologically important effect of cell-cell adhesion; (2) The application of new and improved simulation techniques, direct solutions of the Becker-Doering equations, and simulation and analysis of stochastic models to investigate the role of microscopic correlations in Ostwald ripening; (3) The development ofanalytic asymptotic methods for accurate reduced descriptions of slow stochastic variables properly incorporating residual fluctuation effects with applications to (bio)chemical reaction networks possessing a wide spectrum of reaction rates; (4) An extension of modeling, analysis and simulation methods developed for simple systems to increasingly complex stochastic models in population biology and epidemiology including epidemics in structured populations and extinction of competing species; (5) Spatial inhomogeneities and reaction-rate variations in the stochastic Fisher-Kolmogorov equation, a fundamental paradigm of front propagation and pattern formation. 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 nano-technology, and for quantitative modeling in the life sciences. With regard to the even broader impact of this project, it contributes to the development of the scientific workforce by providing advanced training for postdoctoral researchers and doctoral students in the natural, engineering and applied mathematical sciences.

摘要 这个重点研究小组汇集了来自密歇根大学数学，物理和化学工程系的研究人员，以解决动态过程的建模，模拟和分析的重要问题，其中潜在的离散性在通过确定性连续系统（通常是常微分方程和偏微分方程系统）的大规模描述中起着不可忽视的作用。 该重点研究小组结合了研究人员在理论，建模，分析和科学计算方面的专业知识，研究了材料物理，化学动力学和生命科学的一系列问题，以阐明基本的科学问题并开发适当的定量工具来分析它们。 具体研究的问题是：（1）伤口愈合与细胞增殖和迁移的介观数学模型，包括细胞-细胞粘附的生物学重要作用;（2）应用新的和改进的模拟技术，直接求解Becker-Doering方程，模拟和分析随机模型，研究微观相关性在Ostwald成熟中的作用;（3）发展分析渐近方法，适当地结合剩余涨落效应，对具有宽反应速率谱的（生物）化学反应网络进行精确的简化描述;（4）建模的扩展，分析和模拟方法的发展，为简单的系统，以日益复杂的随机模型，在人口生物学和流行病学，包括流行病的结构化种群和灭绝的竞争物种;（5）空间不均匀性和反应率的变化，在随机费雪-柯尔莫哥洛夫方程，一个基本的范式，前传播和模式的形成。 从这个项目的结果将导致有效的数学描述和高效的计算方案的发展越来越重要的小规模的物理和化学过程中的材料科学和纳米技术的问题，并在生命科学的定量建模。 关于该项目更广泛的影响，它通过为自然、工程和应用数学科学领域的博士后研究人员和博士生提供高级培训，为科学工作者的发展做出了贡献。