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.

摘要这个集中的研究小组将密歇根大学数学，物理和化学工程系的研究人员汇集在一起​​，以解决针对动态过程的建模，模拟和分析的重要问题，在这些过程中，基本离散性在确定性的连续性系统（普通和部分差分公式的系统）中扮演着不可忽视的作用，在大规模的描述中扮演着不可忽视的作用。 这个重点研究小组结合了研究者在理论，建模，分析和科学计算方面的专业知识，以研究材料物理，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。 要研究的具体问题是：（1）通过细胞增殖和迁移的伤口愈合的介观数学模型，以及包括细胞粘附的生物学重要作用； （2）应用新的和改进的仿真技术，贝克式方程的直接解决方案以及随机模型的仿真和分析来研究微观相关性在Ostwald成熟中的作用； （3）渐无分析方法的发展，用于准确减少慢速随机变量的描述，将残余波动效应与（Bio）化学反应网络的应用合适地纳入具有广泛反应速率的化学反应网络； （4）为简单系统开发的建模，分析和仿真方法的扩展，以越来越复杂的人口生物学和流行病学中的随机模型，包括结构化种群的流行和灭绝竞争物种； （5）随机Fisher-Kolmogorov方程中的空间不均匀性和反应速率变化，这是前传播和模式形成的基本范式。 该项目的结果将导致发展有效的数学描述和有效的计算方案，以提高材料科学和纳米技术对小规模的物理和化学过程的重要性，以及生命科学中的定量建模。 关于该项目的更广泛影响，它通过为自然，工程和应用数学科学的博士后研究人员和博士生提供高级培训，从而有助于科学劳动力的发展。