Statistical Mechanics

统计力学

• 批准号: 9213424
• 负责人: Joel Lebowitz
• 金额: $ 30万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-12-15 至 1996-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9213424&HistoricalAwards=false
• 关键词: Statistical; Mechanics

A broad research program in statistical mechanics will be continued with the goal of obtaining a better understanding of the properties of macroscopic matter. The methods used range from rigorous mathematical analysis to computer simulations. The research is supported jointly by the Divisions of Materials Research, Physics and Mathematical Sciences. The research will focus on the derivation of deterministic macroscopic hydrodynamical equations from microscopic dynamics, by suitable scalings of space and time, in order to obtain an understanding of fluctuatiions and sometimes large deviations from these continuum equations - where the atomic nature of matter manifests itself. This should enhance our understanding of shock structure, phase segregation and related phenomena. The nature of stationary nonequilibrium states, including phase transitions in nonequilibrium systems, will be another major focus of our research. We also plan to investigate the statistical mechanics of probablistic cellular automata with possible applications to parallel computations and neural networks. The behavior of diffusion dominated reactions will be explored with particular attention to the spatial patterns formed at long times. %%% A broad program of theoretical research will be conducted in nonequilibrium statistical mechanics. Emphasis will be placed on deriving equations which model fluid flow from their microscopic constituents. This is a very complex and difficult task which will involve state-of-the-art techniques in analysis and computer science. Reflecting the range of the research, funding is provided by the Divisions of Materials Research, Physics and Mathematical Sciences.

将继续进行统计力学的广泛研究计划 目的是更好地理解 宏观物质。 使用的方法从严格的 数学分析到计算机模拟。 这项研究是 由材料研究部、物理部、 和数学科学 研究将集中在确定性的推导 宏观流体动力学方程从微观动力学， 空间和时间的适当缩放，以获得 理解波动，有时大的偏差， 这些连续统方程--物质的原子性质 表现自己。 这应该会增强我们对休克的理解 结构、相分离和相关现象。 的性质 稳定的非平衡态，包括相变 非平衡系统，将是我们的另一个主要焦点 research. 我们还计划研究 概率元胞自动机及其在 并行计算和神经网络。 的行为 扩散为主的反应将探讨与特定的 注意长期形成的空间格局。 %%% 一个广泛的理论研究计划将在 非平衡统计力学 重点将放在 从微观角度推导出流体流动的模型方程 选民。 这是一项非常复杂和艰巨的任务， 涉及最先进的分析和计算机技术 科学 为了反映研究的范围， 由材料研究、物理和数学部门 以理工科为重