Statistical Mechanics

为了更好地理解宏观物质的性质，一个广泛的统计力学研究计划将继续进行。使用的方法从严格的数学分析到计算机模拟。这项研究由材料研究部、物理部和数学科学部联合支持。研究将集中于从微观动力学推导确定性宏观流体动力学方程，通过适当的空间和时间缩放，以获得对这些连续统方程的波动和有时大偏差的理解-在这些连续统方程中物质的原子性质表现出来。这将提高我们对激波结构、相偏析和相关现象的认识。平稳非平衡态的性质，包括非平衡系统中的相变，将是我们研究的另一个主要焦点。我们还计划研究概率元胞自动机的统计力学及其在并行计算和神经网络中的应用。扩散主导反应的行为将被探索，特别注意在长时间形成的空间模式。将在非平衡统计力学方面进行广泛的理论研究。重点将放在从流体微观组成推导流体流动模型的方程上。这是一项非常复杂和困难的任务，将涉及最先进的分析和计算机科学技术。为了反映研究的范围，资金由材料研究部、物理部和数学科学部提供。

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.