Problems in Statistical Mechanics

在物理化学计划的这个项目中，凯斯将 进一步发展液体光散射理论， 研究非平衡统计的其他几个方面 力学 这些项目包括发展一种动力学 输运理论，研究生长模型和旋节线 分析和计算机上的分解，以及 研究无序系统的光散射。 在光散射理论和 非平衡统计力学，最困难的问题， 涉及高密度、大无序、大空间 波动等等，会受到攻击。 强大的方法， 实空间重整化将直接应用于光 从无序材料散射。 的可能性 来自无序系统的光散射不需要探测 平均属性，但实际上可能会给出整个 概率分布和新的信息将是 研究了 液体中的扩散理论将是 通过应用根据《公约》制定的方法， 以前的赠款。 这些包括动力学的推导 一个应该准确描述液体的方程， 变分法，似乎很适合其解决方案， 发展一种新的概念，在解决动力学 方程，找到随机计算机模拟， 方程式 一个全新的方法来运输理论在 过冷液体，基于利用量 从力常数矩阵导出，将继续进行。 这一广泛研究领域的其他几个项目也将 被追求。

In this project in the Physical Chemistry Program, Keyes will further develop the theory of light scattering from liquids and investigate several other aspects of nonequilibrium statistical mechanics. These projects include development of a kinetic theory of transport, studying growth models and spinodal decomposition both analytically and on the computer, and studying light scattering from disordered systems. In the theory of light scattering and in the theory of nonequilibrium statistical mechanics, the hardest problems, involving high density, large disorder, large spatial fluctuations, etc., will be attacked. The powerful method of real-space renormalization will be directly applied to light scattering from disordered materials. The possibility that light scattering from disordered systems need not probe averaged properties only, but may in fact give entire probability distributions and new information will be investigated. The theory of diffusion in liquids will be advanced via application of methods developed under the previous grant. These include the derivation of a kinetic equation which should describe liquids accurately, a variational method which seems well suited to its solution, and development of a new concept in the solution of kinetic equations, finding stochastic computer simulations which solve the equation. An entirely new approach to transport theory in supercooled liquids, based upon the utilization of quantities derived from the force constant matrix, will be pursued. Several other projects in this broad line of research also will be pursued.