RUI: State Selection and Pattern Formation in Non-Equilibrium Systems

这是一笔瑞安基金，用于支持远离平衡的系统的理论研究。尽管在日常生活和重要的技术过程中发生了大量这样的现象，但人们对非平衡系统中状态的选择知之甚少。例如，从餐巾上的咖啡污渍和窗玻璃上的霜冻，到定向有序、固化和粘性指进实验中超导体和蜂窝界面中的涡流模式。虽然不太可能开发一种单一的变分方法来涵盖所有这些现象(就像波尔兹曼原理在平衡中所做的那样)，但有可能为特定类别的现象或行为开发方法。这项研究的目标是刻画一些重要物理系统的状态选择，并为一类相对简单的非平衡系统发展一种变分原理。%这是一项支持远离平衡系统的理论研究的RUI赠款。尽管在日常生活和重要的技术过程中发生了大量这样的现象，但人们对非平衡系统中状态的选择知之甚少。例如，从餐巾上的咖啡污渍和窗玻璃上的霜冻，到定向有序、固化和粘性指进实验中超导体和蜂窝界面中的涡流模式。虽然不太可能开发一种单一的变分方法来涵盖所有这些现象(就像波尔兹曼原理在平衡中所做的那样)，但有可能为特定类别的现象或行为开发方法。这项研究的目标是刻画一些重要物理系统中的状态选择，并为一类相对简单的非平衡系统发展一个变分原理。

0076054ElderThis is a RUI grant to support theoretical research on systems far from equilibrium. The selection of states in non-equilibrium systems is poorly understood despite the vast array of such phenomena occurring in everyday life and technologically important processes. Examples include everything from coffee stains on a napkin and frost on a window pane to vortex flow patterns in superconductors and cellular interfaces in directional ordering, solidification and viscous fingering experiments. While it is unlikely that a single variational method can be developed to encompass all such phenomena (as the Boltzmann principle does in equlibrium) it may be possible to develop methods for specific classes of phenomena or behavior. The goals of this research are to characterize state selection in a number of important physical systems and to develop a variational principle for a relatively simple class of non-equilibrium systems.%%%This is a RUI grant to support theoretical research on systems far from equilibrium. The selection of states in non-equilibrium systems is poorly understood despite the vast array of such phenomena occurring in everyday life and technologically important processes. Examples include everything from coffee stains on a napkin and frost on a window pane to vortex flow patterns in superconductors and cellular interfaces in directional ordering, solidification and viscous fingering experiments. While it is unlikely that a single variational method can be developed to encompass all such phenomena (as the Boltzmann principle does in equlibrium) it may be possible to develop methods for specific classes of phenomena or behavior. The goals of this research are to characterize state selection in a number of important physical systems and to develop a variational principle for a relatively simple class of non-equilibrium systems.***