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

0076054ElderThis是一个RUI赠款，以支持远离平衡系统的理论研究。 尽管在日常生活和技术上重要的过程中发生了大量的非平衡系统中的状态选择，但人们对这种现象的理解仍然很少。 例子包括从餐巾上的咖啡渍和玻璃窗上的霜到超导体中的涡流模式和定向有序、凝固和粘性指状实验中的细胞界面。 虽然不太可能开发出一种单一的变分方法来涵盖所有这些现象（就像玻尔兹曼原理在平衡中所做的那样），但有可能开发出针对特定类别的现象或行为的方法。 本研究的目标是描述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。这是一个RUI赠款，以支持远离平衡系统的理论研究。 尽管在日常生活和技术上重要的过程中发生了大量的非平衡系统中的状态选择，但人们对这种现象的理解仍然很少。 例子包括从餐巾上的咖啡渍和玻璃窗上的霜到超导体中的涡流模式和定向有序、凝固和粘性指状实验中的细胞界面。 虽然不太可能开发出一种单一的变分方法来涵盖所有这些现象（就像玻尔兹曼原理在平衡中所做的那样），但有可能开发出针对特定类别的现象或行为的方法。 本研究的目标是描述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.***