Static and Dynamic Properties of Surfaces

这里提出的研究是上一笔拨款的延续，旨在了解各种表面和界面的统计力学和动力学。有各种有趣和基本的问题，与许多不同的领域相关，仍有待探讨。这些问题大多分为以下几大类：(1)随机流形，如聚合物和膜，从高维空间中嵌入得到。(2)演化的界面，如生长的晶面、膨胀的凝胶或流动的沙堆。(3)随机介质中的界面和路径与各种研究有关，从污秽超导体中的磁通线陷阱，到掺杂半导体中的费曼路径的干扰。

The research proposed here is a continuation of the previous grant, aimed at understanding the statistical mechanics and dynamics of a variety of surfaces and interfaces. There are various interesting and fundamental issues, relevant to many different fields that remain to be probed. Most of these questions fall into the following broad categories: (1) Random Manifolds, such as polymers and membranes, obtained from embeddings in a higher dimensional space. (2) Evolving interfaces, such as a growing crystal facet, swelling gel, or a flowing sandpile. (3) Interfaces and Paths in Random Media are relevant to studies as diverse as the trapping of flux lines in a dirty superconductor, to the interference of Feynman paths in a doped semiconductor.