Static and Dynamic Properties of Surfaces

表面的静态和动态特性

• 批准号: 9303667
• 负责人: Mehran Kardar
• 金额: $ 34.4万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-06-01 至 1998-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9303667&HistoricalAwards=false
• 关键词: Static; Dynamic; Properties; Surfaces

Theoretical research will be aimed at understanding the static and dynamic fluctuations of a variety of polymers, surfaces and networks. The many interesting and fundamental issues that can be probed are relevant to a diverse variety of subjects which can be broadly placed into the following categories: (1) Extended networks, such as polymers, membranes and gels, fluctuating in a higher dimensional space. The interplay between entropic elasticity, rigidity, and microscopic interactions leads to a number of unusual macroscopic phases. (2) Dynamic evolution of surfaces and paths far from equilibrium cannot be described by a Hamiltonian, and is instead probed by appealing to symmetries and conservation laws. Evolution equations relevant to roughening of crystal facets, moving lines, and flowing sandpiles are constructed and their dynamic steady states are explored. (3) Path integrals in random media are relevant to tunnelling of localized electrons, wave propagation in inhomogeneous media and pinning of vortex lines in superconductors. Numerical and analytical methods are developed for performing these path integrals. (4) Substrate roughness and its influence on adsorption and surface phase transitions is investigated. %%% The theoretical research to be conducted on this grant probes the behavior of extended objects such as surfaces and chains, including how these objects grow into various structures. The general treatment is then applied to such systems as polymers, membranes, interfaces and surfaces. The results have wide applicability in materials research and are also fundamental to modern condensed matter physics.

理论研究旨在了解各种聚合物、表面和网络的静态和动态波动。 可以探讨的许多有趣和基本的问题与各种各样的主题相关，这些主题可以大致分为以下几类：（1）扩展网络，例如在更高维度空间中波动的聚合物、膜和凝胶。 熵弹性、刚性和微观相互作用之间的相互作用导致了许多不寻常的宏观相。 (2) 远离平衡的表面和路径的动态演化不能用哈密顿量来描述，而是通过诉诸对称性和守恒定律来探讨。 构建了与晶面粗糙化、移动线和流动沙堆相关的演化方程，并探讨了它们的动态稳态。 (3) 随机介质中的路径积分与局域电子的隧道效应、非均匀介质中的波传播以及超导体中涡线的钉扎有关。 开发了数值和分析方法来执行这些路径积分。 (4)研究了基底粗糙度及其对吸附和表面相变的影响。 %%% 这项资助将进行的理论研究探讨了扩展对象（例如表面和链）的行为，包括这些对象如何成长为各种结构。 然后将一般处理应用于聚合物、膜、界面和表面等系统。 该结果在材料研究中具有广泛的适用性，也是现代凝聚态物理学的基础。