Statistical Field Theories and Collective Phenomena

统计场论和集体现象

• 批准号: 9805833
• 负责人: Mehran Kardar
• 金额: $ 39万
• 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: 1998
• 资助国家: 美国
• 起止时间: 1998-06-01 至 2001-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9805833&HistoricalAwards=false
• 关键词: Statistical; Field; Theories; Collective; Phenomena

9805833 Kardar Complex phenomena often emerge from the collective interactions of simple underlying entities, such as atoms in a crystal, or neurons in the brain. Statistical mechanics provides powerful tools for quantifying collective phenomena, in both average behavior, and fluctuations around average. This research is aimed at understanding static and dynamic fluctuation phenomena in polymers, flux lines, surfaces, networks, and complex fluids. The chief analytical tool for extracting universal features of interacting systems is field theory. Equations governing the variation of a relevant field in space and time are constructed on the basis of various arguments (symmetry, locality, etc.) and then analyzed by well known techniques such as perturbation expansions and renormalization group. Numerical methods are also employed to simulate complex systems. Some less conventional approaches will also be explored in this research: (i) standard field theory can be regarded as a description of fluctuating linear objects (world-lines). A generalization to describe a class of fluctuating manifolds (with fixed connectivity) of arbitrary internal dimensions will be formulated. (ii) Path integral methods are introduced to study boundary effects introduced by extended objects immersed in a complex fluid. Even a simple system such as a moving mirror in vacuum modifies the quantum fluctuations of the electromagnetic field, leading to forces and radiation phenomena that can be calculated by this method. Specific topics of study include: (i) flux phases in type II superconductors: the modification of the phase diagram by the combined effects of thermal fluctuations, pinning by disorder, and destabilizing longitudinal currents. (ii) configurations of polymers and gels with random interactions and crosslinks. (iii) nonlinear patterns formed in biological systems (cortical maps or microtubule assemblies). (iv) description of nonequilibrium fluctuations in growing sys tems and drifting aggregates. (v) fluctuations of a single polyelectrolyte (charged polymer) and interactions between several extended charged objects. %%% Complex phenomena often emerge from the collective interactions of simple underlying entities, such as atoms in a crystal, or neurons in the brain. Statistical mechanics provides powerful tools for quantifying collective phenomena, in both average behavior, and fluctuations around average. This research is aimed at understanding static and dynamic fluctuation phenomena in polymers, flux lines, surfaces, networks, and complex fluids. Specific topics of study include: (i) flux phases in type II superconductors: the modification of the phase diagram by the combined effects of thermal fluctuations, pinning by disorder, and destabilizing longitudinal currents. (ii) configurations of polymers and gels with random interactions and crosslinks. (iii) nonlinear patterns formed in biological systems (cortical maps or microtubule assemblies). (iv) description of nonequilibrium fluctuations in growing systems and drifting aggregates. (v) fluctuations of a single polyelectrolyte (charged polymer) and interactions between several extended charged objects. ***

9805833 卡达尔复杂现象通常是由简单的底层实体（例如晶体中的原子或大脑中的神经元）的集体相互作用产生的。 统计力学为量化集体现象（包括平均行为和平均波动）提供了强大的工具。 这项研究旨在了解聚合物、通量线、表面、网络和复杂流体中的静态和动态波动现象。 提取相互作用系统的普遍特征的主要分析工具是场论。 控制相关场在空间和时间上的变化的方程是基于各种参数（对称性、局部性等）构建的，然后通过众所周知的技术（例如微扰展开和重正化群）进行分析。 数值方法也用于模拟复杂系统。 本研究还将探索一些不太传统的方法：（i）标准场论可以被视为波动线性物体（世界线）的描述。 将制定描述任意内部尺寸的一类脉动流形（具有固定连通性）的概括。 (ii) 引入路径积分方法来研究浸入复杂流体中的扩展物体所引入的边界效应。 即使是一个简单的系统，例如真空中的移动镜子，也会改变电磁场的量子涨落，从而产生可以通过这种方法计算的力和辐射现象。 具体研究主题包括：（i）II 型超导体中的磁通相：热波动、无序钉扎和不稳定纵向电流的综合影响对相图的修改。 (ii) 具有随机相互作用和交联的聚合物和凝胶的构型。 (iii) 生物系统中形成的非线性模式（皮质图或微管组件）。 (iv) 生长系统和漂移总量的非平衡波动的描述。 (v) 单一聚电解质（带电聚合物）的波动和几个扩展带电物体之间的相互作用。 %%% 复杂的现象通常是由简单的底层实体（例如晶体中的原子或大脑中的神经元）的集体相互作用产生的。 统计力学为量化集体现象（包括平均行为和平均波动）提供了强大的工具。 这项研究旨在了解聚合物、通量线、表面、网络和复杂流体中的静态和动态波动现象。 具体研究主题包括：（i）II 型超导体中的磁通相：热波动、无序钉扎和不稳定纵向电流的综合影响对相图的修改。 (ii) 具有随机相互作用和交联的聚合物和凝胶的构型。 (iii) 生物系统中形成的非线性模式（皮质图或微管组件）。 (iv) 生长系统和漂移聚集体中非平衡波动的描述。 (v) 单一聚电解质（带电聚合物）的波动和几个扩展带电物体之间的相互作用。 ***