CAREER: Statistical Physics of Disordered Systems: A Program for the Development and Application of Exact Combinatorial Algorithms to Extended Systems in Disordered Media

0094176曾鸣这一职业奖支持无序主导系统热力学的理论研究。PI试图建立一个框架，其中组合算法被用来研究无序系统，并且从所得到的无序系统的分析中，可以设计出更实用的新的组合算法。建议的工作包括三个部分：(1)组合算法将被用来研究位错环，以及玻璃界面的粗糙度和统计形貌，这对材料科学是重要的，目的是研究随机临界下的普遍特征。(2)使用一种新的有限温度传递矩阵采样技术对介观涡旋系统进行大规模模拟，以研究热力学变量的反常标度、非自平均量的普遍样本方差以及概率分布函数的标度形式。(3)研究了定义在正方形晶格上的无序全填充环模型，重点研究了基态作为环逸度的函数的计算难度。其目的是定位P(多项式和Easy)和NP(非确定多项式和Hard)之间的相变。该奖项的教育部分涉及多学科科学课程的开发和实施。主要的重点将是研究生课程“自然科学中的组合最优化”，其实施方式新颖，包括从生物信息学到凝聚态物理的各种主题。这个职业奖支持统计物理和组合算法的理论研究和教育。研究的重点是无序主导系统的平衡性质，目的是为了建立无序系统热力学的统一理论。材料驱动的例子包括由随机无序钉扎的第二类超导体中的涡旋，无序底物上的聚合物吸收，以及具有随机残基序列的致密蛋白质的构象。

0094176ZengThis CAREER award supports theoretical research on the thermodynamics of disorder-dominated systems. The PI seeks to develop a framework in which combinatorial algorithms are used to study disordered systems, and from the resulting analyses of disordered systems, new combinatorial algorithms of greater utility can be designed. There are three components to the proposed work: (1) combinatorial algorithms will be used to study dislocation loops, and the roughness and statistical topography of glassy interfaces that are important to materials science, with the aim of investigating universal features at random criticality. (2) Large scale simulations on mesoscopic vortex systems using a new finite-temperature transfer matrix sampling technique will be performed to investigate: anomalous scalings of thermodynamic variables, universal sample-to-sample variances for non-self-averaging quantities, and the scaling forms of probability distribution functions. (3) A disordered fully-packed-loop model defined on a square lattice will be studied with a focus on difficulty of computing ground states as a function of loop fugacity. The aim is to locate a phase transition between P (polynomial and easy) and NP (nondeterministic polynomial and hard). The educational component of this award involves the development and implementation of multidisciplinary science courses. The primary focus will be a graduate course "Combinatorial Optimizations in Natural Science" with a novel implementation that includes a diverse range of topics from bioinformantics to condensed matter physics.%%%This CAREER award supports theoretical research and education on statistical physics and combinatorial algorithms. The focus of the research is on the equilibrium properties of systems dominated by disorder with the aim of contributing to a unified theory of the thermodynamics of disordered systems. Materials motivated examples include vortices in type II superconductors that are pinned by random disorder, polymer absorbtion on disordered substrates, and conformation of compact proteins with random residue sequences.***