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

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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.***