New Numerical and Theoretical Methods to Analyse Disordered Materials

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TECHNICAL SUMMARY:This award supports computational and theoretical research on the low-temperature properties of spin glasses and models inspired by strongly disordered materials. The research is based in part on advances made on a project supported through the Information Technology Research initiative. This project involves developing, applying, and communicating new methods to probe structural and dynamical properties of disordered systems and networks, utilizing the renormalization group and the results of research on the Extremal Optimization heuristic. Thrusts of the research include: 1) Frustrated lattices requiring up to a billion variables above and near bond percolation will be simulated to predict low-temperature exponents with the accuracy essential to reveal scaling relations and to tightly constrain theoretical models. 2) New meta-heuristics will be developed; these are indispensable for low-energy properties of glassy materials, combinatorial optimization, or complex networks. 3) Investigating statistical models at the transition between low-dimensional and mean-field behavior using numerical and analytical techniques to elucidate scaling and critical dimensions in glasses, and small-world properties in networks. The PI will explore a wide range of applications for his heuristics and new network models.This award supports the education of students, whose academic training provides the future backbone of our information technology infrastructure. The PI plans to develop sophisticated software in a web-based environment, utilizing a student-administered cluster-computer. All results and software products will be disseminated widely through publications, presentations, and the internet. The projects will provide students with education and research experience in the study of statistical physics. Ties with researchers at Los Alamos National Laboratory will provide students further real-life research experience.NONTECHNICAL SUMMARY:This award supports computational and theoretical research at the interface of statistical physics and computer science. The research is inspired by disordered materials in which atoms or the smallest units of magnetism cannot usefully be viewed as being arranged in a regular crystalline array. The models that are believed to contain essential physics of these materials are examples of complex systems known both to materials research and computer science. Included in this class of problems are how proteins find the optimum configuration of atoms for biological function, circuit design, and the seemingly simple problem of finding the minimum distance a salesman must travel to visit each city of a list of cities only once. These are difficult to solve as they contain conflicting constraints and are characterized by many almost correct solutions. The PI has developed a computer algorithm that may elucidate the properties of disordered magnetic materials at low-temperatures. This award supports a continuation of that work and the more general application of the PI?s computer algorithm to a wider class of problems known as optimization problems. The research is based in part on advances made on a project supported through the Information Technology Research initiative. This award supports the education of students, whose academic training provides the future backbone of our information technology infrastructure. The PI plans to develop sophisticated software in a web-based environment, utilizing a student-administered cluster-computer. All results and software products will be disseminated widely through publications, presentations, and the internet. The projects will provide students with education and research experience in the study of statistical physics. Ties with researchers at Los Alamos National Laboratory will provide students further real-life research experience.