This award supports theoretical research with a computational emphasis and education efforts organized around the study of complex disordered materials. An understanding of the thermodynamics and dynamics of complex materials is necessary both to understand the stability of magnetic memory and to explore novel complex collective effects seen in systems such as mesoscopic "spin ice," vortex matter, or packed colloidal dimers. Through the development of novel algorithms, this project will also strengthen the connections between physical approaches and the study of optimization and sampling developed by computer scientists.
Microscopically heterogeneous materials exhibit unusual and fascinating properties. These materials can exhibit intricate memory, for example through magnetic hysteresis or in a reprise of their thermal history upon warming. Disordered materials possess a highly complex energy landscape, exhibit glassy dynamics, and are believed to be in a critical state over a broad range of temperatures. Though heuristic analytic pictures exist, numerical simulations have been crucial to verifying theories and exploring which models explain experimental results.
In this project, the PI will advance understanding of the dynamics of complex and disordered materials by inventing, implementing, and utilizing advanced algorithms for optimization and dynamics. Two new approaches to spin glass materials will be applied to non-equilibrium dynamics: patchwork dynamics, a heuristic method to explore non-equilibrium dynamics over many time scales, and a recently developed exact sampling technique, to study the effects of temperature. New methods will also be investigated. This project will explore the importance of the correlations in the spatial structure of real physical systems to bulk memory effects and to the performance of algorithms. Simulations on vortex matter and colloidal systems will also be compared with experimental work.
Graduate students, a postdoctoral researcher, and undergraduate students will be trained in advanced computing methods and data analysis. They will learn and use the deep relationships between statistical physics and condensed matter physics and computational methods. This work has strong interdisciplinary connections with computer science and includes developing solvers for difficult optimization and sampling problems. As the problem of disordered interfaces and magnets are prototypical models of disorder and complexity, advances in this area contribute to a better description of complex systems, including both general networks and practical solutions to optimization problems. The PI will make computer codes generally available and will carry out outreach efforts.
This award supports theoretical research with a computational emphasis and education on the general topic of matter that is disordered and complex. Most materials are impure, but these materials are generally less well understood than pure materials. Because of competing forces, impure materials can take a very long time to relax or change. This extreme "glassy" behavior is seen in magnetic materials with impurities and artificially constructed systems such as packed microscopic dumbbell shaped beads or strips of superconducting material. These systems have long term memories and can store complex information in a distributed fashion.
The PI aims to develop new computational approaches to simulate these materials. These approaches speed up the computations sufficiently to be able to simulate materials over long times. More direct brute force calculations are often prohibitively slow. The PI's new techniques are closely connected to those developed by computer scientists and mathematicians to find optimal solutions, such as the shortest route between locations on a map and the random selection items from a complex set of choices. Adopting these techniques to the study of models for materials advances both the computational techniques and our understanding of complex materials.
The PI will work with undergraduate students, graduate students, and a postdoctoral researcher, to train them in the sophisticated computational techniques and physical analyses that are used in this field. The generality of these methods provides valuable training that enables students to solve a variety of problems in computation and science. The PI will make the computer codes used in the project available to the community. The PI shares his scientific expertise and enthusiasm with the area community through presentations and activities related to phase transitions and structure in materials.
