This award supports fundamental theoretical research on the statistical physics of condensed matter systems. Percolation is one of the most venerable problems in the statistical physics of disordered systems. Insights from ordinary percolation have been useful to an extraordinary range of problems. In ordinary percolation, each site must be connected to at least one other site to be part of the percolating cluster. A generalization of this model is k-core percolation, where each site must be connected to at least k other sites. For k>2, this model exhibits behavior that is strikingly different from ordinary percolation: in the mean-field limit the k-core percolation transition is discontinuous with a diverging correlation length, while the ordinary percolation transition is continuous. Work supported by the previous grant suggests that this unusual mixed transition might persist in finite dimensions. The objectives of the first part of the proposal are to elucidate the nature of the k-core percolation transitions in finite dimensions, and to explore variants of the model using analytical theory, rigorous arguments and numerical simulations.
The second part of the proposal is devoted to the statistical physics of systems far out of equilibrium, specifically sheared glassy systems. This particular class of systems seems particularly promising for theoretical study because it appears to follow one of the simplest possible scenarios predicted by mean-field models. In this scenario, a system is well-characterized by two distinct temperature scales the thermal temperature, which controls behavior at short times scales, and an effective temperature, which controls behavior at long times and whose value depends on the shear rate. While much work has been devoted to establishing the validity of effective temperature, almost nothing has been done to explore what such a temperature might tell us about the system. This proposal seeks to redress this imbalance, and to turn effective temperature into a useful tool for understanding materials properties.
Intellectual Merit: K-core percolation is interesting in itself, but it has also been shown to map onto models that produce glassy dynamics, and has been applied to granular materials. Likewise, sheared glasses and granular materials are two of the systems best described by an effective temperature. Thus, the two parts of the proposal represent two different fundamental issues in statistical physicsthe behavior of disordered systems and of systems driven far from equilibrium that are tied together through the concept of jamming, namely the idea that common physics may underlie dynamical arrest in glass-forming liquids, colloidal suspensions, granular materials and foams, etc.
Broader Impacts: Jamming is a field that spans physics, chemistry, materials science, mechanical engineering and chemical engineering. To help develop a common language, the PI co-edited a reprint volume on jamming with Prof. Sidney Nagel. The graduate students and postdoctoral associates in her group (about half of whom are women) benefit from this breadth: they have gone on to successful careers in physics, chemistry, mechanical engineering and defense-related research. To introduce soft matter physics to a wider community, the PI visited 6 predominantly undergraduate institutions as a Phi Beta Kappa Visiting Lecturer during the 2004-5 academic year. On each trip, she gave a public lecture, colloquium and classroom lecture on her research, and met with women students and faculty to discuss issues such as balancing academic careers with family.
The grant supports basic research on a class of materials (condensed matter systems) as might be found in sands, powders, foams, etc. The theoretical research supported and the students trained will study the fundamental physics associated with these types of materials. While addressing fundamental issues related to these condensed matter systems, the results may also be applicable to real-world situations such as the behavior of granular materials and formation of glassy materials.
