Statistical Physics of Disordered and Driven Systems

该奖项支持凝聚态系统统计物理的基础理论研究。 逾渗是无序系统统计物理中最古老的问题之一。从普通渗流中得到的见解对一系列特殊的问题都很有用。在普通的渗流中，每个位点必须与至少一个其他位点相连，才能成为扩散簇的一部分。这个模型的一个推广是k-核心渗流，其中每个站点必须连接到至少k个其他站点。对于k2，这个模型表现出的行为是显着不同的普通渗流：在平均场极限的k-核心渗流过渡是不连续的发散相关长度，而普通的渗流过渡是连续的。由先前资助支持的工作表明，这种不寻常的混合过渡可能会在有限维中持续存在。该计划的第一部分的目标是阐明有限维k-核渗流跃迁的性质，并利用分析理论、严格论证和数值模拟探索该模型的变体;第二部分致力于远离平衡的系统的统计物理学，特别是剪切玻璃系统。这类特殊的系统似乎特别有希望进行理论研究，因为它似乎遵循平均场模型预测的最简单的可能场景之一。在这种情况下，一个系统是由两个不同的温度尺度热温度，它控制在短时间尺度的行为，和一个有效的温度，它控制在长时间的行为，其值取决于剪切速率。虽然许多工作致力于建立有效温度的有效性，但几乎没有做过任何事情来探索这样的温度可能告诉我们关于系统的信息。该建议旨在纠正这种不平衡，并把有效温度变成一个有用的工具，了解materials properties.Intellectual Merit：K-核心渗流本身是有趣的，但它也已被证明映射到模型，产生玻璃态动力学，并已被应用到粒状材料。同样，剪切玻璃和粒状材料是两个最好的系统描述的有效温度。因此，提案的两个部分代表了统计物理学中两个不同的基本问题无序系统的行为和远离平衡的系统的行为，它们通过干扰概念联系在一起，即普通物理学可能是玻璃形成液体、胶体悬浮液、颗粒材料和泡沫等动力学停滞的基础。干扰是一个跨越物理、化学、材料科学、机械工程和化学工程的领域。为了帮助发展一种共同的语言，PI与西德尼内格尔教授共同编辑了一本关于干扰的再版书。她所在小组的研究生和博士后研究员（其中约一半是女性）受益于这一广泛性：他们在物理、化学、机械工程和国防相关研究领域取得了成功。为了向更广泛的社区介绍软物质物理学，PI在2004- 2005学年期间作为Phi Beta Kappa客座讲师访问了6所主要的本科院校。在每一次访问中，她都就她的研究进行了公开演讲、座谈会和课堂演讲，并与女学生和女教师会面，讨论诸如平衡学术事业与家庭等问题。非技术摘要：该基金支持一类材料的基础研究（凝聚物系统），如可能在砂，粉末，泡沫，理论研究的支持和培训的学生将学习与这些类型的材料相关的基础物理。 在解决与这些凝聚态系统相关的基本问题的同时，这些结果也可能适用于现实世界的情况，例如颗粒材料的行为和玻璃状材料的形成。

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 k2, 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.Non-Technical Abstract: 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.