Studies in Statistical Mechanics

技术概述：该奖项支持统计力学各个分支领域的理论研究和教育。这项工作由材料研究部和数学科学部共同支持。这项工作的中心主题是更好地理解起源于微观成分集体行为的宏观系统的特性。所用的方法从精确的数学分析到计算机模拟都有。这些方法弥合了严谨结果和应用之间的差距。PI和合作者所采用的研究课题是多种多样的。使用介观自由能泛函可以研究周期状态，混合物中的润湿和过饱和蒸汽中的液滴形成。对非平衡定态和局部电流的波动和大偏差的研究仍在继续。这包括水动力标度不充分的情况。基础研究继续取得重大进展，例如建立傅立叶？具有非调和相互作用的开放系统中的热传导定律。在量子统计物理中，对大量子系统的子系统的研究导致对这些系统何时具有由正则吉布斯测度给出的密度矩阵的理解。在某些情况下，如时间周期场中模型量子系统的电离研究，在原子和分子中激光诱导跃迁方面也有应用。除了物理学之外，研究人员还将统计力学方法应用于流行病的数学研究，考虑到网络上的相关性和饱和效应。将这些技术扩展到种群动力学和生态学模型涉及通过缩放极限推导反应扩散方程，这些是计划中的研究。研究活动是高度跨学科的，汇集了物理学家，数学家，化学家和那些在生物和社会科学理论领域工作的人。预期的应用是在材料科学，复杂流体和生物系统。该项目还包括每年组织两次会议，在学院气氛中讨论统计力学的核心主题和新发展。研究生、博士后和少数族裔科学家参与其中，就他们的工作发表演讲，并与该领域的知名研究人员进行互动。这些会议还提供了一个建立专业网络的机会，并可能导致新的合作。非技术概述：该奖项支持统计力学各个分支领域的理论研究和教育。这项工作由材料研究部和数学科学部共同支持。这项工作的中心主题是更好地理解源于其基本原子成分集体行为的材料系统的特性。所用的方法从精确的数学分析到计算机模拟都有。这些方法弥合了严谨结果和应用之间的差距。主题范围从经典物理学到量子物理学和高度正式的技术相关应用，甚至疾病传播的动力学。研究活动是高度跨学科的，汇集了物理学家，数学家，化学家和那些在生物和社会科学理论领域工作的人。预期的应用是在材料科学，复杂流体和生物系统。该项目还包括每年组织两次会议，在学院气氛中讨论统计力学的核心主题和新发展。研究生、博士后和少数族裔科学家参与其中，就他们的工作发表演讲，并与该领域的知名研究人员进行互动。这些会议还提供了一个建立专业网络的机会，并可能导致新的合作。

TECHNICAL SUMMARY:This award supports theoretical research and education in a variety of subfields of statistical mechanics. This work is jointly supported by the Division of Materials Research and the Division of Mathematical Sciences. The central theme of the effort is a better understanding of the properties of macroscopic systems originating in the collective behavior of their microscopic constituents. The methods used range from exact mathematical analysis to computer simulations. These approaches bridge the gap between rigorous results and applications.Research topics employed by PI and collaborators are varied. Using mesoscopic free energy functionals allows investigation of periodic states, wetting in mixtures and droplet formation in supersaturated vapor. An ongoing effort continues on fluctuations and large deviations in nonequilibrium stationary states and partial currents. This includes cases where the hydrodynamic scaling is inadequate. Significant advance continue in fundamental studies such as establishing Fourier?s law of heat conduction in open systems with anharmonic interactions. In quantum statistical physics, the study of subsystems of large quantum systems leads to understanding of when these systems have density matrices given by canonical Gibbs measures. In some cases, such as the study of ionization of model quantum systems in time periodic fields, there are applications to laser induced transitions in atoms and molecules. Beyond physics, researchers also apply statistical mechanical methods to the mathematical study of epidemics taking into account correlations as well as saturation effects on networks. Extension of these techniques to models of population dynamics and ecology involves derivation of reaction-diffusion equations via scaling limits and these are planned investigations.The research activities are highly interdisciplinary, bringing together physicists, mathematicians, chemists and those working in theoretical areas of the biological and social sciences. The expected applications are in material science, complex fluids and in biological systems. The project also includes the organization of two conferences every year in which both core subjects and new developments in statistical mechanics are discussed in a collegial atmosphere. Graduate students, postdocs and minority scientists are involved and present talks on their work and interact with established researchers in the field. The conferences also serve as an opportunity for professional networking and can lead to new collaborations. NONTECHNICAL SUMMARY:This award supports theoretical research and education in a variety of subfields of statistical mechanics. This work is jointly supported by the Division of Materials Research and the Division of Mathematical Sciences. The central theme of the effort is a better understanding of the properties of material systems originating in the collective behavior of their elementary atomic constituents. The methods used range from exact mathematical analysis to computer simulations. These approaches bridge the gap between rigorous results and applications. Topics range from classical physics to quantum physics and highly formal to applications of technological relevance and even dynamics of disease propagation.The research activities are highly interdisciplinary, bringing together physicists, mathematicians, chemists and those working in theoretical areas of the biological and social sciences. The expected applications are in material science, complex fluids and in biological systems. The project also includes the organization of two conferences every year in which both core subjects and new developments in statistical mechanics are discussed in a collegial atmosphere. Graduate students, postdocs and minority scientists are involved and present talks on their work and interact with established researchers in the field. The conferences also serve as an opportunity for professional networking and can lead to new collaborations.