Statistical Analysis of Jammed Matter

该奖项支持关于堵塞物质的理论研究和教育。本提议的目标是发展体积波动系综来描述堵塞物质的统计力学，目的是揭示长期存在的表征粒子随机紧密堆积和随机松散堆积的问题。PI将致力于开发一种理论统计方法，目的是用与熵、配位数、体积分数、弹性模量以及体积和接触的概率分布等可观测值相关的状态方程来描述堵塞系统。PI将按照系统的路线将堵塞填料分类为阻塞的相图，从无摩擦颗粒到摩擦颗粒，从硬球体到可变形颗粒，从单分散到多分散，从球形颗粒到非球形凸颗粒（如椭球），试图从统一的角度理解填料问题。我们还将粒子的随机紧密堆积和随机松散堆积的研究推广到其他维度，如二维、三维和无限维的平均场极限。该项目的一个重要影响将是吸引未被充分代表的学生参与拟议的研究，这些学生来自CCNY未被充分代表的物理和工程专业的优秀本科生和研究生。该奖项支持有关干扰的理论研究和教育。在微粒系统中，当微粒的密度增加到一定程度时，所有微粒彼此紧密接触并经历结构阻滞，就会发生干扰现象。一旦堵塞，系统能够承受施加的压力。堵塞系统具有非常不同的特性，从坚硬粗糙的颗粒材料，到可变形无摩擦的乳液液滴，再到胶体悬浮液。探索各种系统的干扰过渡在工业过程和理解这种类型的结构阻滞的基本理论中都具有重要意义。PI旨在建立一个理论框架来描述这一现象。PI设想创建一个相图还是？路线图?简明地捕捉干扰发生的条件和颗粒材料的状态。越来越多的人认识到，颗粒介质的研究给物理学带来了意想不到的挑战，它们的行为不同于液体或固体。一般认为，干扰转变与玻璃化转变有许多共同的特征，发生在冷却足够快的液体中。因此，堵塞物质领域的进展将促进对各种非平衡现象的理解。从实用的角度来看，颗粒物质和乳剂广泛存在，在食品工业、化妆品、制药和地貌学中都有应用。通常，由于缺乏对这些复杂系统的理解，颗粒材料的处理是基于经验方法的。这些系统的基本基础将使开发新的程序和减少处理费用成为可能。该项目的一个重要影响将是吸引未被充分代表的学生参与拟议的研究，这些学生来自CCNY未被充分代表的物理和工程专业的优秀本科生和研究生。

TECHNICAL SUMMARYThis award supports theoretical research and education on jammed matter. The goal of this proposal is to develop the ensemble of volume fluctuations to describe the statistical mechanics of jammed matter with an aim of shedding light to the long-standing problem of characterizing the random close packing and random loose packing of particles.The PI will work to develop a theoretical statistical approach with the aim of describing the jammed system with equations of state relating observables such as entropy, coordination number, volume fraction, elastic moduli as well as the probability distributions of volume and contacts. The PI will follow a systematic route to classify jammed packings into a phase diagram of jamming, from frictionless to frictional particles, from hard spheres to deformable particles, from monodisperse to polydisperse, from spherical particles to nonspherical convex particles such as ellipsoids, in an attempt to understand the packing problem from a unifying perspective. We will also generalize our studies of random close packing and random loose packing of particles to other dimensions such as 2d, nd, and the mean-field limit of infinite dimension.An important impact of the project will be to attract underrepresented students to participate in the proposed research drawn from the excellent pool of underrepresented undergraduate and graduate students from physics and engineering at CCNY.NON-TECHNICAL SUMMARYThis award supports theoretical research and education on jamming. The phenomenon of jamming takes place in particulate systems when the density of particles is increased to a point where all particles are in close contact with one another and experience structural arrest. Once jammed, the system is able to withstand an applied stress. Jammed systems have very different properties, ranging from hard and rough granular materials, to deformable and frictionless emulsion droplets, to colloidal suspensions. Exploring the jamming transition for a variety of systems carries importance in both industrial processes and understanding of the fundamental theory of this type of structural arrest. The PI aims to develop a theoretical framework to describe this phenomenon. The PI envisions creating a phase diagram or ?road map? to concisely capture the conditions under which jamming occurs and the states of granular materials. There is a growing realization that the study of granular media offers unexpected challenges in physics, having behavior unlike that of liquids or solids. Generally, it is believed that the jamming transition shares many features with the glass transition, taking place in liquids cooled down sufficiently fast. Therefore, progress in the field of jammed matter will advance the understanding of a variety of out of equilibrium phenomena.From a practical perspective, granular matter and emulsions are widespread, finding applications in the food industry, cosmetics, pharmaceuticals and geomorphology. Often, the handling of granular materials is based on empirical methods due to a lack of understanding of these complex systems. A fundamental basis for these systems would make it possible to develop new procedures and reduce handling costs. An important impact of the project will be to attract underrepresented students to participate in the proposed research drawn from the excellent pool of underrepresented undergraduate and graduate students from physics and engineering at CCNY.