Statistical Analysis of Jammed Matter

堵塞物统计分析

• 批准号: 0907004
• 负责人: Hernan Makse
• 金额: $ 27万
• 依托单位: CUNY City College
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-15 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0907004&HistoricalAwards=false
• 关键词: Statistical; Analysis; Jammed; Matter

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.

技术摘要这一奖项支持有关障碍物质的理论研究和教育。 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数量和触点的概率分布。 PI将遵循系统的途径，将封装分类为从无摩擦到摩擦颗粒的阶段图，从硬球到可变形的颗粒，从单分散到多分散，从球形颗粒到多颗粒，从球形颗粒到非球形凸面粒子，例如椭圆形的问题，以了解一个单独的问题，从而使一个单一的问题从一个封装的问题中构成了一个独立的问题。 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理论研究与教育有关。当颗粒的密度增加到所有颗粒彼此紧密接触并经历结构停滞的程度时，干扰的现象发生在颗粒系统中。堵塞后，该系统能够承受施加的应力。堵塞的系统具有截然不同的特性，从硬质和粗糙的颗粒材料到可变形和无摩擦乳液液滴到胶体悬浮液。探索各种系统的干扰过渡在工业过程中都具有重要的意义，并且对这种类型的结构停滞的基本理论的理解。 PI旨在开发一个理论框架来描述这种现象。 PI设想创建相图还是路线图？简洁地捕获堵塞发生的条件和颗粒状材料状态。越来越多的意识到，对颗粒培养基的研究与液体或固体不同的行为提供了意想不到的物理挑战。通常，据信，干扰过渡与玻璃过渡具有许多特征，这在液体中进行了足够快的冷却。因此，堵塞物质领域的进展将提高对各种平衡现象的理解。从实际角度来看，颗粒状物质和乳液是广泛的，在食品工业，化妆品，药​​品和地貌学中找到了应用。通常，由于缺乏对这些复杂系统的了解，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制定新程序并降低处理成本成为可能。该项目的一个重要影响是吸引代表性不足的学生参加来自CCNY物理和工程学的优秀代表性不足的本科生和研究生。