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.

技术总结该奖项支持堵塞物的理论研究和教育。该提案的目标是发展体积涨落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颗粒随机紧密堆积和随机松散堆积的问题。PI将致力于发展一种理论统计方法，目的是用与熵等观测量相关的状态方程来描述堵塞系统，配位数、体积分数、弹性模量以及体积和接触的概率分布。PI将遵循一个系统的路线分类堵塞填料到堵塞的相图，从无摩擦到有摩擦的颗粒，从硬球到可变形的颗粒，从单分散到多分散，从球形颗粒到非球形凸颗粒，如椭球体，试图从统一的角度来理解包装问题。我们还将把我们对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，如2d，nd，该项目的一个重要影响将是吸引代表性不足的学生参加拟议的研究，这些研究来自CCNY物理和工程专业代表性不足的优秀本科生和研究生。该奖项支持干扰的理论研究和教育。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时，在颗粒系统中发生堵塞现象。一旦卡住，系统能够承受施加的应力。被堵塞的系统具有非常不同的性质，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。探索各种系统的堵塞过渡在工业过程和理解这种类型的结构制动的基本理论方面都具有重要意义。PI旨在开发一个理论框架来描述这种现象。PI设想创建相图或？路线图？以简明地捕捉发生堵塞的条件和颗粒材料的状态。越来越多的人认识到，颗粒介质的研究在物理学中提供了意想不到的挑战，具有不同于液体或固体的行为。一般认为，堵塞转变与玻璃化转变具有许多共同的特征，发生在足够快冷却的液体中。因此，堵塞物领域的研究进展将促进对各种非平衡现象的理解。从实用的角度来看，颗粒物质和乳状液是广泛存在的，在食品工业、化妆品、制药和地貌学中有着广泛的应用。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。这些系统的基本基础将使开发新程序和降低处理成本成为可能。该项目的一个重要影响将是吸引代表性不足的学生参加拟议的研究，这些研究来自CCNY物理和工程专业代表性不足的优秀本科生和研究生。