CAREER: Correlated Percolation Approaches to Jamming

职业：干扰的相关渗透方法

• 批准号: 0645373
• 负责人: Jennifer Schwarz
• 金额: $ 40万
• 依托单位: Syracuse University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-09-01 至 2013-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0645373&HistoricalAwards=false
• 关键词: CAREER; Correlated; Percolation; Approaches; Jamming

TECHNICAL SUMMARY:This CARRER award supports research and education on the statistical physics of condensed matter systems. Jamming is the transition in a disordered collection of objects from a state where motion is possible to one where it is not. With this definition, the seemingly unrelated systems of traffic, granular materials, glasses, and colloidal glasses all exhibit jamming behavior. Inspired by simple models of the glass transition, the PI and her collaborators have proposed a simple mechanism for the jamming of granular materials based on the model of k-core percolation. The definition of k-core percolation is ordinary percolation with an additional clustering constraint: each site in a percolation cluster must have a minimum number of contacts. While the mean field theory of this model quantitatively reproduces the critical exponents determined by simulations of granular jamming in finite-dimensions, finite-dimensional studies of k-core percolation so far do not. This raises the question: Is the k-core clustering constraint enough to describe the universality class of the jamming transition? Or do we need to consider other constraints, like force-balance? To answer this and related questions, the PI proposes to study various models of correlated percolation as simplified descriptions of jamming to determine which constraints are relevant in the renormalization group sense of the word and which constraints are not. Moreover, the PI will analyze systems where jamming arises due to the interplay between disorder resulting from intrinsic constraints and extrinsic, quenched disorder, with the goal of understanding jamming on rough surfaces. This avenue of investigation will also explore connections between jamming and depinning, where quenched disorder always plays a role. Finally, extension of the notion of jamming to quantum mechanical systems, by considering the jamming cluster as a medium for electronic transport, is introduced with an aim to broaden our understanding of conductivity in disordered materials. Since jamming is such an everyday phenomenon, whether occurring in traffic or coffee beans stuck in a dispenser, it is natural to have a broad outreach component to the educational part of the proposal. Furthermore, the geometrical concepts in jamming result in pictorial explanations that make it easy to convey to the general public. So the PI proposes to collaborate with Syracuse's Museum of Science and Technology (MOST) to give a series of lecture/demonstrations to children and design several stations on jamming and percolation with the ultimate goal of constructing an exhibit showcasing the theory and applications of soft matter. The PI also intends to give other public lectures on the subject. As for the university setting, the PI proposes to use percolation as a computer laboratory project in the undergraduate class "Science and Computing" and teach a graduate seminar on phase transitions with percolation and k-core as its focus.NON-TECHNICAL SUMMARY:This CARRER award supports research and education on the statistical physics of condensed matter systems. Diverse and seemingly unrelated systems of materials like sand, powders, glasses, and colloidal glasses can all exhibit jamming behavior, a transition from a state where motion is possible to one where it is not. The research focuses on understanding the fundamental science underlying this phenomenon. Since jamming is such an everyday and accessible phenomenon, whether occurring in traffic or coffee beans stuck in a dispenser, the PI will collaborate with Syracuse's Museum of Science and Technology (MOST) to give a series of lecture/demonstrations to children and design several stations on jamming and percolation with the ultimate goal of constructing an exhibit showcasing the theory and applications of soft matter. The PI also intends to give other public lectures on the subject. At the university level, the PI aims to use percolation as a computer laboratory project in the undergraduate class "Science and Computing" and teach a graduate seminar.

技术综述：该Carrer奖支持凝聚态系统统计物理的研究和教育。干扰是无序的物体集合中从可以运动的状态到不能运动的状态的转变。在这个定义下，交通、颗粒材料、玻璃和胶体玻璃等看似无关的系统都表现出拥堵行为。受玻璃化转变的简单模型的启发，Pi和她的合作者提出了一个基于k核渗流模型的颗粒材料堵塞的简单机制。K-core渗流的定义是具有附加集群约束的普通渗流：渗流集群中的每个站点必须具有最小数量的联系。虽然这个模型的平均场理论定量地再现了有限维颗粒堵塞模拟所确定的临界指数，但有限维k核渗流的研究到目前为止还不能。这就提出了一个问题：k-core集群约束是否足以描述干扰转换的普适性类？或者我们需要考虑其他限制，比如力量平衡？为了回答这个和相关的问题，PI建议研究各种相关渗流模型作为干扰的简化描述，以确定哪些约束在单词的重整化群义中相关，哪些约束不相关。此外，PI将分析由于内在约束导致的无序和外在的淬火无序之间的相互作用而产生干扰的系统，目的是了解粗糙表面上的干扰。这一调查途径还将探索干扰和脱钉之间的联系，在这一点上，猝灭的无序总是起作用的。最后，将干扰的概念扩展到量子力学系统中，将干扰团簇视为电子传输的媒介，目的是拓宽我们对无序材料中电导的理解。由于交通堵塞是一种日常现象，无论是发生在交通堵塞还是咖啡豆卡住了自动售货机，提案中的教育部分都有广泛的宣传成分是很自然的。此外，干扰中的几何概念导致了图形化的解释，使得它很容易传达给普通公众。因此，国际和平研究所建议与锡拉丘兹科学技术博物馆(MOST)合作，为儿童举办一系列讲座/演示，并设计几个关于干扰和渗流的站，最终目标是建立一个展示软物质理论和应用的展览。公社还打算就这一主题举办其他公开讲座。在大学设置方面，国际和平研究所建议在本科生的《科学与计算》课程中将渗流作为计算机实验室项目，并以渗流和k核为重点讲授相变研究生研讨会。非技术总结：该Carrer奖支持凝聚态系统统计物理的研究和教育。各种看似无关的材料系统，如沙子、粉末、玻璃和胶体玻璃，都会表现出堵塞行为，从可能运动的状态过渡到不可能运动的状态。这项研究的重点是理解这一现象背后的基础科学。由于堵塞是如此常见的现象，无论是发生在交通中还是卡住咖啡豆的自动售货机中，PI都将与锡拉丘兹科学技术博物馆(MOST)合作，为儿童提供一系列讲座/演示，并设计几个关于堵塞和渗滤的站，最终目标是建造一个展示软物质理论和应用的展览。公社还打算就这一主题举办其他公开讲座。在大学层面上，PI的目标是将渗流作为本科生课程《科学与计算》的计算机实验室项目，并教授研究生研讨会。