CAREER: Correlated Percolation Approaches to Jamming

技术概述：这项CARRER奖支持凝聚态系统统计物理学的研究和教育。干扰是指一群无序的物体从可能运动的状态过渡到不可能运动的状态。根据这个定义，看似无关的交通系统、颗粒材料、玻璃和胶体玻璃都表现出堵塞行为。受玻璃化转变简单模型的启发，PI和她的合作者提出了一种基于k核渗透模型的颗粒材料干扰的简单机制。k核渗透的定义是普通的渗透，附加了聚类约束：渗透簇中的每个点必须具有最小接触数。虽然该模型的平均场理论定量地再现了有限维颗粒干扰模拟所确定的临界指数，但迄今为止，k-岩心渗流的有限维研究尚未做到这一点。这就提出了一个问题：k核聚类约束是否足以描述干扰跃迁的普遍性？或者我们是否需要考虑其他约束，比如力量平衡？为了回答这个问题和相关问题，PI建议研究各种相关渗透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意义上是相关的，哪些约束不是。此外，PI将分析由于内在约束和外在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。这条调查途径也将探索干扰和脱钉之间的联系，其中淬火无序总是起作用。最后，通过将干扰簇视为电子输运的介质，将干扰概念扩展到量子力学系统，旨在拓宽我们对无序材料电导率的理解。由于拥堵是一种日常现象，无论是发生在交通中，还是咖啡豆卡在自动售货机里，因此在提案的教育部分中加入广泛的推广内容是很自然的。此外，干扰中的几何概念导致图形解释，使其易于向公众传达。因此，PI建议与锡拉丘兹科学技术博物馆（MOST）合作，为孩子们提供一系列讲座/演示，并设计几个关于干扰和渗透的站点，最终目标是建立一个展示软物质理论和应用的展览。PI还打算就这一主题举行其他公开讲座。在大学设置方面，PI建议在本科课程“科学与计算”中使用渗透作为计算机实验室项目，并教授以渗透和k-core为重点的相变研究生研讨会。非技术总结：这项CARRER奖支持凝聚态系统统计物理学的研究和教育。沙子、粉末、玻璃和胶体玻璃等多种多样且看似无关的材料系统都可能表现出干扰行为，即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。由于干扰是一种日常和可接触的现象，无论是发生在交通中还是咖啡豆卡在自动售货机中，PI将与锡拉丘兹科学技术博物馆（MOST）合作，为孩子们提供一系列讲座/示范，并设计几个关于干扰和渗透的站点，最终目标是建立一个展示软物质理论和应用的展览。PI还打算就这一主题举行其他公开讲座。在大学层面，PI的目标是在本科课程“科学与计算”中使用渗透作为计算机实验室项目，并教授研究生研讨会。

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.