Fluctuations and Response in Granular Matter near Jamming

技术总结该奖项支持由颗粒物理学中的一个关键问题推动的理论研究：如何描述大长度和长时间尺度上干燥颗粒介质的静力学和动力学？PI专注于干扰附近应力传播的性质。我们预测和控制颗粒材料对外部变化的反应的能力取决于我们将在短长度尺度上观察到的力链等特征与颗粒介质的大规模变形联系起来的能力。因此，将颗粒的微观行为和集体行为联系起来的理论框架有可能改变颗粒研究的格局。颗粒材料的一个特性是存在大量宏观上等价的不同微观亚稳态，这是大多数非平凡现象的原因，也是导致大多数理论挑战的原因。这一特征也存在于更广泛类别的处于堵塞状态的材料中。干扰，流体状态到无序固体状态的转变受亚稳态的存在影响，颗粒材料在干扰附近表现出强烈的波动。实验和模拟表明，应力、流场和密度的波动具有定义良好的分布，仅由几个外部参数表征。表征良好的分布的存在导致了对颗粒介质的潜在统计描述的概念。已经提出了类似于平衡统计力学的统计系综，以在微观和宏观、波动和响应之间建立所需的联系。PI将使用最近开发的应力集合来预测静态颗粒填充中的空间波动。对于一组给定的宏观参数，颗粒材料的流变性也受到多个亚稳态的存在的强烈影响。在最近的工作中，应力集合与应力景观中亚稳定的概念相结合。已经能够再现颗粒材料在剪切下的对数强度。该项目的一个目标是利用包含亚稳态、无序性和随机性的模型来更好地理解缓慢变形的颗粒介质的动力学。该项目将为研究生和本科生提供宝贵的教育机会。PI有一个很好的记录，在她的研究中纳入了代表不足的学生和教职员工。PI还通过创建和组织研讨会和会议，在复杂的流体和颗粒社区发挥了领导作用。非技术总结该奖项支持颗粒材料和堵塞现象的理论研究和教育。我们日常生活中遇到的颗粒状物质，如沙、盐或大米，都具有显著的特性。盒子里的谷物摇一摇就会压实，大米只有在小心倒出的时候才会形成金字塔结构，沙子在沙漏里以恒定的速度流动。粮食筒仓的失效是由于当水流停止时施加在侧壁上的不可预测的巨大应力造成的。雪崩和地震是谷物疏通导致水流的例子。然而，我们对颗粒物质的这种行为的理解是有限的。阻碍理解颗粒物质的主要障碍是它从根本上脱离了热平衡。颗粒是通过耗散接触相互作用的宏观物体。相互作用的耗散性质意味着必须不断地提供能量以维持稳定状态。宏观尺寸使得热涨落与颗粒状态的改变无关，而颗粒材料实际上是零温度系统，不会自发平衡。人们越来越意识到，颗粒介质的研究在物理学上带来了意想不到的挑战，具有不同于液体或固体的行为。PI旨在开发一种理论框架，以捕捉颗粒材料所显示的各种现象。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了解，颗粒材料的处理基于经验方法。这些系统的一个基本基础将使开发新的程序和降低处理成本成为可能，从而对工业和美国的竞争力产生重大影响。这个项目将为研究生和本科生提供宝贵的教育机会。PI有一个很好的记录，在她的研究中纳入了代表不足的学生和教职员工。PI还通过创建和组织研讨会和会议，在复杂的流体和颗粒社区发挥了领导作用。

TECHNICAL SUMMARYThis award supports theoretical research that is motivated by a key question in granular physics: how can one describe the statics and dynamics of dry granular media at large length scales and long time scales?The PI focuses on the nature of stress propagation near jamming. Our ability to predict and control the response of granular materials to external changes hinges on our ability to connect features such as force chains observed at short length scales to the large-scale deformation of granular media. Therefore, a theoretical framework that links the microscopic and collective behavior of grains has the potential of transforming the landscape of granular research.A property of granular materials that is responsible for most of the non trivial phenomenology, and leads to most of the theoretical challenges is the existence of a large number of different microscopic metastable states that are macroscopically equivalent. This feature is also present in a broader class of materials in their jammed states. Jamming, the transition from a fluid state to a disordered solid state is influenced by the presence of metastability, and granular materials exhibit strong fluctuations close to jamming. Experiments and simulations have shown that fluctuations in stresses, flow fields, and density have well defined distributions characterized by only a few external parameters. The existence of well-characterized distributions has led to notion of an underlying statistical description for granular media. Statistical ensembles analogous to those of equilibrium statistical mechanics have been proposed to create the desired link between microscopic and macroscopic, fluctuations and response. The PI will use a recently developed stress ensemble to make predictions about spatial fluctuations in static granular packings. The rheology of granular materials is also strongly affected by the existence of multiple, metastable states for a given set of macroscopic parameters. In recent work, the stress-ensemble, combined with a concept of metastability in a ?stress landscape? has been able to reproduce the logarithmic strengthening of granular materials under shear. A goal of the proposed project is to achieve better understanding of the dynamics of slowly deformed granular media using models that incorporate metastabilty, disorder and stochasticity.This project will provide valuable educational opportunities for graduate and undergraduate students. The PI has a strong record of including under-represented students and faculty in her research. The PI has also taken leadership roles in the complex fluids and granular community by founding and organizing workshops and conferences.NON-TECHNICAL SUMMARYThis award supports theoretical research and education on granular materials and the phenomenon of jamming. The granular materials encountered in our daily lives, such as sand, salt, or rice, have remarkable properties. The cereal in the box compactifies when shaken, rice makes pyramidal structures only when poured out carefully, and sand flows at a constant rate in an hourglass. Failures of grain silos are caused by unpredictably large stresses exerted on the sidewalls as the flow arrests. Avalanches and earthquakes are examples of the unjamming of grains leading to flow. Yet, our grasp of such behavior of granular matter is limited. The main obstacle that hinders the understanding of granular matter is that it is fundamentally out of thermal equilibrium. Grains are macroscopic objects that interact through dissipative contact. The dissipative nature of the interactions implies that energy has to be constantly supplied to maintain a steady state. The macroscopic size makes thermal fluctuations irrelevant for changing the state of grains, and granular materials are effectively zero-temperature systems that do not equilibrate spontaneously. There is a growing realization that the study of granular media offers unexpected challenges in physics, having behavior unlike that of liquids or solids. The PI aims to develop a theoretical framework which captures the diverse phenomena displayed by granular materials. 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, thereby having a significant impact on industry and on American competitiveness.This project will provide valuable educational opportunities for graduate and undergraduate students. The PI has a strong record of including under-represented students and faculty in her research. The PI has also taken leadership roles in the complex fluids and granular community by founding and organizing workshops and conferences.