Fluctuations and Response in Granular Matter near Jamming

干扰附近颗粒物质的波动和响应

• 批准号: 0905880
• 负责人: Bulbul Chakraborty
• 金额: $ 28.5万
• 依托单位: Brandeis University
• 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 2012-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0905880&HistoricalAwards=false
• 关键词: Fluctuations; Response; Granular; Matter; near

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.

技术摘要这一奖项支持理论研究，该研究是由粒状物理学中的关键问题激发的：如何描述大尺度和长时间尺度上干颗粒培养基的静态和动态？我们预测和控制颗粒材料对外部变化的响应的能力取决于我们连接特征的能力，例如在短长度尺度上观察到的力链，以与颗粒介质的大规模变形。因此，将谷物的显微镜和集体行为联系起来的理论框架具有改变颗粒状研究的景观的潜力。颗粒状材料的特性负责大多数非琐碎的现象学，并且导致大多数理论挑战是存在大量不同的显微镜中的大量显微镜状态，该状态与不同的显微镜状态相同。此功能也存在于其困扰状态的更广泛的材料中。堵塞，从流体状态到无序固态的过渡受到亚竞争能力的影响，颗粒材料表现出接近阻塞的强烈波动。实验和仿真表明，应力，流场和密度的波动具有仅由少数外部参数来定义的分布。特征良好的分布的存在导致了颗粒介质的基本统计描述的概念。已经提出了类似于平衡统计力学的统计集合，以在显微镜和宏观，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包装中的空间波动。对于给定的一组宏观参数的多个，亚稳态的状态，颗粒材料的流变学也受到了强烈的影响。在最近的工作中，压力集结加上了压力格局中亚稳定性的概念？已经能够重现剪切下颗粒材料的对数增强。拟议项目的一个目标是通过结合转移，混乱和随机性的模型更好地了解缓慢变形的颗粒媒体动态。该项目将为研究生和本科生提供宝贵的教育机会。 PI在她的研究中有良好的记录，其中包括代表性不足的学生和教职员工。 PI还通过建立和组织研讨会和会议在复杂的流体和颗粒状社区中发挥了领导作用。Non-technical摘要这一奖项支持有关颗粒材料以及干扰现象的理论研究和教育。在我们的日常生活中遇到的颗粒材料，例如沙子，盐或大米具有显着的特性。盒子中的谷物在摇动时会压实，米饭只有小心地倒出时才能制成锥体结构，然后以沙漏以恒定的速度流动。谷物孤岛的失败是由于流动逮捕时在侧壁上施加的巨大压力引起的。雪崩和地震是导致流动的谷物不恰当的例子。然而，我们对粒状物质这种行为的理解是有限的。阻碍理解颗粒物的主要障碍是它从根本上摆脱了热平衡。晶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提供能量以维持稳定状态。宏观尺寸使热波动与改变晶粒状态无关，而颗粒材料实际上是零温度的系统，不会自发地平衡。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。 PI旨在开发一个理论框架，该框架捕获了粒状材料所显示的各种现象。从实际的角度来看，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，从而对行业和美国竞争力产生重大影响。该项目将为研究生和本科生提供宝贵的教育机会。 PI在她的研究中有良好的记录，其中包括代表性不足的学生和教职员工。 PI还通过建立和组织研讨会和会议来在复杂的液体和颗粒状社区中发挥领导作用。