Collaborative Research: Experiment, simulation, and theory of slowly driven granular materials --- from micro-state statistics to macroscopic properties

0968013Shattuck项目描述：我们提出了一套协调的实验，数值模拟和理论研究，以提供静态和缓慢驱动的颗粒材料的结构和力学性能的预测和定量描述。致密颗粒介质在自然界中普遍存在，并出现在许多工业应用中。然而，目前还没有基本的理解，如何唯一地表征状态的致密颗粒系统使用宏观描述符。在我们提出的研究中，我们寻求这样一个描述使用系统的，自下而上的方法，我们首先表征微观概率的机械稳定的颗粒填料，然后利用它们来预测宏观行为。 在我们的静态颗粒填料的研究中，我们将测量不同的微观状态（编目的颗粒位置）的概率为不同的包装准备协议和颗粒的性质，如形状，摩擦，和大小多分散性。我们还将确定对应于宏观观测值的微观状态的数量，例如体积分数，弹性常数和机械强度。通过结合我们的微观态概率和宏观态密度的结果，我们将确定显着贡献的微观态的ensembleaveraged量。我们还将研究缓慢驱动系统的演化，其中发生从一个微观状态到另一个微观状态的转变。特别是，我们将测量的过渡概率在实验和数值模拟的攻丝激励和准静态剪切。然后，我们将开发主方程的方法来预测的稳态微观状态分布和相应的宏观变量的驱动mechanism.Intellectual优点的强度的函数：这项工作的一个重要方面是，实验和数值模拟将在一系列的系统尺寸进行。在小的系统（多达几十个粒子），所有的静态包装将被枚举，这样我们就可以解开包装生成协议的几何效应的影响。在中等大小的系统（最多100个粒子）中，我们将获得统计上最相关的状态集。我们还将通过研究具有O（103）粒子的系统来深入了解大系统极限下颗粒系统的宏观性质。因此，我们将能够开发一个统一的图片，连接微观概率分布的机械稳定（MS）包装的宏观性能。 这个建议的另一个关键特点是，我们提出了综合实验，模拟和理论研究。在每个阶段，我们将比较实验和模拟的包装分布，以了解MS包装的性质和包装生成协议的影响。简单的理论模型也将被开发，以确定占主导地位的物理mechanism.Broader影响：虽然我们的调查集中在准静态条件下的颗粒介质的属性，我们的研究结果也将有助于更好地了解其他非晶系统的材料特性，如分子和胶体玻璃和乳液和泡沫。特别是，我们的研究将是相关的理论描述缓慢的动态在玻璃形成流体的固有结构的统计。除了基本的重要性，从拟议的研究中获得的知识将对实际应用产生影响。潜在的工业应用包括开发用于颗粒物质储存、混合、分离和输送的高效技术，以及设计具有所需性质的现代玻璃质材料（例如，高强度金属玻璃）。 拟议的调查将为研究生和本科生提供研究机会（特别是，我们将指导来自耶鲁大学STARS计划和CCNY多元化学生团体的有才华的少数民族学生）。我们将参加纽约市两所高中的项目，让高中生参与我们的研究项目。我们的项目还将通过与波兰基础技术研究所的几位科学家的拟议合作，促进国际知识转让。

0968013ShattuckDescription of the project: We propose a set of coordinated experiments, numerical simulations, and theoretical studies to provide predictive and quantitative descriptions of the structural and mechanical properties of static and slowly driven granular materials. Dense granular media are ubiquitous in nature and occur in many industrial applications. However, there is currently no fundamental understanding of how to uniquely characterize the state of a dense granular system using macroscopic descriptors. In our proposed research, we seek such a description using a systematic, bottom-up approach in which we first characterize microstate probabilities of mechanically stable granular packings and then utilize them to predict macroscopic behavior. In our studies of static particle packings, we will measure the probabilities of distinct microscopic states (cataloged by the particle positions) for different packing preparation protocols and particle properties such as shape, friction, and size polydispersity. We will also determine the number of microscopic states corresponding to macroscopic observables, such as the volume fraction, elastic constants and mechanical strength. By combining our results for microstate probabilities and the density of macro-states, we will determine the microstates that contribute significantly to ensembleaveraged quantities. We will also study the evolution of slowly driven systems, in which transitions from one microstate to another occur. In particular, we will measure the transition probabilities in experiments and numerical simulations of tapping excitations and quasi static shear. We will then develop master equation approaches to predict the steady state microstate distributions and corresponding macroscopic variables as a function of the intensity of the driving mechanism.Intellectual Merit: An important aspect of this work is that the experiments and numerical simulations will be performed over a range of system sizes. In small systems (up to tens of particles), all static packings will be enumerated, so that we can disentangle the influence of the packing generation protocol from geometrical effects. In moderate sized systems (up to one hundred particles), we will obtain the set of states that are statistically most relevant. We will also gain insight into the macroscopic properties of granular systems in the large-system limit by studying systems with O(103) particles. We thus will be able to develop a unified picture that connects microscopic probability distributions of mechanically stable (MS) packings to macroscopic properties. Another key feature of this proposal is that we propose integrated experiments, simulations, and theoretical studies. At each stage, we will compare the packing distributions from experiments and simulations to understand the nature of the MS packings and the effect of the packing generation protocol. Simple theoretical models will also be developed to identify the dominant physical mechanisms.Broader Impacts: While our investigations are focused on the properties of granular media under quasistatic conditions, our results will also contribute to a better understanding of material properties of other amorphous systems, such as molecular and colloidal glasses and emulsions and foams. In particular, our research will be relevant for theories describing slow dynamics in glass-forming fluids in terms of the statistics of inherent structures. Apart from the fundamental importance, the knowledge gained from the proposed studies will have impact on practical applications. Potential industrial applications include development of efficient technologies for storage, mixing, separation, and conveying of granular matter, and design of modern glassy materials of desired properties (e.g., high-strength metallic glasses). The proposed investigations will provide research opportunities for graduate and undergraduate students (in particular, we will mentor talented minority students from the STARS program at Yale and the diverse student body at CCNY). We will participate in programs at two high schools in New York City to involve high school students in our research program. Our project will also promote iternational knowledge transfer through the proposed collaboration with several scientists from the Institute of Fundamental Technological Research in Poland.