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

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，以提供对静态和缓慢驱动的颗粒材料的结构和机械性能的预测性和定量描述。密实的颗粒介质在自然界中普遍存在，并存在于许多工业应用中。然而，目前对于如何使用宏观描述符来唯一地表征稠密颗粒系统的状态还没有基本的理解。在我们提出的研究中，我们使用一种系统的、自下而上的方法来寻求这样的描述，在这种方法中，我们首先表征机械稳定的颗粒堆积的微观状态概率，然后利用它们来预测宏观行为。在静态颗粒填充的研究中，我们将测量不同填充制备方案和颗粒特性(如形状、摩擦和尺寸多分散性)的不同微观状态(按颗粒位置分类)的概率。我们还将确定与宏观观测相对应的微观状态的数量，如体积分数、弹性常数和机械强度。通过结合我们对微态概率和宏态密度的结果，我们将确定对系综平均量有重要贡献的微态。我们还将研究缓慢驱动系统的演化，在该系统中，发生从一个微态到另一个微态的转变。特别是，我们将在实验和数值模拟中测量轻敲激励和准静态剪切的跃迁几率。然后，我们将开发主方程方法来预测稳态微态分布和相应的宏观变量作为驱动机制强度的函数。智能优点：这项工作的一个重要方面是，将在一系列系统尺寸上进行实验和数值模拟。在小系统(多达数十个粒子)中，所有静态填充都将被列举，这样我们就可以将填充生成协议的影响从几何效应中分离出来。在中等大小的系统(多达100个粒子)中，我们将获得统计上最相关的一组状态。我们还将通过研究含有O(103)粒子的系统来深入了解大系统极限下的颗粒系统的宏观性质。因此，我们将能够开发出一幅将机械稳定(MS)填料的微观概率分布与宏观特性联系起来的统一图景。这一建议的另一个关键特点是我们提出了综合的实验、模拟和理论研究。在每个阶段，我们将比较实验和模拟得到的填充分布，以了解MS填充的性质和填充生成协议的影响。我们还将开发简单的理论模型来确定主要的物理机制。布罗德影响：虽然我们的研究重点是准静态条件下颗粒介质的性质，但我们的结果也将有助于更好地理解其他非晶态系统的材料性质，如分子和胶体玻璃、乳液和泡沫。特别是，我们的研究将与描述玻璃形成流体中固有结构统计方面的缓慢动力学的理论相关。除了基本的重要性外，从拟议研究中获得的知识还将对实际应用产生影响。潜在的工业应用包括开发高效的颗粒物质储存、混合、分离和输送技术，以及设计具有所需性能的现代玻璃材料(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STAR项目和CCNY多样化学生群体的有才华的少数族裔学生)。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拟议的与波兰基础技术研究所的几位科学家的合作，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.