Dynamical Systems Special Topics: Dynamics of granular materials: jamming, avalanches, disorder, and localization

为了指导当前的实验、模拟和应用，需要一个关于剪切颗粒材料在阻塞转变附近的动力学的简单解析理论。建立了这样一个模型：(1)确定控制剪切颗粒材料在干扰转变附近的间歇动力学的关键参数；(2)预测滑移雪崩统计量对远离干扰转变的关键参数的依赖关系；(3)对颗粒材料及其相关系统的结构和动力学之间的相互作用提供统一的理解。颗粒状物质，如粉末、沙子、砾石和颗粒，要么在推动下流动，类似于流体，要么堵塞，断断续续地突然停止和滑动，类似于地震。一种简单的数学工具正在开发中，它可以快速预测推进的颗粒材料的行为，预计将在使用分子液体、粉末、建筑材料和农业谷物的过程中得到广泛应用。该工具可以用来预测新实验的结果，在计算机模拟中，也可以在工业应用中，在这些应用中，颗粒物质的堵塞构成了一个重大的操作问题。这项研究的结果也适用于其他大范围的物理系统，从金属晶体和非晶态材料的变形到地震中地壳的变形。该模型为材料无损检测和危险性预测提供了新的途径。该项目还为研究生和高级本科生提供广泛的跨学科培训。学生从物理学、材料科学与工程、动力系统理论、数学物理和计算科学中学习现代数学建模工具。与理论家、实验学家、工程师和地球物理学家的合作拓宽了学生的视野？视角，增加他们解决新问题的多才多艺。

A simple analytic theory of the dynamics of sheared granular materials near the jamming transition is needed to guide current experiments, simulations, and applications. Here such a model is developed that:(1) identifies the key parameters that control the intermittent dynamics of sheared granular materials near the jamming transition,(2) provides predictions for the dependence of the slip avalanche statistics on the key parameters, both near and far from the jamming transition, and(3) provides a unified understanding of the interplay between structure and dynamics of granular materials and related systems. Granular materials, such as powders, sand, gravel, and grain, either flow if pushed, similar to fluids, or they jam, with intermittent sudden stops and slips, similar to earthquakes. A simple mathematical tool to quickly predict the behavior of pushed granular materials is being developed that is expected to have wide applications in processes that use molecular liquids, powders, construction materials, and agricultural grains. The tool can be used to predict the results of new experiments, in computer simulations, and in industrial applications, where jamming of granular matter poses a significant operational problem. The results of this research are relevant also to other physical systems, over a wide range of scales, from the deformation of metallic crystals and amorphous materials to the deformation of the earth's crust in earthquakes. The model provides new approaches to nondestructive materials testing and hazard prediction. The project also provides broad interdisciplinary training to a graduate student and an advanced undergraduate student. The students learn modern mathematical modeling tools from physics, materials science and engineering, dynamical systems theory, mathematical physics, and computational science. Collaboration with theorists, experimentalists, engineers, and geophysicists broaden the students? perspectives and increase their versatility in solving new problems.