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

一个简单的分析理论的剪切颗粒材料附近的干扰过渡的动力学，需要指导当前的实验，模拟和应用。在这里，这样一个模型的开发：（1）识别的关键参数，控制剪切颗粒材料的间歇性动力学附近的堵塞过渡，（2）提供预测的关键参数的滑动雪崩统计的依赖关系，无论是附近和远离堵塞过渡，和（3）提供了一个统一的理解颗粒材料和相关系统的结构和动力学之间的相互作用。 颗粒状物质，如粉末、沙子、砾石和谷物，要么在被推动时流动，类似于流体，要么堵塞，间歇性突然停止和滑动，类似于地震。一个简单的数学工具，以快速预测的推动颗粒状材料的行为正在开发中，预计将有广泛的应用过程中，使用分子液体，粉末，建筑材料和农业谷物。该工具可用于预测新实验的结果，在计算机模拟和工业应用中，颗粒物质的干扰造成了显着的操作问题。这项研究的结果也与其他物理系统有关，范围很广，从金属晶体和非晶材料的变形到地震中地壳的变形。该模型为材料的无损检测和灾害预测提供了新的途径。该项目还为一名研究生和一名高级本科生提供广泛的跨学科培训。学生学习物理学，材料科学与工程，动力系统理论，数学物理和计算科学的现代数学建模工具。与理论家、实验家、工程师和计算机科学家的合作拓宽了学生的视野？观点，并增加他们在解决新问题的多功能性。

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.