FRG-Collaborative Research: Physical, Mathematical, and Engineering Problems in Slow Granular Flow

提案：DMS-0244492PI: David G. schaeffer机构：杜克大学标题：FRG：合作研究：慢颗粒流中的物理、数学和工程问题摘要该提案解决了颗粒材料慢流动中的一系列基础和应用问题。它包括在实验、数学分析、建模和数值模拟方面的协调努力，并得到长期工业合作的支持。从几个角度来看，颗粒材料的连续体模型是可取的，但相关的偏微分方程通常是不适定的，这是一个严重阻碍进展的数学困难，特别是多维流动。这种病态反映了一种真实的不稳定性，即颗粒流中的变形倾向于局部剪切带。围绕连续体描述的基本问题将通过相互关联的项目来解决，这些项目将调查：(i)离散性和非线性在规范不适定连续体描述中的作用；（ii）基于实验和MD模拟，从微观力学考虑出发，提出一个考虑微观速度波动的连续体模型；（iii）多维稳态料仓流动的数学预测和实验测试；（iv）粉末沉降，这是一个工业上重要的两相流问题原型。该研究项目研究了一个基本问题的不同方面：通过将材料建模为连续体，可以理解缓慢流动的颗粒材料的什么行为？对于工业环境来说，这尤其是个问题，比如农业谷物在会聚料斗中的流动：当料仓被排出时，颗粒状材料有点像连续的流体流动，但由于材料的固体状特性及其离散性，料斗壁上的力与流体施加的力不同。从科学上讲，我们希望了解这些特性，特别是材料的离散性在模型中所起的作用。在其他贡献中，本研究有望提高物料处理行业的预测能力，从而提高制造效率。该小组将创造一个研究环境，通过每周的小组会议、参加会议和一门关于颗粒材料的新课程，将研究与学生和博士后的培训结合起来。杜克大学数学系和物理系的临近，以及北卡罗来纳州立大学和杜克大学的pi之间现有的合作，将促进跨领域的合作。

Proposal: DMS-0244492PI: David G. SchaefferInstitution: Duke UniversityTitle: FRG: Collaborative Research: Physical, Mathematical and Engineering Problems in Slow Granular FlowsABSTRACTThis proposal addresses a spectrum of fundamental and applied problems in the slow flow of granular materials. It includes coordinated efforts in experiment, mathematical analysis, modeling, and numerical simulation, supported by a long-standing industrial collaboration. Continuum models of granular materials are desirable from several points of view, but the associated partial differential equations are typically ill-posed, a mathematical difficulty that has severely hampered progress, especially for multidimensional flow. This ill-posedness reflects a real instability, the tendency of the deformation in granular flow to localize into shear bands. Fundamental issues surrounding the continuum description will be addressed through inter-related projects that investigate: (i) the role of discreteness and nonlinearity in regularizing the ill-posed continuum description, (ii) the formulation from micromechanical considerations, based on experiments and MD simulations, of a continuum model that accounts for microscopic velocity fluctuations, (iii) mathematical predictions and experimental tests of multidimensional steady-state hopper flows, and (iv) the settling of powders, an industrially significant prototype two-phase flow problem.The research program attacks different aspects of a basic question: What behavior of slowly flowing granular material can be understood by modeling the material as a continuum? This is particularly an issue for industrial settings such as the flow of agricultural grains in a converging hopper: When a silo is discharged, the granular material flows somewhat like a continuous fluid, but the forces on the hopper walls are unlike those exerted by a fluid due to the solid-like properties of the material and its discreteness. Scientifically, we wish to understand these properties, especially the role that the discreteness of the material plays in the models. Among other contributions, this research is expected to improve predictive capabilities in the materials- handling industry and thereby increase efficiency in manufacturing. The group will create a research environment that integrates research with the training of students and post-docs, through weekly group meetings, participation in conferences and a new course on granular materials. Collaboration across fields will be facilitated by the proximity of the mathematics and physics departments at Duke University, and by the existing collaborations between PIs at NC State and Duke Universities.