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

建议：DMS-0244492PI：David G.Schaeffer研究所：杜克大学标题：FRG：协作研究：慢粒流中的物理、数学和工程问题摘要本建议解决了粒材料慢流中的一系列基本和应用问题。它包括在实验、数学分析、建模和数值模拟方面的协调努力，并得到长期的工业合作的支持。从几个角度来看，颗粒材料的连续介质模型是可取的，但相关的偏微分方程通常是不适定的，这一数学困难严重阻碍了进展，特别是对于多维流动。这种不适性反映了一种真正的不稳定性，即颗粒流中的变形局部化为剪切带的趋势。围绕连续介质描述的基本问题将通过相互关联的项目来解决，这些项目研究：(I)离散性和非线性在病态连续介质描述正则化中的作用，(Ii)基于实验和MD模拟的微观力学考虑，建立解释微观速度波动的连续介质模型，(Iii)多维稳态漏斗流的数学预测和实验测试，以及(Iv)粉末的沉降，这是一个具有工业意义的两相流原型问题。研究计划解决了一个基本问题的不同方面：通过将材料建模为连续介质，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，这是一个特别的问题，例如农业谷物在收敛料斗中的流动：当筒仓卸料时，颗粒物料的流动有点像连续的流体，但由于物料的类似固体的性质及其离散性，料斗壁上的力不同于流体施加的力。从科学上讲，我们希望了解这些性质，特别是材料的离散性在模型中所起的作用。在其他贡献中，这项研究有望改善材料搬运行业的预测能力，从而提高制造业的效率。该小组将通过每周小组会议、参加会议和开设关于颗粒材料的新课程，创造一个将研究与学生和博士后培训相结合的研究环境。杜克大学数学系和物理系的临近，以及北卡罗来纳州州立大学和杜克大学私人投资机构之间现有的合作，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.