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

提案：DMS-0244488 PI：Michael Shearer机构：北卡罗来纳州州立大学标题：FRG：合作研究：缓慢颗粒流中的物理、数学和工程问题摘要本提案解决了颗粒材料缓慢流动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，这是一个数学上的困难，严重阻碍了进展，特别是多维流。这种不适定性反映了一种真实的不稳定性，即颗粒流中变形局部化为剪切带的趋势。 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，这些项目调查：（i）离散性和非线性在正则化不适定连续描述中的作用，（ii）基于实验和MD模拟，从微观力学考虑制定一个考虑微观速度波动的连续模型，（iii）多维稳态料斗流的数学预测和实验测试，以及（iv）粉末的沉降，工业上重要的原型两相流问题。该研究计划从不同方面解决了一个基本问题：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哪些行为？ 这对于工业环境尤其是一个问题，例如农业谷物在会聚料斗中的流动： 当筒仓卸料时，颗粒状物料的流动有点像连续的流体，但由于物料的固体性质及其离散性，料斗壁上的力与流体施加的力不同。 科学上，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。 除其他贡献外，这项研究预计将提高材料处理行业的预测能力，从而提高制造业的效率。 该小组将创造一个研究环境，通过每周小组会议，参加会议和新的颗粒材料课程，将研究与学生和博士后的培训相结合。 跨领域的合作将促进在杜克大学的数学和物理系的接近，并在北卡罗来纳州和杜克大学的PI之间的现有合作。

Proposal: DMS-0244488PI: Michael ShearerInstitution: North Carolina State 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.