IUTAM-ISIMM Symposium Mathematical Modeling and Physical Instances of Granular Flows

美国国家科学基金会-化学，生物工程，环境和运输系统分部颗粒和多相过程计划（1415）摘要提案号：0936892首席研究员：Goddard， joe联系方式：提案题目：IUTAM-ISIMM研讨会颗粒流的数学建模和物理实例这是一份申请NSF旅行资助的提案，用于支持美国参加国际理论力学联合会（IUTAM）和国际力学与数学相互作用协会（ISIMM）的联合研讨会，颗粒流的数学建模和物理实例，2009年9月14-18日，意大利雷焦卡拉布里亚。该研讨会的网站正在建设中，网址是http://mat520.unime.it/granular09/，将在雷焦卡拉布里亚市中心的一家酒店举行。根据IUTAM的规则，经过评审的会议记录将被出版，美国物理研究所（AIP）已签约将其出版为两卷本的AIP会议记录。至少一半的差旅支持将授予年轻的研究人员，包括高级博士研究生、博士后研究人员和初级教员。颗粒材料在自然界和技术中无处不在，从食品到沙质土壤和行星环。这些具有非线性耗散相互作用的多体系统在离散和连续建模中都提出了长期存在的具有挑战性的理论问题。诸如颗粒混合和分离（粒度分离）、振动输运、应变局部化和拱、颗粒压实和地震液化等现象需要更详细的物理理解和数学模型。对于非粘性的干燥颗粒介质，可以识别出三种不同的流动形式：一种准静态（赫兹-库仑）弹塑性状态，其中粒子尺度的惯性可以忽略不计，力学主要由持久的摩擦-弹性接触控制。2 .低密度（Bagnold）“颗粒-气体”状态，由粒子惯性和短时间的碰撞接触所主导；密集快速流动的一种中间的、尚不清楚的状态，使人联想到类液体的行为，其中持久的摩擦-弹性接触是由粒子惯性和重力介导的。IUTAM-ISIMM研讨会将汇集对颗粒物质数学模型的持续发展和应用感兴趣的数学家、物理学家和工程师。其中一个目标是促进新思想和方法的交流，并介绍流变模型、连接连续体和离散模型的均匀化方法、数值模拟和实验观察方面的最新研究。虽然将讨论所有上述流动型态，但重点将放在最不了解的型态3，即密集的快速流动。颗粒介质的数学模型对土木工程、岩土工程和工艺工程至关重要，也已应用于行星环、月球风化层和宇宙尘埃的积聚。虽然这些模型的公式和解决方案本身就提供了基本的数学问题，但在耗散系统的统计力学和凝聚态物质的玻璃态的广泛问题中，潜在的物理是共同的。

National Science Foundation - Division of Chemical, Bioengineering, Environmental, and Transport Systems Particulate & Multiphase Processes Program (1415)ABSTRACTProposal Number: 0936892Principal Investigator: Goddard, JoeAffiliation: University of California-San DiegoProposal Title:IUTAM-ISIMM Symposium Mathematical Modeling and Physical Instances of Granular FlowsThis is a proposal for an NSF travel grant to Support U.S. participation in the joint Symposium of the International Union of Theoretical Mechanics (IUTAM) and the International Society for the Interaction of Mechanics and Mathematics (ISIMM), Mathematical Modeling and Physical Instances of Granular Flows", Reggio Calabria, Italy, September 14-18, 2009. The symposium, whose web site is under construction at http://mat520.unime.it/granular09/, is to be held in a centrally located hotel in the city of Reggio Calabria. In keeping with IUTAM rules, refereed proceedings are to be published, and the American Institute of Physics (AIP) has been contracted to publish these as a two-volume AIP Conference Proceedings. At least half the requested travel support will be awarded to younger researchers, including advanced PhD students, postdoctoral researchers and beginning faculty members.Granular materials are ubiquitous in nature and technology, ranging from alimentary products to sandy soils and planetary rings. These many-body systems with nonlinear, dissipative interactions pose long-standing and challenging theoretical problems in both discrete and continuum modeling. Phenomena such as particulate mixing and de-mixing (size-segregation), vibratory transport, strain localization and arching, granular compaction and seismic liquefaction of soils require more detailed physical understanding and mathematical models. One can identify three distinguished flow regimes for non-cohesive, dry granular media:1.) A quasi-static (Hertz-Coulomb) elastoplastic regime, in which particle-scale inertia is negligible and the mechanics is governed largely by enduring frictional-elastic contacts,2.) A low-density (Bagnold) "granular-gas" regime, dominated by particle inertia and short-duration collisional contacts, and3.) An intermediate and poorly understood regime of dense rapid flow, reminiscent of liquid-like behavior, in which enduring frictional-elastic contacts are mediated by particle inertia and gravity.The IUTAM-ISIMM symposium will bring together mathematicians, physicists and engineers interested in the continuing development and application of mathematical models of granular matter. One objective is to promote the interchange of new ideas and methodologies and to present recent research on rheological models, methods of homogenization for connecting continuum to discrete models, numerical simulation and experimental observations. While all the above flow regimes will be addressed, a major emphasis will be placed on the most poorly understood, Regime 3, dense rapid flows.Mathematical models of granular media, which are essential to civil, geotechnical and process engineering, have also been applied to planetary rings, lunar regolith and accretion of cosmic dust. While the formulation and solution of such models provides basic mathematical problems of interest in their own right, the underlying physics is common to a wide range of problems in the statistical mechanics of dissipative systems and the glassy states of condensed matter.