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

国家科学基金会-化学、生物工程、环境和运输系统颗粒多相过程计划(1415)摘要建议编号：0936892主要研究员：Goddard，JoeAffiliation：加州大学圣迭戈分校建议标题：IUTAM-ISIMM研讨会颗粒流的数学建模和物理实例这是一项NSF旅行补助金的建议，以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”，意大利雷焦卡拉布里亚，2009年9月14日至18日。研讨会的网站正在http://mat520.unime.it/granular09/，建设中，将在雷吉奥卡拉布里亚市中心的一家酒店举行。根据IUTAM的规则，将发表经裁判的会议记录，美国物理研究所(AIP)已签约将这些会议记录作为两卷的AIP会议记录出版。申请的旅行资助至少有一半将授予年轻研究人员，包括高级博士生、博士后研究人员和初任教职人员。颗粒状材料在自然和技术中随处可见，从食物产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介质建模中提出了长期存在的和具有挑战性的理论问题。土壤的颗粒混合和解混(尺寸分离)、振动传输、应变局部化和拱化、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。人们可以确定无粘性、干燥颗粒介质的三种不同的流型：1)一种准静态(赫兹-库仑)弹塑性区域，其中颗粒尺度的惯性可以忽略不计，力学在很大程度上由持久的摩擦-弹性接触来控制。以粒子惯性和短时间碰撞接触为主的低密度(Bagnold)“颗粒气体”区域，以及3。一种中间且鲜为人知的密集快速流动状态，使人联想到类似液体的行为，其中持久的摩擦-弹性接触是由粒子惯性和重力调节的。IUTAM-ISIMM研讨会将把对颗粒物质数学模型的持续发展和应用感兴趣的数学家、物理学家和工程师聚集在一起。其中一个目标是促进新思想和新方法的交流，并介绍流变学模型、将连续介质与离散模型连接的均化方法、数值模拟和实验观察的最新研究。虽然将讨论上述所有流型，但重点将放在最不了解的流型3，即密集的快速流上。对土木工程、岩土工程和过程工程至关重要的颗粒介质的数学模型也已应用于行星环、月球土层和宇宙尘埃的吸积。虽然这些模型的表述和求解本身就提供了感兴趣的基本数学问题，但其基本物理是耗散系统统计力学和凝聚态的玻璃态中的广泛问题的共同之处。

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.