FRG: Collaborative Research: Kinetic Description of Multiscale Phenomena: Modeling, Theory and Computation

FRG：协作研究：多尺度现象的动力学描述：建模、理论和计算

• 批准号: 0757227
• 负责人: Eitan Tadmor
• 金额: $ 69.97万
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-09-01 至 2012-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0757227&HistoricalAwards=false
• 关键词: FRG; Collaborative; Research; Kinetic; Description

Kinetic equations play a central role in many areas of mathematical physics, from micro- and nano-physics to continuum mechanics. They are an indispensable tool in the mathematical description of applications in physical and social sciences, from semi-conductors, polymers and plasma to traffic networking and swarming. The ultimate goal of this proposal is to develop novel analytical and numerical methods based on kinetic descriptions of complex phenomena with multiple scales and with a wide range of applications. The objective is to achieve a better understanding of problems which are in the forefront of current research and to contribute to the solution of long-standing problems by synergetic collaboration of theory, modeling and numerics. To this end, this Focus Research Group (FRG) will provide a platform, led by leading researchers from Universities of Maryland, Brown, Iowa State, Wisconsin-Madison, Arizona State, Austin-Texas and Toulouse, France, who will merge their expertise in the construction, analysis and implementation of kinetic descriptions for a selected suite of problems with crossing scales from quantum and micro scales to the macro scales. Topics to be discussed include kinetic descriptions of microscopic and quantum phenomena, and kinetic descriptions of macroscopic phenomena. As a recent novel example for the kinetic methodology we will use kinetic descriptions to study hyperbolic flows for complex supply chains. The theoretical and modeling aspects of this research program, on both microscopic and macroscopic scales, will be integrated with kinetic-based numerical methods for capturing ``smaller scales phenomena".The rationale behind this proposal is a timely effort to address several important issues in modern applied mathematics. Kinetic theories are not new. Yet, there have been many major developments in kinetic modeling, kinetic theories and related numerical methods, with the potential for a considerable impact on emerging new fields in physical and social sciences. The proposed effort will significantly strengthen the leading role that the US researchers can play in pursuing cutting-edge research and training a new generation of applied mathematicians in this important field. We expect this project to contribute to the development of scientific workforce by advanced training for doctoral and postdoctoral researchers and by providing a platform for interdisciplinary interactions with researchers from related disciplines. Internal and external interactions will be maintained through synergetic collaborations which will come to fruition during the three annual workshops to be held in Maryland (Year 1), France and Brown (Year 2), and Wisconsin (Year 3). International meetings will be held as part of a series of interdisciplinary workshops organized by the Center for Scientific Computation and Mathematical Modeling (CSCAMM) at the University of Maryland. Project researchers will collaborate with the DOE Center for Multiscale Plasma Dynamics in CSCAMM, the DOE Ames Laboratory at Iowa State University, and the Institute for Computational Engineering and Sciences (ICES) at UT Austin.

动力学方程在数学物理的许多领域中发挥着核心作用，从微米和纳米物理到连续介质力学。它们是物理和社会科学应用的数学描述中不可或缺的工具，从半导体、聚合物和等离子体到交通网络和集群。该提案的最终目标是开发基于多尺度和广泛应用的复杂现象的动力学描述的新颖的分析和数值方法。目的是更好地理解当前研究的前沿问题，并通过理论、建模和数值的协同合作为解决长期存在的问题做出贡献。为此，该焦点研究小组（FRG）将提供一个平台，由来自马里兰大学、布朗大学、爱荷华州立大学、威斯康星大学麦迪逊分校、亚利桑那州立大学、德克萨斯大学奥斯汀分校和法国图卢兹大学的顶尖研究人员领导，他们将融合他们在构建、分析和实施动力学描述方面的专业知识，以解决从量子和微观尺度到宏观尺度的跨尺度问题。讨论的主题包括微观和量子现象的动力学描述，以及宏观现象的动力学描述。作为动力学方法论的最新示例，我们将使用动力学描述来研究复杂供应链的双曲流。该研究计划的理论和建模方面，在微观和宏观尺度上，将与基于动力学的数值方法相结合，以捕获“较小尺度的现象”。该提案背后的基本原理是及时努力解决现代应用数学中的几个重要问题。动力学理论并不新鲜。然而，动力学建模、动力学理论和相关领域已经有了许多重大发展。 数值方法，有可能对物理和社会科学新兴领域产生相当大的影响。拟议的努力将显着加强美国研究人员在这一重要领域进行尖端研究和培养新一代应用数学家方面可以发挥的主导作用。我们期望该项目通过对博士和博士后研究人员的高级培训以及提供跨学科互动的平台，为科学劳动力的发展做出贡献。 相关学科的研究人员。将通过协同合作来维持内部和外部互动，这些合作将在马里兰州（第一年）、法国和布朗（第二年）以及威斯康星州（第三年）举行的三个年度研讨会期间取得成果。国际会议将作为马里兰大学科学计算和数学建模中心 (CSCAMM) 组织的一系列跨学科研讨会的一部分举行。项目 研究人员将与 CSCAMM 的 DOE 多尺度等离子体动力学中心、爱荷华州立大学的 DOE Ames 实验室以及 UT Austin 的计算工程与科学研究所 (ICES) 合作。