Collaborative Research: A Unified Dynamical Systems-Simulation-Visualization Approach to Modeling and Analyzing Granular Flow Phenomena

协作研究：用于建模和分析颗粒流现象的统一动力系统-仿真-可视化方法

• 批准号: 1030326
• 负责人: Xavier Tricoche
• 金额: $ 22.74万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-01 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1030326&HistoricalAwards=false
• 关键词: Collaborative; Research; Unified; Dynamical; Systems

A novel interdisciplinary approach, combining the modern theory of dynamical systems, advanced simulation programs, and sophisticated visualization techniques shall be used to investigate complex granular flows having important engineering and industrial applications, with a focus on density relaxation and related phenomena such as jamming and force chains. Approximate continuum infinite-dimensional dynamical models shall be constructed using a method developed by the investigators as well as by taking more conventional long-wave limits. Once these models are constructed, they will be analyzed to determine such behaviors as stability, bifurcations and transitions to chaos. In addition, aspects of these granular flows such as jamming and force chains shall be rigorously characterized and analyzed in the context of nonlinear dynamics. The dynamical systems component will be extensively fine-tuned, tested and verified using a highly developed discrete simulation code and novel computer visualization techniques tailored especially for nonlinear dynamics. Both the code and the visualization techniques have already proven to be effective in predicting macroscopic properties in several granular flow regimes such as vibrating beds, and also in illuminating complex behavior in dynamical systems. The envisaged interplay among the dynamical systems, simulation code, and visualization components will be intimate and encompassing, so as to optimize the outcomes of the proposed project. Granular flow research is a data intensive activity that benefits from multiscale, cross-institutional collaborations, which necessitate extensive cyberinfrastructure (CI) development and reuse. A goal is the creation of algorithms and software for open source CI systems; facilitated via Purdue?s involvement in the TeraGrid Partnership and NJITs commitment to the development of widely accessible computational science resources. The dynamical systems/simulation/visualization (DSSV) approach will be applied as follows: a) Developing an effective paradigm for combining continuum approximations, simulations and visualization towards the goals of analyzing and predicting density relaxation related phenomena, and tailoring the outcomes for CI integration and reuse. b)Rigorously characterizing, analyzing and predicting such behaviors and artifacts as jamming and force chains for a range of granular flows in one, two and three dimensions, and developing novel methods for their detection. c) Proving results about the integrability of the continuum limits of integrable systems as well as new KAM type theorems for these systems; quantifying the accuracy of the approximations; and devising novel simulation and visualization schemes for studying the associated granular flows. This involves the blending of rigorous dynamical systems analysis, simulations and computer visualization to produce new insights and predictive tools for density relaxation, as well as the development of rigorous analysis strategies for jamming and force chain detection. A team comprised of a mathematician and a mechanical engineer at NJIT, and a computer scientist from Purdue, with extensive experience in mathematical modeling, dynamical systems analysis, granular flow simulations, and dynamically oriented visualization, shall conduct the research. This team has a successful track record of combining their expertise to solve outstanding problems related to the proposed project.The project will serve as a paradigm for obtaining effective approximate models for a wide range of granular flows of industrial importance. In addition, dissemination through publications, presentations at conferences, industrial sites and government laboratories, Web posting, CI reuse and the inclusion of outcomes in graduate courses will be done. Moreover, a substantial effort will be made to recruit highly qualified graduate and undergraduate students especially from underrepresented groups as research assistants on the project, thereby providing them with a unique opportunity to participate in leading-edge interdisciplinary research. In addition, a special issue of Mechanics Research Communications devoted to the research focus of this project is planned, and several outcomes from this project are slated to be included in a book on integrability analysis of infinite-dimensional dynamical systems now being completed.

一种新颖的跨学科方法，结合现代动力系统理论，先进的仿真程序和复杂的可视化技术来研究具有重要工程和工业应用的复杂颗粒流，重点关注密度松弛和相关现象，如干扰和力链。近似连续无限维动力学模型将使用研究者开发的方法以及采用更常规的长波极限来构建。一旦这些模型被构建，它们将被分析以确定诸如稳定性、分岔和向混沌过渡等行为。此外，在非线性动力学的背景下，这些颗粒流的各个方面，如堵塞和力链，需要进行严格的表征和分析。动力系统组件将使用高度开发的离散仿真代码和专门为非线性动力学量身定制的新颖计算机可视化技术进行广泛的微调，测试和验证。代码和可视化技术已经被证明是有效的预测宏观性质在一些颗粒流动的状态，如振动床，也在阐明动力系统的复杂行为。设想的动态系统、仿真代码和可视化组件之间的相互作用将是密切和包容的，以便优化所提议项目的结果。颗粒流研究是一项数据密集型活动，得益于多尺度、跨机构的合作，这需要广泛的网络基础设施（CI）开发和重用。目标是为开源CI系统创建算法和软件；通过普渡大学？我们对TeraGrid伙伴关系的参与以及njit对开发广泛可访问的计算科学资源的承诺。动态系统/仿真/可视化（DSSV）方法将应用如下：a)开发一种有效的范式，将连续统近似、仿真和可视化结合起来，以实现分析和预测密度松弛相关现象的目标，并为CI集成和重用定制结果。b)严格地描述、分析和预测这些行为和工件，如干扰和力链，用于一系列颗粒流的一维、二维和三维，并开发新的检测方法。c)证明了可积系统的连续统极限的可积性及其新的KAM型定理；量化近似值的准确性；并设计新的模拟和可视化方案来研究相关的颗粒流。这涉及严格的动力系统分析，模拟和计算机可视化的混合，为密度松弛产生新的见解和预测工具，以及为干扰和力链检测开发严格的分析策略。由NJIT的一名数学家和一名机械工程师以及普渡大学的一名计算机科学家组成的团队将进行研究，他们在数学建模、动力系统分析、颗粒流模拟和动态导向可视化方面具有丰富的经验。这个团队有一个成功的记录，结合他们的专业知识来解决与拟议项目相关的突出问题。该项目将作为一个范例，为具有工业重要性的大范围颗粒流获得有效的近似模型。此外，还将通过出版物进行传播、在会议、工业场所和政府实验室发表演讲、在网络上张贴、重新使用CI以及将成果纳入研究生课程。此外，将作出重大努力，特别是从代表性不足的群体中招募高素质的研究生和本科生担任该项目的研究助理，从而为他们提供参与前沿跨学科研究的独特机会。此外，计划在《力学研究通讯》上专刊一期专门讨论该项目的研究重点，并且该项目的一些成果将被列入一本关于无限维动力系统可积性分析的书中，目前正在完成。