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

一种新的跨学科方法，结合现代动力系统理论，先进的模拟程序和先进的可视化技术，将被用于研究具有重要工程和工业应用的复杂颗粒流动，重点是密度松弛和相关现象，如干扰和力链。应使用研究人员开发的方法以及采用更常规的长波极限来构建近似的连续介质无限维动力学模型。一旦构建了这些模型，将对它们进行分析，以确定稳定性、分叉和向混沌的转变等行为。此外，应在非线性动力学的背景下严格描述和分析这些颗粒流的各个方面，如干扰和力链。动力系统组件将使用高度开发的离散模拟代码和专门为非线性动力学量身定做的新型计算机可视化技术进行广泛的微调、测试和验证。该程序和可视化技术已经被证明在预测几种颗粒流态的宏观性质方面是有效的，例如振动床，以及在揭示动力系统中的复杂行为方面。所设想的动力系统、模拟代码和可视化组件之间的相互作用将是密切和包容的，从而优化拟议项目的成果。颗粒流研究是一项数据密集型活动，受益于多规模、跨机构的合作，这需要广泛的网络基础设施(CI)开发和重用。一个目标是为开源CI系统创建算法和软件；通过普渡？S参与TeraGrid合作伙伴关系和NJIT致力于开发广泛可用的计算科学资源来促进。动力系统/模拟/可视化(DSSV)方法将被应用如下：a)开发一种有效的范例，将连续统近似、模拟和可视化结合起来，以实现分析和预测与密度松弛相关的现象的目标，并为CI整合和再利用量身定制结果。B)严格描述、分析和预测一维、二维和三维颗粒流的干扰和力链等行为和伪影，并开发新的检测方法。C)证明了关于可积系统的连续统极限的可积性的结果以及这些系统的新的Kam型定理；量化了近似的精度；设计了新的模拟和可视化方案来研究相关的颗粒流。这涉及将严格的动力系统分析、模拟和计算机可视化相结合，以产生用于密度松弛的新见解和预测工具，以及开发用于干扰和力链检测的严格分析策略。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这项研究，他们在数学建模、动力系统分析、颗粒流模拟和面向动态的可视化方面具有丰富的经验。这个团队在结合他们的专业知识来解决与拟议项目相关的突出问题方面有着成功的记录。该项目将作为一个范例，为各种具有工业重要性的颗粒流获得有效的近似模型。此外，还将通过出版物、在会议、工业场所和政府实验室的演讲、网络张贴、传播信息的再利用以及将成果纳入研究生课程等方式进行传播。此外，将作出重大努力，特别是从代表性不足的群体中招聘高素质的研究生和本科生作为该项目的研究助理，从而为他们提供参与前沿跨学科研究的独特机会。此外，还计划出版一期《力学研究通讯》，专门讨论这一项目的研究重点，该项目的几个成果将被收录在一本关于无限维动力系统的可积性分析的书中，该书现已完成。

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.