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

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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 Purdues 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.