ITR: Multiscale Analysis, Modeling, and Simulation

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ITR: Multi-scale Analysis, Modeling, and SimulationThis proposal will operate in the context of the Caltech Center for Integrative Multi-scale Modeling and Simulation (CIMMS) whose purpose is to develop, and foster multi-scale innovations in a wide range of areas spanning the physical, mathematical, information, and computational sciences. It provides the infrastructure that allows for the mix of domain experts from fluids, materials and geophysics with specialists in mathematical and computational analysis. This proposal aims to:1. Develop fundamental insights into multi-scale interactions, especially the coarse graining of dynamics and how they affect the accuracy of naive coarse-scale simulations; 2. Assemble existing ideas about multi-scale interactions scattered across a wide range of disciplines into a coherent whole, ready for broad dissemination;3. Codify and develop systematic techniques to accurately model and simulate across space and time scales;4. To test them systematically in a wide range of important scientific settings;5. Develop and distribute software and associated infrastructure supporting the rapid and thorough diffusion of these techniques;6. Raise consciousness among scientists, engineers, educators, and society in general about the importance of accurate physical modeling, the fundamental role of the multi-scale hierarchy as an obstacle to naive modeling and the existence of powerful ideas and convenient tools available to scale the hierarchy.Overarching Research Themes. Two key themes cut across and unifying the scientific research: modeling across scales, and multi-scale algorithms. They reflect two groups of researchers: those developing modeling techniques to get the physics and computations right across scales and those who develop the computational and information technology infrastructure, including algorithms and other mathematical tools, such as ridgelets and curvelets. The first years will concentrate on macromolecules and crystalline materials, and imaging and data analysis. In future years, other areas may be included, such as geophysics, space sciences and additional topics in biology, all of which present challenging multi-scale problems.