ITR: Multiscale Analysis, Modeling, and Simulation

ITR：多尺度分析、建模和仿真本提案将在加州理工学院综合多尺度建模和仿真中心(CIMMS)的背景下运行，该中心的目的是在横跨物理、数学、信息和计算科学的广泛领域开发和促进多尺度创新。它提供的基础设施允许流体、材料和地球物理领域的专家与数学和计算分析方面的专家混合使用。这一建议的目的是：1.发展对多尺度相互作用的基本见解，特别是动力学的粗粒化及其如何影响幼稚的粗略尺度模拟的准确性；2.将分散在广泛学科中的关于多尺度相互作用的现有想法组合成一个连贯的整体，为广泛传播做好准备；3.编纂和开发系统技术，以在空间和时间尺度上准确地建模和模拟；4.在广泛的重要科学环境中系统地测试它们；5.开发和分发支持这些技术的快速和彻底传播的软件和相关基础设施；6.提高科学家、工程师、教育工作者和整个社会的意识，认识到准确的物理模型的重要性，多尺度层次结构作为简单建模的障碍的基本作用，以及存在可用于测量层次结构的强大的想法和方便的工具。两个关键主题贯穿并统一了科学研究：跨尺度建模和多尺度算法。他们反映了两组研究人员：一组开发建模技术，以获得跨尺度的物理和计算；另一组开发计算和信息技术基础设施，包括算法和其他数学工具，如脊线和曲线。第一年将专注于大分子和晶体材料，以及成像和数据分析。在未来几年，可能会包括其他领域，如地球物理、空间科学和生物学的其他主题，所有这些领域都提出了具有挑战性的多尺度问题。

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.