ITR: Multiscale Analysis, Modeling, and Simulation

ITR：多尺度分析、建模和仿真该提案将在加州理工学院综合多尺度建模和仿真中心（CIMMS）的背景下进行，该中心的目的是在跨越物理、数学、信息和计算科学的广泛领域发展和促进多尺度创新。它为流体、材料和地球物理领域的专家与数学和计算分析专家提供了基础设施。本提案旨在：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度以及它们如何影响朴素粗尺度模拟的准确性；2. 2 .将分散在广泛学科范围内的关于多尺度相互作用的现有想法整合成一个连贯的整体，以便广泛传播；编纂和发展系统的技术，以准确地模拟和模拟跨空间和时间尺度；4 .在广泛的重要科学环境中对其进行系统的测试；开发和分发软件和相关的基础设施，以支持这些技术的快速和彻底的传播；提高科学家、工程师、教育工作者和整个社会对准确物理建模的重要性的认识，多尺度层次结构作为幼稚建模障碍的基本作用，以及可用于扩展层次结构的强大思想和方便工具的存在。总体研究主题。跨越和统一科学研究的两个关键主题：跨尺度建模和多尺度算法。它们反映了两组研究人员：那些开发建模技术以获得跨尺度的物理和计算的人，以及那些开发计算和信息技术基础设施的人，包括算法和其他数学工具，如脊波和曲线。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，其他领域可能包括，如地球物理学，空间科学和生物学的附加主题，所有这些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.