SCREMS: Multiscale Computing in Astrophysics, Geophysics, Hydrodynamics, Kinetic and Quantum Applications

SCREMS：天体物理学、地球物理学、流体动力学、动力学和量子应用中的多尺度计算

• 批准号: 0532085
• 负责人: Fabian Waleffe
• 金额: $ 7.3万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-09-15 至 2006-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0532085&HistoricalAwards=false
• 关键词: SCREMS; Multiscale; Computing; Astrophysics; Geophysics

This award supports the purchase of a mid-size computationalsystem that will support computational mathematics researchby four faculty members and their student research associatesin the department of Mathematics at the University of Wisconsin-Madison.The four projects are in distinct areas of science. One project aims to develop and test computational methods tostudy how mass is accreted onto (sucked into) black holes. Black holes are massive compact objects that induce such stronggravity that not even light can escape them andoccur in our universe in several forms includingas super-massive black holes at the center of galaxies andat the scale of stars in the form of x-ray binaries.The detailed physics of the accretion process andthe resulting dynamics are not yet fully understood.The goal of this project is the developmentof accurate and efficient computational methods for furtherunderstanding of these processes.A second project is to study the impact of `small scale' physical effects that have not been explicitly included in currentcomputational models of the atmosphere, oceans and the climate.Those effects are either ignored for lack of computer power,even on today's -- and tomorrow's-- state of the art supercomputers,or are indirectly included through crude, semi-empirical formulas.Computer calculations and theory on `simplified'mathematical models (i.e. the 3D Boussinesq equations for rotatingand stratified flow) of relevance to weather and climate modeling, haveshown that these small scales effects can be very significantand contrary to the semi-empirical formulas.A third project aims to develop and test numerical methods that canefficiently deal with multiscale problems in quantum and classicalmechanics. The study of these problems is central to many areas ofmathematical physics and modern technology (e.g. Nanoscience,plasmas, micro-electro-mechanical-systems [MEMS],...). In recentyears we have made significant progress in devising robust andefficient numerical methods to compute multivalued solutions thatarise in quantum mechanics and geometric optics. In this proposalthat work will be extended to compute solutions with interfacesthat couple classical and quantum regimes. The goal is to provide a semiclassical approach that is slightly more expensive than a classical approach but much less expensive than a quantum simulation based on solving directly the Schrodinger equation. One particularly important application is the nano-scale quantum dots that are a standard product of modern semiconductor manufacturing procedures.The fourth project continues the study of recurrent unstable coherentstates that have been discovered in the flow of simple fluids suchas air or water flowing in pipes, channels or over airplane wings,around boats, cars or other vessels. Such flows are typically in a complex`turbulent' state characterized by apparently random eddy motions,but the newly discovered coherent states (i.e. structured and well-organized)capture many key features and characteristics of turbulent flows.These discoveries suggest that some deep theoretical ideas that havebeen successful for small systems in `chaos' theory may be appliedand extended to much more complex fluid systems. One aim of the projectis to provide a catalog of key unstable coherent states that might beconsidered a `turbulence genome project'.

该奖项支持购买一个中型计算系统，该系统将支持威斯康星大学麦迪逊分校数学系的四名教师及其学生研究助理的计算数学研究。这四个项目分别在不同的科学领域。其中一个项目旨在开发和测试计算方法，以研究质量是如何被吸积到黑洞上的。黑洞是一种质量很大的致密物体，它产生的引力非常强，甚至连光都无法逃脱。黑洞以几种形式存在于我们的宇宙中，包括星系中心的超大质量黑洞和恒星尺度的x-射线双星。吸积过程的详细物理过程和由此产生的动力学尚未完全理解。该项目的目标是发展精确和有效的计算方法第二个项目是研究“小尺度”物理效应的影响，这些效应没有明确地包括在当前的大气、海洋和气候计算模型中。这些效应要么由于缺乏计算机能力而被忽略，即使在今天和明天的最先进的超级计算机上也是如此，要么通过粗略的计算间接地包括在内，半经验公式.计算机计算和“简化”数学模型理论（即三维Boussinesq方程的湍流和分层流）的天气和气候模拟的相关性，已经表明，这些小规模的影响可以是非常显着的，相反的半-第三个项目旨在开发和测试数值方法，可以有效地处理量子和经典力学中的多尺度问题。对这些问题的研究是数学物理和现代技术（如纳米科学，等离子体，微机电系统[MEMS]，.）的许多领域的核心。近年来，我们在设计稳健有效的数值方法来计算量子力学和几何光学中出现的多值解方面取得了重大进展. 在这个proposalthat工作将扩展到计算解决方案的接口耦合经典和量子制度。我们的目标是提供一个半经典的方法，是稍微昂贵的比经典的方法，但便宜得多的量子模拟的基础上直接解决薛定谔方程。其中一个特别重要的应用是纳米级量子点，这是现代半导体制造过程的标准产品。第四个项目继续研究在简单流体流动中发现的周期性不稳定相干态，例如在管道、通道或飞机机翼上流动的空气或水，在船只、汽车或其他船只周围流动。这种流动通常处于一种复杂的“湍流”状态，其特征是明显的随机涡流运动，但新发现的相干态（即结构化和组织良好）捕捉了湍流的许多关键特征和特性。这些发现表明，在“混沌”理论中成功用于小系统的一些深刻的理论思想可以应用并扩展到更复杂的流体系统。该项目的一个目标是提供一个关键的不稳定相干态目录，可以考虑将其作为一个“湍流基因组项目”。