Computational methods for materials science, high frequency wave propagation, and quantum mechanics

材料科学、高频波传播和量子力学的计算方法

• 批准号: 1417053
• 负责人: Smadar Karni
• 金额: $ 35.3万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-07-01 至 2019-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1417053&HistoricalAwards=false
• 关键词: Computational; methods; materials; science; frequency

This project involves modeling, simulation, and efficient computation of technologically important and intellectually interesting problems. In the area of material science the research investigates two new off-lattice methods for the computational modeling of the evolution of crystalline materials in which the lattice structure may change. This is needed when defect formation is important, for example. The project will also address the efficient computation of high frequency wave propagation in nonhomogeneous materials. This classic problem in computational science and applied mathematics has attracted much attention because it is useful for problems in geophysics and optics and it is a mathematically rich problem requiring insight into the behavior of wave equation. The PI also plans to develop numerical methods for studying quantum dynamics of molecules. The importance of quantum mechanics in understanding chemical reactions cannot be overstated, and this research offers the potential of providing detailed insight and predictive power for a variety of photo-induced chemical reactions. The project also involves training of graduate students.The first project involves developement of off-lattice computation models for the evolution of crystalline materials. In one case, the PI plans to formulate an off-lattice kinetic Monte Carlo method for the simulation of epitaxial growth and in other an alternative to the phase field crystal method is proposed. In both cases the underlying energy of the system is a suitable intermolecular potential. In addition, in both cases one will be computing on time scales orders of magnitude larger than molecular dynamics. Another project involves the computation of high frequency solutions of the wave equation. The goal is to exploit the asymptotic structure of high frequency solutions to develop efficient numerical methods that do not have the errors that result from asymptotic approximations that occur when one uses methods that rely on geometrical optics or Gaussian beams. The PI also plans to develop numerical methods for the studying quantum dynamics of molecules when conical intersections play an important role. A full quantum mechanical treatment would mean solving the Schroedinger equation in 20 to 30 dimensions even for small molecules. Our plan is to identify the important modes by using surface hopping methods as a probe of the energy landscape. A full quantum treatment can then be accurately obtained just using this smaller set of modes.

该项目涉及建模，仿真和技术上重要和智力上有趣的问题的有效计算。在材料科学领域，研究了两种新的非晶格方法，用于晶格结构可能发生变化的晶体材料演化的计算建模。例如，当缺陷形成很重要时，就需要这样做。该项目还将解决高频波在非均匀材料中传播的有效计算问题。这是计算科学和应用数学中的经典问题，因为它对物理学和光学中的问题很有用，并且它是一个数学上丰富的问题，需要深入了解波动方程的行为，因此引起了人们的广泛关注。PI还计划开发研究分子量子动力学的数值方法。量子力学在理解化学反应中的重要性怎么强调都不过分，这项研究提供了为各种光诱导化学反应提供详细见解和预测能力的潜力。第一个项目是发展非晶格计算模型，以研究晶体材料的演化。 在一种情况下，PI计划制定一个非晶格动力学蒙特卡罗方法的模拟外延生长，并在其他替代相场晶体方法提出。 在这两种情况下，系统的基本能量都是合适的分子间势。 此外，在这两种情况下，人们将在比分子动力学大的数量级的时间尺度上进行计算。另一个项目涉及波动方程高频解的计算。我们的目标是利用高频解的渐近结构来开发有效的数值方法，这些方法不具有当使用依赖于几何光学或高斯光束的方法时发生的渐近近似的误差。PI还计划开发数值方法来研究圆锥相交发挥重要作用时的分子量子动力学。一个完整的量子力学处理将意味着解决薛定谔方程在20至30维，即使是小分子。我们的计划是通过使用表面跳跃方法作为能量景观的探针来识别重要的模式。然后，仅使用这组较小的模式就可以精确地获得完整的量子处理。