Mathematical Sciences: Variational Methods and Applications

数学科学：变分方法及其应用

• 批准号: 9501148
• 负责人: Giles Auchmuty
• 金额: $ 6万
• 依托单位: University of Houston
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9501148&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Variational; Methods; Applications

9501148 Auchmuty This project will involve the investigation of a number of problems in classical field theories, quantum chemistry, and the theory of rotating self- gravitating fluids. Each of these problems involves non-standard variational principles and it is intended to develop the requisite variational analysis and in some cases also look at numerical problems involved in the simulation of solutions. These problems often are non-convex and special efforts will be devoted to studying certain duality theories and dual problems for these principles. Under this project, the investigator plans to develop new methods for describing fields in various classical continuum theories. This will answer some foundational questions in fluid mechanics, electromagnetic field theory and some areas of materials science. It is also planned to investigate the theory of Hartree-Fock models which are basic models in quantum chemistry and also some hydrodynamical models of planets and stars. For these problems, the major interest is in developing good numerical algorithms for simulating solutions. The proposed algorithms are based on control theoretic ideas and appear to be both more stable and much more efficient than the methods currently being used for simulation of these problems.

小行星9501148 该项目将涉及调查一些问题， 经典场论、量子化学和旋转自引力流体理论。 这些问题都涉及到非标准 变分原理，并打算制定必要的变分 分析，并在某些情况下也看看数字问题涉及的 模拟解决方案。 这些问题往往是非凸的和特殊的 努力将致力于研究某些对偶理论和对偶 这些原则的问题。 在这个项目下，研究人员计划开发新的方法， 描述各种经典连续统理论中的场。 这将回答 流体力学、电磁场、 理论和材料科学的一些领域。 还计划调查 Hartree-Fock模型是量子力学的基本模型， 化学以及行星和恒星的流体动力学模型。 为 这些问题，主要的兴趣是在发展良好的数值 模拟解决方案的算法。 所提出的算法是基于 控制理论的思想，似乎都更稳定， 比目前用于模拟这些的方法更有效 问题