Optimal Weighted and Constrained Energy Configurations and Applications

最佳加权和约束能量配置和应用

• 批准号: 1109266
• 负责人: Douglas Hardin
• 金额: $ 24.91万
• 依托单位: Vanderbilt University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-09-15 至 2015-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1109266&HistoricalAwards=false
• 关键词: Optimal; Weighted; Constrained; Energy; Configurations

HardinDMS-1109266 The investigator and his colleagues study the theory and applications of discrete minimum energy problems that are of significance in the discretization of compact metric spaces. By utilizing minimal weighted Riesz energy configurations, one can generate sequences of points on surfaces that approximate prescribed density functions on that surface. Such constructions have a myriad of possible applications to the physical and biological sciences. Specifically, the team is studying (i) separation and fill-radius estimates for optimal N-point weighted energy configurations; (ii) geometrical properties of optimal and near optimal weighted energy configurations on 2-dimensional surfaces; (iii) algorithms for the fast generation of points distributed on a manifold in accordance with a prescribed density; (iv) properties of greedy energy points; and (v) near optimal discretizations for problems of importance in geophysical applications. The investigator and his colleagues study stable (minimum energy) states of charged particle configurations on curved surfaces and solid materials, especially when such particles are restricted in density or under the influence of external forces. One goal of the project is to determine efficient numerical methods for the generation of optimal or near optimal distributions of point charges that can be used to help understand the convection of the Earth's mantle, for the modeling of the geodynamo, and to gain a better determination of the Earth's gravitational field. This project addresses in several different contexts the fundamental problem of how best to convert from analog to digital.

HardIndms-11109266研究者及其同事研究了离散的最低能量问题的理论和应用，这些问题在紧凑型公制空间的离散化中具有重要意义。 通过利用最小的加权Riesz能量构型，可以在表面上近似规定密度函数的表面上生成点序列。 这种结构在物理和生物科学上有无数的可能应用。 具体而言，该团队正在研究（i）分离和填充拉迪乌斯的估计值，以实现最佳的N点加权能量构型； （ii）在二维表面上最佳和接近最佳加权能量构型的几何特性； （iii）根据规定密度分布在多种多样的快速生成点的算法； （iv）贪婪能量点的特性； （v）几乎是地球物理应用中重要问题的最佳离散化。 研究者及其同事研究稳定的（最小能量）状态在弯曲表面和固体材料上进行带电的颗粒构型，尤其是当这种颗粒受到密度或外部力的影响时。 该项目的一个目标是确定可用于生成最佳或接近最佳分布的点电荷的有效数值方法，这些分布可用于帮助了解地球地幔的对流，对地球的对流的对流，并更好地确定地球的重力场。 该项目在几种不同的情况下解决了如何最好地从模拟转换为数字的基本问题。