Dynamical and Computer-Assisted Methods Applied to Hamiltonian Systems

应用于哈密顿系统的动力学和计算机辅助方法

基本信息

批准号：
2138090
负责人：
Wai Ting Lam
金额：
$ 30万
依托单位：
Lam, Wai Ting
依托单位国家：
美国
项目类别：
Fellowship Award
财政年份：
2021
资助国家：
美国
起止时间：
2021-10-01 至 2024-09-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2138090&HistoricalAwards=false
关键词：
Dynamical Computer Assisted Methods Applied

项目摘要

This award is made as part of the FY 2021 Mathematical and Physical Sciences Ascending Postdoctoral Research Fellowships, MPS-Ascend Program. Wai-Ting Lam is awarded this fellowship to conduct a program of research and education at Florida Atlantic University (FAU) in the mathematical sciences, including applications to other disciplines, under the mentorship of the sponsoring scientist J.D. Mireles-James. This is a research project aimed at the study of dynamics of some celestial mechanics models. In particular, the principal investigator (PI) will investigate a restricted four-body problem arising in modeling dynamics of a spacecraft or moonlet in a vicinity of a Jupiter Trojan asteroid. The PI will use variational methods to obtain realistic physical models for the gravitational potential of irregularly-shaped asteroids within certain families of shapes that are commonly used to model the shapes of asteroids. Along with this research, the PI will be involved in the activities to broaden participation of Underrepresented Minorities in mathematical sciences through the recruitment and retention of students at FAU, a Hispanic Serving Institution, as well as through collaboration with American Indian Science and Engineering society (Florida).In this project the PI will develop advanced numerical algorithms and computer assisted proofs that will lead to a more detailed, rigorous descriptions of the dynamics in a variety of realistic settings. Resonant orbits in the vicinity of an irregularly shaped body will be investigated, and periodic and quasi-periodic orbits, hyperbolic invariant manifolds, and transverse intersections between such manifolds will be obtained via rigorous computations. Such geometric structures will be used to prove the existence of trajectories whose energy undergoes a significant change over time, thus constituting a verification of the Arnold diffusion in a concrete model.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该奖项是 2021 财年数学和物理科学提升博士后研究奖学金 MPS-Ascend 计划的一部分。林伟廷 (Wai-Ting Lam) 获得这项奖学金，以便在赞助科学家 J.D. Mireles-James 的指导下，在佛罗里达大西洋大学 (FAU) 开展数学科学领域的研究和教育项目，包括在其他学科中的应用。这是一个旨在研究一些天体力学模型动力学的研究项目。特别是，首席研究员（PI）将研究木星特洛伊小行星附近的航天器或小卫星的动力学建模中出现的受限四体问题。 PI 将使用变分方法来获取通常用于模拟小行星形状的某些形状族中不规则形状小行星的引力势的真实物理模型。除了这项研究之外，PI 将通过在拉美裔服务机构 FAU 招募和保留学生以及与美洲印第安人科学与工程学会合作，参与扩大少数族裔对数学科学的参与的活动（佛罗里达州）。在这个项目中，PI 将开发先进的数值算法和计算机辅助证明，从而对各种现实环境中的动力学进行更详细、更严格的描述。将研究不规则形状物体附近的共振轨道，并通过严格的计算获得周期和准周期轨道、双曲不变流形以及流形之间的横向交集。这种几何结构将用于证明能量随时间发生显着变化的轨迹的存在，从而构成对具体模型中阿诺德扩散的验证。该奖项反映了 NSF 的法定使命，并通过使用评估认为值得支持基金会的智力价值和更广泛的影响审查标准。