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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.

该奖项是作为2021财年数学和物理科学上升博士后研究奖学金，MPS-Ascend计划的一部分。林伟婷获颁发此奖学金，在赞助科学家J.D.的指导下，在佛罗里达大西洋大学（FAU）进行数学科学的研究和教育计划，包括其他学科的应用。米勒斯-詹姆斯这是一个研究天体力学模型动力学的课题。特别是，首席研究员（PI）将调查在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限制性四体问题。PI将使用变分方法来获得不规则形状小行星引力势的现实物理模型，这些形状通常用于模拟小行星形状。沿着这项研究，PI将参与扩大代表性不足的少数民族参与数学科学的活动，方法是在FAU（一个西班牙裔服务机构）招募和留住学生，以及通过与美国印第安人科学和工程学会（佛罗里达）的合作。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，在各种现实环境中对动态的严格描述。共振轨道附近的不规则形状的身体将被调查，和周期和准周期轨道，双曲不变流形，和横向交叉等流形之间将通过严格的计算获得。这种几何结构将被用来证明其能量随时间发生显著变化的轨迹的存在，从而构成了阿诺德扩散在一个具体的模型中的验证。该奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。