Computing Invariant Manifolds and Assimilating Data in Tipping Problems

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。Emmanuel Fleurantin被授予该奖学金，在位于查佩尔山的北卡罗来纳州大学的文艺复兴计算研究所（RENCI）进行数学科学的研究和教育计划，包括在赞助科学家Christopher K.琼斯该项目将开发新的计算工具，以处理复杂动力系统中的倾翻现象，例如气候子系统中的突然突变。沿着这项研究，Fleurantin将启动培训和推广工作，以扩大代表性不足的少数民族在数学科学中的参与。该项目将通过以下方面的研究，在费率和噪音引起的小费背后的数学中开发新理论：1）计算具有变速率参数的紧致系统中基吸引子和复盆边界的稳定/不稳定流形及其连接轨道，2）通过连接轨道的最可能路径捕获噪声促进倾翻的影响，3）理解在倾翻点问题中产生的复杂系统中歧管交叉点的横向性。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This award is made as part of the FY 2021 Mathematical and Physical Sciences Ascending Postdoctoral Research Fellowships, MPS-Ascend Program. Emmanuel Fleurantin is awarded this fellowship to conduct a program of research and education at the Renaissance Computing Institute (RENCI) located at the University of North Carolina (UNC) at Chapel Hill in the mathematical sciences, including applications to other disciplines, under the mentorship of the sponsoring scientist Prof. Christopher K. Jones. This project will develop new computational tools concerning tipping phenomena in complex dynamical systems, such as sudden abrupt changes in a climate subsystem. Along with this research, Fleurantin will initiate training and outreach efforts to broaden participation of Underrepresented Minorities in mathematical sciences.The project will develop new theory in the mathematics behind rate and noise induced tipping through research on: 1) computations of stable/unstable manifolds of base attractors and complex basin boundaries and their connecting orbits in a compactified system with a varying rate parameter, 2) capturing the effect of noise-facilitated tipping through a most probable path connecting orbit, and 3) understanding transversality of intersections of manifolds in the complex systems arising in tipping point problems.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.