Project Info

Active Subspaces in Landau Damping

Active subspace analysis is an emerging computational tool to identify and exploit the most important directions in the space of a model’s input parameters. These directions depend inherently on the quantity of interest, which can be represented as a function from input parameters to model outputs. As countless models in the study of plasmas depend upon potentially unknown parameter values, active subspaces can be useful tools to understand how certain physical phenomena depend upon fluctuations in these variables. This project will create new computational methods to study the dependence of the nonlinear rate of Landau damping in a collisionless plasma modeled by the Vlasov-Poisson system, the most-widely used electrostatic model in the study of plasma dynamics.

1. My website:
https://sites.google.com/view/spcsmsite

2. A strong reference concerning the numerical simulation of plasmas:
https://www.amazon.com/Plasma-Physics-via-Computer-Simulation/dp/0750310251
http://www.phy.pku.edu.cn/~lei/cp/ppvcs.pdf

3. A review of current Active Subspace methods:
https://epubs.siam.org/doi/book/10.1137/1.9781611973860

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Student Preparation

Qualifications

The student should be proficient in computational science and applied mathematical modeling with a strong background in the numerical solution of differential equations, especially using Matlab, Fortran, and Python.

Time Commitment

25-30 hours/month

Skills/Techniques Gained

The student will hone his or her computational and programming skills while learning about state-of-the-art methods and algorithms in the field of uncertainty quantification, as well as, basic mathematical modeling of physical phenomena in plasma dynamics. A paper will likely be submitted to the journal “Physics of Plasmas” at the conclusion of the undergraduate research experience.

Mentoring Plan

The student will meet weekly with me and my research group (currently, 2 PhD students). Additionally, I will hold a separate one-on-one meeting with the student every two weeks. In addition to standard research mentoring regarding the specifics of the project, I will also work with the student to develop their communication, networking, and presentation skills. In particular, we will work together to create a talk that he or she will present at one or two local or national research conferences, such as the Pikes Peak Regional Undergraduate Mathematics Conference (held annually at UCCS), the SIAM Front Range Applied Mathematics Conference (held annually at CU Denver), or the MAA Mathfest (held annually – 2019 in Cincinnati).