Kun Huang Wins Oden Institute 2024 Outstanding Dissertation Award

Kun Huang has been awarded the 2024 Outstanding Dissertation Award from the Oden Institute for Computational Engineering and Sciences. His dissertation, “A Numerical and Analytical Study of Kinetic Models for Particle-Wave Interaction in Plasmas,”  focuses on advancing numerical methods for solving the kinetic equation in plasma physics. 

Todd Arbogast, professor of mathematics and chair of the Graduate Studies Committee, said Kun’s dissertation was selected “for a beautiful blend of deep mathematical analysis and practical numerical algorithmic development for the kinetic modeling of particle-wave interactions in plasmas.”

Current challenges in the field stem from the limitations of existing models. While the fluid model lacks the capability to capture critical mechanisms, the kinetic equation, which is able to provide the desired microscopic description, is too costly to compute for inhomogeneous plasmas. In order to remedy this, Kun proposes a novel method that uses trajectorial average to reduce the dimension and relax time step restrictions, thus lowering the cost of computation. He has tested and validated his work on 3-dimensional systems with axisymmetry.

In addition, Kun, who is a student in the Applied Mathematics Group at the Institute, also offers a proof of existence of a weak solution to the equation that describes the particle wave interaction in plasmas in the one-dimensional case. 

Reflecting back on his dissertation process, Kun was a bit surprised by the final outcome. “I studied theoretical and applied mechanics in my undergraduate degree, and I came here originally to become a computational physicist. I did not expect to do the analysis part of my work.” He received his B.S. degree in Theoretical and Applied Mechanics from Peking University in 2019.

“Kun is a very creative, thoughtful individual. He has a great mind with extraordinary potential,” remarked Irene Gamba, professor of mathematics and Kun’s Ph.D. advisor. “Advising him has been a smooth ride which has enabled several innovative contributions in the areas of scientific computing, computational and analytical methods of high impact in rigorous non-linear quasilinear models in plasma physics as well as numerical analytical methods and providing novel computational schemes targeting approximations to mean field theories.” Gamba is core faculty at the Oden Institute and leads the Applied Mathematics Group.

Kun reflected on his experience with Gamba, an expert in both the numerical and analysis disciplines, saying, “I was affected by our discussions, and thought to think like a mathematician and try to see if I can make some contribution to the problem I am working on. It was unexpected, and it was not on the schedule. Out of interest we started working on it, and we got some pretty good results.” 

Looking ahead Kun’s plans to implement the algorithm for real-world applications especially to apply his algorithm to a problem that the plasma physics community is widely interested in and concerned about. “I am now working to really implement the algorithm for real-world application. Right now, we know the scheme is good, but we need to let the plasma physics community know about our contribution.” 

“Kun’s work is extraordinary as it brings new computational concepts and tools. He is clearly on a startup path to a stellar scientific career,” added Gamba.