ACM Seminar
The Applied and Computational Mathematics (ACM) seminar series since 2020.
Click HERE for the schedule.
Efficient, positive, and energy stable schemes for Poisson-Nernst-Planck systems
Speaker: Hailiang Liu (Iowa State University)
We are concerned with positive and energy-dissipating schemes for solving the time-dependent system of Poisson-Nernst-Planck (PNP) equations, which has found much use in the modeling of biological membrane channels and semiconductor devices. As a gradient flow in density space, this strongly coupled system of nonlinear equations can take long time evolution to reach steady states. Hence, designing efficient and stable methods is highly desirable. In this talk we shall present a class of methods with structure-preserving properties for the PNP system, and review advances around related models such as the quantum diffusion equation.
Time: February 21, 2020 2:30pm-3:30pm
Location: LC317R
Host: Changhui Tan
Mathematical and numerical analysis to variable-order mobile-immobile time-fractional diffusion equations
Speaker: Xiangcheng Zheng (University of South Carolina)
We proved the wellposedness of variable-order mobile-immobile time-fractional diffusion equations and the regularity of their solutions. Optimal-order finite element approximation was presented and analyzed. Numerical experiments were carried out for demonstration.
Time: January 31, 2020 2:30pm-3:30pm
Location: LC317R
Lagrangian Front Tracking and Applications to Conservation Law, Fluid Mixing, and Phase Transition Problems
Speaker: Xiaolin Li (Stony Brook University)
In this talk, I will review the history of the Lagrangian front tracking method and the computational platform built on this methodology. I will review the front tracking in the study of fluid interface instabilities, including Rayleigh-Taylor instability, Richtmyer Meshkov instability and fluid mixing induced by these instabilities. I will also introduce a fully conservative front tracking scheme and its application in the phase transition problem.
Time: March 20, 2020 2:30pm-3:30pm
Location: LC317R
Host: Xinfeng Liu
Traveling Wave of Gray-Scott System: Results and Perspective
Speaker: Yuanwei Qi (University of Central Florida)
In this talk, I shall report some recent progress on the existence and multiplicity of traveling waves to one of the most important models in Turing Pattern Formation. In addition, I shall pose some questions which are wide open which demand new ideas and fresh approaches. This is a joint-work with Xinfu Chen et al.
Time: January 17, 2020 2:30pm-3:30pm
Location: LC317R
Host: Changhui Tan