School of Mathematical Sciences Academic Report [2025] No. 033  

(High-Level University Construction Series Report No. 1055)  

Lecture Title: A threshold dislocation dynamics method

Speaker: Qin Xiaoxue (Lecturer, Shanghai University)  

Date & Time: 10:30–11:30 AM, Thursday, May 8, 2025  

Venue: Room 501, Huixing Building  

Abstract: We propose an efficient threshold dynamics method for dislocation dynamics in a slip plane. We show that this proposed threshold dislocation dynamics method is able to give two correct leading orders in dislocation velocity, including both the O(logε) local curvature force and the O(1) nonlocal force due to the long-range stress field generated by the dislocations, where ε is the dislocation core size. This is different from the available threshold dynamics methods in the literature which only give the leading order local velocities associated with mean curvature or its anisotropic generalizations of the moving fronts. We also propose a numerical method based on spatial variable stretching to overcome the numerical limitations brought by physical settings in this threshold dislocation dynamics method. Specifically, this variable stretching method is able to correct the mobility and to rescale the velocity, which can be applied generally to any threshold dynamics method. We validate the proposed threshold dislocation dynamics method by numerical simulations of various motions and interaction of dislocations.

Biography: Dr. Qin Xiaoxue is a lecturer and master's supervisor in the Department of Mathematics at Shanghai University, and is recognized as a high-level overseas talent in Shanghai. She graduated from the Department of Mathematics at the Hong Kong University of Science and Technology with a Ph.D. in Science in August 2020. From September 2020 to August 2022, she engaged in postdoctoral research in the Department of Mathematics at the Hong Kong University of Science and Technology. Her main research focuses on the mathematical modeling of defects in crystalline materials and efficient numerical algorithms. In recent years, she has achieved a series of innovative results in the fields of computational mathematics and scientific computing, with related research published in journals such as SIAM Journal on Multiscale Modeling and Simulation (SIAM MMS), Journal of Scientific Computing (JSC), and Communications in Computational Physics (CICP).  

All faculty and students are welcome to attend!

Invited by: Zhang Luchan

School of Mathematical Sciences  

May 7, 2025