McKenzie Black, Changhui Tan. Asymptotic behaviors for the compressible Euler system with nonlinear velocity alignment. Journal of Differential Equations, Volume 380, pp. 198-227 (2024).
Abstract: We consider the pressureless compressible Euler system with a family of nonlinear velocity alignment. The system is a nonlinear extension of the Euler-alignment system in collective dynamics. We show the asymptotic emergent phenomena of the system: alignment and flocking. Different types of nonlinearity and nonlocal communication protocols are investigated, resulting in a variety of different asymptotic behaviors.
This work is supported by NSF grant DMS #2108264 and the U of SC SPARC grant.
Talks & Presentations
Nonlocal Dynamics and Emergent Phenomena in the Pressureless Compressible Euler System with Nonlinear Velocity Alignment, FIU Applied Mathematics Seminar, Florida International University, October 2023
Asymptotic Behaviors For The Compressible Euler System With Nonlinear Velocity Alignment (Poster), Discover USC, April 2023 [Pictured on the top right]
Asymptotic Behaviors For The Compressible Euler System With Nonlinear Velocity Alignment , SIAM Southeastern Atlantic Section Annual Meeting, Virginia Tech, March 2023 (Awarded SIAM SEAS Student Award) [Picture in the bottom right]
Do Birds of a Feather Flock Together? An Overview of Alignment Models, Graduate Colloquium, University of South Carolina, March 2023
Asymptotic Behaviors For The Compressible Euler System With Nonlinear Velocity Alignment , Southeastern-Atlantic Regional Conference on Differential Equations, North Carolina State University, November 2022
It’s a bird. It’s a plane. No, it’s an alignment model!, Applied and Computational (ACM) Student Seminar, University of South Carolina, October 2021.