5 papers
From microscopic social force models to macroscopic continuum models for pedestrian flow
Liangze Yang, Hui Yu, Jie Du
The pedestrian flow is one of the most complex systems, involving large populations of interacting agents. Models at microscopic and macroscopic scales offer different advantages f…
Phase transition of the kinetic Justh-Krishnaprasad type model for nematic alignment
Seung-Yeal Ha, Hui Yu, Baige Zhou
We present a stochastic Justh-Krishnaprasad flocking model and study the phase transition of the Vlasov-McKean-Fokker-Planck (VMFP) equation, which can be obtained in the mean-fiel…
Concentration of cones in the Alt-Phillips problem
Ovidiu Savin, Hui Yu
We study minimizing cones in the Alt-Phillips problem when the exponent γ is close to 1. When γ converges to 1, we show that the cones concentrate around symmetric solutions to the…
Stable and Minimizing Cones in the Alt-Phillips Problem
Ovidiu Savin, Hui Yu
We study homogeneous solutions to the Alt-Phillips problem when the exponent is close to 1. In dimension , we show that the radial cone is minimizing when is close t…
Positivity-preserving and energy-dissipating discontinuous Galerkin methods for nonlinear nonlocal Fokker-Planck equations
José A. Carrillo, Hailiang Liu, Hui Yu
This paper is concerned with structure-preserving numerical approximations for a class of nonlinear nonlocal Fokker-Planck equations, which admit a gradient flow structure and find…