4 papers
Nonlocal modeling of opinion alignment and environmental feedback: Spatial aggregation and non-consensus patterns
Rui Wang, Yunfeng Xiong, Zhengru Zhang +1
The formation of public opinion in modern information environments is shaped by the interplay between social conformity and information exposure. While social interactions promote…
Efficient structure-preserving scheme for chemotaxis PDE system with singular sensitivity in crime and epidemic modeling
Rui Wang, Yunfeng Xiong, Zhengru Zhang
The chemotaxis PDE system with singular sensitivity was originally proposed by Short et al. (Math. Mod. Meth. Appl. Sci., 2008) as the continuum limit of a biased random walk model…
Beyond quantum mean-field approximation: Phase-space formulation of many-body time-dependent density functional theory and efficient spectral approximations
Jiong-Hang Liang, Yunfeng Xiong
As a universal quantum mechanical approach to the dynamical many-body problem, the time-dependent density functional theory (TDDFT) might be inadequate to describe crucial observab…
An efficient stochastic particle method for high-dimensional nonlinear PDEs
Zhengyang Lei, Sihong Shao, Yunfeng Xiong
Numerical resolution of high-dimensional nonlinear PDEs remains a huge challenge due to the curse of dimensionality. Starting from the weak formulation of the Lawson-Euler scheme,…