33 citations · 179 across the 44 of their papers we have counts for
5 papers · 1 filter
Investigating the integrate and fire model as the limit of a random discharge model: a stochastic analysis perspective
Jian-Guo Liu, Ziheng Wang, Yantong Xie +2
In the mean field integrate-and-fire model, the dynamics of a typical neuron within a large network is modeled as a diffusion-jump stochastic process whose jump takes place once th…
A tumor growth model with autophagy: the reaction-(cross-)diffusion system and its free boundary limit
Xu'an Dou, Jian-Guo Liu, Zhennan Zhou
In this paper, we propose a tumor growth model to incorporate and investigate the spatial effects of autophagy. The cells are classified into two phases: normal cells and autophagi…
A unified structure preserving scheme for a multi-species model with a gradient flow structure and nonlocal interactions via singular kernels
Yong Zhang, Yu Zhao, Zhennan Zhou
In this paper, we consider a nonlinear and nonlocal parabolic model for multi-species ionic fluids and introduce a semi-implicit finite volume scheme, which is second order accurat…
Multi-level Monte Carlo path integral molecular dynamics for thermal average calculation in the nonadiabatic regime
Xiaoyu Lei, Zhennan Zhou
With the path integral approach, the thermal average in a multi-electronic-state quantum systems can be approximated by the ring polymer representation on an extended configuration…
Rigorous justification of the Fokker-Planck equations of neural networks based on an iteration perspective
Jian-guo Liu, Ziheng Wang, Yuan Zhang +1
In this work, the primary goal is to establish rigorous connection between the Fokker-Planck equation of neural networks with its microscopic model: the diffusion-jump stochastic p…