134 citations · 161 across the 18 of their papers we have counts for
43 papers
Convergence of Oja's online principal component flow
Jian-Guo Liu, Zibu Liu
Online principal component analysis (PCA) has been an efficient tool in practice to reduce dimension. However, convergence properties of the corresponding ODE are still unknown, in…
On the equilibrium of the Poisson-Nernst-Planck-Bikermann model equipping with the steric and correlation effects
Jian-Guo Liu, Yijia Tang, Yu Zhao
The Poisson-Nernst-Planck-Bikermann (PNPB) model, in which the ions and water molecules are treated as different species with non-uniform sizes and valences with interstitial voids…
In search of local singularities in ideal potential flows with free surface
Jian-Guo Liu, Robert L. Pego
For ideal fluid flow with zero surface tension and gravity, it remains unknown whether local singularities on the free surface can develop in well-posed initial value problems with…
From kinetic to fluid models of liquid crystals by the moment method
Pierre Degond, Amic Frouvelle, Jian-Guo Liu
This paper deals with the convergence of the Doi-Navier-Stokes model of liquid crystals to the Ericksen-Leslie model in the limit of the Deborah number tending to zero. While the l…
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…
Existence and incompressible limit of a tissue growth model with autophagy
Jian-Guo Liu, Xiangsheng Xu
In this paper we study a cross-diffusion system whose coefficient matrix is non-symmetric and degenerate. The system arises in the study of tissue growth with autophagy. The existe…