209 citations · 1.4k across the 114 of their papers we have counts for
116 papers
Phase-Field Models, Sharp Interface Limits, and Numerical Schemes for Contact Line Dynamics
Guosheng Fu, Yuan Gao, Jian-Guo Liu
We study phase-field and sharp-interface models for contact line dynamics of a liquid droplet on a solid substrate within a unified variational framework. The motion of the contact…
High-order Moment Closure Models with Random Batch Method for Efficient Computation of Multiscale Turbulent Systems
Di Qi, Jian-Guo Liu
We propose a high-order stochastic-statistical moment closure model for efficient ensemble prediction of leading-order statistical moments and probability density functions in mult…
Existence of weak solutions to -Navier-Stokes equations
Yuanyuan Feng, Lei Li, Jian-Guo Liu +1
We study the existence of weak solutions to the -Navier-Stokes equations with a symmetric -Laplacian on bounded domains. We construct a particular Schauder basis in $W_0^{1,p…
Diffusion approximations of Oja's online principal component analysis
Jian-Guo Liu, Zibu Liu
Oja's algorithm of principal component analysis (PCA) has been one of the methods utilized in practice to reduce dimension. In this paper, we focus on the convergence property of t…
Geometric ergodicity of SGLD via reflection coupling
Lei Li, Jian-Guo Liu, Yuliang Wang
We consider the geometric ergodicity of the Stochastic Gradient Langevin Dynamics (SGLD) algorithm under nonconvexity settings. Via the technique of reflection coupling, we prove t…
Master equations for finite state mean field games with nonlinear activations
Yuan Gao, Wuchen Li, Jian-Guo Liu
We formulate a class of mean field games on a finite state space with variational principles resembling those in continuous-state mean field games. We construct a controlled contin…
A Random Batch Method for Efficient Ensemble Forecasts of Multiscale Turbulent Systems
Di Qi, Jian-Guo Liu
A new efficient ensemble prediction strategy is developed for a general turbulent model framework with emphasis on the nonlinear interactions between large and small scale variable…
A selection principle for weak KAM solutions via Freidlin-Wentzell large deviation principle of invariant measures
Yuan Gao, Jian-Guo Liu
This paper reinterprets Freidlin-Wentzell's variational construction of the rate function in the large deviation principle for invariant measures from the weak KAM perspective. Thr…
Homogenization of the Landau-Lifshitz-Gilbert equation with natural boundary condition
Jingrun Chen, Jian-Guo Liu, Zhiwei Sun
The full Landau-Lifshitz-Gilbert equation with periodic material coefficients and natural boundary condition is employed to model the magnetization dynamics in composite ferromagne…
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…
Revisit of macroscopic dynamics for some non-equilibrium chemical reactions from a Hamiltonian viewpoint
Yuan Gao, Jian-Guo Liu
Most biochemical reactions in living cells are open systems interacting with environment through chemostats to exchange both energy and materials. At a mesoscopic scale, the number…
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…
Holographic Anomalous Current at a Finite Temperature
Jian-Guo Liu, Rong-Xin Miao
Weyl anomaly leads to novel anomalous currents in a spacetime with boundaries. Recently it is found that the anomalous current can be significantly enhanced by the high temperature…
Surfactant-dependent contact line dynamics and droplet spreading on textured substrates: derivations and computations
Yuan Gao, Jian-Guo Liu
We study spreading of a droplet, with insoluble surfactant covering its capillary surface, on a textured substrate. In this process, the surfactant-dependent surface tension domina…
On the Random Batch Method for second order interacting particle systems
Shi Jin, Lei Li, Yiqun Sun
We investigate several important issues regarding the Random Batch Method (RBM) for second order interacting particle systems. We first show the uniform-in-time strong convergence…
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…
Existence and rigidity of the Peierls-Nabarro model for dislocations in high dimensions
Yuan Gao, Jian-Guo Liu, Zibu Liu
We focus on existence and rigidity problems of the vectorial Peierls-Nabarro (PN) model for dislocations. Under the assumption that the misfit potential on the slip plane only depe…
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…
Projection method for droplet dynamics on groove-textured surface with merging and splitting
Yuan Gao, Jian-Guo Liu
The geometric motion of small droplets placed on an impermeable textured substrate is mainly driven by the capillary effect, the competition among surface tensions of three phases…