107 citations · 345 across the 16 of their papers we have counts for
16 papers
Modeling and simulation of nuclear architecture reorganization process using a phase field approach
Qing Cheng, Pourya Delafrouz, Jie Liang +2
We develop a special phase field/diffusive interface method to model the nuclear architecture reorganization process. In particular, we use a Lagrange multiplier approach in the ph…
Discrete Flux and Velocity Fields of Probability and Their Global Maps in Reaction Systems
Anna Terebus, Chun Liu, Jie Liang
Stochasticity plays important roles in reaction systems. Vector fields of probability flux and velocity characterize time-varying and steady-state properties of these systems, incl…
Coarse-graining Langevin dynamics using reduced-order techniques
Lina Ma, Xiantao Li, Chun Liu
This paper considers the reduction of the Langevin equation arising from bio-molecular models. To facilitate the construction and implementation of the reduced models, the problem…
From Generalized Langevin Equations to Brownian Dynamics and Embedded Brownian Dynamics
Lina Ma, Xiantao Li, Chun Liu
We present the reduction of generalized Langevin equations to a coordinate-only stochastic model, which in its exact form, involves a forcing term with memory and a general Gaussia…
The Derivation and Approximation of Coarse-grained Dynamics from Langevin Dynamics
Lina Ma, Xiantao Li, Chun Liu
We present a derivation of a coarse-grained model from the Langevin dynamics. The focus is placed on the memory kernel function and the fluctuation-dissipation theorem. Also presen…
The Poisson Boltzmann equation and the charge separation phenomenon at the silica-water interface: A holistic approach
Maijia Liao, Li Wan, Shixin Xu +2
The Poisson Boltzmann equation is known for its success in describing the Debye layer that arises from the charge separation phenomenon at the silica/water interface. However, by t…
Boundary Layer Solutions of Charge Conserving Poisson-Boltzmann Equations: One-Dimensional Case
Chiun-Chang Lee, Hijin Lee, YunKyong Hyon +2
For multispecies ions, we study boundary layer solutions of charge conserving Poisson-Boltzmann (CCPB) equations [50] (with a small parameter ǫ) over a finite one-dimensional (1D)…
Transport of Charged Particles: Entropy Production and Maximum Dissipation Principle
Chia-Yu Hsieh, YunKyong Hyon, Hijin Lee +2
In order to describe the dynamics of crowded ions (charged particles), we use an energetic variation approach to derive a modified Poisson-Nernst-Planck (PNP) system which includes…
Computation of the Memory Functions in the Generalized Langevin Models for Collective Dynamics of Macromolecules
Minxin Chen, Xiantao Li, Chun Liu
We present a numerical method to compute the approximation of the memory functions in the generalized Langevin models for collective dynamics of macromolecules. We first derive the…
Finite time singularities for hyperbolic systems
Geng Chen, Tao Huang, Chun Liu
In this paper, we study the formation of finite time singularities in the form of super norm blowup for a spatially inhomogeneous hyperbolic system. The system is related to the va…
Diffusion limit of kinetic equations for multiple species charged particles
Hao Wu, Tai-Chia Lin, Chun Liu
In ionic solutions, there are multi-species charged particles (ions) with different properties like mass, charge etc. Macroscopic continuum models like the Poisson-Nernst-Planck (P…
A Conservative Finite Difference Scheme for Poisson-Nernst-Planck Equations
Allen Flavell, Michael Machen, Bob Eisenberg +2
A macroscopic model to describe the dynamics of ion transport in ion channels is the Poisson-Nernst-Planck(PNP) equations. In this paper, we develop a finite-difference method for…
On the General Ericksen-Leslie System: Parodi's Relation, Well-posedness and Stability
Hao Wu, Xiang Xu, Chun Liu
In this paper we investigate the role of Parodi's relation in the well-posedness and stability of the general Ericksen-Leslie system modeling nematic liquid crystal flows. First, w…
A Model of Electrodiffusion and Osmotic Water Flow and its Energetic Structure
Yoichiro Mori, Chun Liu, Robert S. Eisenberg
We introduce a model for ionic electrodiffusion and osmotic water flow through cells and tissues. The model consists of a system of partial differential equations for ionic concent…
First-Order System Least Squares and the Energetic Variational Approach for Two-Phase Flow
J. H. Adler, J. Brannick, C. Liu +2
This paper develops a first-order system least-squares (FOSLS) formulation for equations of two-phase flow. The main goal is to show that this discretization, along with numerical…
Asymptotic Behavior for a Nematic Liquid Crystal Model with Different Kinematic Transport Properties
Hao Wu, Xiang Xu, Chun Liu
We study the asymptotic behavior of global solutions to hydrodynamical systems modeling the nematic liquid crystal flows under kinematic transports for molecules of different shape…