96 citations · 484 across the 29 of their papers we have counts for
30 papers
Global Finite-Energy Weak Solutions and Sharp Entropy Decay for a Poisson-Nernst-Planck System with Interspecies Drag and Steric Effects
Baoli Hao, Fanze Kong, Kei Fong Lam +1
We derive and analyze a binary Poisson-Nernst-Planck system with steric interactions and interspecies drag through the energetic variational approach. The steric effects are incorp…
On variational principles for polarization responses in electromechanical systems
Yiwei Wang, Chun Liu, Bob Eisenberg
Classical electrodynamics uses a dielectric constant to describe the polarization response of electromechanical systems to changes in an electric field. We generalize that descript…
A second-order accurate, operator splitting scheme for reaction-diffusion systems in an energetic variational formulation
Chun Liu, Cheng Wang, Yiwei Wang
A second-order accurate in time, positivity-preserving, and unconditionally energy stable operator splitting numerical scheme is proposed and analyzed for the system of reaction-di…
On a Reversible Gray-Scott Type System from Energetic Variational Approach and Its Irreversible Limit
Jiangyan Liang, Ning Jiang, Chun Liu +2
Most of the previous studies on the well-known Gray-Scott model view it as an irreversible chemical reaction system. In this paper, we derive a four-species reaction-diffusion syst…
Nonlinear simulation of vascular tumor growth with chemotaxis and the control of necrosis
Min-Jhe Lu, Wenrui Hao, Chun Liu +2
In this paper, we develop a sharp interface tumor growth model in two dimensions to study the effect of both the intratumoral structure using a controlled necrotic core and the ext…
Convergence analysis of the variational operator splitting scheme for a reaction-diffusion system with detailed balance
Chun Liu, Cheng Wang, Yiwei Wang +1
We present a detailed convergence analysis for an operator splitting scheme proposed in [C. Liu et al.,J. Comput. Phys., 436, 110253, 2021] for a reaction-diffusion system with det…
Well-Posedness for the Reaction-Diffusion Equation with Temperature in a critical Besov Space
Chun Liu, Jan-Eric Sulzbach
We derive a model for the non-isothermal reaction-diffusion equation. Combining ideas from non-equilibrium thermodynamics with the energetic variational approach we obtain a genera…
A two species micro-macro model of wormlike micellar solutions and its maximum entropy closure approximations: An energetic variational approach
Yiwei Wang, Teng-Fei Zhang, Chun Liu
Wormlike micelles are self-assemblies of polymer chains that can break and recombine reversibly. In this paper, we derive a thermodynamically consistent two species micro-macro mod…
A structure-preserving, operator splitting scheme for reaction-diffusion equations with detailed balance
Chun Liu, Cheng Wang, Yiwei Wang
In this paper, we propose and analyze a positivity-preserving, energy stable numerical scheme for certain type reaction-diffusion systems involving the Law of Mass Action with the…
A positivity-preserving, energy stable and convergent numerical scheme for the Poisson-Nernst-Planck system
Chun Liu, Cheng Wang, Steven M. Wise +2
In this paper we propose and analyze a finite difference numerical scheme for the Poisson-Nernst-Planck equation (PNP) system. To understand the energy structure of the PNP model,…
Structure-Preserving Numerical Methods for Nonlinear Fokker--Planck Equations with Nonlocal Interactions by an Energetic Variational Approach
Chenghua Duan, Wenbin Chen, Chun Liu +2
In this work, we develop novel structure-preserving numerical schemes for a class of nonlinear Fokker--Planck equations with nonlocal interactions. Such equations can cover many ca…
On second-order and fourth-order elliptic systems consisting of bulk and surface PDEs: Well-posedness, regularity theory and eigenvalue problems
Patrik Knopf, Chun Liu
In this paper, we study second-order and fourth-order elliptic problems which include not only a Poisson equation in the bulk but also an inhomogeneous Laplace--Beltrami equation o…
The Brinkman-Fourier System with Ideal Gas Equilibrium
Chun Liu, Jan-Eric Sulzbach
In this work, we will introduce a general framework to derive the thermodynamics of a fluid mechanical system, which guarantees the consistence between the energetic variational ap…
A second order accurate numerical scheme for the porous medium equation by an energetic variational approach
Chenghua Duan, Wenbin Chen, Chun Liu +2
The porous medium equation (PME) is a typical nonlinear degenerate parabolic equation. An energetic variational approach has been studied in a recent work [6], in which the traject…
Particle-based Energetic Variational Inference
Yiwei Wang, Jiuhai Chen, Chun Liu +1
We introduce a new variational inference (VI) framework, called energetic variational inference (EVI). It minimizes the VI objective function based on a prescribed energy-dissipati…
Phase-field dynamics with transfer of materials: The Cahn--Hilliard equation with reaction rate dependent dynamic boundary conditions
Patrik Knopf, Kei Fong Lam, Chun Liu +1
The Cahn--Hilliard equation is one of the most common models to describe phase separation processes of a mixture of two materials. For a better description of short-range interacti…
A Variational Lagrangian Scheme for a Phase Field Model: A Discrete Energetic Variational Approach
Chun Liu, Yiwei Wang
In this paper, we propose a variational Lagrangian scheme for a modified phase-field model, which can compute the equilibrium states for the original Allen-Cahn type model. Our dis…
Global Existence of the Non-isothermal Poisson-Nernst-Planck-Fourier System
Chia-Yu Hsieh, Tai-Chia Lin, Chun Liu +1
In this paper, we consider a non-isothermal electrokinetic model, which is derived from the Energetic Variational Approach. The charge transport is described through the Poisson-Ne…
Field Theory of Reaction-Diffusion: Mass Action with an Energetic Variational Approach
Yiwei Wang, Chun Liu, Pei Liu +1
We extend the energetic variational approach so it can be applied to a chemical reaction system with general mass action kinetics. Our approach starts with an energy-dissipation la…
Complex Far-Field Geometries Determine the Stability of Solid Tumor Growth with Chemotaxis
Min-Jhe Lu, Chun Liu, John Lowengrub +1
In this paper, we develop a sharp interface tumor growth model to study the effect of the tumor microenvironment using a complex far-field geometry that mimics a heterogeneous dist…
Convergence analysis of a numerical scheme for the porous medium equation by an energetic variational approach
Chenghua Duan, Chun Liu, Cheng Wang +1
The porous medium equation (PME) is a typical nonlinear degenerate parabolic equation. We have studied numerical methods for PME by an energetic variational approach in [C. Duan et…
On Lagrangian schemes for porous medium type generalized diffusion equations: a discrete energetic variational approach
Chun Liu, Yiwei Wang
In this paper, we present a systematic framework to derive a Lagrangian scheme for porous medium type generalized diffusion equations by employing a discrete energetic variational…
Numerical methods for Porous Medium Equation by an Energetic Variational Approach
Chenghua Duan, Chun Liu, Cheng Wang +1
We study numerical methods for porous media equation (PME). There are two important characteristics: the finite speed propagation of the free boundary and the potential waiting tim…
Do Bi-Stable Poisson-Nernst-Planck Models Describe Single Channel Gating?
Nir Gavish, Chun Liu, Bob Eisenberg
Experiments measuring currents through single protein channels show unstable currents, a phenomena called the gating of a single channel. Channels switch between an 'open' state wi…