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A dynamic mass-transport method is proposed for approximately solving the Poisson-Nernst-Planck(PNP) equations. The semi-discrete scheme based on the JKO type variational formulation naturally enforces solution positivity and the energy law…

Numerical Analysis · Mathematics 2022-11-23 H. Liu , W. Maimaitiyiming

We present an efficient and robust numerical model for simulation of electrokinetic phenomena in porous networks over a wide range of applications including energy conversion, desalination, and lab-on-a-chip systems. Coupling between fluid…

Fluid Dynamics · Physics 2016-10-04 Shima Alizadeh , Ali Mani

Understanding how electrolyte-filled porous electrodes respond to an applied potential is important to many electrochemical technologies. Here, we consider a model supercapacitor of two blocking cylindrical pores on either side of a…

Soft Condensed Matter · Physics 2022-04-05 Jie Yang , Mathijs Janssen , Cheng Lian , René van Roij

In this article we propose and investigate a hierarchy of mathematical models based on partial differential equations (PDE) and ordinary differential equations (ODE) for the simulation of the biophysical phenomena occurring in the…

Numerical Analysis · Mathematics 2016-01-20 Emanuela Abbate , Matteo Porro , Thierry Nieus , Riccardo Sacco

We report a multiscale modeling study for charged cylindrical nanopores using three modeling levels that include (1) an all-atom explicit-water model studied with molecular dynamics (MD), and reduced models with implicit water containing…

Ion transport through narrow channels is described by the coupled Poisson--Nernst--Planck--Stokes equations (PNPS) on a continuum scale. However, direct numerical simulations in two or three dimensions of boundary value problems for small…

Analysis of PDEs · Mathematics 2026-03-10 Christine Keller , Andreas Münch , Barbara Wagner

We report here new electrical laws, derived from nonlinear electro-diffusion theory, about the effect of the local geometrical structure, such as curvature, on the electrical properties of a cell. We adopt the Poisson-Nernst-Planck (PNP)…

Subcellular Processes · Quantitative Biology 2017-11-22 Jerome Cartailler , Zeev Schuss , David Holcman

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, we make use of the Energetic Variational Approach (EnVarA),…

Numerical Analysis · Mathematics 2020-09-18 Chun Liu , Cheng Wang , Steven M. Wise , Xingye Yue , Shenggao Zhou

The hard sphere repulsion among ions can be considered in the Poisson-Nernst-Planck (PNP) equations by combining the fundamental measure theory (FMT). To reduce the nonlocal computational complexity in 3D simulation of biological systems, a…

Chemical Physics · Physics 2016-03-23 Yu Qiao , Benzhuo Lu , Minxin Chen

We present a 3D finite element solver for the nonlinear Poisson-Nernst-Planck (PNP) equations for electrodiffusion, coupled to the Stokes system of fluid dynamics. The model serves as a building block for the simulation of macromolecule…

Computational Physics · Physics 2017-04-05 Gregor Mitscha-Baude , Andreas Buttinger-Kreuzhuber , Gerhard Tulzer , Clemens Heitzinger

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 treating only the mobile ionic charges in the liquid, the…

Soft Condensed Matter · Physics 2019-07-30 Maijia Liao , Li Wan , Shixin Xu , Chun Liu , Ping Sheng

Poisson-Nernst-Planck equations are widely used to describe the electrodiffusion of ions in a solvated biomolecular system. Two kinds of two-grid finite element algorithms are proposed to decouple the steady-state Poisson-Nernst-Planck…

Numerical Analysis · Mathematics 2016-09-09 Ying Yang , Benzhuo Lu , Yan Xie

Starting with a microscopic (individual-based) Brownian dynamics model of charged particles (ions), its macroscopic description is derived as a system of partial differential equations that govern the evolution of ion concentrations in…

Computational Physics · Physics 2025-06-25 Jinyuan Zhang , Radek Erban

The Poisson-Nernst-Planck (PNP) equations are one of the most effective model for describing electrostatic interactions and diffusion processes in ion solution systems, and have been widely used in the numerical simulations of biological…

Numerical Analysis · Mathematics 2023-12-19 Yang Liu , Shi Shu , Ying Yang

The Poisson-Boltzmann (PB) theory is widely used to depict ionic systems. As a mean-field theory, the PB theory neglects the correlation effect in the ionic atmosphere and leads to deviations from experimental results as the concentration…

Soft Condensed Matter · Physics 2019-06-25 Mao Su , Zhijie Xu , Yanting Wang

Ion transport in biological and synthetic nanochannels is characterized by phenomena such as ion current fluctuations and rectification. Recently, it has been demonstrated that nanofabricated synthetic pores can mimic transport properties…

Classical Physics · Physics 2009-11-13 I. D. Kosińska , I. Goychuk , M. Kostur , G. Schmid , P. Hänggi

Ion transport, the movement of ions across a cellular membrane, plays a crucial role in a wide variety of biological processes and can be described by the Poisson-Nernst-Planck equations with steric effects (PNP-steric equations). In this…

Analysis of PDEs · Mathematics 2019-07-16 Li-Chang Hung , Mach Nguyet Minh

We study a two-grid strategy for decoupling the time-dependent Poisson-Nernst-Planck equations describing the mass concentration of ions and the electrostatic potential. The computational system is decoupled to smaller systems by using…

Numerical Analysis · Mathematics 2018-08-01 Ruigang Shen , Shi Shu , Ying Yang , Benzhuo Lu

The main goal of this work is to examine the qualitative effect of ion sizes via a steady-state boundary value problem. We study a one-dimensional version of a Poisson-Nernst-Planck system with a local hard-sphere potential model for ionic…

Mathematical Physics · Physics 2022-03-18 Weishi Liu , Hamid Mofidi

We rigorously derive a homogenized model for the Poisson--Nernst--Planck (PNP) equations for the case of multiple species defined on a periodic porous medium in spatial dimensions two and three. This extends the previous homogenization…

Analysis of PDEs · Mathematics 2026-02-02 Apratim Bhattacharya