Related papers: Modeling Concentration Profiles in Electrolytes by…
We have developed a novel differential equation solver software called PND based on the physics-informed neural network for molecular dynamics simulators. Based on automatic differentiation technique provided by Pytorch, our software allows…
Computing equilibrium concentrations of molecular complexes is generally analytically intractable and requires numerical approaches. In this work we focus on the polymer-monomer level, where indivisible molecules (monomers) combine to form…
The linearized of the Poisson-Nernst-Planck (PNP) equation under closed ends around a neutral state is studied. It is reduced to a damped heat equation under non-local boundary conditions, which leads to a stochastic interpretation of the…
A three-dimensional (3D) Poisson solver with longitudinal periodic and transverse open boundary conditions can have important applications in beam physics of particle accelerators. In this paper, we present a fast efficient method to solve…
In this paper, we develop an adaptive finite element method for the nonlinear steady-state Poisson-Nernst-Planck equations, where the spatial adaptivity for geometrical singularities and boundary layer effects are mainly considered. As a…
In this article we study a system of nonlinear PDEs modelling the electrokinetics of a nematic electrolyte material consisting of various ions species contained in a nematic liquid crystal. The evolution is described by a system coupling a…
Cells and cellular organelles are encapsulated by nanometrically thin membranes whose main component is a lipid bilayer. In the presence of electric fields, the ion-impermeable lipid bilayer acts as a capacitor and supports a potential…
A model is constructed to describe the arbitrary deformation of a drop or vesicle that contains and is embedded in an electrolyte solution, where the deformation is caused by an applied electric field. The applied field produces an…
An implicit Euler finite-volume scheme for a degenerate cross-diffusion system describing the ion transport through biological membranes is analyzed. The strongly coupled equations for the ion concentrations include drift terms involving…
A widely used electrostatics model in the biomolecular modeling community, the nonlinear Poisson-Boltzmann equation, along with its finite element approximation, are analyzed in this paper. A regularized Poisson-Boltzmann equation is…
As more and more numerical and analytical solutions to the linear neutron transport equation become available, verification of numerical results is increasingly important. This presentation concerns the development of another benchmark for…
The current study extends previous analytical and numerical solutions of chronopotentiometric response of one-dimensional systems consisting of three layers to the more realistic two-dimensional heterogeneous ion-permselective medium. An…
In this article we propose two novel 3D finite element models, denoted method A and B, for electron and hole Drift-Diffusion (DD) current densities. Method A is based on a primal-mixed formulation of the DD model as a function of the…
We consider electrodiffusion of ions in fluids, described by the Nernst-Planck-Navier-Stokes system, in three dimensional bounded domains, with mixed blocking (no-flux) and selective (Dirichlet) boundary conditions for the ionic…
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…
We present a modeling study of a nanopore-based transistor computed by a mean-field continuum theory (Poisson-Nernst-Planck, PNP) and a hybrid method including particle simulation (Local Equilibrium Monte Carlo, LEMC) that is able to take…
Electrostatic forces play many important roles in molecular biology, but are hard to model due to the complicated interactions between biomolecules and the surrounding solvent, a fluid composed of water and dissolved ions. Continuum model…
We consider the problem of electromigration of a sample ion (analyte) within a uniform background electrolyte when the confining channel undergoes a sudden contraction. One example of such a situation arises in microfluidics in the…
Mathematical models for excitable cells are commonly based on cable theory, which considers a homogenized domain and spatially constant ionic concentrations. Although such models provide valuable insight, the effect of altered ion…
A novel integral equations approach is applied for studying ion pairing in the restricted primitive model (RPM) electrolyte, i. e., the three point extension (TPE) to the Ornstein-Zernike integral equations. In the TPE approach, the…