A Structure-Preserving JKO Scheme for the SizeModified Poisson-Nernst-Planck-Cahn-Hilliard Equations

Poisson-Nernst-Planck equations in a ball

The Poisson Nernst-Planck equations for charge concentration and electric potential in a ball is a model of electro-diffusion of ions in the head of a neuronal dendritic spine. We study the relaxation and the steady state when an initial charge of ions is injected into the ball. The steady state equation is similar to the Liouville-Gelfand-Bratú-type equation with the difference that the bounda...

A Wasserstein Gradient Flow Approach to Poisson-Nernst-Planck Equations

The Poisson-Nernst-Planck system of equations used to model ionic transport is interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of probability measures with finite second moment. A variational scheme is then set up and is the starting point of the construction of global weak solutions in a unified framework for the cases of both linear and nonlinear dif...

Poisson-Boltzmann-Nernst-Planck model.

The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems,...

A structure preserving scheme for the Kolmogorov-Fokker-Planck equation

Article history: Received 11 March 2016 Received in revised form 4 November 2016 Accepted 5 November 2016 Available online 21 November 2016

Preconditioning for Vector-Valued Cahn-Hilliard Equations