Related papers: Electro-Neutral Models for Dynamic Poisson-Nernst-…
We consider a reformulation of the classical $P_N$ method with Marshak boundary conditions for the approximation of the monoenergetic stationary linear transport equation as a system of second-order PDEs. Our derivation allows the automatic…
We propose and study the evolving neural network (ENN) method for solving one-dimensional scalar hyperbolic conservation laws with linear and quadratic spatial fluxes. The ENN method first represents the initial data and the inflow boundary…
The peridynamic theory brings advantages in dealing with discontinuities, dynamic loading, and non-locality. The integro-differential formulation of peridynamics poses challenges to numerical solutions of complicated and practical problems.…
We have developed a molecular mean-field theory -- fourth-order Poisson-Nernst-Planck-Bikerman theory -- for modeling ionic and water flows in biological ion channels by treating ions and water molecules of any volume and shape with…
We propose physics-informed holomorphic neural networks (PIHNNs) as a method to solve boundary value problems where the solution can be represented via holomorphic functions. Specifically, we consider the case of plane linear elasticity…
In physics, accurately modeling large-scale phenomena such as core-collapse supernovae, (CCSN), and neutron star mergers are computationally challenging and require solving large sets of partial and ordinary differential equations.…
The transport of organelles and vesicles in living cells can be well described by a kinetic tug-of-war model advanced by M\"uller, Klumpp and Lipowsky. In which, the cargo is attached by two motor species, kinesin and dynein, and the…
We propose a neural network based approach for extracting models from dynamic data using ordinary and partial differential equations. In particular, given a time-series or spatio-temporal dataset, we seek to identify an accurate governing…
Polymer electrolytes (PEs) are promising candidates for use in next-generation high-voltage batteries, as they possess advantageous elastic and electrochemical properties. However, PEs still suffer from low ionic conductivity and need to be…
We present and analyze two stabilized finite element methods for solving numerically the Poisson--Nernst--Planck equations. The stabilization we consider is carried out by using a shock detector and a discrete graph Laplacian operator for…
The steady state of ions diffusion in polymer electrolytes at arbitrary applied voltage is analyzed in the framework of the Nernst-Planck-Poisson equation (NPP). The exact solution of the set of equations is found without the assumption of…
The accurate electromagnetic modeling of both low- and high-frequency physics is crucial in the signal and power integrity analysis of electrical interconnects. The boundary element method (BEM) is appealing for lossy conductor modeling…
Boundary conditions (BCs) are a key component in every Physics-Informed Neural Network (PINN). By defining the solution to partial differential equations (PDEs) along domain boundaries, BCs constrain the underlying boundary value problem…
Recently, physics informed neural networks (PINNs) have been explored extensively for solving various forward and inverse problems and facilitating querying applications in fluid mechanics applications. However, work on PINNs for unsteady…
We investigate the critical threshold phenomena in a large class of one dimensional pressureless Euler--Poisson (EP) equations, with non-vanishing background states. First, we establish local-in-time well-posedness in proper regularity…
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…
Ionic fluids under conductive confinement are central to technologies such as batteries, supercapacitors, and fuel cells. Their interfacial behavior governs energy storage and electrochemical processes. Despite their importance, the…
It is economical to devise ways and means to simplify a multi-species particle system. The single fluid MHD description of a plasma is sufficiently adequate to study plasma phenomena . A plasma containing multi-species of particles can also…
A connection between the impedance spectroscopy response of anomalous Poisson-Nernst-Planck (PNPA) diffusional models and of equivalent circuits containing constant phase elements (CPE) is established for a typical electrolytic cell. The…
A Poisson-Nernst-Planck-Fermi (PNPF) theory is developed for studying ionic transport through biological ion channels. Our goal is to deal with the finite size of particle using a Fermi like distribution without calculating the forces…