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Accurate calculation of electrostatic potential and gradient on the molecular surface is highly desirable for the continuum and hybrid modeling of large scale deformation of biomolecules in solvent. In this article a new numerical method is…
In ionic solutions, there are multi-species charged particles (ions) with different properties like mass, charge etc. Macroscopic continuum models like the Poisson-Nernst-Planck (PNP) systems have been extensively used to describe the…
We present a generalized approach for computing electron conductance and I-V characteristics in multiterminal junctions from first-principles. Within the framework of Keldysh theory, electron transmission is evaluated employing an O(N)…
In this article we address the study of ion charge transport in the biological channels separating the intra and extracellular regions of a cell. The focus of the investigation is devoted to including thermal driving forces in the…
A full viscous quantum hydrodynamic system for particle density, current density, energy density and electrostatic potential coupled with a Poisson equation in one dimensional bounded intervals is studied. First, the existence and…
Calculations of the ground state of inhomogeneous many-electron systems involve a solving of the Poisson equation for Coulomb potential and the Schroedinger equation for single-particle orbitals. Due to nonlinearity and complexity this set…
In this research, we explore how permanent charges affect the movement of ionic currents through ion channels. We use a quasi-one-dimensional classical Poisson-Nernst-Planck (PNP) model to study two types of ions, one positively charged and…
The self-consistent quantum-electrostatic (also known as Poisson-Schr\"odinger) problem is notoriously difficult in situations where the density of states varies rapidly with energy. At low temperatures, these fluctuations make the problem…
We present an explicit solver of the three-dimensional screened and unscreened Poisson's equation which combines accuracy, computational efficiency and versatility. The solver, based on a mixed plane-wave / interpolating scaling function…
A novel Gaussian-Sinc mixed basis set for the calculation of the one-electron electronic structure within a uniform magnetic field in three dimensions is presented. The one-electron system is used to demonstrate the utility of this new…
The solitary waves are investigated through the Bernstein-Greene-Kruskal integral method with the ion response. We consider two specific cases of ions, i.e., the single stream with the waterbag distribution and the two counter-propagating…
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 derive a set of modified Poisson-Nernst-Planck (mPNP) equations for ion transport from the variation of the free energy functional which includes the many-body Coulomb correlation in media of variable dielectric coefficient. 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…
This work concerns the numerical approximation of a multicomponent compressible Euler system for a fluid mixture in multiple space dimensions on unstructured meshes with a high-order discontinuous Galerkin spectral element method (DGSEM).…
A recent proof-of-principle study proposes a nonlinear electrostatic implicit particle-in-cell (PIC) algorithm in one dimension (Chen, Chacon, Barnes, J. Comput. Phys. 230 (2011) 7018). The algorithm employs a kinetically enslaved…
Modeling the chemical, electric, and thermal transport as well as phase transitions and the accompanying mesoscale microstructure evolution within a material in an electronic device setting involves the solution of partial differential…
Mathematical models for excitable tissue with explicit representation of individual cells are highly detailed and can, unlike classical homogenized models, represent complex cellular geometries and local membrane variations. However, these…
The problem of the one dimensional electro-diffusion of ions in a strong binary electrolyte is considered. In such a system the solute dissociates completely into two species of ions with unlike charges. The mathematical description…
This review describes the theory and implementation of implicit solvation models based on continuum electrostatics. Within quantum chemistry this formalism is sometimes synonymous with the polarizable continuum model, a particular…