Displaying similar documents to “The Child–Langmuir limit for semiconductors: a numerical validation”

A boundary integral Poisson-Boltzmann solvers package for solvated bimolecular simulations

Weihua Geng (2015)

Molecular Based Mathematical Biology

Similarity:

Numerically solving the Poisson-Boltzmann equation is a challenging task due to the existence of the dielectric interface, singular partial charges representing the biomolecule, discontinuity of the electrostatic field, infinite simulation domains, etc. Boundary integral formulation of the Poisson-Boltzmann equation can circumvent these numerical challenges and meanwhile conveniently use the fast numerical algorithms and the latest high performance computers to achieve combined improvement...

Poisson-Fermi Formulation of Nonlocal Electrostatics in Electrolyte Solutions

Jinn-Liang Liu, Dexuan Xie, Bob Eisenberg (2017)

Molecular Based Mathematical Biology

Similarity:

We present a nonlocal electrostatic formulation of nonuniform ions and water molecules with interstitial voids that uses a Fermi-like distribution to account for steric and correlation efects in electrolyte solutions. The formulation is based on the volume exclusion of hard spheres leading to a steric potential and Maxwell’s displacement field with Yukawa-type interactions resulting in a nonlocal electric potential. The classical Poisson-Boltzmann model fails to describe steric and correlation...

Probabilistic Interpretation for the Nonlinear Poisson-Boltzmann Equation in Molecular Dynamics

Nicolas Perrin (2012)

ESAIM: Proceedings

Similarity:

The Poisson-Boltzmann (PB) equation describes the electrostatic potential of a biomolecular system composed by a molecule in a solvent. The electrostatic potential is involved in biomolecular models which are used in molecular simulation. In consequence, finding an efficient method to simulate the numerical solution of PB equation is very useful. As a first step, we establish in this paper a probabilistic interpretation of the nonlinear PB equation with Backward Stochastic Differential...

Raman laser: mathematical and numerical analysis of a model

François Castella, Philippe Chartier, Erwan Faou, Dominique Bayart, Florence Leplingard, Catherine Martinelli (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

In this paper we study a discrete Raman laser amplification model given as a Lotka-Volterra system. We show that in an ideal situation, the equations can be written as a Poisson system with boundary conditions using a global change of coordinates. We address the questions of existence and uniqueness of a solution. We deduce numerical schemes for the approximation of the solution that have good stability.

The Child–Langmuir limit for semiconductors : a numerical validation

María-José Cáceres, José-Antonio Carrillo, Pierre Degond (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Similarity:

The Boltzmann–Poisson system modeling the electron flow in semiconductors is used to discuss the validity of the Child–Langmuir asymptotics. The scattering kernel is approximated by a simple relaxation time operator. The Child–Langmuir limit gives an approximation of the current-voltage characteristic curves by means of a scaling procedure in which the ballistic velocity is much larger that the thermal one. We discuss the validity of the Child–Langmuir regime by performing detailed numerical...

Quantization of pencils with a gl-type Poisson center and braided geometry

Dimitri Gurevich, Pavel Saponov (2011)

Banach Center Publications

Similarity:

We consider Poisson pencils, each generated by a linear Poisson-Lie bracket and a quadratic Poisson bracket corresponding to a so-called Reflection Equation Algebra. We show that any bracket from such a Poisson pencil (and consequently, the whole pencil) can be restricted to any generic leaf of the Poisson-Lie bracket. We realize a quantization of these Poisson pencils (restricted or not) in the framework of braided affine geometry. Also, we introduce super-analogs of all these Poisson...

Computation of Biharmonic Poisson Kernel for the Upper Half Plane

Ali Abkar (2007)

Bollettino dell'Unione Matematica Italiana

Similarity:

We first consider the biharmonic Poisson kernel for the unit disk, and study the boundary behavior of potentials associated to this kernel function. We shall then use some properties of the biharmonic Poisson kernel for the unit disk to compute the analogous biharmonic Poisson kernel for the upper half plane.