Displaying similar documents to “Quasineutral limit of the Euler-Poisson system for ions in a domain with boundaries II”

Numerical approximation of Knudsen layer for the Euler-Poisson system

Fréderique Charles, Nicolas Vauchelet, Christophe Besse, Thierry Goudon, Ingrid Lacroix–Violet, Jean-Paul Dudon, Laurent Navoret (2011)

ESAIM: Proceedings

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In this work, we consider the computation of the boundary conditions for the linearized Euler–Poisson derived from the BGK kinetic model in the small mean free path regime. Boundary layers are generated from the fact that the incoming kinetic flux might be far from the thermodynamical equilibrium. In [2], the authors propose a method to compute numerically the boundary conditions in the hydrodynamic limit relying on an analysis of the...

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

Weihua Geng (2015)

Molecular Based Mathematical Biology

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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

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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...

The Cauchy problem for the two dimensional Euler–Poisson system

Dong Li, Yifei Wu (2014)

Journal of the European Mathematical Society

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The Euler-Poisson system is a fundamental two-fluid model to describe the dynamics of the plasma consisting of compressible electrons and a uniform ion background. In the 3D case Guo [7] first constructed a global smooth irrotational solution by using the dispersive Klein-Gordon effect. It has been conjectured that same results should hold in the two-dimensional case. In our recent work [13], we proved the existence of a family of smooth solutions by constructing the wave operators for...

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

Dimitri Gurevich, Pavel Saponov (2011)

Banach Center Publications

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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

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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.