Quasilinear Schrödinger-Poisson equations involving a nonlocal term and an integral constraint

2021 ◽  
Author(s):  
Xiaojing Dong ◽  
Anmin Mao
Keyword(s):  
Nonlocal Term ◽  
Integral Constraint ◽  
Poisson Equations

scholarly journals Electrodiffusion Phenomena in Neuroscience and the Nernst–Planck–Poisson Equations

Electrochem ◽  
2021 ◽  
Vol 2 (2) ◽  
pp. 197-215
Author(s):  
Jerzy J. Jasielec
Keyword(s):  
Electrical Potential ◽  
Signal Propagation ◽  
Liquid Junction Potential ◽  
Liquid Junction ◽  
Patch Clamp Technique ◽  
Poisson Equations ◽  
Cellular Environment ◽  
Electrochemical Transport ◽  
Insight Into ◽  
Junction Potential

This work is aimed to give an electrochemical insight into the ionic transport phenomena in the cellular environment of organized brain tissue. The Nernst–Planck–Poisson (NPP) model is presented, and its applications in the description of electrodiffusion phenomena relevant in nanoscale neurophysiology are reviewed. These phenomena include: the signal propagation in neurons, the liquid junction potential in extracellular space, electrochemical transport in ion channels, the electrical potential distortions invisible to patch-clamp technique, and calcium transport through mitochondrial membrane. The limitations, as well as the extensions of the NPP model that allow us to overcome these limitations, are also discussed.

Blow-up for the compressible isentropic Navier-Stokes-Poisson equations

2019 ◽  
Vol 70 (1) ◽  
pp. 9-19
Author(s):  
Jianwei Dong ◽  
Junhui Zhu ◽  
Yanping Wang
Keyword(s):  
Blow Up ◽  
Navier Stokes ◽  
Poisson Equations

Improved blowup theorems for the Euler-Poisson equations with attractive forces

2016 ◽  
Vol 57 (7) ◽  
pp. 071505 ◽  
Author(s):  
Rui Li ◽  
Xing Lin ◽  
Zongwei Ma
Keyword(s):  
Poisson Equations

scholarly journals Comparison of Iteration Schemes for the Solution of the Multidimensional Schrödinger-Poisson Equations

VLSI Design ◽  
1998 ◽  
Vol 8 (1-4) ◽  
pp. 105-109 ◽  
Author(s):  
A. Trellakis ◽  
A. T. Galick ◽  
A. Pacelli ◽  
U. Ravaioli
Keyword(s):  
Coupled System ◽  
Iteration Scheme ◽  
Simple Expression ◽  
Software Implementation ◽  
Quantum Structures ◽  
System Of Differential Equations ◽  
Poisson Equations ◽  
Quantum Electron ◽  
Predictor Corrector ◽  
Bound Electron

We present a fast and robust iterative method for obtaining self-consistent solutions to the coupled system of Schrödinger's and Poisson's equations in quantum structures. A simple expression describing the dependence of the quantum electron density on the electrostatic potential is used to implement a predictor – corrector type iteration scheme for the solution of the coupled system of differential equations. This approach simplifies the software implementation of the nonlinear problem, and provides excellent convergence speed and stability. We demonstrate the algorithm by presenting an example for the calculation ofthe two-dimensional bound electron states within the cross-section of a GaAs-AlGaAs based quantum wire. For this example, six times fewer iterations are needed when our predictor – corrector approach is applied, compared to a corresponding underrelaxation algorithm.

Global Solutions to the One-Dimensional Compressible Navier--Stokes--Poisson Equations with Large Data

2013 ◽  
Vol 45 (2) ◽  
pp. 547-571 ◽  
Author(s):  
Zhong Tan ◽  
Tong Yang ◽  
Huijiang Zhao ◽  
Qingyang Zou
Keyword(s):  
Global Solutions ◽  
Large Data ◽  
Navier Stokes ◽  
One Dimensional ◽  
Poisson Equations ◽  
The One
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