A solution of the one-dimensional linear quartic Poisson-Boltzmann equation using lattice-Boltzmann

2018 ◽  
Vol 11 (33) ◽  
pp. 1613-1619
Author(s):  
F. Fonseca
Keyword(s):  
Boltzmann Equation ◽  
Lattice Boltzmann ◽  
One Dimensional ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
The One

Simulation of Electroosmotic Flows in Micro- and Nanochannels Using a Lattice Boltzmann Model

2004 ◽  
Author(s):  
Fuzhi Tian ◽  
Baoming Li ◽  
Daniel Y. Kwok
Keyword(s):  
Boltzmann Equation ◽  
Analytical Solution ◽  
Charge Distribution ◽  
Excellent Agreement ◽  
Lattice Boltzmann ◽  
Lattice Boltzmann Model ◽  
Computational Tool ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Boltzmann Model

A Lattice Boltzman Model (LBM) with the Poisson-Boltzmann equation for charge distribution is presented for the simulation of electroosmotic transport in straight rectangular micro and nanochannels. Our results from the LBM are in excellent agreement with the corresponding analytical solution. We have shown that the Lattice Boltzmann Model in the presence of an external force may be used an effective computational tool to simulate the electroosmotic transport phenomena in micro- and nanochannels.

scholarly journals One-dimensional model of the electrostatic ion acceleration in the ultraintense laser–solid interaction

2004 ◽  
Vol 22 (2) ◽  
pp. 163-169 ◽  
Author(s):  
M. PASSONI ◽  
M. LONTANO
Keyword(s):  
Initial Conditions ◽  
Target Surface ◽  
Ion Acceleration ◽  
Ion Distribution ◽  
One Dimensional ◽  
Vacuum Interface ◽  
Ion Energization ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
The One

Effective ion acceleration of picosecond-duration well-collimated bunches in the strong relativistic interaction of a short laser pulse with a thin solid target has been experimentally demonstrated. In this work, with reference to the sharp rear solid–vacuum interface, where ion energization takes place, the one-dimensional Poisson–Boltzmann equation is analytically solved on a finite spatial interval whose extension is determined by requiring electron energy conservation, resulting in the consistent spatial distributions of the hot electrons created by the laser and of the corresponding electrostatic potential. Then, the equation of motions for an ensemble of test ions, initially distributed in a thin layer of the rear target surface, with different initial conditions, is solved and the energy spectrum corresponding to a given initial ion distribution is determined.

scholarly journals Monte Carlo methods for linear and non-linear Poisson-Boltzmann equation

2015 ◽  
Vol 48 ◽  
pp. 420-446 ◽  
Author(s):  
Mireille Bossy ◽  
Nicolas Champagnat ◽  
Hélène Leman ◽  
Sylvain Maire ◽  
Laurent Violeau ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Boltzmann Equation ◽  
Monte Carlo Methods ◽  
Non Linear ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation
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