Analytical Solution of Poisson‐Boltzmann Equation for Two‐Dimensional Many‐Center Problem

Nobuhisa Imai; Tsuyoshi Onishi

doi:10.1063/1.1730112

Analytical Solution of Poisson‐Boltzmann Equation for Two‐Dimensional Many‐Center Problem

The Journal of Chemical Physics ◽

10.1063/1.1730112 ◽

1959 ◽

Vol 30 (4) ◽

pp. 1115-1116 ◽

Cited By ~ 43

Author(s):

Nobuhisa Imai ◽

Tsuyoshi Onishi

Keyword(s):

Boltzmann Equation ◽

Analytical Solution ◽

Two Dimensional ◽

Center Problem ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation

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Screening of macroions in colloidal plasmas: Accurate analytical solution of the Poisson–Boltzmann equation

Physics Letters A ◽

10.1016/j.physleta.2005.04.028 ◽

2005 ◽

Vol 340 (5-6) ◽

pp. 440-448 ◽

Cited By ~ 13

Author(s):

Lev G. D'yachkov

Keyword(s):

Boltzmann Equation ◽

Analytical Solution ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation

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Poisson–Boltzmann equation for spherical cell model: approximate analytical solution and applications

Colloids and Surfaces A Physicochemical and Engineering Aspects ◽

10.1016/s0927-7757(01)00728-2 ◽

2001 ◽

Vol 192 (1-3) ◽

pp. 235-251 ◽

Cited By ~ 18

Author(s):

Emilij K. Zholkovskij ◽

Stanislav S. Dukhin ◽

Nataliya A. Mishchuk ◽

Jacob H. Masliyah ◽

Jan Czarnecki

Keyword(s):

Boltzmann Equation ◽

Analytical Solution ◽

Approximate Analytical Solution ◽

Cell Model ◽

Spherical Cell ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation

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The Irregular Behavior of a Counter-Ion Density Described by the Application of the Two-Dimensional Poisson-Boltzmann Equation

Journal of the Physical Society of Japan ◽

10.1143/jpsj.58.4235 ◽

1989 ◽

Vol 58 (11) ◽

pp. 4235-4250 ◽

Cited By ~ 2

Author(s):

Tetsuo Kaneko

Keyword(s):

Boltzmann Equation ◽

Two Dimensional ◽

Ion Density ◽

Counter Ion ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation ◽

Irregular Behavior

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A solution of the two-dimensional unbalanced Poisson-Boltzmann equation

Nonlinear Analysis and Differential Equations ◽

10.12988/nade.2016.6638 ◽

2016 ◽

Vol 4 ◽

pp. 393-404

Author(s):

F. Fonseca

Keyword(s):

Boltzmann Equation ◽

Two Dimensional ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation

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Analytical solution of Poisson?Boltzmann equation for interacting plates of arbitrary potentials and same sign

Journal of Colloid and Interface Science ◽

10.1016/j.jcis.2009.09.008 ◽

2010 ◽

Vol 341 (1) ◽

pp. 178-185 ◽

Cited By ~ 17

Author(s):

M. Polat ◽

H. Polat

Keyword(s):

Boltzmann Equation ◽

Analytical Solution ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation

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Analytical Solution of the Poisson–Boltzmann Equation in Cases of Spherical and Axial Symmetry

Technical Physics Letters ◽

10.1134/1.1894433 ◽

2005 ◽

Vol 31 (3) ◽

pp. 204 ◽

Cited By ~ 12

Author(s):

L. G. D’yachkov

Keyword(s):

Boltzmann Equation ◽

Analytical Solution ◽

Axial Symmetry ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation

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A new Green's function Monte Carlo algorithm for the solution of the two-dimensional nonlinear Poisson–Boltzmann equation: Application to the modeling of the communication breakdown problem in space vehicles during re-entry

Journal of Computational Physics ◽

10.1016/j.jcp.2014.07.042 ◽

2014 ◽

Vol 276 ◽

pp. 479-485 ◽

Cited By ~ 1

Author(s):

Kausik Chatterjee ◽

John R. Roadcap ◽

Surendra Singh

Keyword(s):

Monte Carlo ◽

Boltzmann Equation ◽

Green’S Function ◽

Green's Function ◽

Monte Carlo Algorithm ◽

Space Vehicles ◽

Two Dimensional ◽

Communication Breakdown ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation

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A two-dimensional stochastic algorithm for the solution of the non-linear Poisson–Boltzmann equation: validation with finite-difference benchmarks

International Journal for Numerical Methods in Engineering ◽

10.1002/nme.1539 ◽

2006 ◽

Vol 66 (1) ◽

pp. 72-84 ◽

Cited By ~ 2

Author(s):

Kausik Chatterjee ◽

Jonathan Poggie

Keyword(s):

Boltzmann Equation ◽

Finite Difference ◽

Stochastic Algorithm ◽

Two Dimensional ◽

Non Linear ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation

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Exact analytical solution to the Poisson-Boltzmann equation for semiconductor devices

The European Physical Journal Plus ◽

10.1140/epjp/i2014-14104-5 ◽

2014 ◽

Vol 129 (6) ◽

Cited By ~ 7

Author(s):

Elyas Shivanian ◽

Saeid Abbasbandy ◽

Mohammed S. Alhuthali

Keyword(s):

Boltzmann Equation ◽

Analytical Solution ◽

Exact Analytical Solution ◽

Semiconductor Devices ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation

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Analytical solution of the linearized Poisson–Boltzmann equation in cylindrical coordinates

The Journal of Chemical Physics ◽

10.1063/1.441936 ◽

1981 ◽

Vol 75 (11) ◽

pp. 5582-5583 ◽

Cited By ~ 7

Author(s):

Richard E. Rice ◽

Frederick H. Horne

Keyword(s):

Boltzmann Equation ◽

Analytical Solution ◽

Cylindrical Coordinates ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation

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