scholarly journals Roles of Boundary Conditions in DNA Simulations: Analysis of Ion Distributions with the Finite-Difference Poisson-Boltzmann Method

2009 ◽  
Vol 97 (2) ◽  
pp. 554-562 ◽  
Author(s):  
Xiang Ye ◽  
Qin Cai ◽  
Wei Yang ◽  
Ray Luo
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Ion Distributions ◽  
Poisson Boltzmann ◽  
Boltzmann Method

scholarly journals An improved pairwise decomposable finite-difference Poisson–Boltzmann method for computational protein design

2008 ◽  
Vol 29 (7) ◽  
pp. 1153-1162 ◽  
Author(s):  
Christina L. Vizcarra ◽  
Naigong Zhang ◽  
Shannon A. Marshall ◽  
Ned S. Wingreen ◽  
Chen Zeng ◽  
...  
Keyword(s):  
Finite Difference ◽  
Protein Design ◽  
Computational Protein Design ◽  
Poisson Boltzmann ◽  
Boltzmann Method

An Adaptive, Finite Difference Solver for the Nonlinear Poisson-Boltzmann Equation with Applications to Biomolecular Computations

2013 ◽  
Vol 13 (1) ◽  
pp. 150-173 ◽  
Author(s):  
Mohammad Mirzadeh ◽  
Maxime Theillard ◽  
Asdís Helgadöttir ◽  
David Boy ◽  
Frédéric Gibou
Keyword(s):  
Boltzmann Equation ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Level Set ◽  
Level Set Function ◽  
Novel Approach ◽  
Uniform Grids ◽  
Poisson Boltzmann ◽  
Finite Volume Approach ◽  
Poisson Boltzmann Equation

AbstractWe present a solver for the Poisson-Boltzmann equation and demonstrate its applicability for biomolecular electrostatics computation. The solver uses a level set framework to represent sharp, complex interfaces in a simple and robust manner. It also uses non-graded, adaptive octree grids which, in comparison to uniform grids, drastically decrease memory usage and runtime without sacrificing accuracy. The basic solver was introduced in earlier works [16,27], and here is extended to address biomolecular systems. First, a novel approach of calculating the solvent excluded and the solvent accessible surfaces is explained; this allows to accurately represent the location of the molecule’s surface. Next, a hybrid finite difference/finite volume approach is presented for discretizing the nonlinear Poisson-Boltzmann equation and enforcing the jump boundary conditions at the interface. Since the interface is implicitly represented by a level set function, imposing the jump boundary conditions is straightforward and efficient.

Axisymmetric flow near the critical point on the moving boundary

2010 ◽  
Vol 7 ◽  
pp. 182-190
Author(s):  
I.Sh. Nasibullayev ◽  
E.Sh. Nasibullaeva
Keyword(s):  
Fluid Flow ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Axial Velocity ◽  
Moving Boundary ◽  
Axisymmetric Flow ◽  
Boundary Motion ◽  
Newton Raphson ◽  
Raphson Method

In this paper the investigation of the axisymmetric flow of a liquid with a boundary perpendicular to the flow is considered. Analytical equations are derived for the radial and axial velocity and pressure components of fluid flow in a pipe of finite length with a movable right boundary, and boundary conditions on the moving boundary are also defined. A numerical solution of the problem on a finite-difference grid by the iterative Newton-Raphson method for various velocities of the boundary motion is obtained.

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