Ion distributions in lamellar liquid crystals. A comparison between results from Monte Carlo simulations and solutions of the Poisson-Boltzmann equation

1980 ◽  
Vol 84 (17) ◽  
pp. 2179-2185 ◽  
Author(s):  
Bo Joensson ◽  
Haakan Wennerstroem ◽  
Bertil Halle
Keyword(s):  
Monte Carlo ◽  
Liquid Crystals ◽  
Boltzmann Equation ◽  
Monte Carlo Simulations ◽  
Lamellar Liquid Crystals ◽  
Ion Distributions ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

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

Geometry entrapment in Walk-on-Subdomains

2019 ◽  
Vol 25 (4) ◽  
pp. 329-340 ◽  
Author(s):  
Preston Hamlin ◽  
W. John Thrasher ◽  
Walid Keyrouz ◽  
Michael Mascagni
Keyword(s):  
Monte Carlo ◽  
Boltzmann Equation ◽  
Monte Carlo Method ◽  
Electrostatic Energy ◽  
Potential Solution ◽  
Long Time ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Monte Carlo Implementation

Abstract One method of computing the electrostatic energy of a biomolecule in a solution uses a continuum representation of the solution via the Poisson–Boltzmann equation. This can be solved in many ways, and we consider a Monte Carlo method of our design that combines the Walk-on-Spheres and Walk-on-Subdomains algorithms. In the course of examining the Monte Carlo implementation of this method, an issue was discovered in the Walk-on-Subdomains portion of the algorithm which caused the algorithm to sometimes take an abnormally long time to complete. As the problem occurs when a walker repeatedly oscillates between two subdomains, it is something that could cause a large increase in runtime for any method that used a similar algorithm. This issue is described in detail and a potential solution is examined.

Numerical Optimization of a Walk-on-Spheres Solver for the Linear Poisson-Boltzmann Equation

2013 ◽  
Vol 13 (1) ◽  
pp. 195-206 ◽  
Author(s):  
Travis Mackoy ◽  
Robert C. Harris ◽  
Jesse Johnson ◽  
Michael Mascagni ◽  
Marcia O. Fenley
Keyword(s):  
Monte Carlo ◽  
Boltzmann Equation ◽  
Nearest Neighbor ◽  
Optimization Techniques ◽  
Nearest Neighbor Search ◽  
Computational Time ◽  
Neighbor Search ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Exact Nearest Neighbor

AbstractStochastic walk-on-spheres (WOS) algorithms for solving the linearized Poisson-Boltzmann equation (LPBE) provide several attractive features not available in traditional deterministic solvers: Gaussian error bars can be computed easily, the algorithm is readily parallelized and requires minimal memory and multiple solvent environments can be accounted for by reweighting trajectories. However, previously-reported computational times of these Monte Carlo methods were not competitive with existing deterministic numerical methods. The present paper demonstrates a series of numerical optimizations that collectively make the computational time of these Monte Carlo LPBE solvers competitive with deterministic methods. The optimization techniques used are to ensure that each atom’s contribution to the variance of the electrostatic solvation free energy is the same, to optimize the bias-generating parameters in the algorithm and to use an epsilon-approximate rather than exact nearest-neighbor search when determining the size of the next step in the Brownian motion when outside the molecule.

Examining sharp restart in a Monte Carlo method for the linearized Poisson–Boltzmann equation

2020 ◽  
Vol 26 (3) ◽  
pp. 223-244
Author(s):  
W. John Thrasher ◽  
Michael Mascagni
Keyword(s):  
Monte Carlo ◽  
Free Energy ◽  
Monte Carlo Algorithm ◽  
Significant Bias ◽  
Poisson Boltzmann ◽  
Electrostatic Free Energy ◽  
Poisson Boltzmann Equation ◽  
The Stability ◽  
Potential Methods ◽  
The Individual

AbstractIt has been shown that when using a Monte Carlo algorithm to estimate the electrostatic free energy of a biomolecule in a solution, individual random walks can become entrapped in the geometry. We examine a proposed solution, using a sharp restart during the Walk-on-Subdomains step, in more detail. We show that the point at which this solution introduces significant bias is related to properties intrinsic to the molecule being examined. We also examine two potential methods of generating a sharp restart point and show that they both cause no significant bias in the examined molecules and increase the stability of the run times of the individual walks.

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