Last-passage Monte Carlo Algorithm for Charge Density on a Conducting Spherical Surface

2021 ◽  
Vol 88 (3) ◽  
Author(s):  
Unjong Yu ◽  
Young-Min Lee ◽  
Chi-Ok Hwang
Keyword(s):  
Monte Carlo ◽  
Charge Density ◽  
Spherical Surface ◽  
Monte Carlo Algorithm

Off‐Centered Last‐Passage Monte Carlo Algorithm for the Charge Density on a Flat Conducting Surface

2020 ◽  
Vol 3 (8) ◽  
pp. 2000075
Author(s):  
Hoseung Jang ◽  
Unjong Yu ◽  
Youngjoo Chung ◽  
Chi‐Ok Hwang
Keyword(s):  
Monte Carlo ◽  
Charge Density ◽  
Monte Carlo Algorithm ◽  
Conducting Surface

A diffusion Monte Carlo method for charge density on a conducting surface at non-constant potentials

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Unjong Yu ◽  
Hoseung Jang ◽  
Chi-Ok Hwang
Keyword(s):  
Monte Carlo ◽  
Charge Density ◽  
Potential Surface ◽  
Circular Disk ◽  
Monte Carlo Algorithm ◽  
Conducting Surface ◽  
Charge Densities ◽  
Monte Carlo Algorithms ◽  
Constant Potential ◽  
Diffusion Monte Carlo Method

Abstract We develop a last-passage Monte Carlo algorithm on a conducting surface at non-constant potentials. In the previous researches, last-passage Monte Carlo algorithms on conducting surfaces with a constant potential have been developed for charge density at a specific point or on a finite region and a hybrid BIE-WOS algorithm for charge density on a conducting surface at non-constant potentials. In the hybrid BIE-WOS algorithm, they used a deterministic method for the contribution from the lower non-constant potential surface. In this paper, we modify the hybrid BIE-WOS algorithm to a last-passage Monte Carlo algorithm on a conducting surface at non-constant potentials, where we can avoid the singularities on the non-constant potential surface very naturally. We demonstrate the last-passage Monte Carlo algorithm for charge densities on a circular disk and the four rectangle plates with a simple voltage distribution, and update the corner singularities on the unit square plate and cube.

Monte-Carlo Simulation of Ion Transport at the Polymer-Metal Interface

Aerospace ◽  
2005 ◽  
Author(s):  
Xingxi He ◽  
Donald J. Leo
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Electric Field ◽  
Ion Transport ◽  
Charge Density ◽  
Monte Carlo Algorithm ◽  
Coulomb Energy ◽  
Metal Interface ◽  
Polymer Metal ◽  
Hopping Model

The transport of charge due to electric stimulus is the primary mechanism of actuation for a class of polymeric active materials known as ionomeric polymer transducers. Continuum-based models of ion transport have been developed for the purpose of understanding charge transport due to diffusion and migration. In this work a two dimensional ion hopping model has been built to describe ion transport in ionomeric polymer transducer (IPT) with Monte-Carlo simulation. In the simulation, cations are distributed on 50nm × 50nm × 1nm (or 50nm × 10 nm × 1nm) lattice cells of IPT while the same number of negative charges are uniformly scattered and fixed as background. In the simulation, thermally activated cations are hopping between multiwell energy structures by overcoming energy barriers around with a hopping distance of 1nm during each time step. A step voltage is applied between the electrodes of the IPT. In one single simulation step, coulomb energy, external electric potential energy and intrinsic energy of the material are calculated and added up for the energy wells around the cations. And then hopping rates in every potential hopping direction are obtained. Due to the random nature of the ion transitions, a weighting function from Monte-Carlo algorithm is added in to calculate the ion hopping time. Finally hopping time is compared, the minimum hopping time is chosen and one hopping event is completed. Both system time and ions distribution are updated before the next simulation loop. Periodic boundary conditions are applied when ions hop in the direction perpendicular to the electric field. The influence of the electrodes on both faces of IPT is presented by the method of image charges. The charge density at equilibrium state is compared with the result from a continuum-based model. The property of charge density has charge neutrality over the central part of the membrane and the charge imbalance over boundary layers close to the anode and cathode. Electric field distribution is obtained after charge distribution. After it is demonstrated that ion hopping model leads to the results qualitatively matching the property of IPT, the paper uses the model to analyze the polymer-metal interface when the electrode shape inside transducer varies.

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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