First- and last-passage Monte Carlo algorithms for the charge density distribution on a conducting surface

Given, James A.; Hwang, Chi‐Ok; Mascagni, Michael

doi:10.1103/physreve.66.056704

Cited by 29 publications

(62 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Nowadays, owe to the calculation power of the computers, different iterative algorithms are used to solve the equations that govern the behaviour of this type of capacitors [5][6][7][8][9], these algorithms are designed to obtain the surface distributions of load, the values of the electric field and the total capacitance. The disadvantage of these algorithms is that they are designed for specific cases, so that, if geometry changes, the algorithm must almost be reconstructed entirely.…”

Section: Introductionmentioning

confidence: 99%

Capacitance Evaluation on Parallel-Plate Capacitors by Means of Finite Element Analysis

Izquierdo¹,

Bueno-Barrachina²,

Peñuelas³

et al. 2024

RE&PQJ

View full text Add to dashboard Cite

Abstract.The electric field distribution produced by any disposition of insulating and conducting materials is a key aspect in electrical design, but exact values can only be obtained in simple geometries. In this work, using commercially available F.E.M. software we show the influence of the edge-effect on the electric field distribution of a two parallel-plane conducting plates system surrounded by an insulating medium taking into account the thickness of the conducting plates. We compare our results with previous published works. Finally, we obtain the relationship between capacitance and insulation characteristics, insulation gap, plate dimensions and plate thickness.

show abstract

Section: Introductionmentioning

confidence: 99%

Capacitance Evaluation on Parallel-Plate Capacitors by Means of Finite Element Analysis

Izquierdo¹,

Bueno-Barrachina²,

Peñuelas³

et al. 2024

RE&PQJ

View full text Add to dashboard Cite

show abstract

“…Treat x 1 as the new starting point, draw a second ball fully contained in D, make a jump from x 1 to x 2 on the surface of the second ball as before. Repeat this procedure until the path hits a absorption ǫ-shell of the domain [5]. When this happens, we assume that the path has hit the boundary ∂D (see Figure 1(a) for an illustration).…”

Section: Methods Of Walk On Spheres (Wos)mentioning

confidence: 99%

Computation of the local time of reflecting Brownian motion and the probabilistic representation of the Neumann problem

Zhou

Cai

Hsu

2017

Communications in Mathematical Sciences

View full text Add to dashboard Cite

In this paper, we propose numerical methods for computing the boundary local time of reflecting Brownian motion (RBM) in R 3 and its use in the probabilistic representation of the solution of the Laplace equation with the Neumann boundary condition. Approximations of the RBM based on a walk-on-spheres (WOS) and random walk on lattices are discussed and tested for sampling the RBM paths and their applicability in finding accurate approximation of the local time and discretization of the probabilistic formula. Numerical tests for several types of domains (cube, sphere, and ellipsoid) have shown the convergence of the numerical methods as the length of the RBM path and number of paths sampled increase.

show abstract

“…[22][23][24][25] These developments focus on the computation of absorption probability from a point in the suspen-FIG. For completely absorbing traps, the appropriate boundary condition is C 0 = 0 on the surface of the trap because the trapped particle leaves the system.…”

Section: A Probability Of Trapping In a Particle/trap Encountermentioning

confidence: 94%

First-passage approach for permeable traps

Vaughn

2005

The Journal of Chemical Physics

View full text Add to dashboard Cite

Many reactive processes in complex materials involve absorption of diffusing molecules. Recently, there has been interest in particle interaction with partially absorbing (or permeable) traps. Here, we present a simple and efficient method for accounting for the non-diffusion-limited reaction of particles when the flux of particles to the trap is governed by surface permeability. The trapping probability is determined from a one-dimensional Green's function, which results in a simple algebraic expression. This expression, which applies in the region immediately adjacent to the trap, is then used with a first-passage approach far from the trap. When applied to a suspension of permeable traps, the method is seen to give accurate results over the concentration range. The method is applied to the competition of reactive particles in a suspension of permeable spheres with a reactive continuous phase.

show abstract

First- and last-passage Monte Carlo algorithms for the charge density distribution on a conducting surface

Cited by 29 publications

References 10 publications

Capacitance Evaluation on Parallel-Plate Capacitors by Means of Finite Element Analysis

Capacitance Evaluation on Parallel-Plate Capacitors by Means of Finite Element Analysis

Computation of the local time of reflecting Brownian motion and the probabilistic representation of the Neumann problem

First-passage approach for permeable traps

Contact Info

Product

Resources

About