Last‐Passage Algorithm for Charge Distribution Over a Finite Region

Abstract

First‐passage and last‐passage Monte Carlo algorithms have been used for computing charge distribution on a conducting object. First‐passage algorithms are used for an overall charge distribution on a conducting object and Given–Hwang's last‐passage algorithms are used for a charge density at a specific point on a flat or spherical surface of a conductor. In this paper, a last‐passage algorithm for computing charge distribution over a finite region of a conducting object is presented.

Sphere Last‐Passage Algorithm for Charge Density on a Smooth (Convex) Conducting Surface

“…In this section, we compute the corner singularity on the unit cube. The corner singularity exponent is defined as [19] 𝜎(r) = Ar (𝜋∕𝛼−1)−𝛾 (15) where 𝜎(r) is charge density, A constant, r the diagonal distance from the corner, 𝛼 = 3 2 𝜋 the angle between the two intersecting surfaces which form the edge, and 𝛾 the singularity exponent.…”

“…In addition, recently we have developed a last-passage algorithm for computing charge distribution over a finite region of a conducting object. [15] All the previous last-passage algorithms can compute charge density at a specific point on a flat or spherical conducting surface only. Here, in this paper we further develop the last-passage algorithms for charge density at a specific point on a smooth surface, where we can construct a tangent plane and put a sphere, that is, at a point on a smooth (generally convex) surface.…”

“…Schematic diagram for the relation of electrostatic potential $$\phi (r)$$ and the diffusion probability $$p(r)$$: The potential $$\phi (r)$$ is the potential at r when the spherical conductor is at unit potential and the probability $$p(r)$$ is the probability of the Brownian particle starting from the distance r and going to infinity without going back to the spherical conductor. [ 4,5 ] …”

“…In a series of papers, we have been developing the last‐passage algorithms such as last‐passage algorithm, [ 7 ] off‐centered last‐passage algorithm on a flat conducting surface, [ 8 ] quadrupole last‐passage algorithm on an L‐shaped conducting surface, [ 4 ] and last‐passage algorithm on a spherical conducting surface [ 9 ] and so on [10]. In addition, recently we have developed a last‐passage algorithm for computing charge distribution over a finite region of a conducting object.…”

“…In addition, recently we have developed a last‐passage algorithm for computing charge distribution over a finite region of a conducting object. [ 15 ]…”