Walk-on-Hemispheres first-passage algorithm.

Due to the isomorphism between an electrostatic problem and the corresponding Brownian diffusion one, the induced charge density on a conducting surface by a charge is isomorphic to the first-passage probability of the diffusion initiated at the location of the charge. Based on the isomorphism, many diffusion algorithms such as "Walk-on-Spheres" (WOS), "Walk-on-Planes" and so on have been developed. Among them, for fast diffusion simulations WOS algorithm is generally applied with an [Formula: see text]-layer, which is used for diffusion convergence on the boundary but induces another error from the [Formula: see text]-layer in addition to the intrinsic Monte Carlo error.

Six-state clock model on the square lattice: fisher zero approach with Wang-Landau sampling.

We investigate the six-state clock model with nearest-neighbor interactions on the square lattice. We obtain the density of states of the finite systems up to L=28 using the Wang-Landau sampling. With the density of states and the Fisher zero approach, we successfully find two different critical temperatures 0.

Last-passage Monte Carlo algorithm for mutual capacitance.

We develop and test the last-passage diffusion algorithm, a charge-based Monte Carlo algorithm, for the mutual capacitance of a system of conductors. The first-passage algorithm is highly efficient because it is charge based and incorporates importance sampling; it averages over the properties of Brownian paths that initiate outside the conductor and terminate on its surface. However, this algorithm does not seem to generalize to mutual capacitance problems.

Edge distribution method for solving elliptic boundary value problems with boundary singularities.

Elliptic boundary value problems are difficult to treat in the vicinity of singularities, i.e., edges and corners, of the boundary.

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

Recent research shows that Monte Carlo diffusion methods are often the most efficient algorithms for solving certain elliptic boundary value problems. In this paper, we extend this research by providing two efficient algorithms based on the concept of "last-passage diffusion." These algorithms are qualitatively compared with each other (and with the best first-passage diffusion algorithm) in solving the classical problem of computing the charge distribution on a conducting disk held at unit voltage.