Many important classes of problems in materials science and biotechnology require the solution of the Laplace or Poisson equation in disordered two-phase domains in which the phase interface is… (More)

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… (More)

As CMOS devices are scaled down to nanometer regime, it is even more stringent to control the impurity profiles at the front-end process. Especially, ion implantation for ultra shallow junction in… (More)

The “Walk On Spheres” (WOS) algorithm and its relatives have long been used to solve a wide variety of boundary value problems [Ann. Math. Stat. 27 (1956) 569; J. Heat Transfer 89 (1967) 121; J.… (More)

We describe two efficient methods of estimating the fluid permeability of standard models of porous media by using the statistics of continuous Brownian motion paths that initiate outside a sample… (More)

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… (More)

We review efficient grid-free random walk methods for solving boundary value problems for the linearized Poisson-Boltzmann equation (LPBE). First we introduce the “Walk On Spheres” (WOS) algorithm… (More)

In this paper, we present a simple atomistic model for describing the kinetic Monte Carlo (KMC) evolution of interstitial clusters during boron diffusion. It has been known that clusters generated… (More)