Chi-Ok Hwang

Electrical capacitance of the unit cube

It is well known that there is no analytical expression for the electrical capacitance of a cube, even though it has been claimed that one can compute this capacitance numerically to high precision. However, there have been some disparities between reported numerical results of the capacitance of the unit cube. In this article, the “walk on planes” (WOP) algorithm [M. L. Mansfield, J. F. Douglas, and E. J. Garboczi, Phys. Rev. E 64, 061401 (2001)] is used to compute the capacitance of the unit cube. With WOP, we remove the error from the e-absorption layer commonly used in “walk on spheres” computations so that there is no inherent error introduced in these WOP computations except the intrinsic Monte Carlo sampling error of size O(N1/2). This WOP technique comes from the isomorphism, provided by probabilistic potential theory, between the electrostatic Dirichlet problem on a conducting surface, and the corresponding Brownian motion first-passage expectation. The numerical result we obtain with WOP, 0.660 ...

On the rapid estimation of permeability for porous media using Brownian motion paths

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 and terminate on contacting the porous sample. The first method associates the ‘‘penetration depth’’ with a specific property of the Brownian paths, then uses the standard relation between penetration depth and permeability to calculate the latter. The second method uses Brownian paths to calculate an effective capacitance for the sample, then relates the capacitance, via angle-averaging theorems, to the translational hydrodynamic friction of the sample. Finally, a result of Felderhof is used to relate the latter quantity to the permeability of the sample. We find that the penetration depth method is highly accurate in predicting permeability of porous material.

Efficient modified “walk on spheres” algorithm for the linearized Poisson–Bolzmann equation

A discrete random walk method on grids was proposed and used to solve the linearized Poisson–Boltzmann equation (LPBE) [R. Ettelaie, J. Chem. Phys. 103, 3657 (1995)]. Here, we present an efficient grid-free random walk method. Based on a modified “walk on spheres” algorithm [B. S. Elepov and G. A. Mihailov, Sov. Math. Dokl. 14, 1276 (1973)] for the LPBE, this Monte Carlo algorithm uses a survival probability distribution function for the random walker in a continuous and free diffusion region. This simulation method is illustrated by computing four analytically solvable problems. In all cases, excellent agreement is observed.

Ising antiferromagnets in a nonzero uniform magnetic field

We evaluate the density of states g(M, E) as a function of energy E and magnetization M of Ising models on square and triangular lattices, using the exact enumeration method for small systems and the Wang-Landau method for larger systems. From the density of states the average magnetization per spin, m(T, h), of the antiferromagnets has been obtained for any values of temperature T and uniform magnetic field h .A lso, based ong(M, E), the behaviour of m(T, h) is understood microcanonically. The microcanonical approach reveals the differences between the unfrustrated model (on the square lattice) and the frustrated one (on the triangular lattice).

Self-diffusion constants in silicon: Ab initio calculations in combination with classical rate theory

We demonstrate that local-density approximation in combination with the dynamical matrix method is a plausible method for calculating diffusion constants in solids. Especially we compute the diffusivity of the neutral self-interstitial in silicon bulk. The climbing image nudged elastic band method is used for the energy barrier and the transition state atomic configuration. The diffusion prefactor is obtained by using a classical rate theory, the dynamical matrix method. We compare with the diffusivity from another alternative way, ab initio molecular-dynamics simulations, at 1500 K. They are in good agreement.

Nonlinear instability of the one-dimensional Vlasov-Yukawa system

We discuss the nonlinear instability of some class of stationary solutions to the one-dimensional Vlasov–Yukawa system with a mass parameter m. The Vlasov–Yukawa system corresponds to the short-range correction of the repulsive Vlasov–Poisson system arising from plasma physics. We show that the stationary solutions satisfying the Penrose condition are nonlinearly unstable in small mass regime. In a large mass regime, the massiveness of force carrier particles acts as stabilizer in a finite time interval. We present several numerical results to confirm our analytical results.

Yang–Lee zeros of triangular Ising antiferromagnets

In our previous research, by combining both the exact enumeration method (microcanonical transfer matrix) for a small system (L=9) with the Wang–Landau Monte Carlo algorithm for large systems (to L=30) we obtained the exact and approximate densities of states g(M,E), as a function of the magnetization M and exchange energy E, for a triangular-lattice Ising model. In this paper, based on the density of states g(M,E), the precise distribution of the Yang–Lee zeros of triangular-lattice Ising antiferromagnets is obtained in a uniform magnetic field as a function of temperature a=e−2β for a 9×9 lattice system. Also, the feasibility of the Yang–Lee zero approach combined with the Wang–Landau algorithm is demonstrated; as a result, we obtained the magnetic exponents for triangular Ising antiferromagnets at various temperatures.

Simple atomistic modeling of dominant B m I n clusters in boron diffusion

In this paper, we present a simple atomistic model for describing the evolution of interstitial clusters during boron diffusion in kinetic Monte-Carlo (KMC) calculation. It has been known that clusters generated after ion implantation play a decisive role in the enhanced boron diffusion at the tail region while being immobile at the peak region. Our model, which is based on the simple continuum model, takes the intermediate clusters into account as well as dominant clusters for describing the evolutionary behavior of interstitial clusters during boron diffusion. We found that the intermediate clusters such as B3I3 and B2I3 play a significant role during the evolution of clusters despite the fact that the lifetimes of the corresponding intermediate clusters are relatively short due to low binding energies. Further, our investigation revealed that B3I is the most dominant cluster after annealing. We applied our simple atomistic model to the study of boron retardation in arsenic pre-doped substrate. KMC simulation results were compared with experimental SIMS data, which supports our theoretical model.

Study of the Antiferromagnetic Blume-Capel Model on kagomé Lattice

We study the anti-ferromagnetic (AF) Ising model and the AF Blume-Capel (BC) model on the kagome lattice. Using the Wang-Landau sampling method, we estimate the joint density functions for both models on the lattice, and we obtain the exact critical magnetic fields at zero temperature by using the micro-canonical analysis. We also show the patterns of critical lines for the models from micro-canonical analysis.

Phase transitions of 2D triangular antiferromagnetic Ising model in a uniform magnetic field near h=0 and T=0

Using a microcanonical magnetization-energy (ME) diagram, this paper describes all the possible phase transitions of a 2D triangular antiferromagnetic (TAFM) Ising model in a uniform external magnetic field. In particular, we investigate the detailed phase boundary shape of the TAFM near h = 0 and T = 0 using staggered susceptibility.