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 0.632(2) and 0.997(2) for the clock model. It seems that this study supports the recent results by [Lapilli et al.Phys. Rev. Lett. 96, 140603 (2006)] that the transitions are not of Kosterlitz and Thouless type.

In this paper, we report our study on the minimised atomistic model (MAM) and the determination of an evolution path for dominant B _m I _n clusters during boron diffusion in kinetic Monte Carlo (KMC). 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 MAM, based on the simple continuum model and the simple atomistic model, takes the smallest number of intermediate clusters into account as well as dominant clusters for the evolution path of interstitial clusters during boron diffusion. We find that intermediate clusters such as B₂I₃ and B₃I₃ 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. Also, through our simulation results, we find the main evolution path of dominant clusters from B₂I to B₃I during thermal annealing in the MAM. Furthermore, our investigation reveals that the density of BI₂ clusters increases at the beginning of the annealing process while the density of B₃I increases at a later stage. KMC simulation results are compared with experimental SIMS data, which support our theoretical model.

We introduce the discrete p-Schrödinger operator L_p,ω and solve the following p-Schrödinger equation: L_p,ωu = −Δ_p,ωu + q|u|^p−2u = f on networks. To show the uniqueness of solutions of the p-Schrödinger equation, we first solve the eigenvalue problem for the p-Schrödinger operator and obtain some properties of the smallest eigenvalue and its corresponding eigenfunction of the p-Schrödinger operator.

In this paper, we investigate the semiclassical strings in AdS₃ × S², in which the string configuration of AdS₃ is classified to three cases depending on the parameters. Each of these has a different anomalous dimension proportional to log S, S^1/3 and S, where S is a angular momentum on AdS₃. Further we generalize the dispersion relations for various string configuration on AdS₃ × S².

This paper proposes a new nondestructive evaluation method for detecting cracks, voids, and other hidden defects inside concrete structures, called "frequency differential electrical impedance scanning (fdEIS)." The primary benefit of fdEIS over the conventional nondestructive methods is that it is possible to determine the thickness of the voids. In fdEIS, we inject a sequence of electrical currents with various frequencies through the tested concrete wall by applying a sinusoidal voltage difference between a surface electrode and a scan probe, which are placed on opposite surfaces of the wall. Through the probe, we measure the derivative d/dw gw of exit currents (Neumann data) with respect to the angular frequency variable w. We find the fundamental concept in fdEIS relating the thickness of the voids to d/dw gw and derive an approximation formula for estimating the thickness of the voids. We demonstrate the performance of our method in numerical simulations.

Ha, T., Choi, Y., Shin, C.S. and Min, D.-J., 2009. Numerical modeling for 3D acoustic wave
equation in the frequency domain. Joumal of Seisnic Exploration, l8t 57-19.
We investigatea frequency-domainfi nite-elementm ethod for three-dimensionaml odeling
of the acousticw ave equation.F requency-domaimn odelingh ass everala dvantageos ver time-domain
modeling,e ven though it requiresh ugec omputationaml emoryc omparedt o time-domainm odeling.
One of these advantages is that multi-shot modeling can be performed more efficiently in the
frequency domain than in the time domain, and another is the ability to work on a
frequency-by-frequencbya sis,w hich makesi t possiblet o distributef requenciesa crossp rocessors.
Consideringt hat frequency-domainm odeling is popular in waveform inversionb ecauseo f source
wavelet estimationa nd multi-shot modeling, 3D frequency-domainfi nite-elementm odelingc an be
effectively used in 3D waveform inversion. We derive a numerical dispersion relationship for the
3D frequency-domainfi nite-elementm ethoda nd then analyzen umericald ispersiono n the basiso f
dispersion curves. From the dispersion analysis, we determine th€ minimum number of grid points
per wavelength. The validity of the 3D finite-element modelirtg algorithm is examined for a
three-layeredm odel and the SEG/EACE salt model.
KEY WORDS:3D modeling, acousticw ave equation,f requency-domainf,i nite-elemem,
numerical dispersion