Selective lumping finite element method for shallow water flow

A finite element method for solving shallow water flow problems is presented. The standard Galerkin method is employed for spatial discretization. The numerical integration scheme for the time variation is the explicit two step scheme, which was originated by the authors and their co-workers. However, the original scheme has been improved to remove the erroneous artifical damping effect. Since the improved scheme employs a combination of lumped and unlumped coefficients, the scheme is referred to as a selective lumping scheme. Stability conditions and accuracy are investigated by considering several numerical examples. The method has been applied to the tidal flow in Osaka Bay and Yatsushiro Bay.     

刻蚀AlN缓冲层对硅衬底N极性n-GaN表面粗化的影响

研究了等离子体刻蚀AlN缓冲层对硅衬底N极性n-GaN表面粗化行为的影响. 实验结果表明, 表面AlN缓冲层的状态对N极性n-GaN的粗化行为影响很大, 采用等离子体刻蚀去除一部分表面AlN缓冲层即可以有效提高N极性n-GaN在KOH溶液中的粗化效果, AlN缓冲层未经任何刻蚀处理的样品粗化速度过慢, 被刻蚀完全去除AlN缓冲层的样品容易出现粗化过头的现象. 经X射线光电子能谱分析可知, 等离子体刻蚀能够提高样品表面AlN缓冲层Al 2p的电子结合能, 使得样品表面费米能级向导带底靠近, 原子含量测试表明样品表面产生了大量的N空位, N空位提供电子, 使得材料表面费米能级升高, 这降低了KOH溶液和样品表面之间的肖特基势垒, 从而有利于表面粗化的进行. 通过等离子体刻蚀掉表面部分AlN缓冲层, 改善了N极性n-GaN在KOH溶液中的粗化效果, 明显提升了对应发光二级管器件的出光功率.     

Specular and Diffuse Reflectance of Phase‐Separated Polymer Blend Films

Diffuse reflectors have various applications in devices ranging from liquid crystal displays to light emitting diodes, to coatings. Herein, specular and diffuse reflectance from controlled phase separation of polymer blend films, a well‐known self‐organization process, are studied. Temperature‐induced spinodal phase separation of polymer blend films in which one of the components is selectively extracted is shown to exhibit enhanced surface roughness as compared to unextracted films, leading to a notable increase of diffuse reflectance. Diffuse reflectance of UV–visible light from such selectively leached phase‐separated blend films is determined by a synergy of varying lateral scale of phase separation (≈200 nm to 1 μm) and blend film surface roughness (0–40 nm). These critical parameters are controlled by tuning annealing time (0.5–3 h) and temperature (140, 150, 160 °C) of phase separation. Angle‐resolved diffuse reflection studies show that the surface‐roughened polymer films exhibit diffuse reflectance up to 40° from normal incident light in contrast to optically uniform as‐cast films that exhibit largely specular reflectance. Furthermore, the intensity of the diffusively reflected light can be enhanced (300–700 nm) or reduced (220–300 nm) significantly by coating the leached phase‐separated films with a thin silver over layer.

     

Self-consistent mode-coupling theory of the Sun–Guo–Grant equation

The self-consistent mode-coupling approximation of Colaiori and Moore [Phys. Rev. Lett. 86 (2001) 3946] is generalized to the analysis of the Sun–Guo–Grant equation to investigate its dynamic scaling properties in the strong-coupling regime. The corresponding values of the dynamic exponents are calculated for the substrate dimension d=1$d=1$ and 2, respectively, and are also compared with previous analytical and numerical results. It can be seen that our discussion and calculation made in present paper are reasonable and reliable.     

Air–water flow properties in step cavity down a stepped chute

For the last three decades, the research into skimming flows down stepped chutes was driven by needs for better design guidelines. The skimming flow is characterised by some momentum transfer from the main stream to the recirculation zones in the shear layer developing downstream of each step edge. In the present study some physical modelling was conducted in a relatively large facility and detailed air–water flow measurements were conducted at several locations along a triangular cavity. The data implied some self-similarity of the main flow properties in the upper flow region, at step edges as well as at all locations along the step cavity. In the developing shear layer and cavity region (i.e. y/h < 0.3), the air–water flow properties presented some specific features highlighting the development of the mixing layer downstream of the step edge and the strong interactions between cavity recirculation and mainstream skimming flows. Both void fraction and bubble count rate data showed a local maximum in the developing shear layer, although the local maximum void fraction was always located below the local maximum bubble count rate. The velocity profiles had the same shape as the classical mono-phase flow data. The air–water flow properties highlighted some intense turbulence in the mixing layer that would be associated with large shear stresses and bubble–turbulence interactions.     

Thermal and kinetic surface roughening studied by scanning tunneling microscopy and atomic force microscopy

Recent studies of thermal roughening on Si surfaces and kinetic roughening of some growing films, copper and tungsten, by using scanning tunneling microscopy and atomic force microscopy are reviewed. A logarithmic divergence of the surface height fluctuations of Si(111) vicinal surfaces is confirmed, in agreement with the theoretical prediction of rough surface in thermal equilibrium. For the kinetically formed rough surfaces, power law dependences of the interface width on the system size are clearly observed. Furthermore, the tungsten films show a short-range scaling regime and a long-range “smooth” regime. The roughness exponents α are compared with theoretical predictions: for the typical Cu electrode position condition (α=1/2), the exponent appears to be close to that found for local growth models, and for tungsten films (0.7～0.8), it is consistent with recent predictions for growth where surface diffusion is predominant.     

valuation of options on joint minima and maxima

It is shown how to obtain explicit formulae for a variety of popular path-dependent contracts with complex payoffs involving joint distributions of several extrema. More specifically, formulae are given for standard step-up and stepdown barrier options, as well as partial and outside step-up and step-down barrier options, between three and five dimensions. The proposed method can be extended to other exotic path-dependent payoffs as well as to higher dimensions. Numerical results show that the quasi-random integration of these formulae, involving multivariate distributions of correlated Gaussian random variables, provides option values more quickly and more accurately than Monte Carlo simulation.     

Phase-field modeling of epitaxial growth: Applications to step trains and island dynamics

In this paper, we present a new phase-field model including combined effects of edge diffusion, the Ehrlich-Schwoebel barrier, deposition and desorption to simulate epitaxial growth. A new free energy function together with a correction to the initial phase variable profile is used to efficiently capture the morphological evolution when a large deposition flux is imposed. A formal matched asymptotic analysis is performed to show the reduction of the phase-field model to the classical sharp interface Burton-Cabrera-Frank model for step flow when the interfacial thickness vanishes. The phase-field model is solved by a semi-implicit finite difference scheme, and adaptive block-structured Cartesian meshes are used to dramatically increase the efficiency of the solver. The numerical scheme is used to investigate the evolution of perturbed circularly shaped small islands. The effect of edge diffusion is investigated together with the Ehrlich-Schwoebel barrier. We also investigate the linear and nonlinear regimes of a step meandering instability. We reproduce the predicted scaling law for the growth of the meander amplitude, which was based on an analysis of a long wavelength regime. New nonlinear behavior is observed when the meander wavelength is comparable to the terrace width. In particular, a previously unobserved regime of coarsening dynamics is found to occur when the meander wavelength is comparable to the terrace width.     

Stable surface termination on vicinal 6H-SiC(0 0 0 1) surfaces

Ordered nanofacet structures on vicinal 6H-SiC(0 0 0 1) surfaces, consisting of pairs of a (0 0 0 1) basal plane and a facet, are investigated in terms of stable surface stacking of the (0 0 0 1) basal planes. The surface termination of S3 (or S3*), i.e., ABC (or A*C*B*), was suggested by a structural model based on quantized step-bunching, which typically gives a one-unit-cell bunched step configuration at the facet. Here, we evaluate the surface termination at basal planes covered with a layer of silicon oxynitride by means of quantitative low-energy electron diffraction (LEED) analysis combined with scanning tunneling microscopy (STM), and show the validity of the structural model proposed.