American Musicological Society

By using the Onsager principle as an approximation tool, we give a novel derivation for the moving finite element method for gradient flow equations. We show that the discretized problem has the same energy dissipation structure as the continuous one. This enables us to do numerical analysis for the stationary solution of a nonlinear reaction diffusion equation using the approximation theory of free-knot piecewise polynomials. We show that under certain conditions the solution obtained by the moving finite element method converges to a local minimizer of the total energy when time goes to infinity. The global minimizer, once it is detected by the discrete scheme, approximates the continuous stationary solution in optimal order. Numerical examples for a linear diffusion equation and a nonlinear Allen-Cahn equation are given to verify the analytical results.

In this paper, we investigate the uniform regularity for the isentropic compressible Navier--Stokes system with general Navier-slip boundary conditions (1.6) and the inviscid limit to the compressible Euler system. It is shown that there exists a unique strong solution of the compressible Navier--Stokes equations with general Navier-slip boundary conditions in an interval of time which is uniform in the vanishing viscosity limit. The solution is uniformly bounded in a conormal Sobolev space and is uniformly bounded in $W^{1,\infty}$. It is also shown that the boundary layer for the density is weaker than the one for the velocity field. In particular, it is proved that the velocity will be uniformly bounded in $L^\infty(0,T;H^2)$ when the boundary is flat and the Navier--Stokes system is supplemented with the vorticity free boundary condition (1.25). Based on such uniform estimates, we prove the convergence of the viscous solutions to the inviscid ones in $L^\infty(0,T;L^2)$, $L^\infty(0,T;H^1)$ and $L^\infty([0,T]\times\Omega)$ with a rate of convergence.

A thin metal layer is introduced into a slab waveguide grating with guided-mode resonances to reduce the switching intensity in its bistable operational mode. A dielectric grating put on top of the metal layer plays the role of a coupling element between the normally incident light and the guided mode in the slab waveguide grating. The presence of the metal layer increases the reflectivity of the optical device that as a consequence exhibits high-reflection side bands and close-to-zero reflectivity drops. Several structures are designed by changing the grating depths and the metal layer thicknesses, and their influences on linear and nonlinear characteristics are analysed using the finite-difference time-domain method. We found that the metal layer increases the quality factor of guided-mode resonance filters. Numerical results show that the quality factor improves 5.6 times and the switching intensity is reduced 45 times when these devices are compared to typical slab waveguide gratings in the same working conditions, in terms of polarization and operating wavelength.

海南岛万宁地区的辉长岩体及穿插其中的辉绿岩脉均为印支期近时基性侵入体. 我们对辉长岩和辉绿岩脉进行了磁组构研究. 万宁辉长岩体获得61个定向岩芯样品, 边杜村辉长岩获得7个定向岩芯样品. 横跨7条辉绿岩脉共系统钻取53个定向岩芯样品. 岩石磁学分析表明, 辉绿岩和辉长岩主要的磁性矿物分别是多畴贫钛磁铁矿和假单畴-多畴贫钛磁铁矿, 它们为基性岩中的原生磁性矿物. 辉长岩和辉绿岩均具有较低的磁各向异性度(<italic>P_j</italic>&lt;1.2), 它们保留着原生的流动磁组构特征. 辉长岩的最大磁化率主轴(<italic>K</italic>₁, 磁线理方向)分布相对集中, 平均方向为1.9°∠15.7°, 绝大多数样品倾角小于30°, 显示低倾角正北方向倾伏; 7条辉绿岩脉各自的<italic>K</italic>₁主轴集中, 且一致性良好, 分布在NNW-SSE方向, 倾角大致在30°左右. <italic>K</italic>₁分布表明: 万宁辉长岩体的侵位方式为以低仰角由北向南侧向侵位, 而辉绿岩脉则以中至低仰角从NNW向SSE侧向侵位. 它们可能是位于更北部的同源岩浆脉动式侵位的结果, 这意味着在万宁北部的印支期花岗岩之下可能隐伏有该期的基性岩体.

To the Editor Howard Mayer Brown Howard Mayer Brown President American Musicological Society Search for other works by this author on: Oxford Academic Google Scholar Music Theory Spectrum, Volume 1, Issue 1, Spring 1979, Page 129, https://doi.org/10.2307/745785 Published: 01 March 1979