Generalized rayleigh principle and its applications

In this paper, we mainly deal with cigenvalue problems of non-self-adjoint operator. To begin with, the generalized Rayleigh variational principle, the idea of which was due to Morse and Feshbach, is examined in detail and proved more strictly in mathematics. Then, other three equivalent formulations of it are presented. While applying them to approximate calculation we find the condition under which the above variational method can be identified as the same with Galerkin's one. After that we illustrate the generalized variational principle by considering the hydrodynamic stability of plane Poiseuille flow and Bénard convection. Finally, the Rayleigh quotient method is extended to the cases of non-self-adjoint matrix in order to determine its strong eigenvalne in linear algebra.

A new method to analyse the Peierls-Nabarro model of an edge dislocation in a rectangular plate

A new method is presented here to analyse the Peierls-Nabarro model of an edge dislocation in a rectangular plate. The analysis is based on the superposition scheme and series expansions of complex potentials. The stress field and dislocation density field on the slip plane can be expressed as the first and the second Chebyshev polynomial series respectively. Two sets of governing equations are obtained on the slip plane and outer boundary of the rectangular plate respectively. Three numerical methods are used to solve the governing equations.

Intrinsic correlation between fragility and bulk modulus in metallic glasses

A systematic study on the available data of 26 metallic glasses shows that there is an intrinsic correlation between fragility of a liquid and bulk modulus of its glass. The underlying physics can be rationalized within the formalism of potential energy landscape thermodynamics. It is surprising to find that the linear correlation between the fragility and the bulk-shear modulus ratio exists strictly at either absolute zero temperature or very high frequency. Further analyses indicate that a real flow event in bulk metallic glasses is shear dominant, and fragility is in inverse proportion to shear-induced bulk dilatation. Finally, extension of these findings to nonmetallic glasses is discussed.

High Order Multi-Moment Constrained Finite Volume Method. Part I: Basic Formulation

A new high-order finite volume method based on local reconstruction is presented in this paper. The method, so-called the multi-moment constrained finite volume (MCV) method, uses the point values defined within single cell at equally spaced points as the model variables (or unknowns). The time evolution equations used to update the unknowns are derived from a set of constraint conditions imposed on multi kinds of moments, i.e. the cell-averaged value and the point-wise value of the state variable and its derivatives. The finite volume constraint on the cell-average guarantees the numerical conservativeness of the method. Most constraint conditions are imposed on the cell boundaries, where the numerical flux and its derivatives are solved as general Riemann problems. A multi-moment constrained Lagrange interpolation reconstruction for the demanded order of accuracy is constructed over single cell and converts the evolution equations of the moments to those of the unknowns. The presented method provides a general framework to construct efficient schemes of high orders. The basic formulations for hyperbolic conservation laws in 1- and 2D structured grids are detailed with the numerical results of widely used benchmark tests. (C) 2009 Elsevier Inc. All rights reserved.

Self-focusing, Raman, and modulation instability of shaped relativistic laser pulse in plasmas

The interaction of shaped laser pulses with plasmas is studied in a strict theoretical framework without adopting the slow-varying envelope approximation (SVEA). Any physical quantities involved in the interaction are denoted as a summation of different real quantities of respective phases. The relationships among the phases of those real quantities and their moduli are strictly analyzed. Such strict analyses lead to a more exact equation set for the three-dimensional envelope of the laser pulse, which is not based on SVEA. Based on this equation set, self-focusing, Raman, and modulation instabilities could be discussed in a unified framework. The solutions of this equation set for the laser envelope reveal many possible multicolor laser modes in plasmas. The energy and the shape of a pulse determine its propagation through plasmas in a multicolor mode or in a monochromic mode. A global growth rate is introduced to measure the speed of the transition from the monochromic mode in vacuum to a possible mode in plasmas. (c) 2006 American Institute of Physics.

ABCD matrix for reflection and refraction of Gaussian beams at the surface of a parabola of revolution

We report the formulation of an ABCD matrix for reflection and refraction of Gaussian light beams at the surface of a parabola of revolution that separate media of different refractive indices based on optical phase matching. The equations for the spot sizes and wave-front radii of the beams are also obtained by using the ABCD matrix. With these matrices, we can more conveniently design and evaluate some special optical systems, including these kinds of elements. (c) 2005 Optical Society of America

大型干涉仪镜子的支承设计与温度变形分析

在星间激光通信中，涉及对大口径衍射极限激光波面的检测，为保证测量精度，必须严格控制波面十涉仪镜子的自重和温度变形。采用有限元方法对大型干涉仪镜子在不同支承方式下的表面变形进行了分析，结果表明，接触角为180°的钢带支承是较好的支承方式，反射镜表面变形峰-谷(P-V)值仅为1．35nm，均方根(RMS)值为0．363nm根据这一结论，设计了一个同定支承点与浮动支承相结合的超静定钢带支承结构。在该结构下，分析了镜子轴向、径向、周向的温度梯度效应，分析数据表明，镜子的热弹性变形远大于自重变形，建议采取一定的温控

In situ surface topography measurement method of granite base in scanning wafer stage with laser interferometer

Topography of a granite surface has an effect on the vertical positioning of a wafer stage in a lithographic tool, when the wafer stage moves on the granite. The inaccurate measurement of the topography results in a bad leveling and focusing performance. In this paper, an in situ method to measure the topography of a granite surface with high accuracy is present. In this method, a high-order polynomial is set up to express the topography of the granite surface. Two double-frequency laser interferometers are used to measure the tilts of the wafer stage in the X- and Y-directions. From the sampling tilts information, the coefficients of the high-order polynomial can be obtained by a special algorithm. Experiment results shows that the measurement reproducibility of the method is better than 10 nm. (c) 2006 Elsevier GmbH. All rights reserved.

窄带和宽带双曲正割脉冲光束的解析传输式

从近轴波动方程出发推导了窄带和宽带双曲正割脉冲光束的解析传输公式。通过数值计算比较了分别采用复振幅包络(CAE)表示式和复解析信号(CAS)表示式得到的脉冲光束，得出了选择脉冲光束研究方法的条件。结果表明复振幅包络表示式得到的解会存在空间奇异性，使光束出现不符合物理意义的非光束行为。对于宽带光束，复振幅包络解的奇异点的位置距离轴中心较近，使复包络解不能正确表示脉冲光束，而对于奇异点位置远离轴中心的窄带光束，对脉冲光束产生的影响可以忽略。因此，窄带脉冲光束可以采用复振幅包络和复解析信号两种表示式来研究，而对

Propagation properties of off-axis Hermite-cosh-Gaussian beam combinations through a first-order optical system

Based on the Collins integral formula, the analytic expressions of propagation of the coherent and the incoherent off-axis Hermite-cosh-Gaussian (HChG) beam combinations with rectangular symmetry passing through a paraxial first-order optical system are derived, and corresponding numerical examples are given and analysed. The resulting beam quality is discussed in terms of power in the bucket (PIB). The study suggests that the resulting beam cannot keep the initial intensity shape during the propagation and the beam quality for coherent mode is not always better than that for incoherent mode. Reviewing the numerical simulations of Gaussian, Hermite-Gaussian (HG) and cosh Gaussian (ChG) beam combinations indicates that the Hermite polynomial exerts a chief influence on the irradiance profile of composite beam and far field power concentration.

德鲁德分布非均匀膜的光学特性模拟分析

从德鲁德理论出发，对多元共蒸法镀制的非均匀膜的折射率分布与沉积速率的关系进行了探讨；然后利用计算机辅助模拟，对德鲁德分布非均匀光学薄膜，从单周期和多周期、正变和负变、完整周期和存在半周期几个方面对其光学特性进行了系统分析．研究发现：其透射率的极小值和周期数的关系遵从周期数的三次多项式衰减规律，不同规律的德鲁德分布非均匀膜可用来设计不同功能的滤光片．

Bacillus pallidus sp nov., isolated from forest soil

A Gram-positive bacterium, designated strain CW 7(T), was isolated from forest soil in Anhui Province, south-east China. Cells were strictly aerobic, motile with peritrichous flagella and rod-shaped. The strain grew optimally at 30-37 degrees C and pH 7.0-8.0. The major fatty acids of strain CW 7(T) were anteiso-C-15:0, iso-C-15:0 and anteiso-C-17:0. The predominant menaquinone was MK-7. The cell-wall peptidoglycan contained meso-diaminopimelic acid. The G + C content of the genomic DNA was 42.3 mol%. Phylogenetic analysis indicated that strain CW 7(T) belonged to a monophyletic cluster within the genus Bacillus and showed 16S rRNA gene sequence similarities of less than 96.5% to recognized species of the genus Bacillus. The results of the polyphasic taxonomic study, including phenotypic, chemotaxonomic and phylogenetic analyses, showed that strain CW 7(T) represents a novel species of the genus Bacillus, for which the name Bacillus pallidus sp. nov. is proposed. The type strain is CW 7(T) (=KCTC 13200(T)=CCTCC AB 207188(T)=LMG 24451(T)).

Proposal of Sinomonas flava gen. nov., sp nov., and description of Sinomonas atrocyanea comb. nov to accommodate Arthrobacter atrocyaneus

A novel actinomycete strain, designated CW 108(T), was isolated from a forest soil in Anhui Province, China. The cells were strictly aerobic, non-motile, bent rods. The strain grew optimally at 30-37 degrees C and pH 6.0-8.0. Chemotaxonomically, the pepti

On diagonal-Schur complements of block diagonally dominant matrices

It is known that the diagonal-Schur complements of strictly diagonally dominant matrices are strictly diagonally dominant matrices [J.Z. Liu, Y.Q. Huang, Some properties on Schur complements of H-matrices and diagonally dominant matrices, Linear Algebra Appl. 389 (2004) 365-380], and the same is true for nonsingular H-matrices [J.Z. Liu, J.C. Li, Z.T. Huang, X. Kong, Some properties of Schur complements and diagonal-Schur complements of diagonally dominant matrices, Linear Algebra Appl. 428 (2008) 1009-1030]. In this paper, we research the properties on diagonal-Schur complements of block diagonally dominant matrices and prove that the diagonal-Schur complements of block strictly diagonally dominant matrices are block strictly diagonally dominant matrices, and the same holds for generalized block strictly diagonally dominant matrices. (C) 2010 Elsevier Inc. All rights reserved.

Rapid and parallel chromosomal number reductions in muntjac deer inferred from mitochondrial DNA phylogeny

Muntjac deer (Muntiacinae, Cervidae) are of great interest in evolutionary studies because of their dramatic chromosome variations and recent discoveries of several new species. In this paper, we analyze the evolution of karyotypes of muntjac deer in the context of a phylogeny which is based on 1,844-bp mitochondrial DNA sequences of seven generally recognized species in the muntjac subfamily. The phylogenetic results support the hypothesis that karyotypic evolution in muntjac deer has proceeded via reduction in diploid number. However, the reduction in number is not always linear, i.e., not strictly following the order: 46-->14/13-->8/9-->6/7. For example, Muntiacus muntjak (2n = 6/7) shares a common ancestor with Muntiacus feae (2n = 13/14), which indicates that its karyotype was derived in parallel with M. feae's from an ancestral karyotype of 2n greater than or equal to 13/14. The newly discovered giant muntjac (Muntiacus vuquangensis) may represent another pa;allel reduction lineage from the ancestral 2n = 46 karyotype. Our phylogenetic results indicate that the giant muntjac is relatively closer to Muntiacus reevesi than to other muntjacs and may be placed in the genus Muntiacus. Analyses of sequence divergence reveal that the rate of change in chromosome number in muntjac deer is one of the fastest in vertebrates. Within the muntjac subfamily, the fastest evolutionary rate is found in the Fea's lineage, in which two species with different karyotypes diverged in around 0.5 Myr.