双元场和光子的波动方程专题介绍

把电场和磁场组合成双元场,用来表示光子的状态,使得光子的波动方程成为一阶导数型的.该方程既具备宇称变换下的协变性,也体现出电和磁间的对称性,且保持了态函数的统计诠释.文中给出了光子的一些常用算符,并分别在p^和H^,p^z、J^z和H^以及J^2、J^z和H^同时确定的情况下求出了方程的解.不需要给态函数附加Lorentz条件,即能用该波动方程得到只存在两种横光子的结论.     

均布载荷作用下具有光滑中心波纹膜片的非线性分析

采用轴对称旋转壳体的简化Reissner方程，研究了在均布载荷作用下具有光滑中心波纹膜片的非线性弯曲问题。应用格林函数方法，波纹膜片的非线性边值问题化为了非线性积分方程的求解。为了求解积分方程并防止发散，一个插值参数被引入到迭代格式中。计算表明，当载荷很小时，任何插值参数值均能保证迭代的收敛性，取插值参数值接近或等于1获得较快的收敛速度，而当载荷较大时，插值参数值不能取得过大。绘出了波纹膜片的特征曲线，得到的特征曲线可供设计参考。可以断言，当载荷不大时，特征曲线是近似线性的，随着载荷的增大，特征曲线开始向上弯曲，明显偏离线性。本文中提出的解决方法适应于任意轴向截面的波纹壳体。     

反对称斜交叠层板双向弯曲问题的横向基理论解

研究反对称斜交叠层板的双向弯曲问题。根据横向基理论，在厚度方向，给出了三个方向位移沿厚度的分布规律；在面内方向，采用升阶谱位移函数；然后，应用最小势能原理导出叠层板的静力控制方程。通过对多种层数和铺层角的层板力学响应计算分析表明：在典型位置的应力分布，本文解与三维弹性解符合很好，并有较好的收敛性。     

Differential quadrature method for bending of orthotropic plates with finite deformation and transverse shear effects

Based on the Reddy ‘s theory of plates with the effect of higher-order shear deformations, the governing equations for bending of orthotropic plates with finite deformations were established. The differential quadrature ( DQ ) method of nonlinear analysis to the problem was presented. New DQ approach, presented by Wang and Bert ( DQWB), is extended to handle the multiple boundary conditions of plates. The techniques were also further extended to simplify nonlinear computations. The numerical convergence and comparison of solutions were studied. The results show that the DQ method presented is very reliable and valid. Moreover, the influences of geometric and material parameters as well as the transverse shear deformations on nonlinear bending were investigated. Numerical results show the influence of the shear deformation on the static bending of orthotropic moderately thick plate is significant.     

The cut-and-try method in determining the saturate spacing of transverse cracks of composite laminates

In this paper, the saturate spacing of transverse cracks of the 90° ply is originally calculated by the 3-D finite element method. Thus, a new approach is put forward for predicting the saturate spacing of transverse cracks.     

Loss of Ellipticity in Plane Deformation of a Simple Directionally Reinforced Incompressible Nonlinearly Elastic Solid

Change of type in the governing equations of equilibrium is examined in the context of a base neo-Hookean response augmented with unidirectional reinforcing that is characterized by a single additional constitutive parameter for strength of reinforcement. Plane deformations interpreted in terms of both local and global plane strain are considered. Loss of ordinary ellipticity is found to occur for sufficiently large strength of reinforcement under sufficiently severe deformation which necessarily involves contraction in the reinforcing direction. Loss of ellipticity in local plane strain is easily characterized, and its incipient breakdown is associated with the possible emergence of surfaces of weak discontinuity with orientation normals in the reinforcing direction. Loss of ellipticity in global plane strain is given a two-dimensional manifold characterization in a space involving 2 deformation parameters and the strength of reinforcing parameter. Orientation normals for the associated surfaces of weak discontinuity at incipient breakdown do not in general conform to the reinforcing direction. This revised version was published online in August 2006 with corrections to the Cover Date.     

Gravity Affected Lateral Dispersion and Diffusion in a Stationary Horizontal Porous Medium Shear Flow

Transport of dissolved species by a carrier fluid in a porous medium comprises advection and diffusion/dispersion processes. Hydrodynamic dispersion is commonly characterized by an empirical relationship, in which the dispersion mechanism is described by contributions of molecular diffusion and mechanical dispersion expressed as a function of the molecular Peclét number. Mathematically these two phenomena are modeled by a constant diffusion coefficient and by velocity dependent dispersion coefficients, respectively. Here, the commonly utilized Bear--Scheidegger dispersion model of linear proportionality between mechanical dispersion and velocity, and the more complicated Bear--Bachmat model derived on a streamtube array model porous medium and better describing observed dispersion coefficients in the moderate molecular Peclét number range, will be considered. Analyzing the mixing flow of two parallelly flowing confluent fluids with different concentrations of a dissolved species within the frames of boundary layer theory one has to deal with transverse mixing only. With the Boussinesq approximation being adopted approximate analytical solutions of the corresponding boundary layer system of equations show that there is no effect of density coupling on concentration distributions across the mixing layer in the pure molecular diffusion regime case. With the Peclét number of the oncoming flow growing beyond unity, density coupling has an increasing influence on the mixing zone. When the Peclét number grows further this influence is successively reduced until its disappearance in the pure mechanical dispersion regime.     

Extension of Mixed‐Mode Fatigue Cracks in Steel Samples

Experimental studies of the extension of mixedmode fatigue cracks were performed on rail steel samples. The direction of growth of fatigue cracks was studied for three types of loading: alternate transverse shear and transverse and longitudinal shears under compressing stresses. For all tested samples, the following common feature in the extension of fatigue cracks was established: the direction of crack growth coincides with the propagation direction of the principal stresses having minimum absolute values.     

An evaluation of the arcan specimen for determining the shear moduli of fiber-reinforced composites

Moiré interferometry was used to examine the strain distributions in Arcan-type specimens under shear loading. The compact geometry allowed longitudinal and transverse shear behavior to be considered. The best results for longitudinal moduli were obtained with fibers running from notch to notch. As with the losipescu configuration, strain averaging or correction factors were required for modulus determination in all fiber orientations. None of the bending problems that have been encountered in the losipescu specimen were observed. Some twisting was noticed, but its extent (less than 2 percent) was much less than has been noted in shear testing with losipescu specimens.     

Relaxed Energy for Transversely Isotropic Two-Phase Materials

The paper gives a simple derivation of the relaxed energy W ^qc for the quadratic double-well material with equal elastic moduli and analyzes W ^qc in the transversely isotropic case. We observe that the energy W is a sum of a degenerate quadratic quasiconvex function and a function that depends on the strain only through a scalar variable. For such a W, the relaxation reduces to a one-dimensional convexification. W ^qc depends on a constant g defined by a three-dimensional maximum problem. It is shown that in the transversely isotropic case the problem reduces to a maximization of a fraction of two quadratic polynomials over [0,1]. The maximization reveals several regimes and explicit formulas are given in the case of a transversely isotropic, positive definite displacement of the wells. This revised version was published online in June 2006 with corrections to the Cover Date.