Summatory and integral equations in periodic diffraction problems for elastic waves at defects in stratified media

We consider the diffraction problem for an elastic wave on a periodic set of defects located at the interface of stratified media. We reduce the mentioned problem to a pair summatory functional equation with respect to coefficients of the expansion of the desired wave by quasiperiodic waves (the Floquet waves). Using the method of integral identities, we reduce the pair equation to a regular infinite system of linear equations. One can solve this system by the truncation method. We prove that the integral identity is the necessary and sufficient condition for the solvability of the auxiliary overspecified problem for a system of equations in a half-plane in the elasticity theory. We obtain integral equations of the second kind which are equivalent to the initial diffraction problem.     

Separated flow modelling and interfacial transport phenomena

A physical explanation of the different types of interfacial waves that appear in stratified and annular gas-liquid flows is presented. The role of waves in affecting process performance is discussed. Particular attention is paid to interfacial drag, gas absorption, the initiation of slug flow and atomization.This paper was presented at the Shell Conference on Computational Fluid Dynamics in Apeldoorn, December, 1989.     

A fully vectorial technique for scattering and propagation in three-dimensional stratified photonic structures

We present a three-dimensional (3D) technique for computing light scattering and propagation in complex structures formed by scatterers embedded in a stratified background. This approach relies on the Green's tensor associated with the background and requires only the discretization of the scatterers, the entire stratified background being accounted for in the Green's tensor. Further, the boundary conditions at the edges of the computation window and at the different material interfaces in the stratified background are automatically fulfilled. Different examples illustrate the application of the technique to the modeling of photonic integrated circuits: waveguides with protrusions (single element grating) and notches. Subtle effects, like polarization crosstalks in an integrated optics device are also investigated.     

山东电视观众满意度调查抽样方案设计

本文给出山东电视观众满意度调查的抽样方案设计 ,构造了两类目标量的估计量 ,并对估计量的精度进行了分析。     

梯度厚板热应力分层计算方法的改进

为了使功能梯度材料厚板的分层计算具有更快的收敛速度和更好的精度,而采用每层热力系数与梯度材料厚度变化为指数函数的分层方法,来平滑均匀分层法引起材料热力系数的跳跃,使热力系数更逼近实际,并将该方法命名为指数函数有限分层法.通过算例表明,在精度为0.1的情况下,均匀分层法的分层层数是指数函数分层法的分层层数的2倍多,并且随着精度的提高,分层层数相差的倍数就越大.     

Localised forced ignition of globally stoichiometric stratified mixtures: A numerical investigation

Localised forced ignition of globally stoichiometric stratified mixtures (i.e. < φ > =1.0) has been analysed here based on direct numerical simulations for different initial values of velocity and equivalence ratio fluctuations (i.e. u′ and φ′), and the Taylor micro-scale l_φ of equivalence ratio φ variation. The localised ignition is accounted for by a source term in the energy transport equation which deposits energy over a stipulated time interval. It has been found that combustion takes place predominantly under premixed mode in the case of successful ignition. The initial values of φ′ and l_φ have been found to have significant effects on the extent of burning of stratified mixtures following localised ignition. It has been found that an increase in u′(φ′) has adverse effects on the burned gas mass, whereas the effects of l_φ on the extent of burning are non-monotonic and dependent on φ′. Detailed physical explanations have been provided for the observed u′, φ′ and l_φ dependences on the extent of burning in stratified mixtures.     

Numerical modeling of the generation of internal waves by uniform stratified flow over a thin vertical barrier

Numerical simulations of two‐dimensional stratified flow past an obstacle (thin vertical strip) were performed at relatively low Reynolds numbers. A finite differences solver was adopted to simultaneously solve Navier–Stokes equations together with transport equations for salinity (stratifying agent), and the standard Smagorinsky turbulent closure scheme was called in whenever necessary to account for turbulence. The emphases were on the evaluation of code for unsteady stratified flow applications as well as identification of transient and steady internal‐wave processes during flow past obstacles. Simulations were compared with laboratory experiments, where observations were made using a high resolution Schlieren technique and conductivity probes. Blocking was observed upstream of the obstacle, surrounded by near‐zero frequency internal waves, the phase lines of which joined those of lee waves through a transition zone in the proximity of the obstacle. This pattern was preceded by initial transients of the starting flow in which propagating internal waves played a dominant role. Confluence of isopycnals passing over/under the obstacle in the wake led to interesting flow phenomena, including the radiation of internal waves. The numerical simulations were in good agreement with observations, except that some phenomena could not be captured due to resolution issues of either numerical or experimental techniques. The efficacy of the code in point for stratified flow calculations with relevance to the atmosphere and oceans was confirmed. Copyright © 2011 John Wiley & Sons, Ltd.     

On applications of the microlocal parameter method in modelling of temperature distributions in composite cylinders

Summary The problems of transient heat conduction in a periodically stratified medium consisting of a large number of alternating concentric cylinders of two homogeneous isotropic rigid materials and in a rotationally periodic cylinder consisting of a large number of circular homogeneous isotropic rigid sectors are considered. The equations of the homogenized models with microlocal parameters are derived by using the homogenization procedure given in [17]. The obtained models take into account certain microlocal effects connected with the microperiodic structure of the considered composites. Some examples of the application of the presented models to the problems of temperature distributions in composite cylinders are detailed. Received 10 March 1997; accepted for publication 23 October 1997     

Oscillations of a cylinder piercing a linearly stratified fluid layer

The plane problem of the small steady-state oscillations of a horizontal cylinder arbitrarily located in a three-layer fluid whose upper and lower layers are homogeneous and whose middle layer is linearly stratified is considered in the linear formulation using the Boussinesq approximation. The fluid is assumed to be ideal and incompressible. The method of mass sources distributed along the body contour is used in the internal wave generation regime and an integral equation for the fluid pressure is derived in the non-wave regime. The hydrodynamic load acting on the body is calculated as a function of the oscillation frequency of the cylinder and its location. The results are compared with experimental data.