Conformal array realizations of the near and far fields of a complex point source

The complex point source radiates an unusual field without sidelobes in both the near and far zones. The field on a sphere in the near zone closely resembles the far-field pattern. These properties make the complex point-source field desirable in numerous applications in electromagnetics and acoustics. The complex point-source field will be generated using non-resonant arrays with properties that can be realized in the laboratory. Both standard and weighted least-squares techniques determine the array excitation coefficients. The number of array elements required to achieve a certain accuracy of the radiated field can be dramatically reduced if a conformal array structure is employed with the array elements mounted on an impenetrable object. Only the part of the impenetrable object that faces in the beam direction need to be populated with array elements. Numerical examples with array elements consisting of real point sources mounted on a Dirichlet sphere illustrate these findings.     

混合FE-SEA点连接的修正因子研究

针对混合FE-SEA点连接建模提出了一种基于波长的点连接修正因子。目前混合点连接建模主要基于无限结构假设,未考虑边界因素对建模和分析结果的影响。本文首先基于波动理论建立了无限板结构的混合点连接模型,然后根据板结构系统的动力学特性,提出了以判定圆为基准的点连接修正因子。仿真结果表明,本文提出的混合点连接修正因子可有效估计边界对点连接的影响,改进了混合点连接建模的精度。     

Spheroidal wave solutions for sound radiation problems in the near-field of planar structures

Current research in active noise control and in the reconstruction of vibrating sources often requires knowledge of the independent source–field components that best represent the complex acoustical transfer paths observed between a radiating structure and a given control or observation domain. In this paper, closed-form solutions are provided for the singular value expansion of the radiation operator that maps the boundary velocity of a baffled rectangular structure onto the acoustic pressure observed in the half-space domain over a hemi-spheroidal surface located at an arbitrary separation distance from the radiator, including in the near-field zone. Independent contributions of the evanescent and propagating wave components to the complex power are examined for a baffled beam when varying the frequency and the source–field distance parameter. It is shown that the reactive-to-active power ratio induced by each singular mode follows an inverse power law that scales on the product between the reduced frequency and the source–field distance parameter. A transitional region is defined in the space-frequency domain within which the reactive power components are preponderant and should be accounted for when controlling or imaging the near-field zone of a planar radiator. The optimality of the singular source modes is found to be of interest to actively reduce the active and reactive power components in the near-field zone of a radiator with a limited number of independent control channels.     

The mechanisms governing the activation of dislocation sources in aluminum at different strain rates

This article examines the time to activate Frank–Read sources in response to macroscopic strain rates ranging from 10¹ s⁻¹ to 10¹⁰ s⁻¹ in aluminium under athermal conditions. We develop analytical models of the bowing of a pinned dislocation segment as well as numerical simulations of three dimensional dislocation dynamics. We find that the strain rate has a direct influence on both the activation time and the source strength of Frank–Read sources at strain rates up to 10⁶ s⁻¹, and the source strength increases in almost direct proportion to the strain rate. This contributes to the increase in the yield stress of materials at these strain rates. Above 10⁶ s⁻¹, the speed of the bowing segments reaches values that exceed the domain of validity of the linear viscous drag law, and the drag law is modified to account for inertial effects on the motion of the dislocation. As a result the activation times of Frank–Read sources reach a finite limit at strain rates greater than 10⁸ s⁻¹, suggesting that Frank–Read sources are unable to operate before homogeneous nucleation relaxes elastic stresses at the higher strain rates of shock loading. Elastodynamic calculations are carried out to compare the contributions of Frank–Read sources and homogeneous nucleation of dislocations to plastic relaxation. We find that at strain rates of 5×10⁷ s⁻¹ homogeneous nucleation becomes the dominant generation mechanism.     

Efficient field computation using Gaussian beams for both transmission and reception

An exact representation is presented for the field inside a sphere (the observation sphere) due to primary sources enclosed by a second sphere (the source sphere). The regions bounded by the two spheres have no common points. The field of the primary sources is expressed in terms of Gaussian beams whose branch-cut disks are all centered at the origin of the source sphere. The expansion coefficients for the standing spherical waves in the observation sphere are expressed in terms of the output of Gaussian-beam receivers, whose branch-cut disks are all centered at the origin of the observation sphere. In this configuration the patterns of the transmitting and receiving beams “multiply” to produce a higher directivity than is usually seen with Gaussian beams. The areas on the unit sphere, which must be covered by the transmitting and receiving disk normals to achieve a given accuracy, diminish as 1/(ka) for ka → ∞, where a is the disk radius and k is the wavenumber. This 1/(ka) behavior leads to a single-level method with O(N^3/2) complexity for computing matrix-vector multiplications in scattering calculations (N is the number of unknowns).     

Circular crack in a transversely isotropic piezoelectric space under point forces and point charges

In this paper, two kinds of circular crack including external circular crack and penny-shaped crack in a transversely isotropic piezoelectric space are considered. Firstly, we obtain the solution to the problem of an external circular crack in a transversely isotropic piezoelectric space subjected to antisymmetric normal point forces and point charges. Based on this, the solution of one-sided loading of an external circular crack is constructed. Secondly, the real shape of an external circular crack and the opening displacement of a penny-shaped crack under an arbitrary point force and point charge are further obtained. At last, the results are presented in a graphical form. The project supported by the National Natural Science Foundation of China (19872060 and 69982009) and the Postdoctoral Foundation of China     

Complex waves in a dielectric waveguide

Existence of two families of symmetric complex waves in a dielectric waveguide of circular cross section is proved. Eigenvalues of the associated Sturm–Liouville problem on the half-line are determined.     

Advances in scanning electron microscope moiré

The scanning electron microscope (SEM) moiré method for microscopic measurements based on electron beam lithography and an SEM has been well developed. Although it has been a reliable method, some drawbacks exist: reinforcement effects, complicated processing and low sensitivity. To improve the SEM moiré method, new grating-casting techniques and a fringe-viewing technique must be developed. In this study, a carbonaceous grating technique and a total imaging technique are introduced. Accordingly, there are two techniques available for grating-casting (i.e., the carbonaceous grating technique and the existing lithography grating technique) and three techniques available for fringe viewing (i.e., the total imaging technique, the existing, monitor viewing technique and the existing photographic viewing technique). A total of six new imaging techniques of SEM moiré methods are available for microscopic measurements by combining one technique from each of the two groups. This study demonstrates the feasibility of the individual techniques and discusses the characteristics and limitations of each. Based on the presented total imaging technique, the sensitivity of the moiré method is only dependent on the frequency of specimen grating. Because it can be made as high as 10,000 lines/mm, the SEM moiré method can achieve sensitivity as high as 0.01 percent.     

Caristi type hybrid fixed point theorems in menger probabilistic metric space

I.IntroductionandPreliminariesInl976,CaristiprovedtheCaristi'sfixedpointtheoreminIll.Becausethistheoremdoesnotrequirethecontinuityofthemapping.ittindsapplicationsinmanyfields.Inl99l,S.S.Changetal.l'l,broughtforwardCaristi'sfixedpointtheoremandEkeland'svar…     

Thermocapillary convection in a plane liquid layer with concentration heat sources

Thermocapillary instability of a plane liquid binary-mixture layer with time-dependent surface tension is studied under weightlessness conditions. The liquid is heated (or cooled) due to heat release by an active admixture. The heat release rate is proportional to the active-component concentration. The admixture is transported by convection and diffusion. The active component “burns up” with time. The neutral curves for monotonous and oscillating disturbances are found for different values of the nondimensional parameters. Some nonlinear convection regimes are studied numerically by a finite-difference method. The dependence of the convective flow intensity on the Marangoni number is determined. The phase portraits of unsteady regimes are found.     

Minimal and maximal fixed point theorems and iterative technique for nonlinear operators in product spaces

In this paper, we study minimal and maximal fixed point theorems and iterative technique for nonlinear operators in product spaces. As a corollary of our result, some coupled fixed point theorems are obtained, which generalize the coupled fixed point theorems obtained by Guo Da-jun and Lankshmikanthamt and the results obtained by Lan in, and.     

Stagnation point heat flux in hypersonic high enthalpy flow

The paper describes stagnation point heat flux measurements at a range of enthalpies relevant to re-entry speeds of aero-assisted space transfer vehicles (ASTVs) and proposed space planes, using the Australian National University Free Piston Shock Tunnel T3. The unique feature of these experiments is that they were conducted in the straight through (reflectionless) mode which enabled higher enthalpies and densities hitherto unattained.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1992 and the AMS fonts, developed by the American Mathematical Society.     

圆柱管道内运动的小球受到的黏滞阻力的数值分析

为了更好地运用落球法测量研究流体的黏滞系数,研究小球在黏性流体中下落的受力情况,本文对小球在充满黏性流体的圆柱管道的下落过程进行分析。利用COMSOL4.4仿真模拟,建立了合理的仿真模型,并分析了小球受到的黏滞阻力与小球的大小、下落位置的关系。结果表明:选择速度项二阶近似、压强项一阶近似的离散化方法,可以得到和理论值非常相符的仿真结果;当下落过程中小球球心始终在圆柱轴线上时,小球受到的黏滞阻力相对于Stokes力的修正系数,是小球半径与圆柱管道半径的比例函数,本文得到了更大范围的符合理论解的修正系数;当下落过程中小球的球心偏离圆柱轴线时,对于同样大小的小球,黏滞阻力、压强力、黏性力均随着球心到轴线的距离先减小后增大,且具有不同的极小值点。     

流固耦合不可压物质点法及其在晃动问题中的应用

作为一种混合拉格朗日欧拉法,物质点法在流固耦合问题中具有重要的应用前景。对于自由液面的流动问题,基于物质点法框架已建立了弱可压物质点法和完全不可压物质点法,但在处理流固耦合问题时遇到了困难。弱可压物质点法由于采用可压缩状态方程,导致求解时间步长过小,压力振荡严重,产生了非物理的飞溅现象;完全不可压物质点法基于投影算法和不可压条件,消除了弱可压物质点法的压力振荡,提高了时间步长,但难以处理移动边界问题。基于变分形式的投影算法提出了一种新型流固耦合不可压物质点法,得到了体积加权的压力泊松方程PPE(Pressure Poisson Equation),解决了完全不可压物质点法无法处理不规则边界和移动边界的问题。采用流固耦合不可压物质点法研究了运动刚体容器中的液体晃动问题,并与已有实验和数值结果进行对比,验证了算法的正确性和精度。     

Identification of regions of fastest mixing in a system of point vortices

This paper describes a numerical method for efficiently identifying the regions of fastest mixing of a passive dye in a flow due to a system of point vortices. Results obtained from computations are presented for systems of three and four point vortices, both in the unbounded domain and inside a circular cylinder. The flow is two‐dimensional and the fluid is incompressible. The regions where mixing is possible are found by studying the largest Lagrangian Lyapunov exponent distribution with respect to various initial positions of tracer particles. The regions of fastest mixing are then identified from the Lyapunov exponent distribution at small times. The results of the method are verified by quantifying the mixing by using a traditional box counting technique. The technique is then applied to several different initial configurations of vortices and some interesting results are obtained. Some numerical findings about the nature of the exponents computed are also discussed. Copyright © 2002 John Wiley Sons, Ltd.     

Measurements in the vicinity of a stagnation point

This paper presents measurements of a plane jet impinging onto a normal flat plate placed up to five jet widths from the jet outlet. The small spacing ensured that the stagnation streamline remained in the potential core of the jet. The plate shear stress distribution compared well to that from an analytical solution for the laminar development of the plate boundary layer whose external velocity was determined from the measured pressure. By comparing the shear stress measured under the present low level of free stream turbulence (0.35%) at the jet exit with that of Tu and Wood [Exp. Thermal Fluid Sci. 13 (1996) 364–373] made at about 4%, it is concluded that the turbulence level at the nozzle exit has only a second-order influence on the surface shear stress around the stagnation point. Some spanwise non-uniformity was observed in the plate shear stress, but this was confined largely to the transition region. The mean velocity, Reynolds stresses, and fluctuating pressure were measured along the stagnation streamline using a fast-response pressure probe. A significant increase in the streamwise normal stress and the mean square of the pressure fluctuations occurred before they were eventually attenuated by the plate. This increase occurred in the region where the streamwise velocity was decreasing close to the plate causing extra energy production through the normal stresses. Spectra of the velocity and pressure fluctuations showed that the increase in level was mainly due to the low frequency motion, whereas the subsequent decrease occurred at higher frequencies.     

Forced vibration and special effects of revolution shells in turning point range

The forced vibration in the turning point frequency range of a truncated revolution shell subject to a membrane drive or a bending drive at its small end or large end is studied by applying the uniformly valid solutions obtained in a previous paper. The vibration shows a strong coupling between the membrane and bending solutions: either the membrane drive or the bending drive causes motions of both the membrane type and bending type.Three interesting effects characteristic of the forced vibration emerge from the coupling nature:the non-bending effect,the inner-quiescent effect and the inner-membrane-motion-and-outer-bending-motion effect.These effects may have potential applications in engineering.     

在实时单点定位中基于残差信息的改进抗差滤波方法

在利用卫星导航定位系统进行单点导航定位时,为了进一步提高导航定位的精度、实时性和可靠性,针对实时观测信息中存在粗差问题,基于残差分析理论,比较分析了最小二乘法、M估计、抗差滤波估计方法在GNSS单点导航定位中参数估计问题。在此基础上,针对观测量与动力学模型不准确的情况,利用残差信息,构建了有效的改进的基于残差信息的抗差滤波。其特点是观测信息误差比较大的情况下不会导致滤波精度明显下降。在GPS单点导航定位解算中,编程并计算,通过比较分析,结果验证了构建的滤波在单点定位中抗差的优越性,并在导航定位算法选择上得到一些有益结论。     

Two preconditioners for saddle point problems in fluid flows

In this paper two preconditioners for the saddle point problem are analysed: one based on the augmented Lagrangian approach and another involving artificial compressibility. Eigenvalue analysis shows that with these preconditioners small condition numbers can be achieved for the preconditioned saddle point matrix. The preconditioners are compared with commonly used preconditioners from literature for the Stokes and Oseen equation and an ocean flow problem. The numerical results confirm the analysis: the preconditioners are a good alternative to existing ones in fluid flow problems. Copyright © 2006 John Wiley & Sons, Ltd.     

爆炸焊接界面波物质点法三维数值模拟

基于冲击动力学和爆炸焊接理论,采用物质点法对爆炸焊接界面波的形成进行三维数值模拟。通过数值模拟结果与爆炸焊接实验结果的对比,对复合界面材料的塑性流动变形以及界面波形成的机理进行探讨。结果表明:界面波是因为在碰撞点处的金属材料发生熔化并产生涡旋流动形成的;同时也说明采用物质点法模拟爆炸焊接界面波的形成是可行的。