A second-order accurate numerical method for the two-dimensional fractional diffusion equation

Spatially fractional order diffusion equations are generalizations of classical diffusion equations which are used in modeling practical superdiffusive problems in fluid flow, finance and others. In this paper, we present an accurate and efficient numerical method to solve a fractional superdiffusive differential equation. This numerical method combines the alternating directions implicit (ADI) approach with a Crank–Nicolson discretization and a Richardson extrapolation to obtain an unconditionally stable second-order accurate finite difference method. The stability and the consistency of the method are established. Numerical solutions for an example super-diffusion equation with a known analytic solution are obtained and the behavior of the errors are analyzed to demonstrate the order of convergence of the method.     

Reconstruction of holograms generated by using a combination of an iterative method and an error diffusion method

Two-level quantized phase holograms produced by using a combination of an iterative method and an error diffusion method are presented. By using a previously proposed iterative method, images reconstructed from two-level quantized phase holograms are rapidly improved with small amounts of iterative operations but further improvement of the image quality is difficult even if the iterations are greatly increased. Therefore, in order to exceed the improvement limitation of the image quality, the combination of the iterative method and an error diffusion method was used for the hologram-making process. Experimental results using the combination method showed better images than those obtained by the iterative method alone, when referred to results from synthesized holograms.     

Automatic method of fruit object extraction under complex agricultural background for vision system of fruit picking robot

Fruit picking robot is required for agricultural automation for fruit harvest, and vision system is the important and crucial composition of a robot system. An automatic extraction method of fruit object under complex agricultural background for vision system in fruit picking robot is presented in this study. The method is based on an improving Otsu threshold algorithm using a new feature in OHTA color space. Color features are extracted in OHTA color space and then used as an input for the Otsu threshold algorithm which calculates the segmentation threshold value automatically. Four kinds of fruit images are selected to validate the automatic extraction method. The fruit objects are automatically extracted with this method and the outputs are presented in binary images. Numerous of experiments show that the automatic extraction method can extract mature fruit from complex agricultural background and the extraction accuracy is more than 95%. The results indicate an effective fruit object extraction method for vision system of fruit picking robot.     

模拟封闭声场脉冲响应的圆锥束跟踪法

本文简要介绍了声场脉冲响应计算机模拟技术的基本状况,给出了一种将虚源法和声线法相结合的模拟方法－圆锥束跟踪法的原理和算法,并将其对一个实例的计算结果与虚源法进行了比较,最后对其实现过程中需要注意的问题进行了讨论。     

Surface currents of a superconducting axisymmetric body that screen an external coaxial magnetic field

A time-saving method to find currents on the surface of a superconducting axisymmetric body is suggested for the case when the axis of the body and the symmetry axis of an external magnetic field coincide. The method is based on solving a one-dimensional integral equation. Analytical solutions are derived for the superconductor in the form of an ellipsoid of revolution that is placed in a uniform magnetic field and in the form of a sphere placed in a magnetic field varying as a polynominal at the symmetry axis. To find the current density on the surface of an arbitrarily shaped axisymmetric body placed in an arbitrarily varying magnetic field, a method of numerically solving the integral equation is proposed. It is a combination of the iterative regularization method and the projective method with a projector in the form of B splines. The results of numerical reconstruction of the sought functions by the latter method for a number of particular cases are presented.     

能量系统故障诊断的热经济学模型

本文将建立在热力学第二定律基础上的 分析方法与热经济学方法运用于能量系统的故障诊断。通过与常规热力学方法的定量比较,证明了■分析方法与热经济学方法对系统中发生的故障具有更高的敏感度,并建立了进行能量系统故障诊断的 分析模型与热经济学分析模型,并以某 ２００ ＭＷ火电机组为例,分别采用这两种方法对机组在某一况时的故障情况进行了诊断,并对结果进行了分析比较。     

Doublet resonances of an electron in symmetric three-barrier resonant tunneling structures

The evolution and collapse of electron resonances and their spectral parameters in a symmetric three-barrier resonant tunneling structure (TBRTS) are studied theoretically. The resonance energy and width of the quasi-stationary states of an electron are analyzed. The quasi-stationary states are calculated by the transmission coefficient method, the method of the probability distribution function (the probability of finding an electron in a TBRTS), and the scattering cross section method.     

Boundary element-free method for elastodynamics

The moving least-square approximation is discussed first. Sometimes the method can form an ill-conditioned equation system, and thus the solution cannot be obtained correctly. A Hilbert space is presented on which an orthogonal function system mixed a weight function is defined. Next the improved moving least-square approximation is discussed in detail. The improved method has higher computational efficiency and precision than the old method, and cannot form an ill-conditioned equation system. A boundary element-free method (BEFM) for elastodynamics problems is presented by combining the boundary integral equation method for elastodynamics and the improved moving least-square approximation. The boundary element-free method is a meshless method of boundary integral equation and is a direct numerical method compared with others, in which the basic unknowns are the real solutions of the nodal variables and the boundary conditions can be applied easily. The boundary element-free method has a higher computational efficiency and precision. In addition, the numerical procedure of the boundary element-free method for elastodynamics problems is presented in this paper. Finally, some numerical examples are given.     

Design sensitivity analysis for sequential structural-acoustic problems

A design sensitivity analysis of a sequential structural-acoustic problem is presented in which structural and acoustic behaviors are de-coupled. A frequency-response analysis is used to obtain the dynamic behavior of an automotive structure, while the boundary element method is used to solve the pressure response of an interior, acoustic domain. For the purposes of design sensitivity analysis, a direct differentiation method and an adjoint variable method are presented. In the adjoint variable method, an adjoint load is obtained from the acoustic boundary element re-analysis, while the adjoint solution is calculated from the structural dynamic re-analysis. The evaluation of pressure sensitivity only involves a numerical integration process for the structural part. The proposed sensitivity results are compared to finite difference sensitivity results with excellent agreement.     

Non-Scanning Optical Coherence Tomography Using Off-Axis Interferometry with an Angular-Dispersion Imaging Scheme

We present a non-scanning approach for real-time optical coherence tomography (OCT). Our approach is based on an off-axis interferometer that laterally projects the time-of-flight or depth information of the sample onto an image sensor. To facilitate the use of an off-axis interferometer in OCT, an angular-dispersion imaging method has been developed. Theoretical analysis and experimental results are presented to demonstrate that this method is capable of demodulating the interferogram and thus permits a direct inspection of the depth-resolved image. Depth resolution and detection range of the present method are also studied.     

Boundary element-free method for elastodynamics

1 Introduction In recent years, more and more attention has been paid to researches on the meshless (or meshfree) method, which makes it a hot direction of computational mechanics[1,2]. The meshless method is the approximation based on nodes, then the large deformation and crack growth problems can be simulated with the method without the re-meshing technique. And the meshless method has some advantages over the traditional computa- tional methods, such as finite element method (FEM) and boun…     

Color removal method of considering distance in color space

In a color-to-gray conversion, which only considers lightness components, difference of colors are not appropriately reflected in monochrome images. Gooch et al. have proposed a color removal method that considers the differences of colors. Although the method can obtain good results in many cases, there is room for improvement. In this paper, a new color removal method that introduces a weight to Gooch’s algorithm is proposed. In the proposed method, for combinations of colors of each pixel in an input image, weights are determined by distance in color space. In the proposed method, unimportant color combinations are not considered by weight and color information in an input image is appropriately reflected in a monochrome image. The validity of the proposed method is shown by experiments using some images.     

A comparison between analytic and numerical methods for modelling automotive dissipative silencers with mean flow

Identifying an appropriate method for modelling automotive dissipative silencers normally requires one to choose between analytic and numerical methods. It is common in the literature to justify the choice of an analytic method based on the assumption that equivalent numerical techniques are more computationally expensive. The validity of this assumption is investigated here, and the relative speed and accuracy of two analytic methods are compared to two numerical methods for a uniform dissipative silencer that contains a bulk reacting porous material separated from a mean gas flow by a perforated pipe. The numerical methods are developed here with a view to speeding up transmission loss computation, and are based on a mode matching scheme and a hybrid finite element method. The results presented demonstrate excellent agreement between the analytic and numerical models provided a sufficient number of propagating acoustic modes are retained. However, the numerical mode matching method is shown to be the fastest method, significantly outperforming an equivalent analytic technique. Moreover, the hybrid finite element method is demonstrated to be as fast as the analytic technique. Accordingly, both numerical techniques deliver fast and accurate predictions and are capable of outperforming equivalent analytic methods for automotive dissipative silencers.     

半空间球面波函数叠加法重构声源直接辐射声场

提出了基于半空间球面波函数叠加的声场重构方法,以重构含有限声阻抗边界半空间中声源直接辐射的声场。在半空间中多极子声源声压场的解析解的基础上,构造出以边界声阻抗为参量的半空间球面波函数的正交基;通过求逆获得半空间总声压解的基函数系数,同时也获得声源直接辐射声场即自由空间中的基函数系数,进而重构出声源直接辐射的声场。在边界声阻抗已知和边界声阻抗未知两种条件下,对该方法进行了仿真验证和参数分析,并在全消声室内进行了实验验证。结果表明,所提方法能重构出半空间中典型声源即球形声源和平面声源的直接辐射声场;该方法在边界声阻抗已知时的重构精度与稳定性高于在边界声阻抗未知时的情形。      

LS解法和Fisher方程行波系统的定性分析

提出了求解非线性发展方程的新方法——LS解法.LS解法是基于(G’/G)展开法和扩展的双曲正切函数展开法.并引入了Poincar定性理论的思想,然后以Fisher方程为例进行了试验.通过定性分析首先获得了Fisher方程行波系统积分曲线的性质,然后解得了Fisher方程作为耗散系统时单调减少的波前解和作为扩张系统时单调递增的波前解.一些试验结果与Ablowitz所得结果一致.也得到了Fisher方程作为扩张系统时的新结果.LS解法是在定性理论指导下,在已获知解曲线性质的情况下进行精确求解的,求解目标明确.LS解法揭示了线性系统也可以用作辅助方程来求解非线性系统.     

Substructure methods for structural condition assessment

It is commonly known that an accurate analysis of a large structure requires an accurate analytical model. This is also true for the inverse analysis of a structural system where measured structural responses are used as input to assess the structural conditions. However, an accurate model of the structure is always not available in practice. Two substructural identification methods are presented in this paper with the structure divided into substructures and with one substructure assessed at one time. In the first method, an accurate finite element model of the whole structure is assumed known. A state space method is applied to identify the external forces acting on the structure, and a damage identification method is then applied to identify the local damages using time domain information. Iterative model updating method based on the measured acceleration in the selected substructure is employed for the assessment. The second identification method requires only the finite element model of the substructure. The interface forces and the external forces acting on the target substructure are all taken as excitations and they are identified in state space. The substructure is then assessed similar to the first method. Since the target substructure for updating consists of a much reduced number of components and the identification problem is more efficient. The validation of the proposed methods is demonstrated by a truss structure with polluted measured accelerations with promising results.     

Field Analysis of Pillbox Resonator with Radiation Loss Utilizing Finite-Element Beam Propagation Method Formulation

To deal with the radiation from an axially symmetric pillbox resonator embedded in LiNbO₃ substrate, an eigenvalue equation is derived from the expression of the finite-element beam propagation method in a cylindrical coordinate system. By solving the eigenvalue equation iteratively, the field distributions and the angular phase constants of the pillbox resonator are evaluated. The iterative scheme of solving the eigenvalue equation is an extension of our previous direct solution method which was described for a lossless case. The results obtained by this method are compared with those obtained analytically, and excellent agreement is found.     

Accurate carrier-removal technique based on zero padding in Fourier transform method for carrier interferogram analysis

Based on interferogram zero padding and fast Fourier transform (FFT) methods, an effective, straightforward and stable carrier-removal approach in Fourier transform (FT) based method for carrier interferogram analysis is proposed. The spatial carrier interferogram is firstly extrapolated by zero padding method, and the carrier-frequency values within a small fraction of an integral (or a pixel) are estimated from the extrapolation interferogram with FFT method. Then the carrier-phase component is removed by subtracting a pure carrier-frequency phase constructed by the estimated carrier-frequencies in the spatial domain. Numerical simulations and experiments are given to demonstrate the performance of the proposed method and the results show that the proposed method is effective and stable for suppressing the carrier-removal error in the FT method for carrier interferogram analysis.     

An Approximate Approach for Systems of Singular Volterra Integral Equations Based on Taylor Expansion

In this article, an extended Taylor expansion method is proposed to estimate the solution of linear singular Volterra integral equations systems. The method is based on combining the m-th order Taylor polynomial of unknown functions at an arbitrary point and integration method, such that the given system of singular integral equations is converted into a system of linear equations with respect to unknown functions and their derivatives. The required solutions are obtained by solving the resulting linear system. The proposed method gives a very satisfactory solution, which can be performed by any symbolic mathematical packages such as Maple, Mathematica, etc. Our proposed approach provides a significant advantage that the m-th order approximate solutions are equal to exact solutions if the exact solutions are polynomial functions of degree less than or equal to m. We present an error analysis for the proposed method to emphasize its reliability. Six numerical examples are provided to show the accuracy and the efficiency of the suggested scheme for which the exact solutions are known in advance.     

大学物理实验分层次教学与创新能力的培养

建立现代物理实验教学新体系是大学物理实验教学改革的必然趋势,阐述了分层教学法在大学物理实验教学中应用的必要性,分析了分层教学法的优势,探索了更好地发挥分层教学法的方法和原则,从而使大学物理实验在培养学生的动手能力和创新能力方面起到了重要的作用。