耗散对孤波与局地地形相互作用的影响

利用扰动法，由包括耗散和地形的准地转位涡度方程导出了强迫mKdV-Burgers方程，求得了小耗散情形下mKdV-Burgers方程的近似分析解，分析了mKdV孤波质量和能量的时间演变特性。对给定的局地地形，利用拟谱法对强迫mKdV-Burgers方程进行了数值求解。结果显示，小耗散的存在使弧波的振幅和移速随时间缓慢地减小，孤波宽度则随时间缓慢增大；在耗散和地形强迫的非线性系统中，在孤波与地形的相互作用中，耗散的存在使孤波在强迫区附近振荡传播，这有利于大振幅扰动的形成。     

Effect of dust size distribution and dust charge fluctuation on dust ion-acoustic shock waves in a multi-ion dusty plasma

The effects of dust size distribution and dust charge fluctuation of dust grains on the small but finite amplitude nonlinear dust ion-acoustic shock waves, in an unmagnetized multi-ion dusty plasma which contains negative ions, positive ions and electrons, are studied in this paper. A Burgers equation and its stationary solutions are obtained by using the reductive perturbation method. The analytical and numerical results show that the height with polynomial dust size distribution is larger than that of the monosized dusty plasmas with the same dust grains, but the thickness in the case of different dust grains is smaller than that of the monosized dusty plasmas. Furthermore, the moving speed of the shock waves also depend on different dust size distributions.     

浅海随机相位起伏声场中速度估计的互谱分析方法

浅海条件下,目标运动速度是基于波导不变量声源被动定位的关键因素,利用浅海波导环境下的声场简正波理论,研究了浅海随机相位起伏的波束域声场互相关信号的特点,并通过声速剖面的二阶统计量对随机相位扰动进行了有效的补偿,提出利用波束域声场互相关信号进行谱分析的速度估计方法,仿真实验表明了该方法的有效性。利用2013年7月海试实验数据,该方法准确的估计出了目标的速度,并与GPS实测速度对比,速度估计的相对误差在10%以内。     

Numerical solution of 3D Green's function for the dynamic system of anisotropic elasticity

In this Letter, we used homotopy perturbation method to obtain numerical solution of the 3D Green's function for the dynamic system of anisotropic elasticity. Application of homotopy perturbation method to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution. The numerical results obtained from convolution of Green's function and data of the Cauchy problem are compared with the exact solution for cubic media. The results reveal that the proposed method is very effective and simple.     

Application of Davidenko's Method to a Lossy Nonlinear Waveguide

Davidenko's method is implemented for determining the complex propagation constants (Modal index and attenuation coefficient) of nonlinear TE waves guided by an asymmetrical lossy nonlinear dielectric wave-guide. The waveguide structure has a generalized nonlinear substrate with a permittivity of the form | E |and an absorbing cover making the propagation constant to be complex. Davidenko's method shows to be a fast and accurate analysis in finding the complex propagation constants. The effects of initial condition parameter on the propagation characteristics are investigated, analyzed and discussed.     

A note on moving multipole sources of sound

The object of this note is to draw attention to the need, when speaking of a moving multipole source of sound, to state whether it is based on the wave equation for the velocity potential or the wave equation for the perturbation pressure. The theory of moving multipole sources of sound is firmly established, but, owing to lack of precision, some seemingly contradictory results are to be found in the literature. The reasons for these seemingly contradictory results are examined, and various basic relationships between a moving multipole sound field and its method of generation are established.     

Stationary Classical Chaos of Trapped Two-Component Bose-Einstein Condensates in 1-D Optical Lattice Potentials

We study the nonlinear dynamics of two-component Bose-Einstein condensates in one-dimensional periodic optical lattice potentials. The stationary state perturbation solutions of the coupled two-component nonlinear Schrödinger/Gross-Pitaevskii equations are constructed by using the direct perturbation method. Theoretical analysis revels that the perturbation solution is the chaotic one, which indicates the existence of chaos and chaotic region in parameter space. The corresponding numerical calculation results agree well with the analytical results. By applying the chaotic perturbation solution, we demonstrate the atomic spatial population and the energy distribution of the system are chaotic generally.     

An efficient moving mesh spectral method for the phase-field model of two-phase flows

We develop in this paper a moving mesh spectral method for the phase-field model of two-phase flows with non-periodic boundary conditions. The method is based on a variational moving mesh PDE for the phase function, coupled with efficient semi-implicit treatments for advancing the mesh function, the phase function and the velocity and pressure in a decoupled manner. Ample numerical results are presented to demonstrate the accuracy and effectiveness of the moving mesh spectral method.     

Modulational instability and moving gap soliton in Bose–Einstein condensation with Feshbach resonance management

We investigate the modulational instability of symmetric and asymmetric continuous wave solutions in Bose–Einstein condensates in optical lattices with Feshbach resonance managed atomic scattering length. The model is based on a pair of averaged coupled mode Gross–Pitaevskii equations. We analyze the characteristics of the modulational instability in the form of typical dependence of the instability growth rate on the perturbation wavenumber and system’s parameters. We have numerically solved the coupled mode equations by using the split step Fourier method. Convincing agreement has been obtained between analytical and numerical results. Furthermore, the moving and stationary gap solitons in the first spectral gap of the optical lattices for the same amplitude but different phases in the presence and absence of the mean atomic scattering length under the Feshbach resonance management are also constructed.     

一边平夾另一边受均布力矩作用的环形薄板大挠度问题

一.引言 作者曾在文献中指出,用摄动法来处理在均布边缘力矩作用之下的弹性圆薄板大挠度问题,不但远较用数字积分法来得简便,而且还提供了最大挠度以及应力的设计公式,使它们能直接应用到工程设计问题上去。本文则引申之,同样成功地处理了另一些具有实用价值但一直还未被研究过的问题,即外(内)边平夹,而沿内(外)边有均布边缘力矩作用的环形薄板大挠度问题。     

Approximate Solutions of Perturbed Nonlinear Schr(o)dinger Equations

By applying Lou's direct perturbation method to perturbed nonlinear Schr(o)dinger equation and the critical nonlinear Schr(o)dinger equation with a small dispersion, their approximate analytical solutions including the zero-order and the first-order solutions are obtained. Based on these approximate solutions, the analytical forms of parameters of solitons are expressed and the effects of perturbations on solitons are briefly analyzed at the same time. In addition, the perturbed nonlinear Schr(o)dinger equations is directly simulated by split-step Fourier method to check the validity of the direct perturbation method. It turns out that the analytical results given by the direct perturbation method are well supported by numerical calculations.     

渐变折射率光纤标量近似的微扰修正方法

在弱波导近似下,计及了折射率梯度的影响,把▽ε看作微扰项,应用微扰理论,给出了修正到任一级近似的标量场方程,建立了一级修正解的一般表达式,并给出了相关参量的确定方法。最后,以抛物线折射率剖面单模光纤为例,给出了简要分析结果。     

Eigenvalues of structures with uncertain elastic boundary restraints

The eigenvalue problems of structures with random elastic boundary supports are studied in this paper. Using the perturbation method, the differential equations including stochastic distributed parameters and random boundary conditions that govern the eigenproblems are transformed to a series of deterministic differential equations and boundary conditions. Then the differential equations and boundary conditions are discretized utilizing the finite element method (FEM). This process is easy to be implemented since the resulting perturbation equations with different orders own the same FEM meshes. The first-order and second-order sensitivities of eigenvalues are derived through solving the deterministic algebraic equations. Upon determining these sensitivities of eigenvalues, the approximate statistic expressions of random eigenvalues considering uncertain elastic boundary supports are established. At the end, several numerical examples are given to illustrate the application and effectiveness of the present method. Comparison of the present numerical results with those from the Monte-Carlo simulation method verifies the accuracy of the developed method.     

Modified sub-interval perturbation finite element method for 2D acoustic field prediction with large uncertain-but-bounded parameters

Based on the sub-interval perturbation analysis, a modified sub-interval perturbation finite element method is proposed to determine the bounds of sound pressure in the 2D acoustic field with large uncertain-but-bounded parameters. In the proposed method, the inversion of the invertible sub-interval dynamic stiffness matrix is approximated by a modified approximate interval-value Sherman–Morrison–Woodbury formula to overcome the drawbacks arising from the dependency phenomenon of parameters and the unpredictable effect of neglecting the higher order terms in Neumann series. The modified sub-interval perturbation procedures are implemented in a numerical finite element framework. Numerical results on a 2D acoustic tube and a 2D acoustic cavity of a car with large uncertain-but-bounded parameters evidence the remarkable accuracy and effectiveness of the proposed method.     

金属包层渐变折射率介质光波导的传输特性与损耗

用金属包层介质光波导损耗的微扰理论及藉助多层近似法用递推公式分析渐变折射率波导传播常数的方法,对几种类型的金属包层渐变折射率介质光波导的传输特性与损耗进行分析和讨论,得到了与精确数值计算结果相吻合的结果.     

相位微扰法在粗糙面光散射中的应用

根据粗糙面散射理论，用相位微扰法推导出了从随机粗糙介质表面散射的激光雷达散射截面的理论计算公式，计算了几种粗糙表面样品在１．０６μｍ下的单位面积激光雷达散射截面，数值结果与实验数据基本吻合。     

A new numerical solution for the MHD peristaltic flow of a bio-fluid with variable viscosity in a circular cylindrical tube via Adomian decomposition method

In this Letter, we considered a numerical treatment for the solution of the hydromagnetic peristaltic flow of a bio-fluid with variable viscosity in a circular cylindrical tube using Adomian decomposition method and a modified form of this method. The axial velocity is obtained in a closed form. Comparison is made between the results obtained by only three terms of Adomian series with those obtained previously by perturbation technique. It is observed that only few terms of the series expansion are required to obtain the numerical solution with good accuracy.     

Stationary Classical Chaos of Trapped Two-Component Bose-Einstein Condensates in 1-D Optical Lattice Potentials

We study the nonlinear dynamics of two-component Bose-Einstein condensates in one-dimensional periodic optical lattice potentials. The stationary state perturbation solutions of the coupled two-component nonlinear Schr(o)dinger/Gross-Pitaevskii equations are constructed by using the direct perturbation method. Theoretical analysis revels that the perturbation solution is the chaotic one, which indicates the existence of chaos and chaotic region in parameter space. The corresponding numerical calculation results agree well with the analytical results. By applying the chaotic perturbation solution, we demonstrate the atomic spatial population and the energy distribution of the system are chaotic generally.     

Application of He's homotopy perturbation method to boundary layer flow and convection heat transfer over a flat plate

In this Letter, the problem of forced convection over a horizontal flat plate is presented and the homotopy perturbation method (HPM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing on the problem. It has been attempted to show the capabilities and wide-range applications of the homotopy perturbation method in comparison with the previous ones in solving heat transfer problems. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. A clear conclusion can be drawn from the numerical results that the HPM provides highly accurate numerical solutions for nonlinear differential equations.     

The effect of random variations of structure parameters on photonic band gaps of one-dimensional plasma photonic crystals

The electromagnetic properties of one-dimensional plasma photonic crystals influenced by random perturbation of structure parameters are studied through transfer matrix method in the paper. The random perturbation of thicknesses of layers as well as plasma frequency of layers can influence the electromagnetic properties of one-dimensional plasma photonic crystal. The random perturbation of thicknesses of layers tremendously impacts the band structure of one-dimensional plasma photonic crystals in high frequency domain. The random perturbation of plasma frequency, however, contributes to the moving of a cutoff frequency in the low frequency domain. The position of the defect mode of one-dimensional plasma photonic crystal randomly moves due to the random perturbations. The effect of random perturbation of plasma frequency is more significant than that of random perturbation of thickness of layers, which alters not only the transmittance but also the position of the defect mode. An improved quality factor and a shortened moving distance of the defect mode are both acquired by increasing the period number. And then this work may provide a crude but useful instrument in analyzing disordered 1DPPCs.