用傅里叶分析法研究艾里光束远场传播特性

为了从理论上深入分析新型无衍射光束艾里光束在有限能量条件下的远场传播特性,首先,从决定光波在自由空间传播的一维旁轴波动方程入手,采用傅里叶分析法,结合艾里函数的特殊性质,并利用经过指数衰减的有限能量初始条件,完整给出了有限能量条件下用于精确描述一维艾里光束在自由空间传播特性的波动方程解析解.然后,利用所得到解析解分别对一维和二维艾里光束在自由空间的传播特性进行了研究,重点分析了不同参量条件对艾里光束进行无衍射传播和横向自加速的影响.研究表明:当任意横向尺度为100μm,衰减系数为0.03、0.05、0.07、0.1、0.2时,二维艾里光束无衍射传播距离分别为1 014、624、455、338、193mm;当横向尺度保持不变时,衰减系数越小,艾里光束保持无衍射传播的距离越大;当衰减系数保持不变时,横向尺度越小,艾里光束横向自加速越大.所采用的研究方法也可用于研究艾里光束在介质中的传播特性.     

随机相位扰动抑制激发介质中漂移的螺旋波

研究了一类二维变量描述的激发系统中漂移螺旋波的抑制问题.通过在整个系统中局部注入带随机相位的电信号，如在系统256×256格点的边界或中心区域中选取4×4或者5×5格点区域施加一个带随机相位的外部激励电信号，在系统内部产生一个持续的靶波信号，实现靶波对螺旋波的动态竞争.数值计算表明：该方法对于Barkley模型中螺旋波有很强的抑制作用，与简单的局部周期信号驱动比较，具有暂态过程比较短的特点，而且对于时空噪声具有一定的抗干扰性.在一定的噪声范围内，即使系统出现不均匀性，也可以观测到靶波，新出现的靶波对螺旋波有抑制作用. 关键词： 螺旋波 靶波 Barkley模型 随机相位     

An alternative solution of the scattering from an anisotropic cylindrical dielectric shell

A method based on the approximate wave functions for anisotropic media and the mode-matching approach is developed to solve the problem of the electromagnetic scattering from an anisotropic cylindrical dielectric shell. The cylindrical shell is assumed to be infinite in length, and it is illuminated by a plane wave or a cylindrical wave from a line source. The problem is two-dimensional and the solutions to both types of polarization (TE and TM) are presented. The validity of this solution is verified by comparing the numerical results with those in literatures and the previous calculations based on the exact wave functions for anisotropic media. Numerical results show the higher computational efficiency of the present method for bounded anisotropic media.     

Frequency-domain wave equation and its time-domain solutions in attenuating media

Our purpose in this paper is to describe the wave propagation in media whose attenuation obeys a frequency power law. To achieve this, a frequency-domain wave equation was developed using previously derived causal dispersion relations. An inverse space and time Fourier transform of the solution to this algebraic equation results in a time-domain solution. It is shown that this solution satisfies the convolutional time-domain wave equation proposed by Szabo [J. Acoust. Soc. Am. 96, 491-500 (1994)]. The form of the convolutional loss operator contained in this wave equation is obtained. Solutions representing the propagation of both plane sinusoidal and transient waves propagating in media with specific power law attenuation coefficients are investigated as special cases of our solution. Using our solution, comparisons are made for transient one-dimensional propagation in a medium whose attenuation is proportional to frequency with recently obtained numerical solutions of Szabo's equation. These show good agreement.     

Excitable wave patterns in a spatially extended nonlinear optical cavity

We show that finite external excitation can lead to a traveling wave in an excitable passive optical system with one-dimensional space geometry. We have studied the excitable behavior of this system in parallel with that of its diffusive counterpart and show the effects of optical phase on the traveling-wave solution and its velocity. In two-dimensional space we observe numerically rotating optical spiral waves evolving from a truncated planar wave front.     

层状介质时域有限差分方法斜入射平面波引入新方式

应用二维时域有限差分方法分析层状介质中的目标散射时,在总场-散射场边界斜入射平面波源用常规方法难以引入,因为在总场-散射场边界处设置的入射波实际上包含了入射脉冲以及各分层界面的反射和多次反射.为解决这个问题,提出了斜入射平面波的混合引入方式,即对总场-散射场的四个边界面采取不同的处理方式.对于总场-散射场的纵向侧边界,用含有斜入射角度的修正一维时域有限差分方法,只要在自由空间位置加入入射脉冲就会自行产生由各分层界面形成的反射波,包括多次反射.同时,把纵向总场-散射场侧边界向下延伸,使得总场-散射场下边界位于完全匹配层内,这样透射波和散射波均为外向行波而被吸收.对于总场-散射场的上边界,由于完全位于自由空间中,边界上各点的入射波将是总场-散射场纵向边界角点处入射波的带有时间延迟的复制.数值模拟结果表明了本文所提出方法的正确性和有效性. 关键词： 时域有限差分 层状介质 斜入射平面波 修正一维麦克斯韦方程     

Development and transition of spiral wave in the coupled Hindmarsh--Rose neurons in two-dimensional space

The dynamics and the transition of spiral waves in the coupled Hindmarsh--Rose (H--R) neurons in two-dimensional space are investigated in the paper. It is found that the spiral wave can be induced and developed in the coupled HR neurons in two-dimensional space, with appropriate initial values and a parameter region given. However, the spiral wave could encounter instability when the intensity of the external current reaches a threshold value of 1.945. The transition of spiral wave is found to be affected by coupling intensity D and bifurcation parameter r. The spiral wave becomes sparse as the coupling intensity increases, while the spiral wave is eliminated and the whole neuronal system becomes homogeneous as the bifurcation parameter increases to a certain threshold value. Then the coupling action of the four sub-adjacent neurons, which is described by coupling coefficient D’, is also considered, and it is found that the spiral wave begins to breakup due to the introduced coupling action from the sub-adjacent neurons (or sites) and together with the coupling action of the nearest-neighbour neurons, which is described by the coupling intensity D.     

可激发介质中环形异质介质导致自维持靶波

在二维可激发介质中引入环形异质可激发介质,研究了可激发介质中自维持靶波的形成,数值模拟结果表明:当介质的激发性和环的尺寸适当选取时,初始的扰动可在可激发介质中产生自维持靶波,对产生自维持靶波的物理机理作了讨论.     

一维受迫谐振子量子运动的经典特性

对经典一维受迫谐振子量子化,求解量子化后体系的时间演化算符.应用相空间准概率分布函数,研究了体系的量子特性.研究结果表明,初始为真空态,经过时间演化,系统波函数是一个二维高斯波包;波包中心的振幅和相位受到作用力的调制,成为调幅、调相波,波包中心的运动与经典受迫谐振子的运动形式相同.     

Simulation of the vector wave field of a low-frequency sound source in the ocean: Some important features

An approach to the simulation of low frequency vector wave fields in stratified media (mainly in the ocean) is considered. The approach is characterized by an improved stability with respect to dividing the medium into many layers of arbitrary thickness. The model for the sound field of a point source is based on an integral representation of two-dimensional, cylindrically symmetric vector wave fields in inhomogeneous media, so that the contributions of all types of waves are included automatically. The model medium is subdivided into N horizontally homogeneous layers for which 4(N?1) equations are formulated to satisfy the boundary conditions between adjacent layers. The method of the generalized Schmidt matrix is used to obtain the coefficients of the equations; these coefficients are substituted into the expressions (of the Fourier-Bessel integral type) for the local parameters of the field. The latter are calculated according to the numerical procedure, and the results are used to model the distributions of the acoustic pressure and the horizontal and vertical components of the particle velocity in liquid and elastic media. The instability of the calculation procedure may result in a disagreement between the model and the exact solution. However, the disagreement is shown to occur mainly in models containing excessively thick layers. A way for improving the stability of the numerical model is suggested. The simulation results are compared with the exact analytical solution for the simplest example and with the results obtained according to the commonly used generalized matrix procedure (the benchmark problem). The examples of the practical application of the model for investigating more complex seismoacoustic wave fields in the ocean are presented.     

A General Spectral-Domain Formulation of the Electromagnetic Scattering by a Perfectly Conducting Circular Cylinder

A full-wave method for the two-dimensional scattering problem by a perfectly conducting circular cylinder is presented, providing an exact solution for the Helmholtz equation in very general cases. The method is based on the Fourier series expression of the boundary conditions (Dirichlet and Neumann) generated by an arbitrary, finite-power, incident beam, and the analysis is performed in the complex plane of the analytic continuation of a space spectral variable. This approach allows us to define an analytic continuation for cylindrical wave expansions, working with lossy propagation media and with a full incident spectrum, including inhomogeneous waves, both in E and in H polarization. Convergence of the modal expansion is investigated, to verify that very weak hypotheses are needed, and no geometrical or paraxial approximation is required. Extact expressions for the expansion coefficients are given, in terms of complex intergrations involving the Fourier spectrum of the incident beam.     

Stability and ambiguous representation of shock wave discontinuity in thermodynamically nonideal media

The nonlinear analysis of the behavior of a shock wave on a Hugoniot curve fragment that allows for the ambiguous representation of shock wave discontinuity has been performed. The fragment under consideration includes a section where the condition L > 1 + 2M is satisfied, which is a linear criterion of the instability of the shock wave in media with an arbitrary equation of state. The calculations in the model of a viscous heat-conductive gas show that solutions with an instable shock wave are not implemented. In the one-dimensional model, the shock wave decays into two shock waves or a shock wave and a rarefaction wave, which propagate in opposite directions, or can remain in the initial state. The choice of the solution depends on the parameters of the shock wave (position on the Hugoniot curve), as well as on the form and intensity of its perturbation. In the two-dimensional and three-dimensional calculations with a periodic perturbation of the shock wave, a “cellular” structure is formed on the shock front with a finite amplitude of perturbations that does not decrease and increase in time. Such behavior of the shock wave is attributed to the appearance of the triple configurations in the inclined sections of the perturbed shock wave, which interact with each other in the process of propagation along its front.     

Exact solution of Maxwell's equations for optical interactions with a macroscopic random medium

We report what we believe to be the first rigorous numerical solution of the two-dimensional Maxwell equations for optical propagation within, and scattering by, a random medium of macroscopic dimensions. Our solution is based on the pseudospectral time-domain technique, which provides essentially exact results for electromagnetic field spatial modes sampled at the Nyquist rate or better. The results point toward the emerging feasibility of direct, exact Maxwell equations modeling of light propagation through many millimeters of biological tissues. More generally, our results have a wider implication: Namely, the study of electromagnetic wave propagation within random media is moving toward exact rather than approximate solutions of Maxwell's equations.     

Dark soliton in the Bose-Einstein condensates with nonlinearity and harmonic potential managements

The dynamics of dark solitons in one-dimensional Bose-Einstein condensates under the nonlinearity and harmonic potential managements is investigated. It is found that at the large particle limit the macroscopic wave function could evolve self-similarly, which provides a time-varying background for the propagation of dark solitons. The approximate dark soliton solution is derived and its center-of-mass motion is predicted analytically.     

Ocean acoustic tomography with a nonstandard representation of refractive inhomogeneities

The two-dimensional tomography problem of reconstructing a refractive inhomogeneity in the ocean is considered. A distinction of this paper is the expansion of the inhomogeneity under investigation in a nonstandard (nonorthogonal and overfull) basis. This basis makes it possible to overcome some problems inherent in the conventional schemes dividing the ocean into squares, triangles, and other figures with corners. In addition, the perturbation matrix can be easily constructed in such a basis. The proposed approach can be used in its present form for reconstructing flows and solving combined refractive-kinetic problems. The solution of the tomography problem with the use of the proposed basis is carried out in both ray and wave representations.     

The varied nonlinear interface waves in a scale-limited two-medium oscillatory system

We investigate spontaneously generated waves around the interfaces between two different media in a system where the domain scales are limited. These two media are carefully selected so that there exists a theoretical interface wave with the frequency and wave number that can be predicted according to the control parameters. We present the rules of how the frequency and wave number vary with reducing the scales of media domains. We find that the frequency decreases with reducing the scale of antiwave (AW) media, but increases with reducing the scale of normal wave (NW) media in both one-dimensional and two-dimensional systems. The wave number always decreases with reducing scales of either NW or AW media. The least scale to generate the theoretical wave is the predicted wavelength. These special phenomena around the interfaces can be applied to detect the limited scale of a system.     

WKB solution for wave propagation in a time-varying magnetoplasmamedium: longitudinal propagation

The interaction of a right circularly polarized electromagnetic wave of frequency ω₀ with a switched-on-time-varying plasma medium, in the presence of a static magnetic field, is considered. Longitudinal propagation is assumed and ion motion is neglected. The electron density is assumed to vary slowly with time, and the solution is obtained through a WKB approximation. The main effect of switching the time-varying medium is the splitting of the original (incident) wave of frequency ω₀ into three new waves with time-varying frequencies. An exponentially increasing electron density profile is considered to illustrate the solution. The distinguishing feature of the presence of the static magnetic field is the creation of the third wave. The initial value of the instantaneous frequency ω₃ of this wave is equal to the gyrofrequency ω_b, and the final value depends on ω_b, ω₀, and the final value of the plasma frequency. ω₃ decreases with time for the profile under consideration     

多尺度有限差分法模拟复杂介质波传问题

利用有限差分和紧支集正交小波变换对波动方程的时间、空间进行联合近似求解,提出一种适合于一般边界非均匀耗散介质中波传问题数值模拟的快速自适应混合算法——多尺度有限差分(multiresolution finite difference缩写为MRFD)方法.将波传问题的求解转换到小波域中进行,利用小波基的自适应性与消失矩特性,使偏微分算子矩阵稀疏化,有效改善了计算量等.地球物理勘探中的数值实例显示了算法具有良好效率 关键词： MRFD 小波变换 多尺度 波传问题     

梯度耦合下神经元网络中靶波和螺旋波的诱发研究

神经系统内数量众多的神经元电活动的群体行为呈现一定的节律性和自组织性. 当网络局部区域存在异质性或者受到持续周期性刺激, 则在网络内诱发靶波, 且这些靶波如'节拍器'可调制介质中行波的诱发和传播. 基于Hindmarsh-Rose 神经元模型构造了最近邻连接下的二维神经元网络, 研究在非均匀耦合下神经元网络内有序波的诱发问题. 在研究中, 选定网络中心区域的耦合强度最大, 从中心向边界的神经元之间的耦合强度则按照阶梯式下降. 研究结果表明, 在恰当的耦合梯度下, 神经元网络内诱发的靶波或螺旋波可以占据整个网络, 并有效调制神经元网络的群体电活动, 使得整个网络呈现有序性. 特别地, 当初始值为随机值时, 梯度耦合也可以诱发稳定的有序态. 这种梯度耦合对网络群体行为调制的研究结果有助于理解神经元网络的自组织行为.