A Generally Covariant Wave Equation for Grand Unified Field Theory

A generally covariant wave equation is derived geometrically for grand unified field theory. The equation states most generally that the covariant d'Alembertian acting on the vielbein vanishes for the four fields which are thought to exist in nature: gravitation, electromagnetism, weak field and strong field. The various known field equations are derived from the wave equation when the vielbein is the eigenfunction. When the wave equation is applied to gravitation the wave equation is the eigenequation of wave mechanics corresponding to Einstein's field equation in classical mechanics, the vielbein eigenfunction playing the role of the quantized gravitational field. The three Newton laws, Newton's law of universal gravitation, and the Poisson equation are recovered in the classical and nonrelativistic, weak-field limits of the quantized gravitational field. The single particle wave-equation and Klein-Gordon equations are recovered in the relativistic, weak-field limit of the wave equation when scalar components are considered of the vielbein eigenfunction of the quantized gravitational field. The Schrödinger equation is recovered in the non-relativistec, weak-field limit of the Klein-Gordon equation). The Dirac equation is recovered in this weak-field limit of the quantized gravitational field (the nonrelativistic limit of the relativistic, quantezed gravitational field when the vielbein plays the role of the spinor. The wave and field equations of O(3) electrodynamics are recovered when the vielbein becomes the relativistic dreibein (triad) eigenfunction whose three orthonormal space indices become identified with the three complex circular indices (1), (2), (3), and whose four spacetime indices are the indices of non-Euclidean spacetime (the base manifold). This dreibein is the potential dreibein of the O(3) electromagnetic field (an electromagnetic potential four-vector for each index (1), (2), (3)). The wave equation of the parity violating weak field is recovered when the orthonormal space indices of the relativistic dreibein eigenfunction are identified with the indices of the three massive weak field bosons. The wave equation of the strong field is recovered when the orthonormal space indices of the relativistic vielbein eigenfunction become the eight indices defined by the group generators of the SU (3) group.     

Solitary Wave and Wave Front as Viewed From Curvature

The solitary wave and wave front are two important behaviors of nonlinear evolution equations. Geometrically, solitary wave and wave front are all plane curve. In this paper, they can be represented in terms of curvature c(s), which varies with arc length s. For solitary wave when s → ±∞, then its curvature c(s) approaches zero, and when s=0, the curvature c(s) reaches its maximum. For wave front, when s → ±∞, then its curvature c(s) approaches zero, and when s=0, the curvature c(s) is still zero, but c'(s) ≠ 0. That is, s=0 is a turning point. When c(s) is given, the variance at some point (x,y) in stream line with arc length s satisfies a 2-order linear variable-coefficient ordinary differential equation. From this equation, it can be determined qualitatively whether the given curvature is a solitary wave or wave front.     

The hydrothermal wave of large-Prandtl-number fluid in a shallow cavity

The hydrothermal wave was investigated numerically for large-Prandtl-number fluid (Pr = 105.6) in a shallow cavity with different heated sidewalls. The traveling wave appears and propagates in the direction opposite to the surface flow (upstream) in the case of zero gravity when the applied temperature difference grows and over the critical value. The phase relationships of the disturbed velocity, temperature and pressure demonstrate that the traveling wave is driven by the disturbed temperature, which is named hydrothermal wave. The hydrothermal wave is so weak that the oscillatory flow field and temperature distribution can hardly be observed in the liquid layer. The exciting mechanism of hydrothermal wave is analyzed and discussed in the present paper.     

光纤喇曼放大泵浦光与信号光的关联研究

分析了信号光入射后可能发生的效应基于电磁场理论,综合光纤受激喇曼散射(SRS)效应、建立了光纤喇曼放大泵浦光与斯托克斯光、信号光的关联方程,给出了系统增益形成正反馈条件的表达式,结果表明:在光纤参量满足增益正反馈的条件下,当SRS增益对应于非饱和增益工作状态时入射信号光得到放大,SRS增益愈高则放大倍数愈高,并有区段上SRS增益相对低时其关联程度相对高.     

磁场对螺旋波等离子体波和能量吸收影响的数值研究

本文考察在径向电子数密度呈抛物形分布的情况下,外加稳恒磁场,射频通过螺旋波天线在等离子体中激发电磁波的传播性质.采用线性扰动波假设,数值求解Maxwell方程组,得到80—800 G(1 G=10-4T)磁场条件下等离子体中径向电、磁场强度及能量沉积密度的分布情形.计算结果表明,磁场增大(80→800G)时,螺旋波受到的阻尼较小,可深入等离子体传播;Trivelpiece-Gould(TG)波受到的阻尼增大,在等离子体-真空边界处衰减增强;整体的能量吸收向边界集中.磁感应强度小于100 G时,TG波可深入主等离子体区传播,等离子体径向能量吸收相对均匀.     

Two-channel resonance scattering of waves and particles by point and planar defects

The shattering of a wave (quasiparticle) with a dispersion curve consisting of two quadratic branches by a planar defect is discussed. The analog of such a process is the scattering of a similar wave (quasiparticle) in a one-dimensional system by a point defect. It is shown that even when the defect is passive, i.e., has no internal degrees of freedom, scattering may become resonant. The physical explanation of this effect is that a wave with a lower-lying spectrum scattered by the defect is in resonance with a localized (bound) state emerging because of the interaction between the defect and a wave with a higher-lying spectrum. Zh. éksp. Teor. Fiz. 115, 306–317 (January 1999)     

零电磁材料特性模拟及分析

 利用时域有限差分法分别模拟了线源、TM波和偶极子激励下零电磁材料的角度滤波和波形变换特性。仿真结果表明:当电磁波的入射方向垂直于零电磁材料表面时,电磁波可完全穿过零电磁材料;对不同表面形状的零电磁材料,透射波的相位完全由材料输出面决定;在线源或偶极子上覆盖一层输出面为平面的零电磁材料,其辐射可变换成平面波,并且多个线源或偶极子组成的天线阵,单元天线的数目增加至N个时,其辐射场强也提高为N0.5倍。     

等离子体覆盖立方散射体目标雷达散射截面的时域有限差分法分析

采用分段线性电流密度递归卷积时域有限差分（PLJERC-FDTD）算法计算了均匀非磁化等离子体覆盖三维立方体目标的散射特性.分析了等离子体厚度、密度和碰撞频率对雷达散射截面（RCS）的影响.计算结果表明：等离子体包层能有效地减小雷达目标的RCS，当等离子体频率比入射电磁波频率小得多时，主要靠增大等离子体的厚度使立方散射体目标的RCS值减小，增大等离子体碰撞频率对立方散射体目标的RCS值影响不大；当等离子体频率约为入射电磁波频率的一半时，增大等离子体厚度和碰撞频率都对立方散射体目标的RCS值减小有影响；当等 关键词： FDTD算法 电磁波 等离子体隐身 雷达散射截面     

双折射光纤中拉曼效应对参量放大增益谱的影响

根据激光脉冲在光纤中传输时, 所满足的波动方程, 导出了拉曼效应和参量放大共同作用下, 在双折射光纤中所遵循的耦合模方程, 并引入平行拉曼增益的洛伦兹模型, 给出了输入抽运波偏振方向同双折射轴成45^o 时, 拉曼效应和参量放大共同作用所导致的增益. 讨论并分析了拉曼效应在不同色散区对参量放大增益谱的影响. 结果表明, 在考虑拉曼效应后, 使得参量放大斯托克斯波与反斯托克斯波增益谱彼此不对称; 在反常色散区, 产生的增益以反斯托克斯波为主, 正常色散区则以斯托克斯波为主.     

Reflection of spin and spin-elastic waves at the interface of a ferromagnetic half-space

This paper considers the reflection of pure spin and spin-elastic (or magneto-elastic) waves at the interface of a ferromagnetic half-space and a vacuum. For pure spin waves two cases are considered, with exchange effects, and without. It is shown that when exchange effects are taken into account, volume spin waves in the ferromagnetic half space incident at the boundary with the vacuum generate a reflected volume spin wave, and an accompanying compound surface wave propagating along the boundary and consisting of two partial inhomogeneous spin waves in the ferromagnetic half-space and a partial magneto-static inhomogeneous surface wave in the vacuum. When exchange effects are neglected the incident wave generates only a reflected volume wave in the ferromagnetic half-space.

Reflection and transmission of spin-elastic (or magneto-elastic) waves has been considered only in the case of the absence of exchange effects. An incident volume wave generates a volume spin-elastic reflected wave and one inhomogeneous magneto-static accompanying surface wave.

Excitations of the magnetic field are not transmitted into the vacuum in both cases when the exchange effect is neglected. In all cases the reflection of a spin wave has the character of a full internal reflection.     

Ultrafast femtosecond all-optical modulation through nondegenerate two-photon absorption in silicon-on-insulator waveguides

We present numerical investigations of ultrafast femtosecond (with time duration of 100 fs at 1/e intensity point) all-optical modulation of a pump-probe wave arrangement by using nondegenerate two-photon absorption (TPA), namely cross absorption, inside silicon-on-insulator (SOI) optical waveguides. Our results show that when a pump pulse with femtosecond duration and a continuous probe wave are co-propagating along the SOI, the probe wave can be modulated inversely by the ultrafast pump pulse, whose modulation depth depends strongly on the system parameters such as the waveguide length, the peak power and initial chirp of the pump wave, the group velocity dispersion (GVD), etc.; this means that the modulation depth can be improved by an appropriate increase of the waveguide length, the pump peak, and the initial chirp, in addition, which has a larger value for the probe wavelength in the normal dispersion regime compared with the case of abnormal dispersion when the center wavelength of the pump wave is located at the zero-dispersion wavelength.     

Evolution of the exact spatiotemporal periodic wave and soliton solutions of the (3 + 1)-dimensional generalized nonlinear Schrödinger equation with distributed coefficients

In this paper the spatiotemporal evolution of the periodic wave is investigated analytically when the laser passes through the inhomogeneous nonlinear medium. Firstly, the (3 + 1)-dimensional generalized nonlinear Schrödinger equation with distributed coefficients is solved analytically by an improved homogeneous balance principle and F-expansion technique. A number of exact periodic traveling wave and spatiotemporal soliton solutions are obtained. Then, their propagation characteristics are analyzed in detail. It is found that the evolutions of propagation of spatiotemporal soliton and periodic wave solutions are regular when the diffraction and dispersion coefficients are the identical distributed coefficients, but the evolutions of propagation of these solutions are irregular with other coefficients.     

Stochastically excited waves in a 1D random medium – the mean field and power spectrum

Scalar wave propagation is examined when both the wave source and the propagation speed are random. Results are derived for the mean field and the power spectrum using the second-order Born approximation. The results depend on whether the source S(x, t) and the propagation speed c(x, t) are correlated or not. When they are uncorrelated, the mean field is zero. When they are correlated, the mean field is non-zero only when the source is non-stationary. The power spectrum is incoherent to leading order. There is a transfer of energy from lower to higher frequencies owing to wave scattering. The corresponding frequency upshift of the power profile in the (k, ω) domain is mainly caused by the cross power between the direct and the twice scattered field, which represents a second-order incoherent power contribution. The results are confirmed using a numerical solution of the wave equation where the scattered field is expanded to fifth order.     

Ring wave solutions of a n+1-dimensional Sine-Gordon model

The dynamical properties of the ring wave solutions of the model psi(tt)- nabla (n) (2)psi+sin psi+ varepsilon sin (psi/2)+alphapsi(t)=0 (00, alpha=0 (or alpha>0) the return effect of the ring wave does not occur only for well defined values of varepsilon. It will be shown numerically that the dissipative perturbation alphapsi(t) (alpha>0) stabilizes both the velocity and the wave profile of the ring wave when the return effect does not occur. (c) 1997 American Institute of Physics.     

Annihilation and creation of rotating waves by a local light pulse in a protoplasmic droplet of the Physarum plasmodium

Pattern dynamics plays a fundamental role in biological functions from cell to organ in living systems, and the appearance of rotating waves can lead to pathological situations. Basic dynamics of rotating waves of contraction-relaxation activity under local perturbation is studied in a newly developed protoplasmic droplet of the Physarum plasmodium. A light pulse is applied by irradiating circularly a quarter of the droplet showing a single rotating wave. The oscillation pattern changes abruptly only when the irradiation is applied at a part of the droplet near the maximal contraction. The abrupt changes are as follows: the rotating wave disappears or is displaced when the irradiation area is very close to the center of the rotating wave, while new rotating waves are created when the irradiation area is far from the center of the rotating wave. These results support the hypothesis that the phase response curve has a discontinuous change (type 0 resetting) from delay to advance around the maximal contraction. The significance of the results is discussed in relation to “vulnerability” in excitable media and biological systems in general.     

A Recurrent Quantum Neural Network Model to Describe Eye Tracking of Moving Targets

A theoretical quantum neural network model is proposed using a nonlinear Schrödinger wave equation. The model proposes that there exists a nonlinear Schrödinger wave equation that mediates the collective response of a neural lattice. The model is used to explain eye movements when tracking moving targets. Using a recurrent quantum neural network(RQNN) while simulating the eye tracking model, two very interesting phenomena are observed. First, as eye sensor data is processed in a classical neural network, a wave packet is triggered in the quantum neural network.This wave packet moves like a particle. Second, when the eye tracks a fixed target, this wave packet moves not in a continuous but rather in a discrete mode. This result reminds one of the saccadic movements of the eye consisting of ‘jumps’ and ‘rests’. However, such a saccadic movement is intertwined with smooth pursuit movements when the eye has to track a dynamic trajectory. In a sense, this is the first theoretical model explaining the experimental observation reported concerning eye movements in a static scene situation. The resulting prediction is found to be very precise and efficient in comparison to classical objective modeling schemes such as the Kalman filter.     

A semi-automatic processing technique for elastic-wave laboratory data

This paper addresses the problem of determining the onset of transient signals such as seismograms, acoustic emissions or ultrasonic signals. Usual manual techniques of onset-time picking are time consuming when numerous measurements are available. This may occur when dealing with (i) anisotropic rocks requiring many elastic wave velocities measurements in the laboratory, (ii) 4-D seismic field data or (iii) laboratory acoustic emissions data. We present a semi-automatic processing technique devoted to the study of case (i). It is based on ultrasonic signal analysis by wavelet transform and an onset-time picking procedure combining Akaike Information Criterion and cross-correlation method. The first step consists in extracting, from the whole experimentally recorded signal, the frequency component corresponding to the perturbation induced by a typical ultrasonic transducer in the laboratory. The second step is dedicated to the onset-time picking of the phase arrival in the extracted signal. The use of this processing technique based on mathematical arguments reduces human subjectivity. Main outcomes are: (i) increase of signal-to-noise ratio; (ii) measurement of elastic wave velocities at prescribed central frequency; (iii) drastic increase of efficiency in wave data processing; and (iv) increase in reliability (repeatability) of wave data acquisition.     

Ultrasmall volume plasmons, yet with complete retardation effects

Nanoparticle plasmons are attributed to quasistatic oscillations with no wave propagation due to their subwavelength size. However, when located within a band-gap medium (even in air if the particle is small enough), the particle interfaces act as wave mirrors, incurring small negative retardation. The latter, when compensated by a respective (short) propagation within the particle, generates a constructive interference based resonator. The unusual wave interference in the subwavelength regime (modal volume <0.001lambda(3)) significantly enhances the Q factor, e.g., 50 vs 5.5 of the quasistatic limit.     

Omnidirectional reflectance gaps and resonant tunneling effect in a one-dimensional photonic crystal consisting of two metamaterials

We investigate the properties of electromagnetic wave propagating in a one-dimensional photonic crystal (PC) consisting of two metamaterials with different dispersive model. The reflection gaps of metamaterials multilayer system are independent of the incident angle. Not only TE wave but also TM wave, the omnidirectional reflection gaps exhibit the same behavior with different incident angle for metamaterials as double negative material. We also observed that the frequency regimes of zero-transmission bands are different for TE and TM wave with the same incident angle, when one of metamaterials is the permittivity negative (ε < 0) and the other is the double negative. Correspondingly, we show that the result can be act as an efficient polarization splitter. At last, we discuss the resonant tunneling effect. If the total reflection condition is satisfied, the resonant tunneling effect is enhanced as the incident angle increases, even though the propagation wave is evanescent wave in the single layer medium.     

神经元网络中分布式电流诱导靶波机理研究

以四变量的Hodgkin-Huxley神经元模型构建规则网络来研究分布式电流刺激诱导靶波问题. 在一个二维规则网络的局部方形区域输入恒定刺激电流I₁, 其余区域结点上的神经元输入刺激电流I₂ 来刻画分布式电流. 分别研究了耦合强度、刺激电流I₁作用区域(受控神经元个数)、 分布式电流梯度(ΔI=I₁-I₂)对靶波形成的影响. 研究发现: 刺激的区域越小, 需要的电流梯度(ΔI)越大; 耦合强度越大, 诱导靶波所需要的电流梯度(ΔI)也越大. 最后讨论了分布式电流作用和靶波的形成机理. 进一步研究发现, 诱导的靶波对通道噪声有较强的抗干扰性. 关键词： 靶波 神经元网络 分布式电流