Particle-in-Cell Simulation of the Reflection of a Korteweg-de Vries Solitary Wave and an Envelope Solitary Wave at a Solid Boundary

Reflections of a Korteweg-de Vries(KdV) solitary wave and an envelope solitary wave are studied by using the particle-in-cell simulation method.Defining the phase shift of the reflected solitary wave,we notice that there is a phase shift of the reflected KdV solitary wave,while there is no phase shift for an envelope solitary wave.It is also noted that the reflection of a KdV solitary wave at a solid boundary is equivalent to the head-on collision between two identical amplitude solitary waves.     

基于温度效应的无限长压电圆杆纵波分析

利用有限变形理论,以无限长压电圆杆为研究对象,考虑了在横向惯性、等效泊松比效应以及在热电弹藕合共同作用下,基于Hamilton原理,并引入Euler方程推导出压电圆杆的纵向波动方程.采用Jacobi椭圆函数展开法,求解压电圆杆的波动方程和对应的解.最后,通过Matlab软件得到不同波速比下的色散曲线.以及温度场对压电圆杆的波形、波幅和波数的影响曲线.数值分析结果表明:随着温度的升高,波速逐渐降低,温度场的改变可影响和控制孤立波的传播特性.     

A 2D rods-in-air square-lattice photonic crystal optical switch

A 2D photonic crystal optical switch is proposed based on a rods-in-air square-lattice photonic crystal by removing two cross-lines of rods from a 2D square-lattice photonic crystal to form four optical channels. The simulation results show that, when inserting a single rod along the diagonal line of the intersection area of two removed cross-lines of rods, the position of the single inserted rod determines how much incident energy goes into different channels. In the case of transverse magnetic (TM) Gaussian point source, time domain simulation shows that up to 87.3% of the incident energy can be switched into a channel, which is vertical to the source channel. Because there are two diagonal lines in the intersection area of two removed cross-lines of rods, the optical switch feature is achieved by shifting the inserted rod between two diagonal lines. It is also found that the magnitude of the reflected wave in the source channel varies greatly with spatial position of the single inserted rod. The larger the magnitude of the reflected wave in the source channel, the less the energy that goes into the switched channel. The time delay between the incident wave and the reflected wave in the source channel is also related to the position of the single inserted rod. In addition, the large time delay between the incident wave and the reflected wave in the source channel shows that the reflected wave encounters many reflections with the walls of the source channel, instead of waves reflected back from the single inserted rod.     

Propagation of solitary waves in channels of decreasing depth

The changes which occur in a right-going solitary wave as it travels a channel of decreasing depth are discussed. In addition to the changes in the solitary wave, we have found through a judicious use of the conservation laws two secondary structures (a shelf and a reflection). Each of these structures is small with respect to the solitary wave, though the mass flux associated with each is of the same order as that of the solitary wave. Of interest is that the amplitude of the reflected wave does not satisfy Green's law. But rather, the amplitude of the reflected wave is constant along left-going characteristics. This finding allows us to satisfy the mass flux conservation laws to leading order and establishes the perturbed Korteweg-deVries equation as a consistent approximation for the right-going profile.     

Binary collision approximation for solitary waves in a Y-shaped granular chain

We implement a binary collision approximation to study solitary wave propagation in a two-dimensional double Y-shaped granular chain. The solitary wave was transmitted and reflected when it met the interface of the bifurcated branches of the Y-shaped granular chains. We obtain the analytic results of the ratios of the transmitted and reflected speeds to the incident speed of the solitary wave, the maximum force between the two neighbor beads in a solitary wave, and the total time taken by the pulse to pass through each branch. All of the analytic results are in good agreement with the experimental observations from Daraio et al. [Phys. Rev. E 82 036603 (2010)]. Moreover, we also discuss the delay effects on the arrival of split pulses, and predict the recombination of the split waves traveling in branches in the final stem of asymmetric systems. The prediction of pulse recombination is verified by our numerical results.     

Dynamic strain of a longitudinally vibrating viscoelastic rod with an end mass

The dynamic strain of a viscoelastic rod excited into longitudinal simple harmonic vibration, a constant amplitude displacement being maintained by a shaker at one end and a mass terminating the other end, is theoretically investigated in this paper. The general equation of the strain distribution in the rod is derived by solving the one-dimensional wave equation. It is shown that the strain in the rod is the largest at the excited end, at the antiresonant frequencies. Simplified approximate equations are derived for the low loss case to calculate the largest strain in the rod with knowledge of the loss factor.     

Bulk Nonlinear Elastic Strain Waves in a Bilayer Coaxial Cylindrical Rod

The problem of the propagation of long nonlinear elastic strain waves in a bilayer coaxial cylindrical rod with an ideal contact between the layers has been considered. Expressions for transverse displacements through longitudinal displacements have been derived. The former satisfies free boundary conditions and continuity conditions for displacements and stresses at the interlayer interface with the desired accuracy. It has been shown how these expressions generalize the well-known plane-section and Love hypotheses for an isotropic homogeneous rod. An equation for the propagation of a nonlinearly elastic strain longitudinal wave has been derived, and its particular solution in the form of a solitary traveling wave has been studied.     

Generation of elastic stress waves at a T-junction of square rods

Fourier techniques have been used to predict transmitted and reflected waves at a T-joint in rods of square cross-section for an arbitrary longitudinal impulse approaching the joint in the terminating rod. Elementary and Timoshenko beam theory were used for longitudinal and flexural wave motions respectively. Good agreement is obtained between the predicted and experimental results for an input pulse with large wavelengths compared with the lateral dimensions of the rod. The results demonstrate the similarity to transverse impact of an infinite rod and the unidirectional translation of the joint as a valid model.     

Pulsed Sounding of Cracks with the Use of the Modulation of Ultrasound by Vibrations

The possibility of using the effect of the modulation of ultrasound by vibrations due to the presence of cracks for the nonlinear acoustic detection of cracks is demonstrated. The method is based on a pulsed ultrasonic sounding with gating the received signal and simultaneously exciting low-frequency vibrations in the sample. The presence of a crack is characterized by the modulation of the ultrasonic wave reflected from the crack. The visualization of the crack position in a model object (a metal rod) is performed. The possibility of selecting a crack on the background of an intense signal reflected from a cavity is experimentally demonstrated. The manifestation of the nonlinear properties of a crack is studied as a function of the polarization of the flexural vibrations of the rod.     

Bright,dark, and singular solitons in magneto-electro-elastic circular rod

In this article, the bright, dark, and singular solitons are being constructed for nonlinear longitudinal wave equation with dispersion caused by transverse Poisson’s effect in a magneto-electro-elastic circular rod. The solitary wave ansatz is used to carry out these solutions. The constraint conditions, for the existence of the soliton solutions, are also listed. This article provides a lot of encouragement for the researchers in this era.     

粘弹性阻尼对弹性杆内纵向孤波运动的影响

本文用微扰论的计算方法,求出在粘弹性阻尼较小但不可忽略的情况下,弹性杆内纵向孤波的形状、速度及能量随时间的变化规律。结果表明,粘弹性阻尼使孤波逐渐变矮、增宽、速度减慢,能量逐渐耗散,最后导致孤波的消失。 关键词：     

粘弹性阻尼对弹性杆内纵向孤波运动的影响

本文用微扰论的计算方法, 求出在粘弹性阻尼较小但不可忽略的情况下, 弹性杆内纵向孤波的形状、速度及能量随时间的变化规律. 结果表明, 粘弹性阻尼使孤波逐渐变矮、增宽、速度减漫, 能量逐渐耗散, 最后导致孤波的消失. 关键词：     

Optodynamic description of a linear momentum transfer from a laser induced ultrasonic wave to a rod

We present a new optodynamic experimental technique to measure the linear momentum obtained by a rod during a nanosecond laser pulse ablation of the rod’s front face on the basis of the displacement due to an ultrasonic wave reflection at its rear end. With the help of a simple theory, we explained the step-like motion of the rod’s free end. This theory conforms well with the general shape of the measured displacement history curve. The acquired momentum can be directly estimated by measuring the height of a step from the step-like motion of the rod’s end. Measurements based on an arm-compensated Michelson interferometer also enabled us to follow the attenuation of an ultrasonic wave and so to determine the characteristic attenuation time. This quantity plays a major role in the transfer of linear momentum from within the initial ultrasonic wave to the final net uniform motion of the specimen. PACS  52.38.Mf; 43.35.Yb; 43.35.Cg     

Solitary wave emission from a non-linear waveguide with a PTS cladding

We present numerical simulations of solitary wave emission from a waveguide in which the cladding is the non-linear material polydiacetylene para-toluene sulfphonate (PTS). In addition to a self-focusing cubic non-linearity PTS exhibits a defocusing quintic non- linearity, which imposes a limit on the peak non-linear index change. The influence of this limiting on solitary wave emission is studied in detail in one transverse dimension, and we show that it can increase the fraction of the incident power transferred into the emitted solitary wave. Fabrication issues arising from the limiting are also discussed. Numerical simulations in two transverse dimensions are also presented showing stable emitted solitary waves due to the stabilizing effect of the limiting, in contrast to the self-focusing collapse which occurs for a cubic non-linearity.     

Improved description of longitudinal strain solitary waves

It is found that simultaneous existence of compressive and tensile localized strain solitary waves in a rod can be described by the model equation containing both quadratic and cubic nonlinear terms. Only propagation of these waves is described by exact travelling wave solutions. However, numerical solution demonstrates that both kinds of these waves may be generated from an arbitrary input and interact each other keeping their shape and velocity. Moreover, one and the same input gives rise to a different number of these kinds of waves, and it is quadratic nonlinearity that determines it.     

Nonlinear Wave Propagation in a Disordered Medium

In this paper we consider the problem of solitary wave propagation in a weakly disordered potential. Through a series of careful numerical experiments we have observed behavior which is in agreement with the theoretical predictions of Kivshar et al., Bronski, and Gamier. In particular we observe numerically the existence of two regimes of propagation. In the first regime the mass of the solitary wave decays exponentially, while the velocity of the solitary wave approaches a constant. This exponential decay is what one would expect from known results in the theory of localization for the linear Schrödinger equation. In the second regime, where nonlinear effects dominate, we observe the anomalous behavior which was originally predicted by Kivshar et al. In this regime the mass of the solitary wave approaches a constant, while the velocity of the solitary wave displays an anomalously slow decay. For sufficiently small velocities (when the theory is no longer valid) we observe phenomena of total reflection and trapping.     

孤立波在一维复合颗粒链中传播特性的模拟研究

采用分子动力学方法模拟研究了孤立波在重轻颗粒相间排列的一维复合颗粒链中的传播特性.结果发现,在轻重颗粒的质量比较大或较小时,散射作用较弱,颗粒的速度和孤立波的速度衰减较慢.在轻重颗粒的质量比为中等时,散射作用较强,颗粒的速度和孤立波的速度衰减较快.孤立波在通过重-轻颗粒界面时,存在有增速效应,可以提高孤立波的传播速度.并且,轻重颗粒的质量比越小增速效应越强.在散射作用和增速效应的共同作用下,改变轻重颗粒的质量比可以调控孤立波在重-轻颗粒链中的传播时间.     

Simulation studies of the scattering of a solitary wave by a mass impurity in a chain of nonlinear oscillators

We have simulated large amplitude motion in cyclic one-dimensional lattices of Morse potential oscillators with a mass impurity, and have observed an unexpected persistence of solitary wave behavior for which we are unable to discover a satisfactory explanation. In solitary wave motion as a function of cycle length and of initial energy, the most common feature of the dynamics is an initial energy plateau with regular oscillatory energy exchange between the solitary wave and other excitations of the lattice, followed by rapid decay. Some systems show no decay at all through 1000 impurity interactions, while others show no significant plateau before decaying. For some cycle lengths there are energy bands in which the solitary wave propagates indefinitely long, with small amplitude oscillatory exchange of energy with the lattice. No regularities were found.     

Exact solutions of equation of transverse vibrations for a bar with a specific cross section variation law

Flexural wave propagation along a bar whose thickness smoothly decreases down to zero within its end piece is considered. The propagation velocity tends to zero as the tapered end of the bar is approached, and the time of wave propagation to the tapered end is infinite. As a consequence, waves propagating along the bar are not reflected from the end. Previous quantitative study of the effect in the WKB approximation shows that, in the case of parabolic tapering, the WKB approximation yields a uniform asymptotics, which is valid (or invalid) for any of the bar’s cross sections. In the case of a bar with parabolic tapering, the equation of flexural vibrations of the bar has exact analytic solutions in the form of power functions. Based on these solutions, a modified WKB approximation is proposed to solve equations for bars with nonparabolic thickness variation laws. The input impedance of a bar with a parabolic tapering is calculated and analyzed.     

宽度缓慢均匀变化水槽中的非传播表面孤波

用多重尺度微扰理论导出了宽度均匀缓变水糟中非传播孤波所服从的非线性方程及其解析解。结果指出，孤波恒向宽度较窄的一端近加速移动。加速度正比于宽度的变化率．本文所用的方法原则上可以推广于其他均匀缓变波导中线性波和非线性波的理论研究。 关键词：