Spatial separation of the traveling and evanescent parts of dipole radiation

Electric dipole radiation consists of traveling and evanescent plane waves. When radiation is detected in the far field, only the traveling waves will contribute to the intensity distribution, as the evanescent waves decay exponentially. We propose a method to spatially separate the traveling and evanescent waves before detection. It is shown that when the radiation passes through an interface, evanescent waves can be converted into traveling waves and can subsequently be observed in the far field. Let the radiation be observed under angle theta(t) with the normal. Then there exists an angle theta(ac) such that for 0 < or = theta(t) < theta(ac) all intensity originates in traveling waves, whereas for theta(ac) < theta(t) < pi/2 only evanescent waves contribute. It is shown that with this technique and under the appropriate conditions almost all far-field power can be provided by evanescent waves.     

Relaxation of the director field in the form of a traveling wave in twisted nematic cells

The orientational relaxation of the director field toward its equilibrium orientation in the form of a traveling wave is investigated. It is shown that the nonlinear relaxation can occur in the form of a traveling wave in a twisted nematic cell under specific conditions for the external electric field and material parameters characterizing the nematic liquid crystal. The calculations of the relaxation processes in the form of traveling waves have demonstrated that these nonlinear processes in the twisted nematic cell proceed more easily when the initial perturbation of the director is induced in the vicinity of one of the bounding cell surfaces.     

Excitation and sensing of multiple vibrating traveling waves in one-dimensional structures

Lightly damped vibrating structures normally exhibit vibration patterns that are a combination of standing waves, i.e. mode shapes. Traveling waves, on the other hand, occur only under special circumstances. In this work, the theoretical conditions under which traveling waves prevail in finite structure are investigated. These conditions are highly sensitive to the geometrical and material parameters of the structure and in particular the vibration pattern is sensitive to the boundary conditions. There are several combinations under which traveling waves cannot be formed and these ill-posed cases are analyzed in some detail. To overcome the unavoidable uncertainties in a model, a tuning process based on identification and optimization of the excitation is suggested. The identification process uses a parametric algorithm to estimate the wavenumbers of the measured vibrations. Then, the waves are decomposed into traveling and standing parts and the external excitation is tuned until a pure traveling wave is formed.     

Chaotic particle motion under linear surface waves

We investigate the motion of infinitesimal particles in the flow field inside the fluid under a traveling surface wave. It is shown that, even for two-dimensional waves, a superposition of two or more traveling harmonic waves is enough to generate chaotic particle motion, i.e., Lagrangian chaos. (c) 1996 American Institute of Physics.     

一般变换下的Jacobi椭圆函数展开法及应用

将在行波变换下的Jacobi椭圆函数展开法推广到范围非常广泛的一般函数变换下进行，利用这一方法求得了一些非线性发展方程的精确周期解，这些解包括了在行波变换下所求得的周期解. 证明了一些非线性发展方程的周期解一定是行波解. 关键词： 非线性发展方程 周期解 行波解 Jacobi椭圆函数     

Instability of traveling waves in an optical waveguide

Instability of traveling IR waves within a waveguide structure is discussed. A practical model of a traveling wave amplifier of a solid state is proposed, utilizing an optical waveguide. The mechanism of instability is interpreted in terms of an interaction between a plasmon wave and a circuit one under a constraining boundary condition. Properties of the traveling amplification and related problems are discussed, with appropriately suggested semiconductor materials and device designs. The features of the amplifier are a simple structure, a low DC biasing power dissipation for room-temperature operation, unidirectionality, and a wide wavelength range from IR or submillimeter order, suited to various applications.     

A note on poroacoustic traveling waves under Forchheimerʼs law

Acoustic traveling waves in a gas that saturates a rigid porous medium is investigated under the assumption that the drag experienced by the gas is modeled by Forchheimer?s law. Exact traveling wave solutions (TWS)s, as well as approximate and asymptotic expressions, are obtained; decay rates are determined; and acceleration wave results are presented. In addition, special cases are considered, critical values of the wave variable and parameters are derived, and comparisons with predictions based on Darcy?s law are performed. It is shown that, with respect to the Darcy case, most of the metrics that characterize such waveforms exhibit an increase in magnitude under Forchheimer?s law.     

Basin boundaries in asymmetric vibrations of a circular plate

In order to investigate further nonlinear asymmetric vibrations of a clamped circular plate under a harmonic excitation, we reexamine a primary resonance, studied by Yeo and Lee [Corrected solvability conditions for non-linear asymmetric vibrations of a circular plate, Journal of Sound and Vibration 257 (2002) 653-665] in which at most three stable steady-state responses (one standing wave and two traveling waves) are observed to exist. Further examination, however, tells that there exist at most five stable steady-state responses: one standing wave and four traveling waves. Two of the traveling waves lose their stability by Hopf bifurcation and have a sequence of period-doubling bifurcations leading to chaos. When the system has five attractors: three equilibrium solutions (one standing wave and two traveling waves) and two chaotic attractors (two modulated traveling waves), the basin boundaries of the attractors on the principal plane are obtained. Also examined is how basin boundaries of the modulated motions (quasi-periodic and chaotic motions) evolve as a system parameter varies. The basin boundaries of the modulated motions turn out to have the fractal nature.     

Different types of nonlinear convective oscillations in a multilayer system under the joint action of buoyancy and thermocapillary effect

The nonlinear development of oscillatory instability under the joint action of buoyant and thermocapillary effects in a multilayer system, is investigated. The nonlinear convective regimes are studied by the finite difference method. Two different types of boundary conditions – periodic boundary conditions and rigid heat-insulated lateral walls, are considered. It is found that in the case of periodic boundary conditions, the competition of both mechanisms of instability may lead to the development of specific types of flow: buoyant-thermocapillary traveling wave and pulsating traveling wave. In the case of rigid heat-insulated boundaries, various types of nonlinear flows – symmetric and asymmetric oscillations, have been found.     

One-parameter localized traveling waves in nonlinear Schrödinger lattices

We address the existence of traveling single-humped localized solutions in the spatially discrete nonlinear Schrödinger (NLS) equation. A mathematical technique is developed for analysis of persistence of these solutions from a certain limit in which the dispersion relation of linear waves contains a triple zero. The technique is based on using the Implicit Function Theorem for solution of an appropriate differential advance-delay equation in exponentially weighted spaces. The resulting Melnikov calculation relies on a number of assumptions on the spectrum of the linearization around the pulse, which are checked numerically. We apply the technique to the so-called Salerno model and the translationally invariant discrete NLS equation with a cubic nonlinearity. We show that the traveling solutions terminate in the Salerno model whereas they generally persist in the translationally invariant NLS lattice as a one-parameter family of solutions. These results are found to be in a close correspondence with numerical approximations of traveling solutions with zero radiation tails. Analysis of persistence also predicts the spectral stability of the one-parameter family of traveling solutions under time evolution of the discrete NLS equation.     

行波和驻波模式下热声振荡的临界温度梯度

热声机械作为一种能量转化装置。其效率于传统发动机还有较大差距。本文讨论了热声发动机在驻波和行波两种不同工作状态下,其声功率产生的临界温度梯度与流道尺寸和工作介质的关系,得出了两种模式下最佳的工作条件。结果表明;采用行波形式的热声发动机结构,可以有效降低临界温度梯度,提高热致声的效率,同时可以利用一些低品位来做为热声发动机的高温端。     

Stability of the viscous fluid film flow on a uniformly heated substrate

The linear stability is investigated of a viscous fluid film on a uniformly heated substrate under an arbitrary angle of inclination against the horizon. At the substrate, the heat flux is set; at the film surface, the fluid-gas heat transfer coefficient is specified. The waves are considered in the film propagating in an arbitrary direction. Within the frame of the integral model, the dispersion ratios are obtained for the wave increment and phase velocity. The analysis is performed of the dispersion ratios, and the flow instability range is determined. At the Marangoni numbers above a certain threshold, standing wave or traveling wave type disturbances take place; the waves increase in the horizontal direction. For the traveling waves, the Marangoni number threshold value is significantly lower than the same for the standing waves.     

Phonon-polariton waves on the surface of SiC crystal

The excitation and propagation of traveling phonon-polariton waves on the surface of silicon carbide (SiC) excited by light at a frequency close to the lattice resonance have been investigated. These waves are excited in the presence of the boundary of a metal mask deposited on the crystal surface. The use of the Green’s function has been shown to provide good qualitative agreement with the observed distribution of the amplitude and phase of the field on the surface under these experimental conditions. It has been shown that only consideration of the mask boundary as an extended source of traveling surface waves, which removes the inhibition of the generation of waves in the noncoincidence of the wave vector, cannot quantitatively describe the phenomenon. The spatial resolution of the used scanning near-field optical microscope is no worse than 150 nm at a wavelength of 10 μm.     

Pressure potential and stability analysis in an acoustical noncontact transportation

Near field acoustic traveling wave is one of the most popular principles in noncontact manipulations and transportations. The stability behavior is a key factor in the industrial applications of acoustical noncontact transportation. We present here an in-depth analysis of the transportation stability of a planar object levitated in near field acoustic traveling waves. To more accurately describe the pressure distributions on the radiation surface, a 3D nonlinear traveling wave model is presented. A closed form solution is derived based on the pressure potential to quantitatively calculate the restoring forces and moments under small disturbances. The physical explanations of the effects of fluid inertia and the effects of non-uniform pressure distributions are provided in detail. It is found that a vibration rail with tapered cross section provides more stable transportation than a rail with rectangular cross section. The present study sheds light on the issue of quantitative evaluation of stability in acoustic traveling waves and proposes three main factors that influence the stability: (a) vibration shape, (b) pressure distribution and (c) restoring force/moment. It helps to provide a better understanding of the physics behind the near field acoustic transportation and provide useful design and optimization tools for industrial applications.     

真空中线性啁啾时空高斯脉冲传输特性的分析

利用稳态相位点的方法研究了线性啁啾时空高斯脉冲传输过程中的相位特性，并在二阶近似的情况下讨论了其传输过程中的时空特性，两种方法从不同侧面得出了相同的结论，即：时空高斯脉冲在传输的过程中，在无穷远处交退化为球面波，或者在旁轴近似的情况下退化为平面波。     

Wave trains in a model of gypsy moth population dynamics

A recent model of gypsy moth [Lymantria dispar (Lepidoptera: Lymantriidae)] populations led to the observation of traveling waves in a one-dimensional spatial model. In this work, these waves are studied in more detail and their nature investigated. It was observed that when there are no spatial effects the model behaves chaotically under certain conditions. Under the same conditions, when diffusion is allowed, traveling waves develop. The biomass densities involved in the model, when examined at one point in the spatial domain, are found to correspond to a limit cycle lying on the surface of the chaotic attractor of the spatially homogeneous model. Also observed are wave trains that have modulating maxima, and which when examined at one point in the spatial domain show a quasiperiodic temporal behavior. This complex behavior is determined to be due to the interaction of the traveling wave and the chaotic background dynamics. (c) 1995 American Institute of Physics.     

Non-Reflective Magnetohydrodynamic Waves in an Inhomogeneous Plasma

Radiophysics and Quantum Electronics - The existence of traveling waves in a strongly inhomogeneous magnetized plasma is studied. It is shown that under certain conditions for characteristics of...     

On the stability of periodic solutions of the generalized Benjamin-Bona-Mahony equation

We study the stability of a four-parameter family of spatially periodic traveling wave solutions of the generalized Benjamin-Bona-Mahony equation under two classes of perturbations: periodic perturbations with the same periodic structure as the underlying wave, and long wavelength localized perturbations. In particular, we derive necessary conditions for spectral instability under perturbation for both classes of perturbations by deriving appropriate asymptotic expansions of the periodic Evans function, and we outline a theory of nonlinear stability under periodic perturbations based on variational methods which effectively extends our periodic spectral stability results.     

Mode-splitting and quasi-degeneracies in circular plate vibration problems: The example of free vibrations of the stator of a traveling wave ultrasonic motor

In systems with rotational symmetry, bending modes occur in doubly-degenerate pairs with two independent vibration modes for each repeated natural frequency. In circular plates, the standing waves of two such degenerate bending modes can be superposed with a 1/4 period separation in time to yield a traveling wave response. This is the principle of a traveling wave ultrasonic motor (TWUM), in which a traveling bending wave in a stator drives the rotor through a friction contact. The stator contains teeth to increase the speed at the contact region, and these affect the rotational symmetry of the plate. When systems with rotational symmetry are modified either in their geometry, or by spatially varying their properties or boundary conditions, some mode-pairs split into singlet modes having distinct frequencies. In addition, coupling between some pairs of distinct unperturbed modes also causes quasi-degeneracies in the perturbed modes, which leads their frequency curves to approach and veer away in some regions of the parameter space. This paper discusses the effects of tooth geometry on the behavior of plate modes under free vibration. It investigates mode splitting and quasi-degeneracies and derives analytic expressions to predict these phenomena, using variational methods and a degenerate perturbation scheme for the solution to the plate’s discrete eigenvalue problem; these expressions are confirmed by solving the discrete eigenvalue problem of the plate with teeth.     

Periodic Wave,Solitary Wave and Compacton Solutions of a Nonlinear Wave Equation with Degenerate Dispersion

In this letter, we investigate traveling wave solutions of a nonlinear wave equation with degenerate dispersion. The phase portraits of corresponding traveling wave system are given under different parametric conditions. Some periodic wave and smooth solitary wave solutions of the equation are obtained. Moreover, we find some new hyperbolic function compactons instead of well-known trigonometric function compactons by analyzing nilpotent points.