On a certain energy relationship for waves in systems having traveling parameters

A relationship is derived that couples the total energies and frequencies of quasimonochromatic wave packets that propagate in linear systems having parameters that vary in time and space according to the law governing a traveling wave having an arbitrary profile.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 15, No. 1, pp. 51–54, January, 1972.The author thanks N. S. Stepanov for raising the problem and his help with the work, and likewise M. A. Miller and L. A. Ostrovskii for their helpful comments.     

Scattering of surface waves by a sub-surface crack

The scattering of Rayleigh waves by a two-dimensional sub-surface crack, which is perpendicular to the free surface of an elastic half-space, is investigated. The boundary-value problem for the scattered field is stated, and reduced to an uncoupled system of integral equations which are solved numerically. At large distances from the crack the scattered field is shown to consist of outgoing Rayleigh waves and cylindrical body waves. Graphs of the variation of the amplitude and phase of the forward and backward scattered Rayleigh waves with the frequency and the geometrical parameters of the crack are presented. The stress intensity factors at both crack tips have also been obtained.     

Wavelength halving in a transition between standing waves and traveling waves

In the Belousov-Zhabotinsky reaction-diffusion system dispersed in a newly developed water-in-oil aerosol OT/Span-20 microemulsion, the transition between standing waves and traveling waves is accompanied by a halving of the wavelength.     

Holes and chaotic pulses of traveling waves coupled to a long-wave mode

It is shown that localized traveling-wave pulses and holes can be stabilized by a coupling to a long-wave mode. Simulations of suitable real Ginzburg-Landau equations reveal a small parameter regime in which the pulses exhibit a breathing motion (presumably related to a front bifurcation), which subsequently becomes chaotic via period-doubling bifurcations.     

The transfer of ultrasonic energy in the diffraction technique for crack sizing

During the past five years a programme of work has been carried out at the Harwell NDT Centre concerned with the use of scattered or diffracted ultrasound in the sizing of defects. The progress made in this direction and some of the possible lines of further research have been indicated in other papers.^1–3 This diffraction technique has been evaluated on a number of fatigue cracked specimens and it has been found that accuracies in crack sizing consistently better than $\text{1}\text{2}$ mm have been achieved. The technique is thus thought to be on the verge of application to practical ndt problems.The basis of the sizing technique is the recognition and subsequent timing of various discrete ultrasonic pulses, as will be outlined later. The scope of the technique thus depends on these signals remaining both well separated and large enough to be resolved in a wide range of examination geometries. The purpose of the present paper is to consider the mechanisms by which two of the ultrasonic pulses of importance in the diffraction technique are produced. In this connection the current theoretical situation is reviewed and this is compared, where appropriate, with experimental measurements taken during the period of this work.     

Gaussian beam diffraction by a quasi-optical grating for coupling to lower-hybrid plasma waves

This paper is dedicated to the theoretical approach to the problem of modelling quasi-optical launchers of plasma waves in the lower-hybrid range of frequencies, when a gaussian beam is the incident field. Numerical results are presented and discussed comparing the cases of a gaussian beam and a plane wave as an incident field [1].     

Cooperation of traveling and quasi-cutoff waves in a cyclotron-resonance maser

A new version of a cyclotron-resonance maser is studied theoretically and experimentally. Here, a spatially periodic helical electron beam couples traveling (autoresonance) and quasi-cutoff (gyrotron) waves of the same frequency, interacting with them at different cyclotron harmonics. The theory and early experimental results show that this maser can effectively generate a traveling wave with low quasi-cutoff wave excitation losses using a very simple feedback system.     

Dynamics of traveling waves in the transverse section of a laser

We analyze the general features of the formation and interaction of transverse traveling waves and the appearance of filamentation in broad area semiconductor lasers with current profiling. For small apertures, the emitted profile is symmetric consisting of two counterpropagating transverse traveling waves, both emanating from the center of the device. For larger apertures, the emission becomes asymmetric as one of the traveling waves expands to occupy an increased area while the other occupies the remaining, smaller spatial region. In both devices, the pattern becomes unstable at higher injection currents due to optical filamentation, although an intermediate state is present in the wider device whereby the dominant wave undergoes a Hopf bifurcation before filamentation occurs.     

Bifurcations and traveling waves in a delayed partial differential equation

Here cell population dynamics in which there is simultaneous proliferation and maturation is considered. The resulting mathematical model is a nonlinear first-order partial differential equation for the cell density u(t,x) in which there is retardation in both temporal (t) and maturation variables (x), and contains three parameters. The solution behavior depends on the initial function varphi(x) and a three component parameter vector P=(delta,lambda,r). For strictly positive initial functions, varphi(0) greater, similar 0, there are three homogeneous solutions of biological (i.e., non-negative) importance: a trivial solution u(t) identical with 0, a positive stationary solution u(st), and a time periodic solution u(p)(t). For varphi(0)=0 there are a number of different solution types depending on P: the trivial solution u(t), a spatially inhomogeneous stationary solution u(nh)(x), a spatially homogeneous singular solution u(s), a traveling wave solution u(tw)(t,x), slow traveling waves u(stw)(t,x), and slow traveling chaotic waves u(scw)(t,x). The regions of parameter space in which these solutions exist and are locally stable are delineated and studied.     

High-frequency modulation of light in diffraction by the Bragg grating with a refractive index traveling wave

The diffraction by a Bragg grating with high-frequency modulation of the refractive index of the medium is analyzed theoretically. The effect of the grating parameters and parameters of an rf signal on the efficiency of modulation of optical signals at frequencies above 10 GHz is investigated.     

Symmetric waves are traveling waves for a shallow water equation modeling surface waves of moderate amplitude

Following a general principle introduced by Ehrnström, Holden and Raynaud in 2009, we prove that for an equation modeling the free surface evolution of moderate amplitude waves in shallow water, all symmetric waves are traveling waves.     

Enhanced localization of waves in one-dimensional random media due to nonlinearity: Fixed input case

We study the influence of nonlinearity on wave localization in one-dimensional random media. Using a discrete nonlinear Schrödinger equation with a random on-site energy term, we calculate the localization length in a numerically exact manner. Unlike in many previous works, we fix the intensity of the incident wave and calculate quantities as a function of other parameters. We find that localization is enhanced due to nonlinearity for the focusing and defocusing nonlinearities. For small nonlinearity, the localization length is a decreasing function of nonlinearity. For sufficiently large nonlinearity, however, the localization length is found to approach a saturation value.     

Control of traveling waves in the Mammalian cortex

We experimentally confirmed predictions that modulation of the neuronal threshold with electrical fields can speed up, slow down, and even block traveling waves in neocortical slices. The predictions are based on a Wilson-Cowan-type integro-differential equation model of propagating neocortical activity. Wave propagation could be modified quickly and reversibly within targeted regions of the network. To the best of our knowledge, this is the first example of direct modulation of the threshold to control wave propagation in a neural system.     

Experimental observation of traveling waves in the transverse section of a laser

The selection of a transverse traveling wave by an inhomogeneous pump profile has been experimentally observed in a class B laser structure. The laser structure consisted of a wide-aperture edge-emitting laser diode operating in pulsed mode to avoid thermal guiding effects. The injection current's profile was modified from the usual top-hat configuration to a Lorentzian-like profile by the inclusion of a 10-mum p-type expitaxial spreading layer. Spatial dependance of the far field on the near field was observed. The same behavior is also demonstrated numerically by use of Maxwell-Bloch equations for semiconductor lasers.     

Resonance blocking of traveling waves by a system of cracks in an elastic layer

Wave processes that occur in an elastic layer when waves traveling in it are diffracted by a system of horizontal cracks are investigated. Integral representations of wave fields are constructed in terms of the convolution of Green’s matrices and unknown jumps of displacements at the cracks. The displacement jumps are determined from the boundary integral equations, which are obtained from the initial boundary-value problem with the boundary conditions at crack faces being satisfied. The spectrum of the integral operator is studied for different variants of mutual crack arrangement and is compared with the spectrum of the corresponding operators for individual cracks; the relationship between the spectrum and the blocking effects is analyzed. The possibility of obtaining an extended frequency band of waveguide blocking in the case of groups of cracks is demonstrated.