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.     

Dynamics of defects and traveling waves in an interfacial finger pattern

We present the results of an experimental study of one-dimensional traveling finger patterns dominated by source and sink defects. The system studied is a driven fluid–air interface, and the traveling-wave state arises via a subcritical bifurcation. We analyze space–time images of the patterns to obtain the amplitude and local wave number of the left- and right-going traveling waves near the defects. We determine the width of the defects, and find that the width of the sinks does not vary significantly with distance above the bifurcation over the range of our experiments, while the source width increases as the bifurcation is approached from above. We also observe both localized depressions or enhancements in wave amplitude and periodic modulations of the pattern amplitude and wave number.     

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.     

Interaction of intense laser radiation with weak electromagnetic waves in an evacuated section of a ring laser

A laboratory experiment for the study of nonlinear interaction of electromagnetic waves in vacuum is proposed. The basic idea of the experiment is as follows. If one separates a certain region of the circuit in a ring laser from the remaining part with gas-impenetrable partitions, evacuates it, and forms external electromagnetic fields there, the oscillation frequencies and the polarization states of the electromagnetic waves traveling in this ring laser in counter directions are different. A calculation is made for the oscillation frequencies of electromagnetic waves traveling in a ring laser in opposite directions in the case when they interact in an evacuated section of the ring laser circuit with intense laser radiation. It is shown that the effect can be observed in experiments using presently available pulsed lasers of ultrahigh power.     

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.     

Collisional damping of transverse waves in a plasma

The effect of collisions on transverse waves in a homogeneous, field free plasma is investigated by means of Gross-Krook collision model. The dispersion relation is calculated by assuming the collision frequency to be small andKλ _D ?1. The damping rate ω _I is obtained as $$\omega _I = \frac{{\nu _{ei} }}{2}\frac{{\omega _p^2 }}{{\omega _0^2 }}\left[ {1 + \frac{{3K^2 \lambda _D^2 \omega _p^2 }}{{\omega _0^2 }} - \frac{{K^2 \lambda _D^2 \omega _p^4 }}{{\omega _0^4 }}} \right] + \frac{{\nu _{ee} }}{2}\frac{{\omega _p^2 }}{{\omega _0^2 }}\left( {\frac{{K^2 \lambda _D^2 \omega _p^2 }}{{\omega _0^2 }}} \right)$$ where ω ₀ ² =c ² K ²+ω ₂ ^p , andv _ei andv _ee are electron-ion and electron-electron collision frequency respectively.     

Ultrasonic engine based on traveling waves in a plate

Velocity dispersion curves and phase relationships between the surface displacement components are calculated in the case of waves propagating in XZ-, YZ-, and ZY-cut LiNbO₃ plates. The dispersion curves agree with experimental frequency dependences of the excitation efficiency for various modes in the plates. The displacements of ZnS microparticles placed on the surface of the plates qualitatively agree with the analytical phase relationships between the displacement components. Results obtained indicate that the plate may be used as an ultrasonic engine capable of transferring microparticles in various physical and industrial processes.     

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.     

Oscillatory traveling waves in excitable media

A new type of waves in an excitable medium, characterized by oscillatory profile, is described. The excitable medium is modeled by a two-component activator-inhibitor system. Reaction-diffusion systems with diagonal and cross diffusion are examined. As an example, a front (kink) represented by a heteroclinic orbit in the phase space is considered. The wave shape and velocity are analyzed with the use of exact analytical solutions for wave profiles.     

Parametric excitation of traveling waves in a circular non-dispersive medium

This paper discusses a special type of propagating waves created by parametric excitation in a circular taught string. The string, being a non-dispersive medium propagates deformations in a similar manner to electromagnetic waves in vacuum, both have simple wavelength–frequency relationship that play an important role here. Nonlinear equations are derived under the assumption of finite deformations, whose solution produces a square-wave like, limited-amplitude, traveling wave. Closed-form expressions are obtained for the parametric excitation characteristics of the nonlinear system and the steady-state traveling waves are described by a generalized eigenvalue problem. The latter relates the nonlinear elongation of the neutral axis to the participating wavelengths forming the propagating wave. Detailed numerical simulations are provided to validate the solution and to illustrate graphically the waveforms. It is shown that propagating sinusoidal parametric excitation gives rise to various square-wave like deformation shapes which a unique phenomenon is arising in non-dispersive media.     

Dynamics of detonation waves in a channel with variable cross section and filled with bubbly fluid

The flow of bubbly fluid comprising a mixture of bubbles filled with explosive and inert gases, which is driven through a converging channel, was studied. Depending on the velocity of the hummer hitting the bubbly fluid boundary, the flow may be accompanied by the development of detonation waves which compress the bubbles with inert gas.     

Dynamics of traveling reaction pulses

The growth of activator losses is accompanied by the decay of a traveling reaction pulse. In a ring reactor, this propagation threshold is present simultaneously with a threshold related to the ring diameter. The results of numerical experiments with pulses of an exothermal reaction reveal the transition from pulse propagation to a homogeneous hot regime, established regimes with periodic variations of the pulse velocity, and oscillatory decay of the pulse. When the medium becomes “bistable” as a result of the variation in parameters, this factor does not prevent the propagation of pulses, but leads to changes in the pulse structure.     

Dynamics of a charged particle in a linearly polarized traveling wave

The basic physical processes in laser-matter interaction, up to (for a neodymium laser) are now well understood, on the other hand, new phenomena evidenced in PIC code simulations have to be investigated above . Thus, the relativistic motion of a charged particle in a linearly polarized homogeneous electromagnetic wave is studied, here, using the Hamiltonian formalism. First, the motion of a single particle in a linearly polarized traveling wave propagating in a non-magnetized space is explored. The problem is shown to be integrable. The results obtained are compared to those derived considering a cold electron plasma model. When the phase velocity is close to c, it is shown that the two approaches are in good agreement during a finite time. After this short time, when the plasma response is taken into account no chaos take place at least when considering low densities and/or high wave intensities. The case of a charged particle in a traveling wave propagating along a constant homogeneous magnetic field is then considered. The problem is shown to be integrable when the wave propagates in vacuum. The existence of a synchronous solution is shown very simply. In the case when the wave propagates in a low density plasma, using a simplifying Lorentz transformation, it is shown that the system can be reduced to a time-dependent system with two degrees of freedom. The system is shown to be nonintegrable, chaos appears when a secondary resonance and a primary resonance overlap. Finally, stochastic instabilities are studied by considering the motion of one particle in a very high intensity wave perturbed by one or two low intensity traveling waves. Resonances are identified and conditions for resonance overlap are studied.     

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.     

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.