Localization of a nonlinear switching wave in an active bistable medium with an isolated inhomogeneity

An analysis is made of the one-dimensional propagation of a switching wave in an active medium when one of the parameters of the medium is a function of the coordinate over a certain region and remains constant outside this region. The possibility of localization (stopping) of the wave at this type of inhomogeneity is investigated. An analytical expression is obtained for the wave shift in the case of a small-amplitude inhomogeneity. Constraints on the amplitude and length of the inhomogeneity at which localization takes place are obtained for an inhomogeneity of finite dimensions. Zh. Tekh. Fiz. 67, 14–20 (August 1997)     

On localized structures of radiation in a wide-aperture laser with a transverse inhomogeneity

The analysis of the stability of the generationless regime in a laser with a smooth transverse inhomogeneity of the resonator length is performed. Localized structures of radiation are considered that are possible in this laser when the nonlinearity of the gain and of the refractive index of the medium is taken into account.     

Localization of an absorbing inhomogeneity in a scattering medium in a statistical framework

An approach for the fast localization and detection of an absorbing inhomogeneity in a tissuelike scattering medium is presented. The probability of detection as a function of the size, location, and absorptive properties of the inhomogeneity is investigated. The detection sensitivity in relation to the source and detector location serves as a basis for instrument design.     

Analysis of the spectral variation of a dye laser by gain medium inhomogeneity

In this paper, an analysis of spectral variation of a high repetition rate dye laser by an optical inhomogeneity developed inside the gain medium is presented. The passive band-pass, responsible for bandwidth, set (in homogeneous medium) by dispersive optical element in its resonator is modulated by scale length of the inhomogeneity introduced in the gain medium. Inhomogeneities, introduced by temperature in laminar flow (at low Reynolds number) and fractional change in flow-induced scale length (at higher Reynolds number) have an effect on the wavelength of dye laser.     

Radiation reflection from an optical inhomogeneity moving in a right- and left-handed medium

The parametric Doppler effect in a medium whose dielectric permittivity and magnetic permeability become negative in some spectral range is analyzed with respect to uniform plane waves. The regime in which the medium is right-handed (the refractive index is positive) for incident radiation and left-handed (the refractive index is negative) for reflected wave is demonstrated. The possibility of the occurrence of additional branches in the dispersion dependences is demonstrated.     

Thermal evolution of residual stress in IN718 alloy subjected to laser peening

The thermal relaxation behaviors of residual stresses induced by laser peening (LP) in IN718 alloy were investigated using an integrated numerical simulation and experimental approach. LP and heat treatments (HT) were carried out after which the X-ray diffraction (XRD) technique was employed in measuring the residual stresses. Micro-structures were observed using an optic microscope (OM) and transmission electron microscope (TEM). Dislocations induced by LP were also observed by TEM and characterized using the XRD technique. The effects of the applied temperature and the exposure time on residual stress and micro-structures were investigated. The results show that the extent of the residual stresses relaxation increased accordingly with the increase in the applied temperature. The relaxation rate was initially high and tended to stabilize for a longer exposure time. Grain size evolution during the process was subsequently discussed. Furthermore, a conceivable mechanism of residual stresses thermal relaxation behavior was obtained.     

Transient combined radiation and conduction in a one-dimensional non-gray participating medium with anisotropic optical properties subjected to radiative flux at the boundaries

Transient combined heat transfer by radiation and conduction is investigated in non-gray participating media with anisotropic optical properties. The medium is irradiated by a time-dependent source. Different kinds of boundaries are considered: black, opaque, transparent and semi-transparent. The heat transfer equations are solved numerically in a one-dimensional configuration. Comparisons are made with test cases taken from the literature, and the results obtained demonstrate the accuracy of the present numerical model. The influence of transparent, semi-transparent and opaque boundaries on an insulating fibrous medium is also studied.     

Nonlinear oscillations of a drop moving at a constant velocity in an insulating medium subjected to an electrostatic field

Nonlinear asymptotic calculations of the second order of smallness in the amplitude of the initial deformation of an ideally conducting liquid drop show that the laminar flow of an ideal conducting incompressible dielectric liquid flowing about the drop in an external electrostatic field parallel to the flow causes oscillation mode’s interaction in the first and second orders of smallness. Both linear and nonlinear interactions between the oscillation modes of the drop excite modes that are absent in the spectrum of modes governing the initial deformation of the drop’s equilibrium shape. In the second order of smallness, the mode interaction decreases the electrostatic field strength, as well as the velocity and density of the environment, that are critical for development of instability of the drop against the polarization charge.     

Dynamics of localized wave packets of rotational states of a molecule in a strong laser field

Numerical simulations are performed to examine the rotational dynamics of a molecule in a strong laser field when the molecular axis is initially oriented in a certain direction. The results obtained by solving the quantum-mechanical problem are compared with those computed in the framework of classical mechanics. It is found that certain characteristics of rotational motion cannot be described by classical theory, particularly for light molecules. It is demonstrated that the axis of a heteronuclear molecule can be reversed by tunneling.     

Anisotropic ellipsoidal inclusion with an anisotropic shell in an isotropic medium subjected to a uniform electric field

An electrostatic problem has been solved for a dielectric inclusion that consists of an anisotropic core and an anisotropic shell. The inclusion is immersed in a uniform isotropic medium (matrix) subjected to a uniform electric field. It is assumed that the outer boundaries of the core and shell are ellipsoidal and become confocal after a linear nonorthogonal transformation that removes the anisotropy of the dielectric properties of the shell. Analytical expressions have been derived for the potential and strength of the electric field in the matrix and also in the shell and core of the inclusion, and an expression for the polarizability tensor of the inclusion has been deduced. It has been shown that the results agree with the well-known solutions in partial (limiting) cases.     

Bifurcation and locking in an multi-quantum-well laser subjected to external injection

Bifurcation and dynamic stability as well as locking in an external light injection multi-quantum-well (MQW) laser are studied. Different dynamic regimes in locking diagram are analyzed with the injection level and frequency detuning. Bifurcate behavior is numerically simulated via the external injection light intensity, frequency detuning, current, linewidth enhance factor, photon loss rate and carrier loss rate, respectively. And the route to chaos from bifurcation, period-doubling and quasi-period are described by numerical analysis. A perturbation equation of four-dimension model and the bifurcation condition are demonstrated. Dynamic stability of the laser is theoretically and numerically analyzed. The bifurcate expression is theoretically given while the maximum locking frequency domain is given. The variational characteristic of the oscillation frequency in the self-pulse regimes versus the injection and detuning are numerically analyzed to find that the relaxation frequency is reduced with adding the detuning in the smaller detuning or with adding the injection in the smaller injection while the relaxation frequency will be increased with adding the detuning in the larger detuning or with adding the injection in the larger injection. We find also that the chaotic spectra are broadened with adding the detuning or narrowed with adding the injection or the current.     

Charged particle motion in a medium along an electromagnetic wave

The solution of the relativistic equation of motion is discussed for a charged particle interacting with an electromagnetic wave in a medium.     

Plane wave propagation in a uniaxial bianisotropic medium with an application to a polarization transformer

Uniaxial bianisotropic medium is a generalization of the well-studied bi-isotropic and chiral media. It is obtained, for example, when microscopic helices with parallel axes are positioned in a host dielectric in random locations. Plane wave propagation in such a medium is studied and a simple solution for the dispersion equation and for the eigenwaves are found. As a numerical example, polarization properties of a transverse wave propagating in a uniaxial bianisotropic medium is considered. The results give a simple possibility to construct a polarization transformer with a transversely uniaxial chiral medium for changing the polarization of a propagating plane wave.     

Flow structures around an inclined substrate subjected to a supersonic impinging jet in laser cutting

In laser cutting, the flow structure around a substrate significantly affects the material removal rate, the cutting depth and the surface finish of the cutting front. In this paper, the phenomena of shock wave that is induced by a supersonic impinging jet emanating from a straight nozzle onto a substrate with varying inclined angles has been simulated numerically and visualized experimentally. The numerical model offers fairly good prediction in comparison with the experiments. It transpires that the angle of inclination has a significant and dramatic effect on the flow structure and that a large wall pressure with a steep gradient can be built up when the angle is large.     

Scattering of an Alfvén wave by an inhomogeneity in the solar wind density

The interaction between a nonlinear Alfvén wave and intense inhomogeneities in the density of interplanetary plasma is considered in the magnetohydrodynamic (MHD) approximation. The cold-plasma approximation was used to carry out a more correct study of the interaction since the thermal pressure can introduce pronounced changes into the shape of specified inhomogeneities in the plasma density. Results of numerical solution of the well-known MHD equations are presented in the form of three films demonstrating different scenarios of development of the nonlinear dynamics. The films allow us to observe the dynamic evolution of the form of an Alfvén perturbation and the changes in the density inhomogeneities. For small-amplitude Alfvén waves this corresponds to the process of linear transformation by the density inhomogeneities, which does not lend itself to comprehensive analytical study. Numerical simulation reveals the phenomena of reflection from regions of sharp density variation, which are very sensitive to the spatial scales of the interacting objects. The same method is used to investigate the scattering of strong waves. After reversible changes in shape in a high-density region (where oscillations of the shock-wave front are attenuated), a moderate-amplitude Alfvén wave is recovered in a more rarefied medium. A strong scattered Alfvén wave brings about irreversible changes in the shape of the density inhomogeneity. The results obtained illustrate the process of interaction between Alfvén waves and strong density perturbations related to piston or explosive shock waves in the solar wind. State Pedagogikal University, Nizhny Novgorod, Russia; Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 2, pp. 152–163, February, 1998.     

The propagation of a nonlinear sound wave in an unconsolidated granular medium

The propagation of a high-intensity sound wave in an unconsolidated medium is considered. Dissipation effects are taken into account on the basis of Buckingham’s theory of a relaxation mechanism of sound attenuation in a saturated sediment. The nonlinear evolution equation for the relaxing medium is obtained, and the solutions of this equation are analyzed. The second-harmonic generation in such a medium decays, as does the linear sound wave of the same frequency. The stationary weak shock profile has a specific form due to relaxation effects.