Neutrino propagation in a weakly magnetized medium

Neutrino-photon processes, forbidden in vacuum, can take place in the presence of a thermal medium and/or an external electro-magnetic field, mediated by the corresponding charged leptons (real or virtual). Such interactions affect the propagation of neutrinos through a magnetized plasma. We investigate the neutrino-photon absorptive processes, at the one-loop level, for massless neutrinos in a weakly magnetized plasma. We find that there is no correction to the absorptive part of the axial-vector-vector amplitude due to the presence of a magnetic field, to the linear order in the field strength.     

Sound and light propagation in a weakly inhomogeneous atmosphere

Small-scale inhomogeneities caused by atmospheric turbulence have a considerable effect on sound and light propagation, producing the fluctuations of these wave fields. V A Krasilnikov [1, 2] performed experiments on phase and amplitude variations of a sound wave propagating through the atmosphere. Fluctuations of light-wave parameters occur, for example, in the well known phenomenon of star scintillation, apparently strongly connected with turbulent irregularities of the atmospheric temperature field [3, 4]‡.

Some calculations of phase (arrival angle) and amplitude fluctuations for a wave propagating through a turbulent medium are described by Krasilnikov [1, 3, 8]. All these and similar calculations are based on the geometrical optics (acoustics) approximation, which may be the reason for disagreement between calculation and experimental data in some cases. Thus, for example, amplitude fluctuations in the geometrical approximation turn out to be proportional to the distance of propagation through a turbulent medium to the power of 3/2. However, observations usually show much slower fluctuation growth.

This paper represents an attempt to consider the problem of amplitude and phase variations for a scalar wave field in terms of more general equations including some diffraction effects. Incidentally, the range of validity of geometrical optics theory becomes clear.     

Beam propagation in a randomly inhomogeneous medium

An integrodifferential equation describing the angular distribution of beams is analyzed for a medium with random inhomogeneities. Beams are trapped because inhomogeneities give rise to wave localization at random locations and random times. The expressions obtained for the mean square deviation from the initial direction of beam propagation generalize the “3/2 law.”     

Damping of light in a weakly resonant inhomogeneous medium

On the basis of an expression obtained earlier for the permittivity in the form of a series in powers of the atomic polarizability, the mechanism of damping of light caused by the processes of reemission between two atoms is considered. It is shown that, on an increase in the polarizability, as a consequence of the light frequency approaching the resonance frequency, this mechanism leads to a sharp increase in the extinction coefficient. This effect is caused by the collective behavior of the atoms and is not connected with the natural absorption near the resonance.     

Plane waves in a layered weakly dissipative randomly inhomogeneous medium

In the framework of the embedding method the authors consider the stationary and non-stationary problem of a plane-wave incident on a randomly inhomogeneous medium. For the stationary problem there are three regions of sufficiently different behaviour of the wavefield intensity moments inside a weakly dissipative medium. For the non-stationary problem they succeeded in calculating the average intensity at t→+∞ by means of analytical prolongation of the stationary problem solution with respect to the absorption parameter. The time asymptotic of the averaged intensity on the boundary slab is also obtained for a finite-thickness slab.     

Plane waves in a layered weakly dissipative randomly inhomogeneous medium

Abstract

In the framework of the embedding method the authors consider the stationary and non-stationary problem of a plane-wave incident on a randomly inhomogeneous medium. For the stationary problem there are three regions of sufficiently different behaviour of the wavefield intensity moments inside a weakly dissipative medium. For the non-stationary problem they succeeded in calculating the average intensity at t→+∞ by means of analytical prolongation of the stationary problem solution with respect to the absorption parameter. The time asymptotic of the averaged intensity on the boundary slab is also obtained for a finite-thickness slab.     

Wave scattering in a multiscale random inhomogeneous medium

In this paper, using the Fock method of the fifth parameter and weighted Fourier-transform with respect to the coordinates of the source and observer, an integral representation is obtained for the wave field in a randomly inhomogeneous medium without invoking the assumption about small-angle propagation. Random trajectory variations to a first approximation are taken into account in calculating the partial wave phase (the expression under the integral sign). The expressions for the field in a medium with different-scale irregularities and for the scintillation index, obtained using this integral representation, are compared with known results. The good agreement with results from the theory of single scattering in a medium with background irregularities, and with investigations of the scintillation index made in terms of Rytov's method and path integrals, indicates that it is possible to use the approach developed in this study to describe the effects of simultaneous influence of different-scale irregularities.     

Energy transfer of a wave-packet in a weakly inhomogeneous medium WKB approximation

It is shown that the physical assumptions used in the local theory to derive expressions for the energy density, the energy flux density and the energy dissipation density of a wave-packet are sufficient for these expressions to be applicable in the whole range of validity of the WKB approximation for the packet under investigation. Further, it is shown that besides the actual growth rate, the local growth rate (depending on spatial co-ordinates) has also a useful physical interpretation for the waves studied. It determines the part of the wave energy density which is dissipated (or obtained from the medium) per unit time in a unit volume.     

Wave beam with minimum divergence in a smoothly inhomogeneous medium

We consider acoustic wave beams propagating in a smoothly inhomogeneous medium along a given reference ray. It is shown that in the aberration-free approximation, a Gaussian beam diverges with distance (on the average) less than any other beam with the same initial width. This result has been obtained by solving a variational problem that is similar to the well-known quantum-mechanical problem of seeking the quantum state with minimum uncertainty (coherent state). An example of the beam with minimum divergence in the realistic model of a deep-ocean acoustic waveguide is considered. An approximate analytical estimate for the amplitudes of normal modes forming the beam is obtained. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 52, No. 1, pp. 46–54, January 2009.     

Wave propagation in a one-dimensional randomly perturbed periodic medium

We study the variance of the solution of a periodic randomly perturbed one-dimensional Schrödinger operator after propagation through N periods. It is shown that if the frequency of propagation lies inside the band, then the total variance is proportional to Nσ², where σ is the intensity of the white noise. However, if the wave frequency is close to the band edge (where the transfer matrix has a Jordan block structure), the resulting variance is proportional to Nσ^2/3. Thus, propagation becomes highly sensitive to random perturbations.

Numerical simulations reveal that even low noise in a periodic potential can suppress transmission near the band edges and make it strongly irregular inside the band. Further increase of the noise amplitude leads to intermittent behaviour of the transmission coefficient, and makes transmission possible only for a few random frequencies in the band.     

Simulation of the propagation of a light pulse in a randomly inhomogeneous medium

The propagation of a Gaussian pulse in an inhomogeneous medium is considered. The detected pulse is represented as a series in the scattering multiplicities. The developed approach enables one to describe the passage of a pulse through a randomly inhomogeneous medium in the general case, beyond the framework of the diffusion approximation. The known results of the diffusion approximation are shown to represent limiting cases of the expansion constructed in the scattering multiplicities. The calculations are performed by the Monte Carlo method for cases of singly and multiply scattering media. The agreement between the results of the theoretical analysis and the numerical simulation allows one to use the approach developed in both optical problems and investigation of propagation of waves of other nature, in particular, seismic waves.     

The propagation of a polarized gaussian beam in a smoothly inhomogeneous isotropic medium

In the frame of the eikonal-based complex geometrical optics, which describes the phase front and cross section of a light beam using the quadratic expansion of a complex-valued eikonal, we investigate the transverse deflections of a polarized Gaussian beam (GB) in a smoothly inhomogeneous isotropic medium, which is called the spin Hall effect of the beam. The linear complex-valued eikonal terms are introduced firstly to describe the polarization-dependent transverse shifts of the beam in the inhomogeneous medium. We find that the polarization-dependent transverse shifts of the beams include two parts: one originates from the coupling between the spin angular momentum and the extrinsic orbital angular momentum due to the curve trajectory of the center of gravity of the polarized GB, and the other from the coupling between the spin angular momentum and the intrinsic orbital angular momentum due to the rotation of the beam with respect to the central ray.     

Wave propagation in embedded inhomogeneous nanoscale plates incorporating thermal effects

In this article, an analytical approach is developed to study the effects of thermal loading on the wave propagation characteristics of an embedded functionally graded (FG) nanoplate based on refined four-variable plate theory. The heat conduction equation is solved to derive the nonlinear temperature distribution across the thickness. Temperature-dependent material properties of nanoplate are graded using Mori–Tanaka model. The nonlocal elasticity theory of Eringen is introduced to consider small-scale effects. The governing equations are derived by the means of Hamilton’s principle. Obtained frequencies are validated with those of previously published works. Effects of different parameters such as temperature distribution, foundation parameters, nonlocal parameter, and gradient index on the wave propagation response of size-dependent FG nanoplates have been investigated.     

Light transmission in inhomogeneous birefringent medium as a function of propagation and observation angles

We use the Mueller matrix for inhomogeneous linear birefringent media derived in Savenkov et al. [Mueller-matrix model of an inhomogeneous linear birefringent medium: single scattering case. JQSRT 2007;106:475–86] to generate new results on the forward scattering of light using Cloude's coherence matrix method. We show that the intensity of scattered light (m₁₁) as a function of observation angle depends on the difference between refractive indices along the eigen polarizations resulting in intensity lost when unpolarized light propagates parallel to the optical axes compared to propagation orthogonal to the optical axis. For a given inhomogeneity (roughness), depolarization strongly depends on the direction of light propagation in the medium. The depolarization at 90° propagation angle is minimal for any value of inhomogeneity. Sample calculations are based on calcite.     

Wave propagation in an excitable medium with a negatively sloped restitution curve

Recent experimental studies show that the restitution curve of cardiac tissue can have a negative slope. We study how the negative slope of the restitution curve can influence basic processes in excitable media, such as periodic forcing of an excitable cell, circulation of a pulse in a ring, and spiral wave rotation in two dimensions. We show that negatively sloped restitution curve can result in instabilities if the slope of the restitution curve is steeper than -1 and report different manifestations of this instability. (c) 2002 American Institute of Physics.