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A theory for the characterization of the fourth-order moment of electromagnetic wave beams is presented in the case when the source is partially coherent. A Gaussian–Schell model is used for the partially coherent random source. The white-noise paraxial regime is considered, which holds when the wavelength is much smaller than the correlation radius of the source, the beam radius of the source, and the correlation length of the medium, which are themselves much smaller than the propagation distance. The complex wave amplitude field can then be described by the Itô-Schrödinger equation. This equation gives closed evolution equations for the wave field moments at all orders and here the fourth-order moment equations are considered. The general fourth-order moment equations are solved explicitly in the scintillation regime (when the correlation radius of the source is of the same order as the correlation radius of the medium, but the beam radius is much larger) and the result gives a characterization of the intensity covariance function. The form of the intensity covariance function derives from the solution of the transport equation for the Wigner distribution associated with the second-order wave moment. The fourth-order moment results for polarized waves are used in an application for imaging of partially coherent sources. [ABSTRACT FROM AUTHOR]

In this paper, we carried out a critical investigation of the strong fluctuation theory using a quantum field theoretic approach [Tatarskii VI. The effects of the turbulent atmosphere on wave propagation. Jerusalem: IPST; 1971]. We employed the Dyson and Bethe-Salpeter equations to derive the radiative transfer equation (RTE) for the Green's function of the radiant intensity. We proceeded to obtain estimates of the domain of validity of the RTE. The results thus obtained satisfy both the optical theorem for waves in random media and energy conservation. We also derived the RTE for our problem by employing a recently developed scale-separated asymptotic theory [Bal G., Komorowski T, Ryzhik L. Kinetic limits of waves in random media. Kinet Relat Models. 2010;3:529–644]. Although the RTE obtained by the two approaches are identical, we explain that the applicability regimes, and hence validity conditions are different. [ABSTRACT FROM AUTHOR]

Extensive research has been reported on MIMO systems for complex environments. It is noted that many communications studies make use of the channel matrix of transmitters and receivers, signal vectors, SNR, and eigenvalues. However, the channel matrix is often expressed in terms of channel modeling, and the detailed statistical characteristics of the channel in terms of physical characteristics of atmospheric turbulence, particulate matter, and rough surfaces and terrain are often not explicitly shown. This paper discusses the inclusion of expressions of physical characteristics of the random medium in the channel matrix. Therefore, the key point of this paper is that the channel matrix is explicitly given in terms of the actual physical parameters of the random environment using the mutual coherence function and stochastic Green's functions; we call this a 'physics-based' communications model. This paper presents a formulation of physics-based communications models in the presence of a random medium based on analytical statistical EM theory. We use the keyhole MIMO as an example to show the key points of this approach. It is hoped that this study may help extend channel modeling to include analytical statistical EM theory for atmospheric turbulence, ocean turbulence, and rough terrain. [ABSTRACT FROM AUTHOR]

The paper addresses the problem of determining the field of a reflected wave in a multiscale inhomogeneous medium, which consists of a background deterministic large-scale irregularity and multiscale random irregularities with scales both larger and smaller than the wavelength. A layer with a linear permittivity profile is taken as the background irregularity. The small-scale irregularities are responsible for wide-angle scattering including backscattering. The first approximation of the perturbation theory is used to account for scattering from these irregularities. As the zero approximation and Green's function in determining the field backscattered by small-scale irregularities, we utilize the integral representation of the field, obtained in our earlier work by combining the method of double weighted Fourier transform (DWFT) and the Fock proper-time method. Asymptotic methods are used to reduce the sevenfold integral representation of a field to lower-order integrals. Conditions for validity of such representations are obtained. Formulas of the frequency coherence functions of waves reflected and backscattered from the turbulent plasma layer are given. The paper presents the results of the simulation of pulse sounding of a randomly inhomogeneous reflecting plasma layer demonstrating the effect of large-scale irregularities on backscattering by small-scale irregularities. [ABSTRACT FROM AUTHOR]

The Markov approximation is widely used in wave propagation in random media. This approximation is valid if the propagation path length is greater than the scale of the medium inhomogeneities affecting a particular statistical moment of a wave field and the moment changes insignificantly over this scale. These conditions might be violated for the variance of the phase fluctuations and other statistical moments of acoustic signals that have propagated through atmospheric turbulence: the scale of the largest eddies can be hundreds of meters, and fluctuations in the acoustic refractive index are relatively strong. In the current article, the phase variance of a spherical sound wave in statistically inhomogeneous turbulence is formulated without the Markov approximation. For propagation ranges smaller than the scale of the largest eddies, the phase variance without the Markov approximation is significantly smaller than when this approximation is employed. As the range increases, the difference between the two results tends toward a constant value (a 'memory' effect), which might be significant in many applications. The phase variance without the Markov approximation agrees better with the experimental data on sound propagation through the atmosphere, while the variance calculated with this approximation significantly overpredicts the data. [ABSTRACT FROM AUTHOR]

Numerical calculations of light propagation in random media demand the multiply scattered Stokes intensities to be written in a common fixed reference. In multiple-scattering schemes, a particularly useful way to perform automatically these basis transformations between reference frames is to write the scattered intensities in the Chandrasekhar-Sekera representation. The main drawback with this representation is the necessity of numerical tests to deal with the limiting situations of the small particle (Rayleigh) and forward/backward scattering. Here, a new set of basis functions is presented to describe the scattering of light by spherical particles (Mie scattering) in the Chandrasekhar-Sekera representation. These basis functions can be implemented in a new algorithm to calculate the Mie scattering amplitudes, which leads straightforwardly to all the scattering quantities. In contrast to the traditional implementation, this set of basis functions implies to natural numerical convergence to the above mentioned limiting cases, which are thoroughly discussed. [ABSTRACT FROM AUTHOR]

Single-well imaging plays an increasingly important role in the exploration and production of hydrocarbon in horizontal wells. Depending on the scattering strength, reflections from lateral sections below heterogeneous regions around the borehole suffer signal distortion and amplitude loss, which complicates the imaging of deeper structures. Thus, the understanding of scattering phenomena and their impact on single-well imaging is of significant interest for hydrocarbon exploration. This paper establishes a complex horizontal well numerical model with which the effects of heterogeneous overburden on deep reflection imaging are studied using dipole acoustic logging. Synthetic data were analyzed with respect to the observed reflectivity in the heterogeneous layer and along the deep reflection. The results show that strong velocity fluctuations increase the severity of the scattering effect when correlation distances are in the order of the dominant wavelength. The reflection images migrate and reveal additional structural details of the medium. Low frequency band imaging enables the extraction of undistorted real reflectors by using the Reflection Image Spectroscopy method. The results explain the influence of the heterogeneous overburden on single-well imaging results and provide theoretical guidance for logging interpretation. [ABSTRACT FROM AUTHOR]

On October 13, 2019 is the ninetieth birthday of the renowned physicist Professor Valerian I. Tatarskii. He is one of the founders of the international journal Waves in Random and Complex Media and its Associate Editor from 1991 to 1998. Outstanding seminal works of Professor V. I. Tatarskii made a global impact on physical science. The article describes main milestones of his life in science and his achievements in the theory of wave propagation in random media. [ABSTRACT FROM AUTHOR]

The dynamic analysis of random fibrous networks (RFNs) is a novel topic, which has many applications since these networks are very often subjected to dynamical loading conditions such as mechanical vibrations. In order to bypass the complexity of performing dynamic computations at the microscopic scale of RFN, we develop and identify couple-stress and second gradient models as effective continua at the mesoscopic level of windows of analysis. The static mechanical properties which are at the basis of the dynamical analysis are computed thanks to FE simulations performed over windows of analysis subjected to mixed boundary conditions allowing to capture the classical and non-classical effective moduli. The acoustic properties are captured by the dispersion diagrams and phase velocity plots; we analyze the influence on the dynamic properties of the fiber bending length, and the fiber network density. The impact of these parameters is successively assessed for the couple-stress and strain gradient substitution continua. A comparison of the acoustic properties of the two effective media is provided, showing that the couple-stress medium is essentially non-dispersive for the longitudinal mode and dispersive for the shear mode, whereas the strain gradient medium behaves in a dispersive manner for both modes. [ABSTRACT FROM AUTHOR]

We consider the problem of localizing one or more sources in a two-dimensional waveguide with horizontal flat boundaries and random sound speed fluctuations. Our data are the acoustic pressure field, measured on a vertical array of hydrophones that may span the entire depth of the waveguide or a part of it. We use randomness to model the effect of internal waves on the sound channel. Although the strength of the fluctuations is small, the transmitted signal is significantly affected from the multiple scattering of the waves with the random inhomogeneities, especially since we consider large propagation distances between the sources and the receiver array. Source localization is performed following an incoherent approach relying on a transport system of equations that describes wave propagation in random waveguides and that takes into account modal dispersion and energy transfer between modes. [ABSTRACT FROM AUTHOR]

We study detection and imaging of small reflectors in heavy clutter, using an array of transducers that emits and receives sound waves. Heavy clutter means that multiple scattering of the waves in the heterogeneous host medium is strong and overwhelms the arrivals from the small reflectors. Building on the adaptive time-frequency filter of [Borcea et al, SIIMS 2011;4(3)], we propose a robust method for detecting the direction of arrival of the direct echoes from the small reflectors, and suppressing the unwanted clutter backscatter. This improves the resolution of imaging. We illustrate the performance of the method with realistic numerical simulations in a non-destructive testing setup. [ABSTRACT FROM AUTHOR]

Taking the attenuation character of the Kelvin wake and the limitation of the traditional two-scale method into account, the practical electromagnetic (EM) scattering model of the Kelvin wake is obtained by using a facet-based model; and for a turbulent ship wake, it is produced by dealing with the wave energy loss rate due to turbulence with the width of turbulent wake closely following a moving ship. The volume scattering theory of foam or bubbles, by using the vector radiation transfer equation, is introduced to modify the traditional two-scale method, a special method for the EM scattering of a turbulent wake, which brings the scattering of ship wakes into better agreement with the real situation. [ABSTRACT FROM AUTHOR]

Calculations of the second-order statistical characteristics of a polarized, lowest-order Gaussian beam which propagates through a jet-stream layer, in the upper troposphere and lower stratosphere (UTLS) environment, are carried out. Comparison of the results based on the refractive-index structure parameter [image omitted] as predicted by a Hufnagel-Valley model and based on data taken at a recent campaign of measurements and high-resolution numerical simulations shows that the jet-stream can significantly affect the intensity distribution and spreading of the beam, especially at high zenith angles. [ABSTRACT FROM AUTHOR]