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A dynamical system under extreme physical disorder has the tendency to evolve toward the equilibrium state characterized by an inverse power law power spectrum. In this paper, a practical, implemen...

In nonclassical transport, the free-path length variable s is modeled as an independent variable, and a nonclassical linear Boltzmann transport equation incorporating s has been derived. To model t...

Scattering from a grounded chiral slab with rough interface is studied using perturbation theory. A system of equations for zeroth and higher order solution is written, which can be solved to get c...

In a homogeneous medium, the far-field generated by a localized source can be expanded in terms of multipoles; the coefficients are determined by the moments of the localized charge distribution. We show that this structure survives to some extent for a random medium in the sense of quantitative stochastic homogenization: In three space dimensions, the effective dipole and quadrupole - but not the octupole - can be inferred without knowing the realization of the random medium far away from the (overall neutral) source and the point of interest. Mathematically, this is achieved by using the two-scale expansion to higher order to construct isomorphisms between the hetero- and homogeneous versions of spaces of harmonic functions that grow at a certain rate, or decay at a certain rate away from the singularity (near the origin); these isomorphisms crucially respect the natural pairing between growing and decaying harmonic functions given by the second Green's formula. This not only yields effective multipoles (the quotient of the spaces of decaying functions) but also intrinsic moments (taken with respect to the elements of the spaces of growing functions). The construction of these rigid isomorphisms relies on a good (and dimension-dependent) control on the higher-order correctors and their flux potentials., Comment: 60 pages

The current paper is devoted to the study of existence and non-existence of transition fronts for two species competition lattice system in random media, and explore the influence of randomness of the media on the wave profiles and wave speeds of such transition fronts. We first establish comparison principle for sub-solutions and super-solutions of the related cooperative system. Next, under some proper assumptions, we construct appropriate sub-solutions and super-solutions for the cooperative system. Finally, we show that random transition fronts exist if their least mean speed is greater than an explicit threshold and there is no random transition front with least mean speed less than the threshold., Comment: 25 pages

Algorithms of Monte Carlo method for estimating probabilistic moments of the parameter of time exponential asymptotics of particle flux with multiplication in a random medium are constructed. It was analytically and numerically shown that the asymptotics of the mean number of particles is close to an exponential one with the factor containing a summand proportional to square of time.

We present a novel approach for stochastic finite-element (FE) modeling of the electromagnetic field in ferrites, combining a thin shell model (TSM) for highly permittive grain boundaries with a Voronoi-tessellation-based geometry generation algorithm. The TSM is validated in the case of a periodic grain structure in a linear 2-D time-harmonic case over a frequency range of 10 kHz-1 GHz, and problems related to standard FE discretization are discussed. The TSM is then applied in a stochastic study for simulating the effect of varying grain structure on the effective resistivity, losses, and reactive power densities of a ferrite core., SCOPUS: ar.j, info:eu-repo/semantics/published

This paper presents a theory of the time-domain radar cross section (RCS) of objects in discrete random media. The time-domain formula is obtained by applying the inverse Fourier transform of the t...

In this paper, we study a macroscopic description on the ensemble of Kuramoto oscillators with finite inertia in a random media characterized by a white noise. In a mesoscopic regime, it is well kn...

We extend the scalar elliptical multi-Gaussian Schell-model (EMGSM) beams with twist phase to the electromagnetic domain and obtain the analytical expression for the propagation of the electromagnetic twisted EMGSM beams through random media. The twist phase-induced changes of the spectral density and degree of polarization of such beams on propagation are studied numerically. Results show that by adjusting the twist factor and the correlated parameters of the source, both the spectral density and degree of polarization not only rotate around the propagation axis but also exhibit diverse shapes. The flattopped ellipse-like and diamond-like shape maintain over a relatively long propagation distance and finally involve into Gaussian-like shape due to stronger atmospheric turbulence. The results will be useful in optical trapping and optical communication.

The propagation of longitudinal and shear elastic waves through a multi-phase material was studied and the effective elastic properties of the medium were evaluated. The distribution of the reinforcing inclusions was considered random throughout the matrix. The effective dynamic properties of the composites, including their effective bulk and shear moduli and effective densities, were examined along with the effective phase velocity and attenuation of the incident P and S waves. The Sabina–Willis model was employed to study the wave propagation behavior, and the model performance was analyzed through comparison with experimental data from the literature. The results indicated that wave propagation significantly depended on the physical and mechanical properties of inclusions relative to those of the matrix and the normalized wave number of the propagated elastic wave. Moreover, despite the fact that the elastic properties of the incidence in the P and S waves exhibited a similar trend, their values differed significantly. The results can serve as a design criterion for composite materials under dynamic loading.

The central theme of my thesis is to develop various analytical and numerical methods, for the coherent control of waves to assist various wavefront shaping applications in random disordered media. This resulted in the development of 2D scalar wave transport modelling frameworks, analytically and computationally, from the scratch. The modelling frameworks cover both frequency domain and time domain. In the frequency domain, the generalised scattering matrix (S matrix) incorporating evanescent modes is used to the study the transport properties. The wavefront shaping methods in the frequency domain involve eigenchannels and iterative phase conjugation for the enhancement of total transmission through slab disorders and disordered constrictions. The generalisation of the conventional Fisher-Lee relations to incorporate evanescent modes is presented in the thesis. S matrices of spatially correlated disorders are estimated using the generalised Fisher-Lee relations, incorporating the Green’s function perturbation method. The comparison between the conventional diffusion theory and the wave transport theory is presented, which involves the cascading of S matrices and the transmission scaling law. The relationship between the spatial correlation of the disorder and various transport properties are also investigated in this comparison. In the time domain, using the finite difference time domain scheme, wavefront shaping involving iterative phase conjugation onto a space-time modulated (STM) guide-star region operating in the Raman-Nath regime, is investigated. The intention of studying the STM is to investigate the potential of the acousto-optic effect for imaging through random media. In the time domain, the effect of sample decorrelation due to Brownian motion on the stability of the focussing is also studied using the Langevin equation. The discussion of the analytical and numerical aspects of the developed models, along with the availability of simulation codes written in Matlab, may be of interest to wavefront shaping researchers interested in characterisation of various wave transport behaviours.

This work concerns the asymptotic analysis of high-frequency wave propagation in randomly layered media with fast variations and long-range correlations. The analysis takes place in the 3D physical space and weak-coupling regime. The role played by the slow decay of the correlations on a propagating pulse is two fold. First we observe a random travel time characterized by a fractional Brownian motion that appears to have a standard deviation larger than the pulse width, which is in contrast with the standard O'Doherty-Anstey theory for random propagation media with mixing properties. Second, a deterministic pulse deformation is described as the solution of a paraxial wave equation involving a pseudo-differential operator. This operator is characterized by the autocorrelation function of the medium fluctuations. In case of fluctuations with long-range correlations this operator is close to a fractional Weyl derivative whose order, between 1 and 2, depends on the power decay of the autocorrelation function. In the frequency domain, the pseudo-differential operator exhibits a frequency-dependent power law attenuation with exponent corresponding to the order of the fractional derivative, and a frequency-dependent phase modulation, both ensuring the causality of the limiting paraxial wave equation as well as the Kramers-Kronig relations. The mathematical analysis is based on an approximation-diffusion theorem for random ordinary differential equation with long-range correlations., Comment: 33 pages, 8 figures

International audience; This paper considers the problem of fully distributed channel allocation in clustered wireless networks when the propagation medium is random. We extend here the existing Trial and Error (TE) framework developed in the deterministic case and for which strong convergence properties hold. We prove that using directly this solution in the random context leads to unsatisfactory solutions. Then we propose an adaptation of the original Trial and Error Learning (TEL) algorithm, called Robust TEL (RTEL), assuming that the random channel effects translate into a bounded stochastic disturbance of the utility function. The solution consists in introducing thresholds in the transitions of the TEL’s Finite State Controller (FSC). We prove that this new solution restores the good convergence property inherited from the TEL. Furthermore, we provide analysis of the stochastic utilities in the Rayleigh fading case in order to check the bounded assumption. Finally, we develop an online algorithm that dynamically estimates the optimal threshold values to adapt to the instantaneous disturbance. Numerical results corroborate our theoretical claims.

We present a class of diffraction-free partially coherent beams each member of which is comprised of a finite power, non-accelerating Airy bump residing on a statistically homogeneous, Gaussian-correlated background. We examine free-space propagation of soft apertured realizations of the proposed beams and show that their evolution is governed by two spatial scales: the coherence width of the background and aperture size. A relative magnitude of these factors determines the practical range of propagation distances over which the novel beams can withstand diffraction. The proposed beams can find applications to imaging and optical communications through random media., 5 pages, 5 figures

A first-order optical system with arbitrary multiple masks placed at arbitrary positions is the basic scheme of various optical systems. Generally, masks in optical systems have a non-shift invariant (SI) effect, thus, the individual effect of each mask on the output cannot be entirely separated. The goal of this paper is to develop a technique where complete separation might be achieved in the common case of random phase screens (RPSs) as masks. RPSs are commonly used to model light propagation through the atmosphere or through biological tissues. We demonstrate the utility of the technique on an optical system with multiple RPSs that model random scattering media.

Properties of vortex beams are significantly affected upon interaction with random phase screens. We provide a quantitative description of the measurable vorticity as a function of variance and spatial correlation properties of distorting media.

The fluctuations of the number of scattering and multiplying particles in a random medium are investigated as functions of time. For this purpose, randomized Monte Carlo algorithms for estimating the probabilistic moments of the corresponding exponential asymptotic parameter are constructed.

In this paper, wavefield storage optimization strategies are discussed with respect to reverse-time migration (RTM) imaging in reflection-acoustic logging, considering the problem of massive wavefield data storage in RTM itself. In doing so, two optimization methods are proposed and implemented to avoid wavefield storage. Firstly, the RTM based on the excitation-amplitude imaging condition uses the excitation time to judge the imaging time, and accordingly, we only need to store a small part of wavefield, such as the wavefield data of dozens of time points, the instances prove that they can even be imaged by only two time points. The traditional RTM usually needs to store the wavefield data of thousands of time points, compared with which the data storage can be reduced by tens or even thousands of times. Secondly, the RTM based on the random boundary uses the idea that the wavefield scatters rather than reflects in a random medium to reconstruct the wavefield source and thereby directly avoid storing the forward wavefield data. Numerical examples show that compared with other migration algorithms and the traditional RTM, both methods can effectively reduce wavefield data storage as well as improve data-processing efficiency while ensuring imaging accuracy, thereby providing the means for high-efficiency and high-precision imaging of fractures and caves by boreholes.

Work to detect and locate distributed subsurface cracks in concrete by extracting non-propagating oscillatory fields is presented. The medium of interest is concrete, but the approach also applies to other types of inhomogeneous media. The theoretical basis of the work is first presented through a one-dimensional point-scatterer model that considers the wavefield set up by multiple distinct scatterers. More complex scattering scenarios are then investigated using numerical simulation. The numerical models consider two types of scatterers: elliptic large-scale particles distributed throughout a medium, and small-sized cracks localized within a damage zone. The theoretical and numerical analyses show that forward propagating waves undergo distinct scattering behavior within the crack damaged zone: non-propagating resonance-like oscillatory fields are set up within the cracked zone, and are distinct from the scatter caused by the large-scale particles. Frequency-wavenumber (f-k) domain analyses to extract the energy of non-propagating oscillatory fields and thus to detect and locate zones of distributed cracking are employed. The proposed approach is evaluated using numerical simulation and experimental data collected from concrete specimens that contain simulated distributed cracks. The results demonstrate that the location of distributed crack zones in discrete random media, such as concrete, can be successfully detected.

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 section...

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...

Effective coefficients for convective diffusion equations are obtained. Correlated random fields of conductivity and porosity are approximated by multiplicative cascades with log-normal distributions of probabilities. The theoretical result is checked numerically for the case of 3D plane flow of an incompressible fluid.

A novel class of random media with designed correlation functions are introduced. When light waves are scattered by this kind of media, the spectral density distributions of the scattered field present concentric rings-like profiles. By adjusting different parameters of the media, the number and the size of concentric rings can be modulated properly. Besides, it is found that the spectral density function of the scattered field and the non-negative definiteness function of the media belong to the same kind of functions. Our results have potential applications in optical trapping and particle manipulation.

In a recent paper, we described the development of a method for calculating exact collision probabilities between different regions (namely, fuel kernels, graphite matrix, moderator, and co...