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Criticality control of random media such as fuel debris is one of the most important safety issues in postaccident management. A 1/fβ spectrum randomizing model is expected to simulate such random ...

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

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...

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...

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...

Stochastic media problems present a severe impact on the properties of the electromagnetic fields that usually deterministic methods tend to overlook. In this paper, we present a finite-dif...

This work is to select precisely the proper frequency range that reduces the dependence of the laser radar cross-section (LRCS) on the incident wave parameters. In doing this, we investigate the effect of these parameters including incident angle and the beam width on the LRCS. We present a numerical analysis of the effect of the H-wave polarization on the radar detection capability in random medium and hence compare it with the freespace case. In doing this, our calculations use a boundary value method considering surface current on the whole contour of the object. As a result, the performance of the LRCS is studied with the target configuration assuming the creeping waves that have remarkable influence especially in the resonance range.

This book is timely summarization of recent advances in the multiscale theory of composites and random media. The theories in the book can be used in many disciplines, including geophysics, materia...

In this study, a review of various research works dealing with the numerical modelling of soil–structure interaction problems is presented. Numerical models have been illustrated to show the performance of techniques used for resolving soil–pipe interaction problems by considering the non-linear and random aspects of soil. Non-linear analysis has been carried out by using an elasto-perfectly plastic model where soil geo-mechanical characteristics have been determined by means of a probabilistic approach “Monte Carlo method” to quantify the influence of the spatial variability of soil geo-mechanical characteristics on the longitudinal responses of a part of sewer. Numerical illustrations are based on the combination of the soil non-linearities and the probabilistic determination of its geo-mechanical properties which can allow us to describe the mechanical behaviour of buried structures in dispersed environments at the stage where the complexity of soil–structure interaction problem is relatively more pron...

Two time-reversal algorithms for identifying, imaging, and tracking moving targets in clutter are introduced. The first algorithm classifies existing scatterers into stationary versus moving targets. Multistatic data matrices (MDMs) corresponding to successive radar acquisitions (snapshots) of the scene are recorded. Singular value decomposition of the (time-)averaged MDM provides information on stationary targets, whereas singular value decomposition of the differential MDM provides information on moving targets. The second algorithm yields real-time selective tracking of each moving target by means of differential time-reversal. It requires minimal processing and memory resources, and exploits distinctive features of time-reversal such as statistical stability and super-resolution. Numerical simulations are used to illustrate the capabilities of the proposed algorithms in different scenarios involving clutter from discrete secondary scatterers and from inhomogeneous random medium backgrounds.

We are concerned with homogenization of stochastic differential equations (SDE) with stationary coefficients driven by Poisson random measures and Brownian motions in the critical case, that is, when the limiting equation admits both a Brownian part as well as a pure jump part. We state an annealed convergence theorem. This problem is deeply connected with homogenization of integral partial differential equations.

This paper concerns the asymptotic structure of the scintillation function in the simplified setting of wave propagation modeled by an Ito–Schrodinger equation. We show that the size of the scintil...

This paper addresses some parameters that have a significant effect on wave scattering in random media. These parameters are: target configuration, including size and curvature; random media strength, represented in the spatial coherence length; and incident wave polarization. Here, I present numerical calculations for the radar cross-section (RCS) of conducting targets and analyze the backscattering enhancement with different configurations. I postulate a concave illumination region and consider targets taking large sizes of about five wavelengths. In this aspect, waves scattering from targets are assumed to propagate in free space and a random medium with H-polarization. This polarization produces what is well known as creeping waves which in turn have an additional effect on the scattering waves that is absent in the case of E-polarization.

In a previous study, the radar cross-section (RCS) was shown to be influenced largely by the curvature of the illumination region of the target. Scattering data from smooth concave–convex contours reveals the obvious impact of specular reflections on the behavior of RCS. This effect needs to be investigated more especially with relatively complex surfaces. Here, we work on a numerical calculation of the RCS and analyze its characteristics with different target configurations including complexity and size. We postulate a concave illumination region and consider targets that are taking large sizes of about five wavelengths. In this communication, we assume wave propagation and scattering from targets in free space and random medium with consideration of horizontal incident wave polarization.

Light localization is revealed by analyzing the spectral intensity and lasing threshold in two-dimensional (2D) media made of uniaxial scatterers arranged to be ordered in spatial location and disordered in orientation of their optical axes. Different system parameters such as surface-filling fraction and sample size are chosen for numerical simulations. Results show that, as the surface-filling fraction and sample size increases, the lasing threshold decreases rapidly, indicating the lightwave transits from a weak scattering state to a localized one.

In Ref. [1] (Appendix A) we derived equations governing the frequency and spatial spectrum of radiation propagating in three-dimensional time-dependent random media with randomly varying sound speed c ( x , t). From the spectral equations we determine equations for the energy flux in both the forward and backward directions. We consider media that are spatially homogeneous and isotropic and stationary in time. In order to allow an independence assumption the analysis is restricted to fluctuations that satisfy the conditions τμ ≫ L z /c 0 and τμ ≪ L FS/c 0 where τμ is the characteristic time of the fluctuations, k 0 is the mean radiation wavenumber, L z is the characteristic correlation length of the random fluctuations in the mean propagation direction and L FS is a mean scattering length. We consider various values of γ = (k 0 L z )2/2. When γ ≪ 1 we find the usual radiation transfer equations. When γ ≫ 1, but back-scattering can be neglected, we find the forward-scattering equations. We also consider γ ...

Theoretical and experimental investigation of self-ordering in a fused quartz under strong light pumping is presented. It is shown that uniform radiation drives a self-organization process in a random medium and macroscopic spatially ordered structure is formed.

Microwave-Induced Thermo-Acoustic Tomography (MITAT) is a promising technique in biomedical imaging. It has predominant advantages in both contrast and resolution compared with conventional microwave or ultrasound imaging system for malignant tumors. In this paper, Time Reversal Mirror (TRM) imaging technique based on numeric method Pseudo-Spectrum Time Domain (PSTD) for MITAT imaging is studied computationally. The proportion relationship between the deposited microwave energy and the induced thermo-acoustic initial source is deduced by analytic method. Due to the globe higher order character and the efficiency, the PSTD method is employed to implement the forward core of the TRM and to model the complex biologic tissue. In order to illustrate the performance of the TRM technique applied in MITAT, some thermo-acoustic objects with different initial pressure distributions are simulated, then designed and imaged by this technique to represent the complex biologic tissue case in a random media. Under the co...

Propagation of waves in a composite elastic rod consisting of rods with alternating properties of random length is considered. We calculate exactly the Lyapunov exponent and find its short and long wave asymptotics. Finally, we discuss conditions for propagation and localization of waves in a binary random medium.

In steel fiber reinforced concrete, steel fibers are randomly oriented in the concrete host. This article presents a full-wave homogenization technique for the computation of the effective permittivity of perfectly conducting wires embedded in a dielectric host. The technique is illustrated with numerical examples and is compared with predictions from a classical mixing formula.

The origins of the long, high-intensity ribbons that occur when a wave propagates through a multiply scattering random medium are examined. It is shown that such ribbons are initiated when the cumulative phase deviation imposed on the wavefront in the direction of propagation becomes large. Estimates are made of the number of such ribbons that might be encountered in typical cases of multiple scatter, and of their expected separation transverse to the direction of propagation. Finally, it is shown that motion of the source in the transverse direction does not lead to appreciable movement of the ribbons.

The model based on the method of finite-difference time-domain is applied to calculate the general feature of localized modes in active random media. The evolution of the localized modes from passive random media to active ones is investigated. By varying the gain lineshape for an active random medium, we have observed a selective excitation of localized modes, including both single-mode and multi-mode excitations. When the eigenfrequencies for some localized modes are near the centre of the gain spectrum, the optical gain offers coherent amplification to them so that they can obtain more amplification and have stronger field amplitude than other modes. The pumping level dependence of the field amplitude of the localized modes exhibits a threshold behaviour.

We study the homogenization of “viscous” Hamilton–Jacobi equations in stationary ergodic media. The “viscosity” and the spatial oscillations are assumed to be of the same order. We identify the asy...

The polarization of incident waves is one of the key factors in radar detection and remote sensing problems. In a previous study, attention was drawn to the anomalous increase in the radar crosssection (RCS) of a target in a random medium that occurs with H-polarization. This large increase occurs with a small-size target and is attributed to the coupling between the direct and creeping waves. In this work, we aim to probe the effect of the creeping waves on the scattering waves for circular wave polarization and compare it with the previous results. Therefore, we can control the target detection by choosing the proper polarization, which does not lead to anomalous phenomena. In doing so, we present numerical results for RCS and analyse the characteristics of the enhancement in the RCS (ERCS) behaviour of targets in random media. In this regard, we assume partially convex targets of different configurations. We consider the case in which a directly incident wave is produced by a line source distributed uniformly along the axis parallel to the conducting cylinder (target) axis. Then we can deal with this scattering problem two-dimensionally under the condition of strong continuous random media with large local scale size.

The spatial and temporal structures of time-dependent signals can be appreciably affected by random changes of the parameters of the medium characteristic of almost all geophysical environments. The dispersive properties of random media cause distortions in the propagating signal, particularly in pulse broadening and time delay. When there is also spatial variation of the background refractive index, the observer can be accessed by a number of background rays. In order to compute the pulse characteristics along each separate ray, there is a need to know the behaviour of the two-frequency mutual coherence function. In this work, we formulate the equation of the two-frequency mutual coherence function along a curved background ray trajectory. To solve this equation, a recently developed reference-wave method is applied. This method is based on embedding the problem into a higher dimensional space and is accompanied by the introduction of additional coordinates. Choosing a proper transform of the ex...

The equation for the fourth moment of a wave propagating in a multiply scattering random medium has been solved by various methods. When the analytical solutions are compared with numerical solutions of the equation it is found that the fundamental solution together with a first-order correction term agree very closely with the numerical results over a wide range of distances and scattering strengths. Unfortunately, the correction term involves multiple integrals and so is difficult to evaluate. This paper shows how some of these integrations can be carried out and the results combined in such a way that an analytical form similar to the fundamental solution is obtained involving only a single integral. This simplified combined solution also agrees very closely with the numerical results.

A new microwave heating process for ceramic materials is proposed and analyzed. Instead of processing material in the bulk state, material under processing is subdivided into many pellets randomly distributed in a suitable low-density, low- thermal-conductivity host medium. Theoretical and numerical models allow studying the dielectric properties of the mixture and analyzing power deposition into the 3D random medium.

In our previous work, we have proved that the spatial coherence length (SCL) of th ei ncident waves around the target together with the target configuration play al eading role in the determination of the enhancement in the radar cross-section (ERCS) of a target in a random medium. Owing to the double-passage effect, the ERCS is almost two when the SCL is much smaller or larger than the target size. However, for a SCL comparable with the target size, the ERCS deviates from two, depending on the target parameters and the SCL. The last conclusion was proved onl yf orE-polarization. The polarization of incident waves is one of the key parameters in scattering problems. In this work, we extend our study and investigate the effect of H -polarization on the radar cross-section and the ERCS for large-size targets.

The shape of the target constitutes an important factor in the radar detection problem. In a previous study, the enhancement in the radar cross section (ERCS) has proved to be affected largely by the target parameters as well as the effects of the double passage and the spatial coherence length of incident waves around the target. However, the target size was limited to about less than one wavelength. Here, we estimate numerically the RCS of targets taking large sizes of more than three wavelengths, and analyse the characteristics of RCS. Moreover, we investigate the ERCS phenomenon of such targets under different circumstances of random medium and target configuration. In this regard, we assume partially convex targets in continuous random media and also horizontal incident wave polarization (E-wave incidence).

In this work a new reference wave method for solving parabolic-type equations is proposed. The performance of the method is demonstrated by applying it to the equation governing the propagation of the two-frequency mutual coherence function in a random medium. An analytic solution is presented for arbitrary correlation properties of the medium. It is shown that when approximating the transverse structure function of the medium by a quadratic form, the solution reduces to the exact result derived previously. Extensions to more general types of media are considered.

Recently time-reversal techniques have emerged as a new, important and fascinating discipline within wave propagation. Many of the problems involved can best be understood, analysed and optimized based on a random field model for the medium. Here we discuss stable refocusing of second-order time-reversed reflections. This phenomenon may appear as surprising at first. However, we show how it can be understood in very simple terms viewing the wavefield as a stochastic process. We give sufficient conditions on the Green function of the propagation problem for the phenomenon to happen. In particular we discuss acoustic wave propagation in the regime of weak random medium fluctuations and give explicitly the derivation of stable refocusing in this case, illustrating it with numerical examples. (Some figures in this article are in colour only in the electronic version)

We perform one-dimensional numerical simulations of both driven and impulsively generated sound waves propagating through a medium whose mass density admits time-independent, random fluctuations. While the amplitude of both types of wave is always attenuated, driven sound waves can be either retarded or speeded up depending on their wavenumber and amplitude and on the strength of the random field. The speed of a pulse propagating in the random medium is also altered, in agreement with the findings for the driven waves. The concomitant action of nonlinearity and randomness results in wave speeding for wavenumbers which are of the order of the size of an average random density fluctuation, whereas it gives retardation for larger wavenumbers.

In this paper, we prove the stabilization and the space–time refocusing of a time-reversed transmitted pulse traveling in a randomly layered medium. This work is a generalization of (5) in the three-dimensional stratified space.

Equations for incoherent intensities are obtained for electromagnetic waves in a random medium layer with plane parallel boundaries. These are based on the Bethe–Salpeter equation under the ladder approximation. These equations are then compared with the radiative transfer equations for this problem. Differences between these two approaches are pointed out and discussed. The Muller matrix is derived based on a first-order approximation to the equations for incoherent intensities which is then used to highlight the significance of the above-mentioned differences in radar cross-section computations.

The integral equation model (IEM) has been developed over the last decade and, since its first presentation by Fung and Pan (1986 Proc. Int. Symp. on Multiple Scattering of Waves in Random Media and Random Surface (PA: Pennsylvania State University Press) pp 701–14), it has become one of the theoretical models most widely used for rough surface scattering in microwave remote sensing. The aim of this model was the study of the scattering by random rough surfaces under more general conditions than the Kirchhoff or the small-perturbation approximations. Furthermore, the IEM was meant to include multiple-scattering effects at second order. The IEM has been gradually corrected in two later releases by its original authors (Hsieh C-Y et al 1997 IEEE Trans. Geosci. Remote Sensing 35 901–9, Chen et al 2000 IEEE Trans. Geosci. Remote Sensing 38 249–56). However, the model still presents several theoretical hiatuses in its current formulation which call for a new revision. Most importantly, the IEM in its ...

The problem of scattering from a random medium layer with rough boundaries is formulated as an integral equation in which the random fluctuations are represented as a zero-mean random operator. The analysis for the diffuse fields is based on the ladder-approximated Bethe–Salpeter equation. An integral equation for the diffuse intensities thus derived displays the various multiple-scattering processes involved in our problem. Transport equations are also derived and several special cases are considered to illustrate the characteristics of the results and to compare them with those in the literature.

We study the high-frequency propagation of acoustic plane and spherical waves in random media. With the geometrical optics and the perturbation approach, we obtain the travel-time mean and travel-time variance at the second order. The main hypotheses are the Gaussian distribution of the acoustic speed perturbation and a factorized form for its correlation function. The second-order travel-time variance explains the nonlinear behaviour at large propagation distance observed with numerical experiments based on ray tracing. Usually, homogeneity and isotropy of the refractive index are considered. Using the geometrical anisotropy hypothesis we extend the theory to a general class of statistically anisotropic random media.

In a previous paper (Whitman et al 1999 Waves Random Media 9 1–11) we discussed the scattering of acoustic waves by random sound-speed fluctuations in a two-dimensional channel and presented an asymptotic form for an acoustic pulse propagating in the channel. Here we include the three-dimensional effect of transverse scattering. We find an asymptotic solution in which initially the two-dimensional mode-transfer effect is more important than the transverse scattering effect. However, for large enough propagation distances the transverse scattering effect dominates the pulse spread. In this paper we shall show the form of the pulse shape in both propagation ranges as well as in the transition regime. We shall begin with a discussion of the physics of the problem and then present a mathematical discussion.

Analytic expressions are derived for the normalized radar cross sections (NRCS) of a random medium layer. These are calculated from the first-order solutions for diffuse intensities which are based on a multiple-scattering wave theoretical analysis. The permittivity fluctuations are assumed to be small and to obey stationary Gaussian statistics. On studying the expressions for the NRCS, some of their characteristics are pointed out. Three different correlation functions are considered and expressions for the coherent propagation constants are provided. Numerical examples are used to verify theoretical results and highlight some interesting characteristics of NRCS.

A novel effective medium theory is derived for the Euler-Bernoulli equation, allowing the transport behaviour of flexural waves encountering random variations in density to be found. As an example the energy transport velocities for multiply scattered, flexural waves propagating in a thin plate with circular inclusions of different density are computed. Small transport velocities are observed for small to moderate density anomalies implying suppression of the wave diffusion constant. For large-density anomalies the diffusive description is found to fail when the localization parameter falls below a critical value.

We consider acoustic pulse propagation in inhomogeneous media over relatively long propagation distances. Our main objective is to characterize the spreading of the travelling pulse due to microscale variations in the medium parameters. The pulse is generated by a point source and the medium is modelled by a smooth three-dimensional background that is modulated by stratified random fluctuations. We refer to such media as locally layered . We show that, when the pulse is observed relative to its random arrival time, it stabilizes to a shape determined by the slowly varying background convolved with a Gaussian. The width of the Gaussian and the random travel time are determined by the medium parameters along the ray connecting the source and the point of observation. The ray is determined by high-frequency asymptotics (geometrical optics). If we observe the pulse in a deterministic frame moving with the effective slowness , it does not stabilize and its mean is broader because of the random compone...

Electromagnetic properties of resonant inhomogeneous media are investigated. A new type of transverse electromagnetic wave arising due to the effective spatial dispersion is studied. It is shown that scattering on the fluctuations of the resonant frequency of the medium shifts the Cherenkov threshold and reduces the intensity of the Cherenkov radiation.

We present a study of the effects of quenched disorder on kinetic phase transitions in catalytic model in 1 + 1 dimensions. We find that even a small disorder changes the critical dynamically properties in a significant manner.