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We theoretically investigate the scaling behavior of the localization length for s-polarized electromagnetic waves incident at a critical angle on stratified random media with short-range correlated disorder. By employing the invariant embedding method, extended to waves in correlated random media, and utilizing the Shapiro–Loginov formula of differentiation, we accurately compute the localization length ξ of s waves incident obliquely on stratified random media that exhibit short-range correlated dichotomous randomness in the dielectric permittivity. The random component of the permittivity is characterized by the disorder strength parameter σ2 and the disorder correlation length lc. Away from the critical angle, ξ depends on these parameters independently. However, precisely at the critical angle, we discover that for waves with wavenumber k, kξ depends on the single parameter klcσ2, satisfying a universal equation kξ≈1.3717klcσ2−1/3 across the entire range of parameter values. Additionally, we find that ξ scales as λ4/3 for the entire range of the wavelength λ, regardless of the values of σ2 and lc. We demonstrate that under sufficiently strong disorder, the scaling behavior of the localization length for all other incident angles converges to that for the critical incidence.

Abstract Random granular media can exhibit characteristics that are often related to ordered media. In the present work, this feature is observed in the polarized Second Harmonic Generation (SHG) response from reduced iron‐doped lithium niobate (LN:Fe) powders, which is an unexpected effect due to multiple scattering. In addition, the subsisting‐order properties of the powders can be further controlled by magnetic induction to tailor the SHG response. The samples are characterized by X‐ray Diffraction (XRD), X‐ray Photoelectron Spectroscopy (XPS), and confocal Raman Spectroscopy. The SHG response in the absence and presence of an external static magnetic field is then studied as the fundamental beam focus is translated from air into the powder. The SHG intensity polarization state is studied as a function of the linear polarization of the fundamental beam at the focus depth position, where the maximum SHG recorded intensity is observed. These results demonstrate that the SHG response of LN:Fe powders can be modified by post‐thermal treatment in a reducing atmosphere for photonic applications.

This article presents an analysis of P-band radio signal propagation through forest based on 3D Numerical Method of Maxwell's equations (NMM3D). The simulation domain of the forested region covers an area of 35.8 × 35.8 m2 that includes 112–121 coniferous trees with a height in the range of 8–16 m. The modeled trees have primary and secondary branches to account for their impact on scattering and attenuation at P-band. The fast hybrid method (FHM) has been successfully developed to complete the NMM3D full wave simulations of trees with efficient use of CPU time and memory. The accuracy of the proposed FHM model is validated by comparing scattered fields to that of FEKO for the case with nine trees. To account for the seasonal variation of water content in trees and hence dielectric constant, the wave scattering model is applied to a range of dielectric constants. Analysis of the P-band signal propagation is performed by computing the average loss and correlation of the transmission fields. The results show that the transmissivities are about 0.9 for winter conditions (low dielectric constant) and about 0.7 for summer conditions (high dielectric constant). Simulations with randomly positioned trees (off the periodic grid) demonstrate that the transmissivity shows a maximum variation of 4.3% relative to the nonrandomly positioned trees. The correlation analysis of P-band radio signals with two different dielectric constants indicates a high correlation amplitude above 0.89 and a phase change of less than 6°. A sensitivity analysis is carried out for a range of tree heights and trunk radii.

Precipitation and in particular rain present a random medium with constituent particles having dimensions comparable to the wavelength at millimeter-wave frequencies. Due to considerable scattering of waves from such particles, significant signal attenuation and phase front aberration can take place which are important factors that must be considered in modern communication system or radar design. This paper presents a fast and accurate numerical method for phase coherent modeling of wave propagation and scattering in random media, like rain. In this approach, the random medium is divided into sufficiently large finite slabs and each slab is modeled as a network with multiple input/output ports where ports represent rays with different polarizations propagating in different directions entering and leaving the slabs. The cascaded networks of slabs can be used to find the response of the random medium to any arbitrary source. The proposed method considers multiple scattering among all scatterers and thus the entire physics of wave-particle interactions is accounted for. In addition, the method can model both the mean and the fluctuating parts of waves in the random medium. To demonstrate the applicability of the proposed method, it is used for the calculation of the specific attenuation in rain media as a function of rain rates and frequency within the millimeter-wave band. The results show a good match with the available rain attenuation data in the literature.

Microwave remote sensing is significantly altered when passing through clouds or dense ice. This phenomenon is not unique to microwaves; for instance, ultrasound is also disrupted when traversing through heterogeneous tissues. Understanding the average transmission in particle-filled environments is central to improve data extraction or even to create materials that can selectively block or absorb certain wave frequencies. Most methods that calculate the average transmitted field assume that it satisfies a wave equation with a complex effective wavenumber. However, recent theoretical work has predicted more than one effective wave propagating even in a material which is statistically isotropic and for scalar waves. In this work we provide the first clear evidence of these predicted multiple effective waves by using high-fidelity Monte-Carlo simulations that do not make any statistical assumptions. To achieve this, it was necessary to fill in a missing link in the theory for particulate materials: we prove that the incident wave does not propagate within the material, which is usually taken as an assumption called the Ewald–Oseen extinction theorem. By proving this we conclude that the extinction length—the distance it takes for the incident wave to be extinct—is equal to the correlation length between the particles.

The full-wave simulations of 3D Maxwell equations of forests at L-band are carried out with a two-step hybrid method. The tallest trees considered include one 8-meter tall trunk, 18 primary branches and 108 secondary branches. In the first step, the T-matrix of a single tree in the representation of vector cylindrical waves (VCW) is calculated by using the far-field scattering amplitudes obtained from the commercial solver FEKO. In the second step, the wave multiple scattering theory (W-MST) as represented by the Foldy-Lax equations is used to account for the wave interactions among different trees. The accuracy of the hybrid method is validated by showing that the computed solutions of three trees are in good agreement with those solved from FEKO. Next the hybrid method is used for Monte Carlo simulations of forest stands with up to 30 trees. The dependences of the solutions on tree heights and tree densities are illustrated. The results show that the full-wave based transmissivities are much larger than those obtained from the radiative transfer equation (RTE) model.

We study how atmospheric turbulence affects twisted space-time beams, which are non-stationary random optical fields whose space and time dimensions are coupled with a stochastic twist. Applying the extended Huygens–Fresnel principle, we derive the mutual coherence function of a twisted space-time beam after propagating a distance z through atmospheric turbulence of arbitrary strength. We specialize the result to derive the ensemble-averaged irradiance and discuss how turbulence affects the beam’s spatial size, pulse width, and space-time twist. Lastly, we generate, in simulation, twisted space-time beam field realizations and propagate them through atmospheric phase screens to validate our analysis.

Increasing the frequency range of physics-based predictions of earthquake ground motions requires to account for small-scale heterogeneities, which can only be described in a stochastic way. Although many studies have addressed the impact of random heterogeneities on ground motion intensity parameters obtained by numerical simulation, very few have verified the accuracy of their numerical solutions or controlled the scattering regime they were simulating. Here we present a comprehensive analysis of SH wave propagation in 2D random media which covers a broad range of propagation regimes from ballistic to diffusive. The coherent and incoherent parts of the wavefield are examined independently. The random media consist in correlated density and velocity fluctuations described by a von Kármán autocorrelation function with a Hurst coefficient of 0.25 and a correlation length a = 500 m. The Birch correlation coefficient which relates density to velocity fluctuations takes 4 possible values between 0.5 and 1, and the standard deviation of the perturbations is either 5% or 10%. Spectral element simulations of SH wave propagation excited by a plane wave are performed for normalized wavenumbers (ka) up to 5. Analysis of the decay of the coherent wave amplitude, obtained through different averaging procedures, allows for a direct measure of the scattering attenuation, which we successfully compare with the predictions of the Dyson mean field theory. We also present the comparison between the energy envelopes measured from the synthetics and their theoretical counterpart provided by the radiative transfer theory and the diffusion approximation. Excellent agreement is found between numerical simulations and theoretical predictions of radiative transfer theory for the mean intensity. The numerical study highlights the difference of attenuation length between the mean field and the mean intensity. In the forward scattering regime, the peak intensity appears to decay exponentially over a length scale known as the transport mean free path. Furthermore, the fluctuations of intensity in the ballistic peak exhibit a transition from Log-normal to Exponential statistics. This transition occurs for a propagation distance of the order of the mean free path, which offers an alternative method of estimating this parameter.

Multiple optical scattering occurs when light propagates in a non-uniform medium. During the multiple scattering, images were distorted and the spatial information they carried became scrambled. However, the image information is not lost but presents in the form of speckle patterns (SPs). In this study, we built up an optical random scattering system based on an liquid crystal display (LCD) and an RGB laser source. We found that the image classification can be improved by the help of random scattering which is considered as a feedforward neural network to extracts features from image. Along with the ridge classification deployed on computer, we achieved excellent classification accuracy higher than 94%, for a variety of data sets covering medical, agricultural, environmental protection and other fields. In addition, the proposed optical scattering system has the advantages of high speed, low power consumption, and miniaturization, which is suitable for deploying in edge computing applications.

This article studies the existence and non-existence of transition fronts for a two species competition lattice system in random media, and explores 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.

Abstract In order to investigate the small-scale scattering heterogeneities underneath the northern Tien Shan, we analyze the P wavefield from teleseismic events. By using the teleseismic fluctuation method, we separate the total wavefield into coherent and fluctuating parts in the frequency band of 0.1–8.0 Hz. Subsequently, we investigate the scattering characteristics by analyzing the frequency-dependent intensities of the coherent and fluctuating wavefield between 0.3 and 2.5 Hz. We further constrain the velocity perturbations and correlation lengths by modeling the P-wave coda envelope with the Monte Carlo simulation. Strong scattering heterogeneities are revealed beneath the northern Tien Shan. The preferred scattering model can be described as a ~ 55- to 130-km-thick randomly heterogeneous layer with velocity perturbations of 6–9% and correlation lengths on the order of 0.4 km. We attribute these small-scale scatterers to isolated melt pockets from the upwelling hot mantle materials.

In this study, the problem of the influence of a horizontally inhomogeneous liquid bottom impedance, given by random Gaussian function of the speed of sound and by density, on the propagation of low-frequency sound in a shallow-water waveguide is considered. The model parameters are referenced to the conditions of sound propagation in the regions of the seas of the Russian Arctic shelf. By the example of statistical modeling of the sound field intensity, we show that sound speed fluctuations in the bottom lead to similar effects that were previously established for volumetric fluctuations of the speed of sound in the water layer. With the distance from the source, the decrease in the average intensity slows down in comparison with a deterministic medium in which there are no fluctuations. This deceleration of the decay of the intensity in a random waveguide can be significant already at short distances. Changes in the law of decay of intensity at a fixed frequency are mainly determined by the correlation radius of inhomogeneities and the average penetrability of the bottom, which leads to attenuation of sound propagating in the waveguide.

An investigation of transient second sound phenomena due to moving heat sources on planar random media is conducted. The spatial material randomness of the relaxation time is modeled by Cauchy or Dagum random fields allowing for decoupling of fractal and Hurst effects. The Maxwell–Cattaneo model is solved by a second-order central differencing. The resulting stochastic fluctuations of Mach wedges are examined and compared to unperturbed Mach wedges resulting from the heat source traveling in a homogeneous domain. All the examined cases are illustrated by simulation movies linked to this paper.

How do you take a reliable measurement of a material whose microstructure is random? When using wave scattering, the answer is often to take an ensemble average (average over time or space). By ensemble averaging we can calculate the average scattered wave and the effective wavenumber. To date, the literature has focused on calculating the effective wavenumber for a plate filled with particles. One clear unanswered question was how to extend this approach to a material of any geometry and for any source. For example, does the effective wavenumber depend on only the microstructure, or also on the material geometry? In this work, we demonstrate that the effective wavenumbers depend on only microstructure, though beyond the long wavelength limit there are multiple effective wavenumbers for one fixed incident frequency. We show how to calculate the average wave scattered from a random particulate material of any shape, and for broad frequency ranges. As an example, we show how to calculate the average wave scattered from a sphere filled with particles.

We investigated the effect of β on effective multiplication factor(keff) in the 1/fβ spectrum random system. The random system was generated by the 1/fβ noise model. The model is a continuous space model based on the Randomized Weierstrass function and describes the component spatial distribution with a power spectrum of 1/fβ, where f and β are the frequency domain variable and the characteristic parameter related to randomness, respectively. In this work, the two-group Monte Carlo calculations were performed to obtain the keff for a simple cubic geometry that consisted of two materials (fuel burned to 12 GWd/t and concrete). A large number of replicas having different spatial distribution and characterized by the representative β values were generated using the model, and the distribution on keff was analyzed. We found the dependency on β of standard deviation, skewness, and kurtosis of keff distribution. This result is expected to help to predict the keff distribution due to the randomizing model.

Random media emerge in several applications in reactor physics and safety analysis. Most often, models of stochastic media assume spatial homogeneity, whereas real-world complex materials, such as fuel chunks resulting from core degradation, typically display apparent heterogeneities. In a series of previous works, we have shown that stochastic tessellations can be successfully used in order to describe the material properties of several classes of random media. In this paper we extend these results to the case of heterogeneous random media by using Voronoi tessellations with space-dependent seed distributions, allowing for spatial gradients.

This paper deals with discrete-time semi-Markov random evolutions (DTSMRE) in reduced random media. The reduction can be done for ergodic and non ergodic media. Asymptotic approximations of random evolutions living in reducible random media (random environment) are obtained. Namely, averaging, diffusion approximation and normal deviation or diffusion approximation with equilibrium by martingale weak convergence method are obtained. Applications of the above results to the additive functionals and dynamical systems in discrete-time produce the above tree types of asymptotic results.

Fully bistatic radar scattering from rough surfaces is of vital importance in terrain remote sensing, but results in bulky data volume. The scattering is dependent on physical parameters of the media and is controlled by the radar observation geometry. Together, the two sets of parameters determine the scattering patterns in a bistatic plane confined by incident and polar angles in both incident and scattering directions. For radar remote sensing, it is desirable to infer surface parameters of interest, with satisfactory accuracy, from large volumes of measured data sets. This is essentially a task of data mining. In this paper, we present model-generated bistatic radar scattering data, followed by a sensitivity analysis, to identify a suitable configuration in terms of parameter inversion from fully bistatic measurements by a Kalman filter-trained dynamic learning neural network (DLNN). Results indicate that with bistatic observation, superior retrieval performance (as compared to backscattering observation) can be readily achieved.

In the framework of the Silent Wall ANR project, the CMM and the US2B are associated in order to characterize and to model fibrous media studying 3D images acquired with an X-Ray tomograph used by the US2B. The device can make 3D images of maximal 23043 voxels with resolutions in the range of 2 μm to 15 μm. Using mathematical morphology, measurements on the 3D X-Ray CT images are used to characterize materials. For example measuring the covariance on these images of an acoustic insulating material made of wooden fibres highlights the isotropy of the fibres orientations in the longitudinal planes which are perpendicular to the compression Oz axis. Moreover, it is possible to extract other morphological properties from these image processing methods such as the size distribution either of the fibres or of the pores by estimating the morphological opening granulometry of the considered medium. Using the theory of random sets introduced by Georges Matheron in the early 1970's, the aim of this work is to model such a fibrous material by parametric random media in 3D according to the prior knowledge of its morphological properties (covariance, porosity, size distributions, etc.). A Boolean model of random cylinders in 3D stacked in planes parallel to each other and perpendicular to the Oz compression axis is first considered. The granulometry results provide gamma distributions for the radii of the fibres. In addition, a uniform distribution of the orientations is chosen, according to the experimental isotropy measurements in the longitudinal planes. Finally the third statistical factor is the length distribution of the fibres which can be fitted by an exponential distribution. Thus it is possible to estimate the validity of this model first by trying to fit the experimental transverse and longitudinal covariances of the pores with the theoretical ones taking into account the statistical distributions of the dimensions of the random cylinders. The second method to validate the model consists in comparing morphological measurements (density profiles, covariance, opening granulometry, tortuosity, specific surface area) processed on real and on simulated media.

The micromechanics based on the Hill-Mandel condition indicates that the majority of stochastic finite element methods hinge on random field (RF) models of material properties (such as Hooke’s law) having no physical content, or even at odds with physics. At the same time, that condition allows one to set up the RFs of stiffness and compliance tensors in function of the mesoscale and actual random microstructure of the given material. The mesoscale is defined through a Statistical Volume Element (SVE), i.e. a material domain below the Representative Volume Element (RVE) level. The paper outlines a procedure for stochastic scale-dependent homogenization leading to a determination of mesoscale one-point and two-point statistics and, thus, a construction of analytical RF models.

Keller’s theorem relates the components of the macroscopic dielectric response of a binary two-dimensional composite system with those of the reciprocal system obtained by interchanging its components. We present a derivation of the theorem that, unlike previous ones, does not employ the common assumption that the response function relates an irrotational to a solenoidal field and that is valid for dispersive and dissipative anisotropic systems. We show that the usual statement of Keller’s theorem in terms of the conductivity is strictly valid only at zero frequency and we obtain a new generalization for finite frequencies. We develop applications of the theorem to the study of the optical properties of systems such as superlattices, 2D isotropic and anisotropic metamaterials and random media, to test the accuracy of theories and computational schemes, and to increase the accuracy of approximate calculations.

Application of CTRW (continuous time random walks) to dipole hopping transport is reviewed. Conditions of applicability of basic kinetic equations to spin systems are indicated. Correct versions of derivation of the CTRW-equations are presented. Existence of different forms of memory kernels is demonstrated. Correction of Scher-Lax memory kernel within geometrical memory approach is fulfilled in accordance with leading terms of concentration expansion. Approximate solution for autocorrelation function is considered. Modern state of numerical simulation and experimental measurements of autocorrelation function in nuclear polarization delocalization are described. It is shown, that application of the CTRW was more successful in description of dipole transport than for hopping conductivity.

This paper aims to conduct a comparative study on four different models of effective field and effective medium for modeling propagation of plane elastic waves through the composites containing spherical particles with random distribution. Effective elastic properties along with the normalized phase velocity and attenuation of the average wave was numerically evaluated by the models. The plane incident wave was considered longitudinal to get the results. The numerical analyses were performed on four types of composites in the range of low to intermediate frequency and different volume fractions. Judgment about this comparative study is done based on physical and theoretical concepts in the wave propagation phenomenon. The obtained results provide a good viewpoint in using different models for studying propagation of the plane elastic waves in various particulate composites.