Properties Of Heterogeneous Media Research Articles

Seismic scattering regimes from multiscale entropy and frequency correlations

SUMMARY Seismic-wave scattering is observed, to variable degrees, on Earth, its moon and Mars. Current scattering models and data processing typically rely on two end-member phenomena: weak, single- or multiple-scattering events (ballistic) on the one hand, or intense scattering such that the wavefield retains no path information or bearing on its origin (diffuse).This study explores the existence of scattering behaviour intermediate between these end-members, as well as the properties of heterogeneous media that facilitate a transition between them. We apply multiscale entropy and frequency-correlation analysis to seismic coda, and observe a distinct transitional behaviour is present within a part of the investigated parameter space. Analysis of terrestrial, lunar and Martian seismograms further demonstrate the applicability of these new methods across a wide range of scattering behaviours, while also highlighting their shortcomings. Results from the planetary data indicate partially non-diffuse behaviour and low complexity within specific bandwidths of lunar wavefields, potentially contradicting the current paradigm that lunar wavefields are diffuse, and require continued study. Furthermore, Martian seismograms are shown to possess greater statistical entropy than lunar seismograms and diffuse energy properties, yet still display distinct phase arrivals, suggesting substantial scattering and transitional scattering behaviour on Mars. The robust, comparative nature of multiscale entropy and frequency-correlation analysis, applied to idealised simulation as well as three separate planetary bodies, provides a promising framework for future exploration of scattered wavefields across ballistic, transitional and diffuse regimes, that complements existing methods.

Multi-physics flux coupling for hydraulic fracturing modelling within INMOST platform

AbstractThis work presents an overview of techniques that enable the construction of collocated finite volume method for complex multi-physics models in multiple domains. Each domain is characterized by the properties of heterogeneous media and features a distinctive multi-physics model. Coupling together systems of equations, corresponding to multiple unknowns, results in a vector flux. The finite volume method requires continuity of intradomain and interdomain vector fluxes. The continuous flux is derived using an extension of the harmonic averaging point concept. Often, the collocated coupling of the equations results in a saddle-point problem subject to inf-sup stability issues. These issues are addressed by the eigen-splitting of indefinite matrix coefficients encountered in the flux expression. The application of the techniques implemented within INMOST platform to hydraulic fracturing problem is demonstrated.

An efficient and accurate hybrid weak-form meshless method for transient nonlinear heterogeneous heat conduction problems

Our purpose is to establish a numerical method meeting the requirements of efficiency, stability, accuracy and easy-using. Faced with these demands, in this paper, a hybrid method combining the advantages of 2 weak-form meshless methods is proposed for solving steady and transient heat conduction problems with temperature-dependent thermophysical properties in heterogeneous media. In the process of the calculation for an arbitrary model discretized by the hybrid method, two different weak-form methods are used for the nodes categorized as: (1) boundary nodes, (2) near boundary interior nodes and (3) interior nodes. A Galerkin free element method (GFREM) is proposed for the interior nodes of the Cartesian grid; and the local radial point interpolation method (LRPIM) is used for the other two types of nodes. The GFREM using the Cartesian grid can greatly improve the accuracy and efficiency of the hybrid scheme. Special decomposition technology to determine the irregular integral domain for LRPIM can increase the flexibility for complex models. In addition, the full implicit finite difference scheme and Newton–Raphson method are used for solving transient nonlinear problems. And non-crossing interface integral domain and support domain are employed for heterogeneous media. Compared with other methods, numerical results show better accuracy, stability and efficiency from the numerical experiments.

Estimation of Spatially Distributed Thermal Properties of Heterogeneous Media with Non-Intrusive Measurement

This article deals with estimation of spatially distributed thermal properties of two-dimensional heterogeneous media from the solution of inverse heat conduction problem. The experimental procedure involves sequential heating of sample at four discrete locations on one side and recording transient temperature on the other side non-intrusively. The inverse problem formulation is carried out as parameter estimation problem and the unknown parameters are estimated through minimization of sum of squared error between measured and simulated temperatures using Levenberg–Marquardt algorithm. The huge computational time required to calculate sensitivity matrix is reduced through parallel computation strategy. Numerical estimations are carried out with synthetic temperature and it is found that the resolution and accuracy of estimated spatially distributed thermal conductivity is in better agreement with the exact distribution when compared to volumetric heat capacity even at an error level of ± 0.1 K. Transient temperature response of the fabricated heterogeneous prototype is recorded using infrared radiation camera and the same is used for estimation of unknown parameters. The estimated thermal conductivity closely mimics the actual distribution. Therefore, this simple proposed method can be directly used in thermal tomography applications for identifying the shape and size of inclusions/inhomogeneities from the estimated thermal conductivity distribution alone.

Optical properties reconstruction using the adjoint method based on the radiative transfer equation

An efficient algorithm is proposed to reconstruct the spatial distribution of optical properties in heterogeneous media like biological tissues. The light transport through such media is accurately described by the radiative transfer equation in the frequency-domain. The adjoint method is used to efficiently compute the objective function gradient with respect to optical parameters. Numerical tests show that the algorithm is accurate and robust to retrieve simultaneously the absorption µa and scattering µs coefficients for lowly and highly absorbing medium. Moreover, the simultaneous reconstruction of µs and the anisotropy factor g of the Henyey–Greenstein phase function is achieved with a reasonable accuracy. The main novelty in this work is the reconstruction of g which might open the possibility to image this parameter in tissues as an additional contrast agent in optical tomography.

Characterization of heterogeneous media using nonlinear Stokes–Mueller polarimetry

The nonlinear optical properties of heterogeneous media are described by an algebraic decomposition of the correlation matrix X(n) of the nth-order nonlinear susceptibility tensor values, obtained from the generalized nonlinear Stokes–Mueller polarimetry measurements. The correlation matrix X(n) forms a square Hermitian semidefinite positive matrix, which can be further decomposed into separate components using projection matrices and calculating eigenvalues and the corresponding eigenvectors for pure states of the heterogeneous media. Up to eight pure states can be deduced for the sum-frequency generation process and up to sixteen states can be presented for a four-wave mixing process. The obtained eigenvalues are used to define the entropy characterizing a heterogeneous media. Filtering and maximum-likelihood estimation approaches are presented to determine the physically realizable values of the nonlinear susceptibility from the X(n) matrix that is obtained by the Stokes–Mueller polarimetry experiments. The Cholesky decomposition is employed for the maximum-likelihood estimation of the correlation matrix X(n). The structural characterization can be used, for example, in nonlinear microscopy for determining the ultrastructure organization of heterogeneous biological samples.

Taming the degeneration of Bessel beams at an anisotropic-isotropic interface: Toward three-dimensional control of confined vortical waves.

Despite their self-reconstruction properties in heterogeneous media, Bessel beams are known to degenerate when they are refracted from an isotropic to an anisotropic medium. In this paper, we study the converse situation wherein an anisotropic Bessel beam is refracted into an isotropic medium. It is shown that these anisotropic Bessel beams also degenerate, leading to confined vortical waves that may serve as localized particle trap for acoustical tweezers. The linear nature of this degeneration allows the three-dimensional control of this trap position by wavefront correction. Theory is confronted to experiments performed in the field of acoustics. A swirling surface acoustic wave is synthesized at the surface of a piezoelectric crystal by a microelectromechanical integrated system and radiated inside a miniature liquid vessel. The wavefront correction is operated with inverse filter technique. This work opens perspectives for contactless on-chip manipulation devices.

A hybrid averaging approach to predict overall properties of nanocomposites

A new method is proposed to consider the characterizations of the fillers in overall properties of heterogeneous media, and in particular, nanocomposites. According to this method, named ‘Hybrid averaging,’ the effective properties of a general nanocomposite containing several phases and orientations can be found using the results from a number of simple unidirectional two-phase nanocomposites. The results for the simple media might be obtained from any roots including analytical approaches, numerical simulations, and experimental analyses. In this article, M—T as the analytical and FE as the numerical approaches are combined with the proposed hybrid method. To perform FE analysis, RRVE with periodic boundary conditions is employed. In addition, the influential parameters consisting of RRVE size and mesh density on the numerical results are justified by satisfying certain criteria. Numerical investigations are then done for two case studies of nanocomposites in which boron nitride nanotubes, as fillers, are distributed using two different functions. Furthermore, comparisons are made between the results obtained from different approaches for these materials.

Inverse analysis with integral transformed temperature fields: Identification of thermophysical properties in heterogeneous media

The objective of this work is to introduce the use of integral transformed temperature measured data for the solution of inverse heat transfer problems, instead of the common local transient temperature measurements. The proposed approach is capable of significantly compressing the measured data through the integral transformation, without losing the information contained in the measurements and required for the solution of the inverse problem. The data compression is of special interest for modern measurement techniques, such as the infrared thermography, that allows for fine spatial resolutions and large frequencies, possibly resulting on a very large amount of measured data. In order to critically address the use of integral transformed measurements, we examine in this paper the simultaneous estimation of spatially variable thermal conductivity and thermal diffusivity in one-dimensional heat conduction within heterogeneous media. The direct problem solution is analytically obtained via integral transforms and the related eigenvalue problem is solved by the Generalized Integral Transform Technique (GITT). The inverse problem is handled with Bayesian inference by employing a Markov Chain Monte Carlo (MCMC) method. The unknown functions appearing in the formulation are expanded in terms of eigenfunctions as well, so that the unknown parameters become the corresponding series coefficients. Such projection of the functions in an infinite dimensional space onto a parametric space of finite dimension also permits that several quantities appearing in the solution of the direct problem be analytically computed. Simulated measurements are used in the inverse analysis; they are assumed to be additive, uncorrelated, normally distributed, with zero means and known covariances. Both Gaussian and non-informative uniform distributions are used as priors for demonstrating the robustness of the estimation procedure.

A multiscale microstructure model of carbon black distribution in rubber

The increase of observations and computational capabilities favoured the numerical simulation of microstructure to derive the effective properties of materials. Indeed, the multiscale approaches, that use homogenization techniques, enable us to estimate or to give bounds of the overall properties of heterogeneous media. In this work, the objective is to develop a three-dimensional mathematical model of the morphology of the microstructure of rubber composite containing carbon black nano-fillers. This multiscale model consists of a combination of some primary models that correspond to the physical scales of the microstructure. It is identified according to an original method that uses statistical moments from experimental transmission electronic microscope (TEM) image data and from numerical TEM simulations. This method leads to three-dimensional representative simulations of microstructures that take the complex clustering effect of particles in aggregates, into account. Finally, the identified model of the morphology satisfies the experimental percolation rate of the carbon black aggregates in the material.

The long-wave theory of N pairwise alternate homogeneous and heterogeneous layers difraction

Basic physics of theory is comparison of electrodynamic properties of heterogeneous media of nonuniform layer with chaotic or regular distribution of scatterers with small wave size and uniform anisotropic media with efficient values of components of dielectric permittivity and magnetic permeability tensors. Scattering coefficients of perpendicular and parallel polarization waves of bounded sequence are obtained by using circuit theory and matrix functions methods. We consider thick periodic grates of magnetodielectric bars with equal and orthogonal symmetry lines orientation and different geometrical and material parameters as two periodic nonuniform layers. We proved direct analytic formulas, which describe width and position of quasitransparency (quasicutoff) zones of band-pass and resonant wave passage and its dynamics on parametric relations of reflection factors. It is discovered effects that prove an opportunity of investigated structure usage in multifunctional electromagnetic field directors.

Evaluation of effective electromagnetic properties in heterogeneous media

This paper presents the application of a homogenisation technique, based on the multi-scale expansion theory, to the analysis of heterogeneous materials constituted of magnetic inclusions dispersed in a dielectric lattice. The role of the shape and dimensions of the inclusions is analysed with reference to the effective electromagnetic properties and energy losses. The investigation is extended to the influence of flux waveforms with harmonic distortion, focusing the attention on the energy loss dependency on the harmonic content.

High refractive index and other optical properties of heterogeneous media

Anomalously high values of the resonant refractive index, Rayleigh scattering extinction coefficient, and absorption or amplification are predicted for a heterogeneous medium composed of metallic nanoballs suspended in a transparent matrix. Optical characteristics of original materials do not posses resonant features.

Quantitative prediction of effective material properties of heterogeneous media

Effective electrical conductivity and electrical permittivity of water-saturated natural sandstones are evaluated on the basis of local porosity theory (LPT). In contrast to earlier methods, which characterize the underlying microstructure only through the volume fraction, LPT incorporates geometric information about the stochastic microstructure in terms of local porosity distribution and local percolation probabilities. We compare the prediction of LPT and of traditional effective medium theory with the exact results. The exact results for the conductivity and permittivity are obtained by solving the microscopic mixed boundary value problem for the Maxwell equations in the quasistatic approximation. Contrary to the predictions from effective medium theory, the predictions of LPT are in better quantitative agreement with the exact results.

Experimental validation on granular metallic films of an optical model based on the entropic analysis of their morphology

We have developed two models for the optical properties of heterogeneous media, based on the entropic analysis of their morphology. These models have been applied to actual granular metallic media close to the percolation. The models account well for the measured optical properties: the plasmon resonance and the infrared behavior are especially well accounted.

Optical Properties of Granular Metallic Media Near the Percolation Transition

ABSTRACTThis review covers most of new physical aspects opened by the recent interest in the optical properties of heterogeneous media close to the percolation transition: relevant parameters and lengths, caracteristic optical behaviour (transmittance, reflectance and absorptance), theoretical models, dimensionali ty effects, discrimination between optical, electrical and morphological percolation transitions. Morphological aspects are emphasized as the key of optical properties at percolation.

A theory of dynamic elastic constants of heteroge[ngrave]eous media

Abstract A theory of dynamic elastic constants is described. The approach taken is deterministic in nature and the elastic wave scattering off a single ellipsoidal inhomogeneity, a self-consistency scheme, and an averaging theorem over strain energy and kinetic energy are presented. The solution for a single ellipsoidal inhomogeneity embedded in an infinite solid under a time-harmonic plane incident wave-field is first given. The formulation depends on the use of the concept of transformation strains which now become frequency dependent. When the incident wavelength λ is much longer than the effective size of the ellipsoid the theory gives the well-known result for the Rayleigh limit. The effective properties of heterogeneous media with multicomponents depend upon a second-rank tensor D and a fourth-rank tensor A. Their derivation is presented by way of a self-consistency scheme. The dynamic effective moduli and mass density are found to be dispersive. Calculations for special cases will depend upon the e...