Wave Propagation In Complex Media Research Articles

Exploring the physical characteristics and nonlinear wave dynamics of a (3+1)-dimensional integrable evolution system

This study comprehensively explores the [Formula: see text]-dimensional Mikhailov–Novikov–Wang [Formula: see text] integrable equation, with the primary objective of elucidating its physical manifestations and establishing connections with analogous nonlinear evolution equations. The investigated model holds significant physical meaning across various disciplines within mathematical physics. Primarily, it serves as a fundamental model for understanding nonlinear wave propagation phenomena, offering insights into wave behaviors in complex media. Moreover, its relevance extends to nonlinear optics, where it governs the dynamics of optical pulses and solitons crucial for optical communication and signal processing technologies. Employing analytical methodologies, namely the unified [Formula: see text], Khater II ([Formula: see text]hat.II) method, and He’s variational iteration [Formula: see text] method, both numerical and analytical solutions are meticulously examined. Through this investigation, the intricate behaviors of the equation are systematically unveiled, shedding illuminating insights on various physical phenomena, notably including wave propagation in complex media and nonlinear optics. The outcomes not only underscore the efficacy of the analytical techniques deployed but also accentuate the equation’s pivotal role in modeling a broad spectrum of nonlinear wave dynamics. Consequently, this research significantly advances our comprehension of complex physical systems governed by nonlinear dynamics, thereby contributing notably to interdisciplinary pursuits in mathematical physics.

On the Application of Fractional Derivative Operator Theory to the Electromagnetic Modeling of Frequency Dispersive Media

Fractional derivative operators are finding applications in a wide variety of fields with their ability to better model certain phenomena exhibiting spatial and temporal nonlocality. One area in which these operators are applicable is in the field of electromagnetism, thereby modelling transient wave propagation in complex media. To apply fractional derivative operators to electromagnetic problems, the operator must adhere to certain principles, like the trigonometric functions invariance property. The Grünwald–Letnikov and Marchaud fractional derivative operators comply with these principles and therefore could be applied. The fractional derivative arises when modelling frequency-dispersive dielectric media. The time-domain convolution integral in the relation between the electric displacement and the polarisation density, containing an empirical extension of the Debye model, is approximated directly. A common approach is to recursively update the convolution integral by approximating the time series by a truncated sum of decaying exponentials, with the coefficients found through means of optimisation or fitting. The finite-difference time-domain schemes using this approach have shown to be more computationally efficient compared to other approaches using auxiliary differential equation methods.

Localization and classification of scattered nonlinear ultrasonic signatures in bio-mechanical media using time reversal approach.

This paper deals with the time reversal approach along with signal classification using ϕ-divergences in biomedical applications for localization and statistical classification of ultrasonic nonlinearities. The time reversal (TR) approach in combination with nonlinear elastic wave spectroscopy (NEWS) is used to obtain the nonlinear signature of air bubbles with different sizes and ultrasound contrast agents in a liquid. An optimized chirp-coded signal in the range of 0.6-3 MHz is used as a compression coding. The signal classification is performed using the fuzzy classification method and the divergence decision tree algorithm using specific ϕ-divergence spectral measures extracted from the received ultrasonic response containing acoustic nonlinearities. The classification results prove that different types of nonlinearities extracted with classical "pulse inversion" based coding methods can be identified. Simultaneously, the different positions of scattered sources are distinguished by ϕ-divergence methods. The potential of time reversal nonlinear elastic wave spectroscopy methods for understanding of ultrasonic wave propagation in complex media is clearly exhibited.

Viscoacoustic wave simulation with the lattice Boltzmann method

The lattice Boltzmann method (LBM), widely used in computational fluid mechanics, is introduced as a novel mesoscopic numerical scheme for viscoacoustic wavefield simulation. Through mathematical derivation, a mapping model between the relaxation time of LBM and the quality factor based on the Kelvin-Voigt model is established, which provides a theoretical background for the comparison of the viscoacoustic wavefields obtained, respectively, by LBM and finite-difference method (FDM) formulated on the traditional wave equation. By defining the transmission and reflection coefficients and adopting a Newton interpolation algorithm to modify the streaming process of the LBM, we have extended the conventional LBM to simulate the wavefields in complex media with acceptable accuracy. A 2D homogeneous model, two 2D layered models, and the modified Marmousi model are tested in the numerical simulation experiments. The simulation results of LBM are comparable to those of FDM, and the relative errors are all within a reasonable range, which can verify the effectiveness of the forward modeling kernel. The modified LBM offers a new numerical scheme in seismology to simulate viscoacoustic wave propagation in complex media and even in porous media considering its flexible boundary condition and high discrete characteristic.

An Adaptive High-Order Transient Algorithm to Solve Large-Scale Anisotropic Maxwell’s Equations

This article presents a stabilized nodal discontinuous Galerkin pseudospectral time-domain (DG-PSTD) algorithm for fully anisotropic electromagnetic waves. This solver permits arbitrary high-order basis functions and adaptive hexahedral elements, thus very efficient for large-scale wave propagation in complex media. Maxwell’s equations are reformulated in a unified hyperbolic form, where a localized anisotropic Riemann solver is derived to serve as a numerical flux to exchange information across adjacent elements in the DG-PSTD scheme. This local analysis method also helps impose the time-domain anisotropic plane wave incidence in the total/scattering field framework. Numerical validations and applications demonstrate the efficiency, accuracy, and capability of this new high-order solver for 3-D large-scale generally anisotropic electromagnetic media.

Statistical classification of scatterer ultrasonic signature in bio-mechanical media and spatial localization of digital data using nonlinear time reversal

Various nonlinear methods have been investigated in recent years offering improvements of over conventional B-mode in medical imaging and non-destructive testing (NDT) [1], including Nonlinear Elastic Wave Spectroscopy (NEWS) methods. Furthermore, new optimized excitations such as Nonlinear Time Reversal (TR) based methods are classified within TR-NEWS methods [2]. In this context, one of the strategic plan of the international NDT community is to define standards for developing advanced and digitalized automated NDT set-up in modern mass production, defining the concept of NDT 4.0 or NDE 4.0 [3]. In the typical NDE4.0 TR-NEWS equipment, an optimized chirp-coded signal in the range of 0.6–3 MHz is used as a compression coding. The signal classification is performed using the Fuzzy Classification (FC) method and the Divergence Decision Tree (DDT) algorithm using specific $\phi$-divergence spectral measures extracted from the received ultrasonic response containing acoustic nonlinearities. Finally, experimental setup and scatterer classification procedures have been further validated in ondotology with tooth echodentographic experiment where the ultrasonic responses to chirp-coded signals were monitored with a standard Polytec vibrometer, showing the efficiency of TR-NEWS methods for understanding of ultrasonic wave propagation in complex media.

Fractional powersof Bessel operator and its numerical calculation

The article discusses the fractional powers of the Bessel operator and their numerical implementation. An extensive literature is devoted to the study of fractional powers of the Laplace operator and their applications. Such degrees are used in the construction of functional spaces, in the natural generalization of the Schrodinger equation in quantum theory, in the construction of the models of acoustic wave propagation in complex media (for example, biological tissues) and space-time models of anomalous (very slow or very fast) diffusion, in spectral theory etc. If we assume the radiality of the function on which the Laplace operator acts, then we receive the problem of constructing the fractional power of the Bessel operator. We propose to use a compositional method for constructing the operators mentioned earlier, which leads to constructions similar in their properties to the Riesz derivatives. The Hankel transform is considered as a basic integral transformation. On its basis, the compositional method proposed by V.V. Katrakhov and S.M. Sitnik, negative powers of the Bessel operator are constructed. The resulting operator contains the Gaussian hypergeometric function in the kernel. For further study, the generalized translation operator is considered in the article, and its properties are proved. For constructing a positive fractional power of the Bessel operator known methods of regularization of the integral are considered. Then, a scheme for the numerical calculation of fractional powers of the Bessel operator is proposed. This scheme is based on the Taylor--Delsarte formula obtained by B.M. Levitan.

High-Order Locally A-Stable Implicit Schemes for Linear ODEs

Accurate simulations of wave propagation in complex media like Earth subsurface can be performed with a reasonable computational burden by using hybrid meshes stuffing fine and coarse cells. Locally implicit time discretizations are then of great interest. They indeed allow using unconditionally stable Schemes in the regions of computational domain covered by small cells. The receivable values of the time step are then increased which reduces the computational costs while limiting the dispersion effects. In this work we construct a method that combines optimized explicit Schemes and implicit Schemes to form locally implicit schemes for linear ODEs, including in particular semi-discretized wave problems that are considered herein for numerical experiments. Both the explicit and implicit schemes used are one-step methods constructed using their stability function. The stability function of the explicit schemes are computed by maximizing the time step that can be chosen. The implicit schemes used are unconditionally stable and do not necessary require the same number of stages as the explicit schemes. The performance assessment we provide shows a very good level of accuracy for locally implicit schemes. It also shows that a locally implicit scheme is a good compromise between purely explicit and purely implicit schemes in terms of computational time and memory usage.

Coda wave interferometry during the heating of deep geothermal reservoir rocks

Coda wave interferometry (CWI) is a high-resolution technique that aims at tracking small changes in a diffusive medium from the time correlation of seismic waveforms. CWI has been widely used in recent years to monitor the fine-scale evolution of fault zones and more recently of deep reservoirs. However, to provide a quantitative interpretation of the reservoir, direct modeling of physical effects like the influence of temperature on seismic wave scattering is required to investigate temperature effects from measurements of velocity changes. Here, we propose to quantify the impact of thermo-elastic deformation on CWI measurements by comparing experimental results obtained from a previous study on Westerly Granite to a numerical approach based on two combined codes (SPECFEM2D and Code_Aster) for modeling wave propagation in complex media during thermo-elastic deformation. We obtain two major results. First, we show that multiple reflections on the boundaries of our simplified numerical sample reproduce well the wave scattering properties of the experimental granitic sample characterized by a complex mineral assembly and a large set of microcracks. We based our comparison on the wave diffusion model that describes both the experimental and numerical samples (similarity in energy density function and mean free path). We also show that both samples share a similar thermo-elastic behavior, but only after the second heating and cooling cycle. Second, the stretching technique used for CWI measurements on both samples reveals reversible time shifts correlated with the thermo-elastic deformation of the sample. However, the influence of thermo-elastic deformation is different between our numerical proxy and the experimental sample. We discuss the role of irreversible deformation (e.g., microcracking) for the observed discrepancy by introducing temperature dependence of elastic moduli in the model. These results suggest that there are open perspectives to monitor thermal strain in geothermal reservoirs using CWI.

Intensity-only measurement of partially uncontrollable transmission matrix: demonstration with wave-field shaping in a microwave cavity.

Transmission matrices (TMs) have become a powerful and widely used tool to describe and control wave propagation in complex media. In certain scenarios the TM is partially uncontrollable, complicating its identification and use. In standard optical wavefront shaping experiments, uncontrollable reflections or imperfect illumination may be the cause; in reverberating cavities, uncontrollable reflections off the walls have that effect. Here we employ phase retrieval techniques to identify such a partially uncontrollable TM solely based on random intensity-only reference measurements. We demonstrate the feasibility of our method by focusing both on a single target as well as on multiple targets in a microwave cavity, using a phase-binary Spatial-Microwave-Modulator.

From Loschmidt daemons to time-reversed waves.

Time-reversal invariance can be exploited in wave physics to control wave propagation in complex media. Because time and space play a similar role in wave propagation, time-reversed waves can be obtained by manipulating spatial boundaries or by manipulating time boundaries. The two dual approaches will be discussed in this paper. The first approach uses 'time-reversal mirrors' with a wave manipulation along a spatial boundary sampled by a finite number of antennas. Related to this method, the role of the spatio-temporal degrees of freedom of the wavefield will be emphasized. In a second approach, waves are manipulated from a time boundary and we show that 'instantaneous time mirrors', mimicking the Loschmidt point of view, simultaneously acting in the entire space at once can also radiate time-reversed waves.

Optimized excitation for nonlinear wave propagation in complex media: From biomedical acoustic imaging to nondestructive testing of cultural heritage

The interaction between an acoustic wave and a complex media has an increase interest for both nondestructive testing (NDT) applications and for biomedical ultrasound. Today, new optimized excitations are generated thanks to the analysis of symmetry properties of the system such as reciprocity, nonlinear time reversal (TR) and other pulse-inverted (PI) techniques. Generalized TR based NEWS (Nonlinear Elastic Wave Spectroscopy) methods and their associate symmetry skeleton will be taken as an example. Among these family of “pulse coded excitation,” solitonic coding constitutes a new scheme in the sense that solitary waves are the best candidates for pulse propagation in nonlinear and layered media, such as tooth or skin. As another application of mixing properties in a wide frequency range, new broadband techniques are needed in the domain of the preservation of cultural heritage. The analysis of the composition of the stones is one of the key parameters in the study of aging historic buildings. The use of TR-NEWS based analysis combined with a FTIR-based system has shown a specific property of the tuffeau limestone where damaged sample contains calcite. In both domains, aging properties of complex medium are extracted thanks to the use of enhanced nonlinear signal processing tools.

Sensors, dynamics, and control: Program overview and relevance to acoustics research

The talk will provide an overview of the sensors, dynamics, and control program, its goals, its funding levels, and its priorities. Specifically, the talk will address topics and research directions that are relevant to the acoustics community at large. Such topics include vibration and noise control, dynamic-based structural health monitoring, wave propagation in complex media, nonlinear dynamics, and acoustic metamaterials. Examples of currently funded projects and ideas for future investigations will be provided to facilitate the discussion. The SDC program supports fundamental research on the analysis, measurement, monitoring, and control of dynamic systems, including development of new analytical, computational and experimental tools, and novel applications to engineered and natural systems. Dynamics is the science of systems that change in time. Control concerns the use of external influences to produce desired dynamic behaviors. Diagnostics concerns the use of observation to infer information about a dynamic system. Objectives of the SDC program are the discovery of new phenomena and the investigation of innovative methods and applications in dynamics, control and diagnostics. The intellectual merit of proposals submitted to the SDC program will be evaluated on the basis of fundamental innovation in foundational areas, on alignment with the core disciplines of the CMMI Division, and on potential for transformative impact within and across disciplinary boundaries.

Numerical simulations of elastic wave propagation using graphical processing units—Comparative study of high-performance computing capabilities

Abstract High-performance computing is important in many areas of engineering. Increasing capabilities of modern workstations open new possibilities in scientific computing. This paper demonstrates how graphical processing units can be used efficiently for large models of elastic wave propagation in complex media. The method is based on the local interaction simulation approach and a parallel algorithm architecture. The focus of the work presented is on numerical implementation and covers aspects related to software modular architecture, computer memory organisation and optimisation. A domain decomposition approach allowing for calculations using multiple-GPU configurations is proposed, implemented and examined. The performance of the proposed simulation framework is tested for numerical models of different sizes, various computing precisions and hardware platforms. The results obtained are discussed in terms of graphical processing unit limitations. Obtained results indicate significant speed-up factors comparing to calculations using central processing units or different modelling approaches.

Fast Fourier homogenization for elastic wave propagation in complex media

In the context of acoustic or elastic wave propagation, the non-periodic asymptotic homogenization method allows one to determine a smooth effective medium and equations associated with the wave propagation in a given complex elastic or acoustic medium down to a given minimum wavelength. By smoothing all discontinuities and fine scales of the original medium, the homogenization technique considerably reduces meshing difficulties as well as the numerical cost associated with the wave equation solver, while producing the same waveform as for the original medium (up to the desired accuracy). Nevertheless, finding the effective medium requires one to solve the so-called “cell problem”, which corresponds to an elasto-static equation with a finite set of distinct loadings. For general elastic or acoustic media, the cell problem is a large problem that has to be solved on the whole domain and its resolution implies the use of a finite element solver and a mesh of the fine scale medium. Even if solving the cell problem is simpler than solving the wave equation in the original medium (because it is time and source independent, based on simple tetrahedral meshes and embarrassingly parallel) it is still a challenge. In this work, we present an alternative method to the finite element approach for solving the cell problem. It is based on a well-known method designed by H. Moulinec and P. Suquet in 1998 in structural mechanics. This iterative technique relies on Green functions of a simple reference medium and extensively uses Fast Fourier Transforms. It is easy to implement, very efficient and relies on a simple regular gridding of the medium. Through examples we show that the method gives excellent results, even, under some conditions, for discontinuous media.

Residual homogenization for elastic wave propagation in complex media

In the context of elastic wave propagation, the non-periodic homogenization asymptotic method allows to find a smooth effective medium and equations that correspond to the wave propagation in a given complex elastic or acoustic medium down to a given minimum wavelength. By smoothing all discontinuities and fine scales of the original medium, the homogenization technique considerably reduces meshing difficulties as well as the numerical cost associated with the wave equation solver, while producing the same waveform as for the original medium (up to the wanted accuracy). We present here a variation of the original method, allowing to homogenize the difference, or residual, between an original medium and a reference medium. This makes it possible to, for example, homogenize some specific parts of a model or to leave unchanged a specific interface while homogenizing the rest of the model. We present two examples of applications, one implying a complex geological shallow structure and the other involving the combination of deterministic and stochastic elastic models.

Attenuated Fractional Wave Equations With Anisotropy.

This paper develops new fractional calculus models for wave propagation. These models permit a different attenuation index in each coordinate to fully capture the anisotropic nature of wave propagation in complex media. Analytical expressions that describe power law attenuation and anomalous dispersion in each direction are derived for these fractional calculus models.

Spectral-element simulations of elastic wave propagation in exploration and geotechnical applications

We apply the spectral-element method (SEM), a high-order finite-element method (FEM) to simulate seismic wave propagation in complex media for exploration and geotechnical problems. The SEM accurately treats geometrical complexities through its flexible FEM mesh and accurately interpolates wavefields through high-order Lagrange polynomials. It has been a numerical solver used extensively in earthquake seismology. We demonstrate the applicability of SEM for selected 2D exploration and geotechnical velocity models with an open-source SEM software package SPECFEM2D. The first scenario involves a marine survey for a salt dome with the presence of major internal discontinuities, and the second example simulates seismic wave propagation for an open-pit mine with complex surface topography. Wavefield snapshots, synthetic seismograms, and peak particle velocity maps are presented to illustrate the promising use of SEM for industrial problems.

Comparison between experimental and 2-D numerical studies of multiple scattering in Inconel600® by means of array probes

Ultrasonic non-destructive testing of polycrystalline structures can be disturbed by scattering at grain boundaries. Understanding and modeling this so-called “structural noise” is crucial for characterization as well as detection purposes. Structural noise can be considered as a fingerprint of the material under investigation, since it contains information about its microstructure. The interpretation of experimental data necessitates an accurate comprehension of complex phenomena that occur in multiple scattering media and thus robust scattering models. In particular, numerical models can offer the opportunity to realize parametrical studies on controlled microstructures. However, the ability of the model to simulate wave propagation in complex media must be validated. In that perspective, the main objective of the present work is to evaluate the ability of the finite-element code ATHENA 2D to reproduce typical features of multiple wave scattering in the context of ultrasonic non-destructive evaluation, with an array of sources and receivers. Experiments were carried out with a 64-element array, around 2MHz. The sample was a mock-up of Inconel600® exhibiting a coarse grain structure with a known grain size distribution. The numerical model of this microstructure is based on Voronoi diagrams. Two physical parameters were used to compare numerical and experimental data: the coherent backscattering peak, and the singular value distribution of the array response matrix. Though the simulations are 2-D, a good agreement was found between simulated and experimental data.

NUMERICAL AND ULTRASONIC EXPERIMENTAL SIMULATIONS OF ELASTIC WAVE PROPAGATION AROUND HOLLOW CYLINDER

A laser-ultrasonic experimental setup was used to study, at a reduced scale, the wave propagation inside and around fluid-filled wells. Simulations tools were also developed and calibrated from comparisons with experimental signals. These tools serve as a connection to realistic scale. A semi-analytical approach, the discrete wave number method was first used to compute signals in a simplified geometrical configuration. This method is fast enough to be used in the identification of the main parameters that describe at best the experimental signals. Then a finite difference scheme was implemented in order to describe accurately the actual well. The two methods describe the attenuation mechanisms by using the Kelvin–Voigt model for the solid and the Maxwell model for the fluid. Comparisons between numerical and experimental waveforms, obtained in the two fundamental elastic configurations: the fast and the slow formations, show very good agreement in arrival times, waveforms and relative amplitudes. This satisfactory result provides insights useful for the recognition and interpretation of wave propagation in complex media. Such is the case of modern sonic-logging technology.