Wave Propagation In Inhomogeneous Media Research Articles

MODELING OF POROUS DRY MATERIALS USING RHEOLOGICALDYNAMICAL ANALOGY

<p class="ABSTRACT">A theoretical model for porous viscoelastoplastic (VEP) materials under dry conditions is examined based on the principles of mass and energy conservation using rheological-dynamical analogy (RDA). The model provides the expressions for the creep coefficient, Poisson's ratio, modulus of elasticity, damage variable and strength in the function of porosity and/or void volume fraction (VVF). Compared with numerous versions of acoustic emission monitoring developed to analyze the behavior of the total wave propagation in inhomogeneous media with density variation, the RDA model is found to be comprehensive in interpretation and consistent with physical understanding. The reliability of the proposed model is confirmed by the comparison of numerical results with experimental ones on hardened concrete and rocks.</p>

Modeling of porous-hardened concrete by rheological-dynamical analogy

PurposeThe purpose of this paper is to describe various aspects of the visco-elastoplastic (VEP) behavior of porous-hardened concrete samples in relation to standard tests.Design/methodology/approachThe problem is formulated on the basis of the rheological-dynamic analogy (RDA). In this study, changes in creep coefficient, Poisson's ratio, damage variables, modulus of elasticity, strength and angle of internal friction as a function of porosity are defined by P and S wave velocities. The RDA model provides a description of the degradation process of material properties from their peak state to their ultimate values using void volume fraction (VVF).FindingsCompared to numerous versions of acoustic emission tracking developed to analyze the behavior of total wave propagation in inhomogeneous media with density variations, the proposed model is comprehensive in interpretation and consistent with physical understanding. The comparison of the damage variables with the theoretical variables under the assumption of spherical voids in the spherical representative volume element (RVE) shows a satisfactory agreement of the results for all analyzed samples if the maximum porosities are used for comparison.Originality/valueThe paper presents a new mathematical-physical method for examining the effect of porosity on the characteristics of hardened concrete. Porosity is essentially related to density variations. Therefore, it was logical to define the limit values of porosity using the strain energy density.

A hybrid implicit-explicit discontinuous Galerkin spectral element time domain (DG-SETD) method for computational elastodynamics

SUMMARY A hybrid implicit-explicit (IMEX) discontinuous Galerkin spectral element time domain (DG-SETD) algorithm is proposed to simulate 3D elastic wave propagation in inhomogeneous media. In this method, the original problem can be divided into a number of well designed subdomains, and the mesh generation of different subdomains is completely independent, thus allowing flexible spatial discretization of complex geometry. The neighboring subdomains are connected by a Riemann transmission condition (RTC), and spectral elements with different interpolation orders can be used in different subdomains to maximize the computational efficiency of multiscale problems to facilitate parallel computing for different subdomains. In particular, the explicit or implicit time iteration scheme can be appropriately selected for a subdomain according to the size of its mesh elements to increase the global time step increment, thus giving higher computational efficiency: For subdomains with coarse meshes, the explicit time integration scheme is used and the time step increment is limited by the Courant−Friedrichs−Lewy (CFL) stability condition; for subdomain with fine structures and thus fine meshes, an implicit time integration scheme is used so that a large time step increment can be used without affecting the stability. In addition, a jump condition of displacement and velocity is introduced to accurately simulating fractures and faults, including lossless and viscous fractures with plane, curve or cross structures. This avoids the volume modeling of the extremely thin fracture structures, and effectively reduces the number of degrees of freedoms (DoFs) in the discretized system without the loss of accuracy. The accuracy, robustness and efficiency of the DG-SETD algorithm are demonstrated by quantitative comparisons of the waveforms with the commercial finite element software COMSOL.

Existence and regularity results for semilinear stochastic time-tempered fractional wave equations with multiplicative Gaussian noise and additive fractional Gaussian noise

To model wave propagation in inhomogeneous media with frequency-dependent power-law attenuation, it is needed to use the fractional powers of symmetric coercive elliptic operators in space and the Caputo tempered fractional derivative in time. The model studied in this paper is semilinear stochastic space-time fractional wave equations driven by infinite dimensional multiplicative Gaussian noise and fractional Gaussian noise, because of the potential fluctuations of the external sources. We first give a representation of the mild solution and some stability estimates for the homogeneous problem, and then prove the existence and uniqueness of the mild solution by using fixed point theorem. Finally, the decay and regularity theory of the solution are provided.

MATRIX-MFO Tandem Workshop/Small Collaboration: Rough Wave Equations

The consideration of wave propagation in inhomogeneous media or the modelling of nonlinear waves often requires the study of wave equations with low regularity data and/or coefficients. Several Australian-European collaborations have recently led to deeper analytical understanding of rough wave equations. This tandem workshop provided a platform for such collaborations and brought together early career researchers and leading experts in harmonic analysis, microlocal analysis and spectral theory. The workshop focused on collaboration and technical knowledge exchange on topics such as local smoothing, spectral multipliers, restriction estimates, Hardy spaces for Fourier integral operators, and nonlinear partial differential equations.

Wave propagation in inhomogeneous media via FE/PML method

AbstractThe Perfectly Matched Layer (PML) method is an efficient approach to imposing radiation conditions at the bounded region of interest in case of wave propagation in unbounded domains. This paper presents and validates 3D FE/PML numerical schemes based on two different PML formulations for homogeneous and inhomogeneous geological media exhibiting discrete or continuous inhomogeneity. In the equation of motion for the PML domain the applied stretching behavior is expressed either as complex material properties or as complex coordinates. Both PML formulations are implemented in the FEM and verified against analytical solutions. Three different types of material inhomogeneity are considered: layered half‐space, continuously inhomogeneous half‐space with linear velocity profile and continuously inhomogeneous half‐space with nonlinear velocity profile. Sensitivity analyses are conducted, and the performance of the developed numerical schemes is investigated taking into account a broad variation of the PML parameters. Recommendations are given for the optimal values of the PML parameters for the case of homogeneous and inhomogeneous geological media.

Physics-informed Supervised Residual Learning for Electromagnetic Modeling

In this paper, we propose a non-stationary iterative physics-informed supervised residual learning scheme (NSIP-ISRL) as a general framework for modeling electromagnetic wave propagation in inhomogeneous medium. NSIPISRL is based on the residual neural network (ResNet) that maps the residuals of matrix equation to the update of solutions [1]. It incorporates the concept of non-stationary iterative method, in which physical principles are embedded in the solution process through matrix-vector multiplication. NSIPISRL is applied to solve 2D volume integral equations in order to model electromagnetic wave interaction with lossy scatterers. The results show that NSIPISRL has a good accuracy and a strong generalization ability. The trained network can be applied to various scenarios with different scatterers, different incident angles, and different frequencies and still maintain a good accuracy.

Comparison of distributed memory algorithms for X-ray wave propagation in inhomogeneous media.

Calculations of X-ray wave propagation in large objects are needed for modeling diffractive X-ray optics and for optimization-based approaches to image reconstruction for objects that extend beyond the depth of focus. We describe three methods for calculating wave propagation with large arrays on parallel computing systems with distributed memory: (1) a full-array Fresnel multislice approach, (2) a tiling-based short-distance Fresnel multislice approach, and (3) a finite difference approach. We find that the first approach suffers from internode communication delays when the transverse array size becomes large, while the second and third approaches have similar scaling to large array size problems (with the second approach offering about three times the compute speed).

Analysis of transient wave propagation in inhomogeneous media using edge-based gradient smoothing technique and bathe time integration method

As is known to all, the classical finite element method (FEM) always fails to effectively solve the wave problems in the relatively large wave numbers due to the troublesome numerical error issue. In this paper, the standard FEM with edge-based gradient smoothing technique and Bathe time integration method is developed to analyze the transient wave propagation problems in inhomogeneous media. We explicitly show that the numerical error of the calculated solutions for transient wave propagation problems consists of two different parts, namely the spatial discretization error and the temporal discretization error. Due to the edge-based gradient smoothing technique and the appropriate numerical dissipation effects from Bathe time integration scheme, it is found that the total numerical error can be significantly suppressed and more accurate numerical solutions can be obtained. Several typical numerical examples have been conducted to examine the capacity of the proposed method in solving transient wave propagation problems in inhomogeneous media.

Transient wave propagation in inhomogeneous media with enriched overlapping triangular elements

We study and use overlapping triangular finite elements enriched by trigonometric functions and implicit time integration to solve transient wave propagations in inhomogeneous media. We show explicitly that the total dispersion error of the calculated solutions can be split into two parts, the spatial error and temporal error. The study of the spatial dispersion error shows the effectiveness of the enriched overlapping finite elements compared to the traditional finite elements and the overlapping finite elements without enrichment. The study of the temporal error of the Bathe time integration scheme shows monotonic convergence to zero with decreasing time step size. The result is that we see monotonic convergence to exact solutions as the mesh of enriched overlapping finite elements is refined and the time step is decreased. We demonstrate the effectiveness of using the proposed scheme in the solution of waves traveling in inhomogeneous media at different speeds, where reflected and transmitted waves are predicted accurately by “simply” using a fine enough mesh and small enough time step.

RETRACTED: A hybrid Finite element-Meshfree method based on partition of unity for transient wave propagation problems in homogeneous and inhomogeneous media

This article has been retracted: please see Elsevier Policy on Article Withdrawal ( https://www.elsevier.com/about/our-business/policies/article-withdrawal ). This article has been retracted at the request of the Editor-in-Chief and the authors. There is duplication between this Applied Mathematical Modelling article and a subsequent paper by the one of the authors, Dr. Y. Chai with Professor K.J. Bathe as co-author: ‘Transient wave propagation in inhomogeneous media with enriched overlapping triangular elements’, Comput. Struct. 237(2020) 106273. DOI: doi.org/10.1016/j.compstruc.2020.106273. Although a completely different numerical method is used for spatial discretization in the earlier Applied Mathematical Modelling paper, several specific and important derivations were done by Dr. Y. Chai and Professor K.J Bathe, and the Applied Mathematical Modelling paper benefited during its revision from this collaboration before later on publishing their joint paper. The authors apologize for their mistake and for any inconvenience this may have caused to readers and researchers citing this paper.

Time-Dependent One-Dimensional Electromagnetic Wave Propagation in Inhomogeneous Media: Exact Solution in Terms of Transmutations and Neumann Series of Bessel Functions

The time-dependent Maxwell system describing electromagnetic wave propagation in inhomogeneous isotropic media in the one-dimensional case reduces to a Vekua-type equation for bicomplex-valued functions of a hyperbolic variable, see [7]. In [5] using this reduction a representation of a general solution of the system was obtained in terms of a couple of Darboux-associated transmutation operators [8]. In [6] a Fourier–Legendre expansion of transmutation integral kernels was obtained. This expansion is used in the present work for obtaining an exact solution of the problem of the transmission of a normally incident electromagnetic time-dependent plane wave through an arbitrary inhomogeneous layer. The result can be used for efficient computation of the transmitted modulated signals. In particular, it is shown that in the classical situation of a signal represented in terms of a trigonometric Fourier series the solution of the problem can be written in the form of Neumann series of Bessel functions with exact formulas for the coefficients. The representation lends itself to numerical computation.

Method of Spherical Phase Screens for Modeling the Propagation of Diverging Beams in Inhomogeneous Media

The phase-screen (split-step) method is widely used for modeling wave propagation in inhomogeneous media. The method of plane phase screens is best known. However, for modeling a 2D problem of radio occultation sounding of the Earth’s atmosphere, the method of cylindrical phase screen was developed many years ago. In this paper, we propose a further generalization of this method for the 3D problem on the basis of spherical phase screens. In the paraxial approximation, we derive the formula for the vacuum screen-to-screen propagator. We also infer the expression for the phase thickness of a thin layer of aisotropic random media. We describe a numerical implementation of this method and give numerical examples of its application for modeling a diverging laser beam propagating on a 25-km-long atmospheric path.

Extra-wide-angle parabolic equation for wave propagation in inhomogeneous media

To describe wave propagation at large angles with respect to a nominal direction, wide-angle parabolic equations (WAPEs) have been widely used in atmospheric and ocean acoustics, geophysics, electromagnetic wave propagation, and other fields of physics. This paper considers an application of an extra-wide-angle parabolic equation (EWAPE) for such problems. For small variations of the refractive index of a medium, the EWAPE describes wave propagation up to 90 deg with respect to the nominal direction and is more general than the WAPEs used in the literature. The EWAPE can be written in an integral form or as a pseudo-differential equation and may be solved by a split-step spectral algorithm or the Padé series expansions of the pseudo-differential operators. The EWAPE is also generalized to large variations in the refractive index, sound propagation above an impedance boundary, and a moving medium with small or large Mach numbers. For sound propagation in a moving medium, the EWAPE enables derivation of new WAPEs which are accurate and simpler to implement than those currently available in the literature. Numerical examples illustrating the application of these new WAPEs to sound propagation in a moving atmosphere are presented.

A multiscale method for wave propagation in 3D heterogeneous poroelastic media

A new multiscale method for wave simulation in 3D heterogeneous poroelastic media is developed. Wave propagation in inhomogeneous media involves many different scales of media. The physical parameters in the real media usually vary greatly within a very small scale. For the direct numerical methods for wave simulation, a refined grid is required in mesh generation to maintain the match between the mesh size and the material variations in the spatial scale. This greatly increases the computational cost and computer memory requirements. The multiscale method can overcome this difficulty due to the scale difference. The basic idea of our multiscale method is to construct computational schemes on two sets of meshes, i.e., coarse grids and fine grids. The finite-volume method is applied on the coarse grids, whereas the multiscale basis functions are computed with the finite-element method by solving a local problem on the fine grids. Moreover, the local problem only needs to be solved once before time stepping. This allows us to use a coarse grid while still capturing the information of the physical property variations in the small scale. Therefore, it has better accuracy than the single-scale method when they use the same coarse grids. The theoretical method and the dispersion analysis are investigated. Numerical computations with the perfectly matched layer boundary conditions are completed for 3D inhomogeneous poroelastic models with randomly distributed small scatterers. The results indicate that our multiscale method can effectively simulate wave propagation in 3D heterogeneous poroelastic media with a significant reduction in computation cost.

A Novel and Systematic Approach to Inhomogeneous Dielectric Lens Design Based on Curved Ray Geometrical Optics and Particle Swarm Optimization

A numerical synthesis algorithm is presented to design inhomogeneous 3-D-printed lenses for any aperture field and, hence, beam pattern. The algorithm is based on geometrical optics (GO), a numerical method for wave propagation in inhomogeneous media, particle swarm optimization, and a global stochastic optimization technique. The approach allows the synthesis of either optimal geometry with known constant permittivity (shape only), optimal nonconstant permittivity with known geometry (material only), or optimal geometry and nonconstant permittivity (shape and material). The presented approach is validated against the analytic test case of the Maxwell fish eye and is shown to provide excellent agreement. A spherical lens is optimized for nonconstant permittivity function and is shown to recover the permittivity of the Luneburg lens. Instructions on how to fabricate the resultant inhomogeneous lenses via 3-D-printing techniques is given. Examples of optimum inhomogeneous lenses synthesized with our approach are provided along with the full-wave simulation verification. A 30 cm inhomogeneous lens is fabricated via 3-D-printing and measured in the UCLA’s plane bipolar near-field measurement range and compared with the results of the GO algorithm.

Gradient index phononic crystals and metamaterials

Abstract Phononic crystals and acoustic metamaterials are periodic structures whose effective properties can be tailored at will to achieve extreme control on wave propagation. Their refractive index is obtained from the homogenization of the infinite periodic system, but it is possible to locally change the properties of a finite crystal in such a way that it results in an effective gradient of the refractive index. In such case the propagation of waves can be accurately described by means of ray theory, and different refractive devices can be designed in the framework of wave propagation in inhomogeneous media. In this paper we review the different devices that have been studied for the control of both bulk and guided acoustic waves based on graded phononic crystals.

An Immersed Discontinuous Galerkin Method for Acoustic Wave Propagation in Inhomogeneous Media

We present an immersed discontinuous Galerkin finite element method on Cartesian meshes for two dimensional acoustic wave propagation problems in inhomogeneous media where elements are allowed to b...

Method of spherical phase screens for the modeling of propagation of diverging beams in inhomogeneous media

The phase-screen (split-step) method is widely used for the modeling of wave propagation in inhomogeneous media. Most known is the method of flat phase screens. An optimized approach based on cylindrical phase screen was introduced for the 2-D modeling of radio occultation sounding of the Earth’s atmosphere. In this paper, we propose a further generalization of this method for the 3-D problem of propagation of diverging beams. Our generalization is based on spherical phase screens. In the paraxial approximation, we derive the formula for the vacuum screen- to-screen propagator. We also derive the expression for the phase thickness of a thin layer of an isotropic random media. We describe a numerical implementation of this method and give numerical examples of its application for the modeling of a diverging laser beam propagating on a 25 km long atmospheric path.

Received signal strength based localization in inhomogeneous underwater medium

Abstract Localization is one of the fundamental tasks in underwater acoustic sensor network (UASN) which is a challenging issue due to inhomogeneity and bandwidth limitation of underwater medium. Time of flight (TOF) and received signal strength (RSS) measurements are two major techniques used for localization. The TOF based localization achieves high resolution when available bandwidth is high enough and also transmitter and receiver can be synchronized well. However, in the RSS, sensors do not need to be synchronized. In this paper we propose a new RSS based localization method for inhomogeneous underwater medium with an isogradient sound speed profile in which acoustic waves propagate along curvature path. To develop the localization algorithm, at the first step, we obtain the relation of transmission loss for acoustic wave propagation in inhomogeneous medium. Then, an oversampled matched filter based method for RSS measurement (OSMF-RSS) is proposed in asynchronous transmitter–receiver scenario. After that, an iterative localization algorithm is derived based on the RSS measurements. Moreover, we examine how the performance of our proposed algorithm affects by flat fading phenomenon which is a challenge of RSS based algorithms. We evaluate the performance of the proposed OSMF-RSS method by computer simulations under different conditions. The results show that the OSMF-RSS method outperforms the TOF based method in accuracy sense when the bandwidth of received signal is less than specific level. Note that, this achievement of the OSMF-RSS method is attained in asynchronous scenario, while in the TOF method transmitter–receiver should be synchronized.