Homogeneous Anisotropic Layers Research Articles

Couette–Poiseuille flow of variable viscosity in a multilayered channel partially filled with a homogeneous anisotropic porous layer: Role of the glycocalyx in attenuating shear stress on endothelial cells

We present an analytical solution for the Couette–Poiseuille flow of variable viscosity in a multilayered channel partially filled with a homogeneous anisotropic porous layer. We establish a critical criterion that dictates the dominating factor when the flow is under the influence of shear and pressure gradient combined. This multilayered system resembles blood flow inside an artery where the fluid layer 1, fluid layer 2, and anisotropic porous layer describe the red blood cell layer, plasma layer, and glycocalyx layer, respectively. One of the novel features of this work is to understand the shear stress distribution on the liquid–porous interface (plasma membrane) and the bottom plate (endothelial cell layer) considering the variable viscosity of the fluid layer 1 while accounting for the anisotropic permeability of the porous medium. We use the obtained analytical solution to investigate the effect of the glycocalyx layer on the transmission of the fluid shear stress to the endothelial cell layer. We perceive that the shear stress distribution is more effective at the outer edge of the glycocalyx (plasma membrane) than the endothelial cell layer. On the other hand, the impact of the anisotropy on the shear stress distribution is more significant on the endothelial cell layer. This model is amenable to analytical solutions of the multilayered system considering the variable viscosity property of the blood and providing a framework for designing microfluidic systems that replicate biological glycocalyx, such as glycocalyx scaffolding.

Additively-Manufactured All-Dielectric Microwave Polarization Converters Using Ceramic Stereolithography

We report a class of all-dielectric, additively-manufactured polarization converters with tailored temporal frequency responses within the Ku and Ka microwave bands (15 – 40 GHz). These multi-layer devices consist of cascaded, subwavelength, high-contrast gratings with different fill fractions and orientations, providing control over the effective anisotropic properties of each layer. In design, the subwavelength gratings are modeled as homogeneous anisotropic layers. This allows the overall metastructure to be treated as a stratified dielectric medium. Therefore, it can be analyzed and optimized using plane-wave transfer matrix techniques that fully account for multiple reflections between layers. Using this cascaded grating geometry, a variety of high-efficiency microwave polarization converters can be realized with broadband, multiband, or multifunctional behavior. The transmissive metastructures do not require anti-reflection layers since impedance matching is incorporated into their design. Three example devices based on alumina/air gratings have been monolithically fabricated using ceramic stereolithography: a broadband reflective half-wave plate, a broadband isotropic polarization rotator, and a dual-band linear-to-circular polarization converter.

Guided waves in periodically stratified plates: Deficiency of homogenizations

The problem of dispersion of guided waves propagating in stratified composite plates containing layers with alternating physical properties is analyzed by using combination of sextic formalism Cauchy, exponential fundamental matrices and Thomson – Haskell method for constructing transfer matrices. The developed method is applicable to analyzing stratified media containing homogeneous anisotropic periodic layers with arbitrary elastic anisotropy.It is revealed that the dispersion portraits of guided waves in plates containing even (asymmetric layout) or odd (symmetric layout) number of alternating layers are significantly different, remaining different even at large number of alternating layers. It is also found that the observed discrepancy between even and odd sets should in principle, be persistent for any composite plates with odd and even numbers of alternating layers. The latter circumstance prevents application of the existing methods of homogenization for obtaining dispersion portraits of guided waves in the stratified media with alternating layers.

Traveltime parameters in tilted orthorhombic medium

Traveltime parameters, defined through the series coefficients of the traveltime squared as a function of the horizontal offset projections, play an important role in moveout approximations and corrections, and in model parameter inversion. We evaluate an approach to derive the traveltime parameters in a single homogeneous anisotropic layer of tilted orthorhombic symmetry for one- and two-way traveling waves. The approach allows us to obtain the traveltime parameters of pure and converted modes. We use numerical models to illustrate the dependence of the high-order traveltime parameters on the Euler angles and the anisotropy parameters. The traveltime parameter inversion is a strongly ill-posed problem in anisotropic media, and improvements due to inclusion of the high-order traveltime parameters can sufficiently reduce the space of equivalent kinematic models. We perform a numerical model parameter inversion using the concept of artificial neural networks to demonstrate the accuracy improvements due to inclusion of the high-order traveltime parameters over the inversion of the second-order coefficient, conventionally known as normal moveout velocity, only. We demonstrate algebraically and numerically that the presented approach to calculate the traveltime parameters is easily extended to multilayered media. It can be used for Dix-type inversion to obtain the interval medium parameters.

Allowing for inhomogeneous anisotropy of a welded joint when reconstructing reflector images from echo signals received by an ultrasonic antenna array

In order to improve the quality of reflector images in welded joints, a modification of the C-SAFT algorithm has been proposed that allows for inhomogeneous anisotropic properties of a test object. Two algorithms have been considered for calculating the times of delay of propagation of a pulse along a ray, viz. a geometrical ray-construction algorithm and an algorithm based on the ray tube description. The geometrical algorithm proceeds from the assumption that an inhomogeneous anisotropic medium can be divided into a set of homogeneous anisotropic layers. Ray construction is performed with allowance for ray refraction on the boundaries of these layers. The geometrical algorithm makes it possible to allow for two types of waves, their conversion, and uneven boundaries of the domains in the test object. Special cases of ray propagation have been considered that demonstrate limitations of calculating delay times by geometrical tracing. The algorithm based on the ray tube description is more versatile and makes it possible to calculate not only the propagation time of a pulse along a ray in an inhomogeneous anisotropic medium but also the pulse amplitude. The operability of the proposed approach has been demonstrated by numerical experiments on processing echo signals that have been calculated by the method of finite differences in a time domain.

Analysis of the Out-of-Plane Coordinate Transformation to Obtain Anisotropic Layered Cloaks

A possible strategy for avoiding singular material parameters in a transformation-based invisibility cloak involves an out-of-plane stretching, calculated to compensate the in-plane singular transformation. In this paper, we used numerical simulations to analyze the relation among the out-of-plane transformation, the resulting material anisotropy, and the total scattering cross width. Moreover, we show how this information can be used to optimize a cloak with homogeneous anisotropic layers.

Approximate electromagnetic cloaking of a conducting cylinder using homogeneous isotropic multi-layered materials

Cloaking refers to hiding a body from detection by surrounding it with a coating consisting of an unusual anisotropic nonhomogeneous material. Its function is to deflect the rays that would have struck the object, guide them around the object, and return them to their original trajectory, thus no waves are scattered from the body. The permittivity and permeability of such a cloak are determined by the coordinate transformation of compressing a hidden body into a point or a line. Some components of the electrical parameters of the cloaking material (ɛ, μ) are required to have infinite or zero value at the boundary of the hidden object. Approximate cloaking can be achieved by transforming the cylindrical body (dielectric and conducting) virtually into a small cylinder rather than a line, which eliminates the zero or infinite values of the electrical parameters. The radially-dependent cylindrical cloaking shell can be approximately discretized into many homogeneous anisotropic layers; each anisotropic layer can be replaced by a pair of equivalent isotropic sub-layers, where the effective medium approximation is used to find the parameters of these two equivalent sub-layers. In this work, the scattering properties of cloaked perfectly conducting cylinder is investigated using a combination of approximate cloaking, together with discretizing the cloaking material using pairs of homogeneous isotropic sub-layers. The solution is obtained by rigorously solving Maxwell equations using angular harmonics expansion. The scattering pattern, and the back scattering cross section against the frequency are studied for both transverse magnetic (TMz) and transverse electric (TEz) polarizations of the incident plane wave for different transformed body radii.

Novel electromagnetic modeling approach of carbon fiber-reinforced polymer laminate for calculation of eddy currents and eddy current testing signals

Due to the heterogeneous nature and electric anisotropy, it is challenging to establish a numerical model to analyze the electromagnetic properties of multilayer carbon fiber-reinforced polymer (CFRP) laminate. In this study, we focus on the exploration of an effective electromagnetic modeling approach for calculation of eddy currents in CFRP laminate composite, as well as eddy current testing signals due to surface cracks. In order to prove the feasibility of modeling CFRP laminate with homogeneous anisotropic layers, the electrical parameters in the three directions are measured, and eddy current path in CFRP is investigated according to the measurement results. A finite element solver based on reduced magnetic vector potential ( A r) formulation and edge elements is developed to enable the eddy current simulation of anisotropic CFRP material, which avoids matching the discretization of source coils with the rest of conductor mesh, and can easily solve the field continuity problem in the interface between two adjacent fiber layers of CFRP laminate. The A r formulation and way to calculate the eddy current testing signals are described. To validate of the developed simulation code, a comparison is conducted between the calculated signals and experimental results of thin-opening cracks in a CFRP test piece, which indicates the simulation code can predict eddy current testing signals with good precision.

Optical characterization of free electron concentration in heteroepitaxial InN layers using Fourier transform infrared spectroscopy and a 2 × 2 transfer-matrix algebra

Fourier Transform Infrared (FTIR) reflectance spectroscopy has been implemented as a non-destructive, non-invasive, tool for the optical characterization of a set of c-plane InN single heteroepitaxial layers spanning a wide range of thicknesses (30–2000 nm). The c-plane (0001) InN epilayers were grown by plasma-assisted molecular beam epitaxy (PAMBE) on GaN(0001) buffer layers which had been grown on Al2O3(0001) substrates. It is shown that for arbitrary multilayers with homogeneous anisotropic layers having their principal axes coincident with the laboratory coordinates, a 2 × 2 matrix algebra based on a general transfer-matrix method (GTMM) is adequate to interpret their optical response. Analysis of optical reflectance in the far and mid infrared spectral range has been found capable to discriminate between the bulk, the surface and interface contributions of free carriers in the InN epilayers revealing the existence of electron accumulation layers with carrier concentrations in mid 1019 cm−3 at both the InN surface and the InN/GaN interface. The spectra could be fitted with a three-layer model, determining the different electron concentration and mobility values of the bulk and of the surface and the interface electron accumulation layers in the InN films. The variation of these values with increasing InN thickness could be also sensitively detected by the optical measurements. The comparison between the optically determined drift mobility and the Hall mobility of the thickest sample reveals a value of rH = 1.49 for the Hall factor of InN at a carrier concentration of 1.11 × 1019 cm−3 at 300° Κ.

Approximate Electromagnetic Cloaking of a Dielectric Sphere Using Homogeneous Isotropic Multi-Layered Materials

In cloaking, a body is hidden from detection by surrounding it by a coating consisting of an unusual anisotropic nonhomogeneous material. The permittivity and permeability of such a cloak are determined by the coordinate transformation of compressing a hidden body into a point or a line. The radially-dependent spherical cloaking shell can be approximately discretized into many homogeneous anisotropic layers; each anisotropic layer can be replaced by a pair of equivalent isotropic sub-layers, where the effective medium approximation is used to find the parameters of these two equivalent sub-layers. In this work, the scattering properties of cloaked dielectric sphere is investigated using a combination of approximate cloaking, where the dielectric sphere is transformed into a small sphere rather than to a point, together with discretizing the cloaking material using pairs of homogeneous isotropic sub-layers. The back-scattering normalized radar cross section, the scattering patterns are studied and the total scattering cross section against the frequency for different number of layers and transformed radius.

Approximate Electromagnetic Cloaking of Spherical Bodies Using Nonlinear Transformation with Improved Total Scattering

Cloaking refers to hiding a body from detection by surrounding it with a coating consisting of an unusual anisotropic nonhomogeneous material. The permittivity and permeability of such a cloak are determined by the coordinate transformation of compressing a hidden body into a point or a line. In this work, the scattering properties of cloaked spherical bodies (conducting and dielectric) are investigated using a combination of approximate cloaking, where the conducting sphere is transformed into a small sphere rather than to a point, and using two types of nonlinear transformations; concave-up and concave-down. The radially-dependent spherical cloaking shell is approximately discretized into many homogeneous anisotropic layers, provided that the thickness of each layer is much less than the wavelength, and this discretization raises the level of scattering as the number of layers decreases. Each anisotropic layer can be replaced by a pair of equivalent isotropic sub-layers, where the effective medium approximation is used to find the parameters of these two equivalent sub-layers. The effect of nonlinearity in the coordinate transformation on the scattering performance is studied. The back-scattering normalized radar cross section, the scattering pattern are studied and the total scattering cross section against the frequency for different number of layers and transformed radius.

Electromagnetic Scattering by Approximately Cloaked Cylindrical Bodies Using Homogeneous Isotropic Multi-Layered Materials

In cloaking, a body is hidden from detection by surrounding it by a coating consisting of an unusual anisotropic nonhomogeneous material. Its function is to deflect the rays that would have struck the object, guide them around the object, and return them to their original trajectory, thus no waves are scattered from the body. The permittivity and permeability of such a cloak are determined by the coordinate transformation of compressing a hidden body into a point or a line.Some components of the electrical parameters of the cloaking material(ε,μ) are required to have infinite or zero value at the boundary of the hidden object. Approximate cloaking can be achieved by transforming the cylindrical body (dielectric and conducting) virtually into a small cylinder rather than a line, which eliminates the zero or infinite values of the electrical parameters. The radially-dependent cylindrical cloaking shell can be approximately discretized into many homogeneous anisotropic layers; each anisotropic layer can be replaced by a pair of equivalent isotropic sub-layers, where the effective medium approximation is used to find the parameters of these two equivalent sub-layers. In this work, the scattering properties of cloaked cylindrical bodies (dielectric and conducting) are investigated using a combination of approximate cloaking, together with discretizing the cloaking material using pairs of homogeneous isotropic sub-layers. The solution is obtained by rigorously solving Maxwell equations using angular harmonics expansion. The scattering pattern, and the back scattering cross section against the frequency are studied for both transverse magnetic (TMz) and transverse electric (TEz) polarizations of the incident plane wave for different transformed body radii.

The potential for convection and implications for geothermal energy in the Perth Basin, Western Australia

Convection of groundwater in aquifers can create areas of anomalously high temperature at shallow depths which could be exploited for geothermal energy. Temperature measurements in the Perth Basin (Western Australia) reveal thermal patterns that are consistent with convection in the Yarragadee Aquifer. This observation is supported by Rayleigh number calculations, which show that convection is possible within the range of aquifer thickness, geothermal gradient, salinity gradient and permeability encountered in the Yarragadee Aquifer, assuming that the aquifer can be treated as a homogeneous anisotropic layer. Numerical simulations of convection in a simplified model of the Yarragadee Aquifer show that: (1) the spacing of convective upwellings can be predicted from aquifer thickness and permeability anisotropy; (2) convective upwellings may be circular or elongate in plan view; (3) convective upwellings create significant temperature enhancements relative to the conductive profile; (4) convective flow rates are similar to regional groundwater flow rates; and (5) convection homogenises salinity within the aquifer. Further work is required to constrain the average horizontal and vertical permeability of the Yarragadee Aquifer, to assess the validity of treating the aquifer as a homogeneous anisotropic layer, and to determine the impact of realistic aquifer geometry and advection on convection.

Anisotropic stratification beneath Africa from joint inversion of SKS and P receiver functions

The analysis of rock anisotropy revealed by seismic waves provides fundamental constraints on stress‐strain field in the lithosphere and asthenosphere. Nevertheless, the anisotropic models resolved for the crust and the upper mantle using seismic waves sometimes show substantial discrepancies depending on the type of data analyzed. In particular, at several permanent stations located in Africa, previous studies revealed that the observations of SKS splitting are accounted for by models with a single and homogeneous anisotropic layer whereas 3‐D tomographic models derived from surface waves exhibit clear anisotropic stratification. Here we tackle the issue of depth‐dependent anisotropy by performing joint inversion of receiver functions (RF) and SKS waveforms at four permanent broadband stations along the East African Rift System (EARS) and also on the Congo Craton. For three out of the four stations studied, stratified models allow for the best fit of the data. The vertical variations in the anisotropic pattern show interesting correlations with changes in the thermomechanical state of the mantle associated with the lithosphere‐asthenosphere transition and with the presence of hot mantle beneath the Afar region and beneath the EARS branches that surround the Tanzanian Craton. Our interpretation is consistent with the conclusion of earlier studies that suggest that beneath individual stations, multiple sources of anisotropy, chiefly olivine lattice preferred orientation and melt pocket shape preferred orientation in our case, exist at different depths. Our study further emphasizes that multiple layers of anisotropy must often be considered to obtain realistic models of the crust and upper mantle.

Parabolic equation modeling of anisotropic waves in heterogeneous media.

Wave propagation in heterogeneous media can be modeled efficiently with the parabolic equation method, which has been extended to problems with homogeneous anisotropic layers [A. J. Fredricks et al., Wave Motion 31, 139–146 (2000)]. This approach is currently being extended to the heterogeneous case, including piecewise continuous vertical dependence and horizontal dependence that is relatively gradual but which may be large over sufficient distances. Vertical dependence is included by applying appropriate heterogeneous depth operators in the equations of motion. Horizontal dependence is included by extending the single‐scattering solution [E. T. Kusel et al., J. Acoust. Soc. Am. 121, 808–813 (2007)] to the anisotropic case. [Work supported by the Office of Naval Research.]

Cloaking with optimized homogeneous anisotropic layers

We present a method to reduce the scattering from arbitrary objects by surrounding them with shells composed of several layers of homogeneous anisotropic materials. An optimization procedure is used to find the material parameters for each layer, the starting point of which is a discretized approximation of a coordinate transformation cloaking shell. We show that an optimized, three-layer shell can reduce the maximum scattering of an object by as much as $15\phantom{\rule{0.3em}{0ex}}\mathrm{dB}$ more than a 100-layer realization of a coordinate transformation cloaking shell. Moreover, using an optimization procedure can yield high-performance cloaking shell solutions that also meet external constraints, such as the maximum value of permittivity or permeability. This design approach can substantially simplify the fabrication of moderate-size cloaking shells.

PP/PSWavefield separation by independent component analysis

SUMMARY In blind signal separation one seeks to retrieve the original source signals that are observed as a linear mixture on an array of sensors. No a priori information is available about waveforms or polarizations of the desired source signals—hence the term blind. Blind signal separation can be achieved using independent component analysis (ICA), which is a rapidly emerging technology in the field of advanced signal processing. It separates a set of observed signals into the statistically most independent components by appealing to higher-order statistics. ICA retrieves the original source signals blindly if they are statistically independent without the need of further a priori information. There are many promising applications of ICA in geophysical signal analysis. ICA can be used to separate P and S waves in three-component seismic reflection data without knowledge of P- and S-wave near-surface velocities or density. Wavefield separation is achieved by exploiting statistical differences between P- and S waves only. The usual problems of amplitude indeterminacy and signal identification that occur in ICA are overcome by examining the inner products of the independent components with the original observations to ensure that the retrieved P and S waves have the appropriate signs and energies. Mode identification is realized by comparing current polarizations with forward predicted ones for each mode while maximizing the coherence with previously determined modes. The ICA wavefield separation technique is exact in a laterally inhomogeneous anisotropic earth with a homogeneous anisotropic near-surface layer if only upgoing waves are present.

Electromagnetic scattering by an inhomogeneous plasma anisotropic sphere of multilayers

Electromagnetic scattering by an inhomogeneous plasma anisotropic sphere is formulated and obtained, where the inhomogeneous plasma anisotropic sphere is divided into (s-1) homogeneous anisotropic spherical layers. The electromagnetic fields in the inner spherical multilayers and outer free space of the inhomogeneous plasma anisotropic spherical structure can be expanded in terms of the spherical vector wave functions in plasma anisotropic medium and in isotropic medium, respectively. By applying the continuous boundary conditions of electromagnetic fields on the spherical interfaces of the (s-1)-layered homogeneous anisotropic plasma medium, the unknown expansion coefficients of fields in the multilayered plasma spherical structure are obtained, and then the electromagnetic field distributions are calculated. Numerical results for the very general inhomogeneous plasma dielectric material sphere are given and the data in a special case are obtained using the present method and the method of moments accelerated with the conjugate-gradient fast-Fourier-transform approach and compared to each other to verify the correctness and applicability of the present analysis.

Traveltime approximation for a reflected wave in a homogeneous anisotropic elastic layer

An approximation to the traveltime field is calculated for an elastic wave that propagates in a homogeneous anisotropic layer and is reflected at a plane boundary. The traveltime is approximated by a Taylor series expansion with the third derivative of the traveltime being taken into account. The coefficients of the series refer to the seismic ray, which is locally the fastest ray. Simple formulae are obtained for orthorhombic media in the crystal coordinate system, which relate the traveltimes of the reflected waves to the elastic constants of the medium. A numerical example is presented for wave propagation in orthorhombic olivine, which is a constituent of the Earth's mantle. A second example is given by an isotropic host rock with a set of parallel cracks, which is an important model for wave propagation in the Earth's crust. The elastic parameters can be determined by measuring the reflection times as a function of source–receiver offset. The approximate traveltime–distance curves are compared with traveltimes obtained from seismic ray tracing.

NMO‐velocity surfaces and Dix‐type formulas in anisotropic heterogeneous media

Reflection moveout of pure modes recorded on conventional‐length spreads is described by a normal‐moveout (NMO) velocity that depends on the orientation of the common‐midpoint (CMP) line. Here, we introduce the concept of NMO‐velocity surfaces, which are obtained by plotting the NMO velocity as the radius‐vector along all possible directions in 3‐D space, and use it to develop Dix‐type averaging and differentiation algorithms in anisotropic heterogeneous media.The intersection of the NMO‐velocity surface with the horizontal plane represents the NMO ellipse that can be estimated from wide‐azimuth reflection data. We demonstrate that the NMO ellipse and conventional‐spread moveout as a whole can be modeled by Dix‐type averaging of specifically oriented cross‐sections of the NMO‐velocity surfaces along the zero‐offset reflection raypath. This formalism is particularly simple to implement for a stack of homogeneous anisotropic layers separated by plane dipping boundaries. Since our method involves computing just a single (zero‐offset) ray for a given reflection event, it can be efficiently used in anisotropic stacking‐velocity tomography.Application of the Dix‐type averaging to layered transversely isotropic media with a vertical symmetry axis (VTI) shows that the presence of dipping interfaces above the reflector makes the P‐wave NMO ellipse dependent on the vertical velocity and anisotropic coefficients ε and δ. In contrast, P‐wave moveout in VTI models with a horizontally layered overburden is fully controlled by the NMO velocity of horizontal events and the Alkhalifah‐Tsvankin coefficient η ≈ ε − δ. Hence, in some laterally heterogeneous, layered VTI models P‐wave reflection data may provide enough information for anisotropic depth processing.