3D Inhomogeneities Research Articles

Examination of the microstructures of the lower cervical facet based on micro-computed tomography: A cadaver study

The cervical facet has complicated 3D microstructures and inhomogeneities. The cervical facet joint, which also participates in the formation, plays a certain role in regulating and limiting the movement of the spine. Correct identification and evaluation of its microstructure can help in the diagnosis of orthopedic disease and predict early phases of fracture risk. To evaluate the safety of the cervical spine by measuring and analyzing the microstructures and morphometric parameters of bone trabeculae in the normal cervical facet with high-resolution 3D micro-computed tomography. Thirty-one sets of C3 to C7 lower cervical vertebrae (155 vertebrae) were scanned using micro-computed tomography. The morphological characteristics and direction of trabecular bone in the facet of the lower cervical vertebrae were observed by selecting and rebuilding the areas of interest, and the changes in the microstructure of the areas of interest were calculated to reveal the structural characteristics and weak areas. Images indicated an ossified center between the superior and inferior articular processes of the lower cervical spine. The cellular bone trabeculae of the articular process had complex reticular microstructures. The trabecular bone plate near the cortical bone was lamellar and relatively dense, and it extended around and transformed into a network structure, and then into the rod-shaped trabecular bone. The rod-shaped trabeculae converged with the plate-shaped trabeculae with only 1 to 2 layers surrounding the trabeculae cavity. Statistical results of the morphological parameters of the trabecular bone showed that trabecular bone volume fraction values were significantly higher for C7 than for C3 to C6 (P < .05). There were significant differences between C7 and C3 to C5 and between C6 and C4 in bone surface area/bone volume (P < .05). There was a significant difference between C7 and C3 to C6 in trabecular bone thickness values (P < .05). The degree of anisotropy value was significantly smaller for C3 than for C6 and C7 (P < .05). The changes in the C3 to C7 microstructure were summarized in this study. The loading capacity and stress of the C7 articular process tended to be limited, and the risk of injury tended to be higher for the C7 articular process.

Magnetotelluric Sounding in the Arctic Using a Drifting Station on an Ice Floe (Numerical Experiment)

Abstract —The magnetotelluric sounding (MTS) method implemented on drifting ice floes in the Arctic is suitable for detection of 3D inhomogeneities in crustal conductivity while recording the transverse magnetic (TM) mode potential of the electromagnetic field. Highconductivity layers of seawater and sediments shield the underlying 3D inhomogeneity. Their presence virtually does not affect changes in the standard responses of the medium used in MTS but is quite noticeable in the characteristics of the TM mode. To register them, one can use a circular electric dipole (CED) located at the surface of an ice floe. During the drift, the electric field can be measured on the ice floe using electrodes in seawater. We propose to lower the magnetic sensors beneath the ice, in seawater, because ice deformations interfere with the magnetic-field component measurements. The coordinates of the observation station during MT soundings on the ice floe in the Arctic (similarly to earlier observations at the North Pole stations) can change significantly. To take into account the effect of horizontal movements of the drifting station, we propose to complement all the recorded time series with the coordinates of measurement points. We have developed a technique for processing such data to take into account nonplane-wave effects, which can occur in the Arctic because of the proximity of ionospheric current jets. We carry out the synchronization of all observations in the investigated area, using a model of spatial and temporal field variations and data accumulation. To test our approach, we use the synthetic experimental data for the model that considers the existence of seawater, sediment, resistive crust, crustal object, and underlying mantle. We determine the crustal 3D object parameters with account of the TM-mode potential distributions at the seawater surface restored from the synthetic experimental data obtained at the drifting station during the drift. We use the Nelder–Mead method for optimization of the object characteristics. The parameters of the object become highly similar to their test values if the trajectory of the drifting station passes through an object, covering it most fully.

Modification of the Alfvén wave spectrum by pellet injection

Alfvén eigenmodes driven by energetic particles are routinely observed in tokamak plasmas. These modes consist of poloidal harmonics of shear Alfvén waves coupled by inhomogeneity in the magnetic field. Further coupling is introduced by 3D inhomogeneities in the ion density during the assimilation of injected pellets. This additional coupling modifies the Alfvén continuum and discrete eigenmode spectrum. The frequencies of Alfvén eigenmodes drop dramatically when a pellet is injected in JET. From these observations, information about the changes in the ion density caused by a pellet can be inferred. To use Alfvén eigenmodes for MHD spectroscopy of pellet injected plasmas, the 3D MHD codes Stellgap and AE3D were generalised to incorporate 3D density profiles. A model for the expansion of the ionised pellet plasmoid along a magnetic field line was derived from the fluid equations. Thereby, the time evolution of the Alfvén eigenfrequency is reproduced. By comparing the numerical frequency drop of a toroidal Alfvén eigenmode (TAE) to experimental observations, the initial ion density of a cigar-shaped ablation region of length 4 cm is estimated to be m−3 at the TAE location (). The frequency sweeping of an Alfvén eigenmode ends when the ion density homogenises poloidally. Modelling suggests that the time for poloidal homogenisation of the ion density at the TAE position is ms for inboard pellet injection, and ms for outboard pellet injection. By reproducing the frequency evolution of the elliptical Alfvén eigenmode (EAE), the initial ion density at the EAE location () can be estimated to be m−3. Poloidal homogenisation of the ion density takes 2.7 times longer at the EAE location than at the TAE location for both inboard and outboard pellet injection.

New interpretation of the reduction phenomenon in the electrical resistivity of rock masses before local earthquakes

Based on long-term observational data from the area of Peter the Great Ridge (Pamir), a decrease in the electrical resistivity of the rock massif before local earthquakes has been observed. To explain the observed phenomenon, a hypothesis has been proposed: the structure of the pore space of a rock in the focal zone of an earthquake changes during the compression/tension associated with earthquake preparation. However, the models proposed have only qualitatively interpreted the experimental data. This article attempts to quantify this hypothesis based on 3D modeling of the observed electromagnetic effects. It is shown that variations in the apparent resistivity are due to changes in the electrical resistivity in a narrow fault zone located at the focus of the dipole-dipole sounding system. The changes occur at depths of <2–2.5 km and are due to low-resistivity fluid saturation of the highly porous fracture crushing zone. Small, smooth changes in the resistivity of the containing medium on both sides of the fault are associated with regional stresses in blocks of rocks and are not associated with the local earthquakes. An analysis of electromagnetic monitoring data at the Bishkek test site (Tien Shan) showed that the observed variations in apparent resistivity during pulse soundings are related to stresses and deformations of rocks in a wide region and cannot be used as a tool for predicting earthquakes. It is shown that, for studies of variations in the resistivity of rock massifs, measuring the response of the medium by grounded electrodes is ineffective due to the “static shift effect” generated by 3D inhomogeneities of the upper layer of the medium. To eliminate this effect, it was proposed that pulse technologies with magnetic field measurements made by ungrounded antennas be used.

Fast computation of MT curves for a horizontally layered earth with laterally inhomogeneous conductivity perturbations

A new algorithm is proposed to compute magnetotelluric (MT) curves for a horizontally layered earth with laterally inhomogeneous conductivity. It is fast and ensures correction of induced eddy currents and galvanic distortions of MT curves produced by 3D inhomogeneities. The computation time is short (~1 min) due to the use of the perturbation method for solving Maxwell’s equations. The suggested algorithm has a better performance than the more costly classical Trefftz method but has an applicability limitation.

Shape optimizations of inhomogeneities of two dimensional (2D) and three dimensional (3D) steady state heat conduction problems by the boundary element method

The shape optimizations of inhomogeneities for 2D and 3D steady state heat conductions in an infinite medium are respectively studied by the boundary element method (BEM). Interest in the shape optimization by the BEM is mainly due to its high computation accuracy and simplicity in meshing. The boundary integral equations and the heat energy formulations in this paper only contain the temperature on each inhomogeneity–matrix interface. The heat energy increment in the inhomogeneous medium is taken as the objective function. The method of moving asymptotes (MMA) is adopted to carry out numerical implementation of the shape optimizations of 2D and 3D inhomogeneities.

Propagation in 3D of microwaves through density perturbations

Simulations using 3D and 2D full-wave codes have shown that edge filaments in tokamak plasmas can significantly affect the propagation of microwaves across a broad frequency spectrum, resulting in scattering angles of up to 46°. Parameter scans were carried out for density perturbations comparable in width and amplitude to MAST filaments and the effect on the measured emission was calculated. 3D effects were discovered in the case of an obliquely incident beam.In general, the problem of electromagnetic propagation past wavelength-sized 3D inhomogeneities is not well understood, yet is of importance for both heating and diagnostic applications in the electron cyclotron frequency range for tokamaks, as well as atmospheric physics. To improve this understanding, a new cold-plasma code, EMIT-3D, was written to extend full-wave microwave simulations in magnetized plasmas to 3D, and make comparisons to the existing 2D code IPF-FDMC. This work supports MAST experiments using the SAMI diagnostic to image microwave emission from the plasma edge due to mode conversion from electron Bernstein waves. Significant fluctuations in the SAMI data mean that detailed modelling is required to improve its interpretation.

Magnetoelastic Resonance in Media with the Inhomogeneous Coupling Parameter

The matrix Greens function of coupled spin and elastic waves for media with the 3D inhomogeneities of the coupling parameter is studied. It has been shown that the difference in shapes of the Greens functions for the cases of 1D and 3D inhomogeneities appears only for the sufficiently large correlation wave number of the inhomogeneities.

Vertical electric source in transient marine CSEM: Effect of 3D inhomogeneities on the late time response

The time-domain marine controlled-source electromagnetic method, based on injection of electric currents into the sea via a vertical cable and measurements of the transient vertical electric field, is characterized by high sensitivity to resistive reservoirs and robustness with respect to distorting effects of lateral heterogeneities. This is due to the fact that a vertical electric dipole induces in a stratified medium only a transverse magnetic (TM) field. In addition, the vertical electric field is not directly contributed by the transverse electric (TE) component of the field scattered by heterogeneities. Nevertheless, a closed-form solution shows that the first order effect of a lateral heterogeneity displays itself as a parallel shift of the late time response curves. The effect is also observed in 3D responses evaluated by numerical solutions of the integral equation of the modified iterative dissipative method. Moreover, in “favorable” conditions, scattering on heterogeneities may change the law of the field decay. The parallel shift of the late time curves is caused by vertical polarization of the scatterer, while its horizontal polarization leads to an abnormally fast decay of the vertical electric field. The latter effect, observed against the background of the general decay of the free electromagnetic field, can be associated with “energy channeling from the TM to TE field.” Neither of the effects necessarily deteriorates the method sensitivity. Unlike the vertical electric field, the horizontal electromagnetic field is contributed by the scattered TE field. As a result, the abnormally fast decay of the vertical electric field is accompanied by an abnormally slow decay of the horizontal components. The transient horizontal electric field may become almost insensitive to the reservoir resistivity. In addition to unrealistically harsh requirements to the transmitter tilt, this may render accurate measurements of the horizontal electromagnetic field of a vertical electric bipole not feasible.

Enhancing rigid frame porous layer absorption with three-dimensional periodic irregularities

This papers reports a three-dimensional (3D) extension of the model proposed by Groby et al. [J. Acoust. Soc. Am. 127, 2865-2874 (2010)]. The acoustic properties of a porous layer backed by a rigid plate with periodic rectangular irregularities are investigated. The Johnson-Champoux-Allard model is used to predict the complex bulk modulus and density of the equivalent fluid in the porous material. The method of variable separation is used together with the radiation conditions and Floquet theorem to derive the analytical expression for the acoustic reflection coefficient from the porous layer with 3D inhomogeneities. Finite element method is also used to validate the proposed analytical solution. The theoretical and numerical predictions agree well with the experimental data obtained from an impedance tube experiment. It is shown that the measured acoustic absorption coefficient spectrum exhibits a quasi-total absorption peak at the predicted frequency of the mode trapped in the porous layer. When more than one irregularity per spatial period is considered, additional absorption peaks are observed.

Spectral properties of waves in superlattices with 2D and 3D inhomogeneities

We investigate the dynamic susceptibility and one-dimensional density of states in an initially sinusoidal superlattice containing simultaneously 2D phase inhomogeneities simulating correlated rough-nesses of superlattice interfaces and 3D amplitude inhomogeneities of the superlattice layer materials. The analytic expression for the averaged Green’s function of the sinusoidal superlattice with two phase inhomogeneities is derived in the Bourret approximation. It is shown that the effect of increasing asymmetry in the peak heights of dynamic susceptibility at the Brillouin zone boundary of the superlattice, which was discovered earlier [15] upon an increase in root-mean-square (rms) fluctuations, also takes place upon an increase in the correlation wavenumber of inhomogeneities. However, the peaks in this case also become closer, and the width and depth of the gap in the density of states decrease thereby. It is shown that the enhancement of rms fluctuations of 3D amplitude inhomogeneities in a superlattice containing 2D phase inhomogeneities suppresses the effect of dynamic susceptibility asymmetry and leads to a slight broadening of the gap in the density of states and a decrease in its depth. Targeted experiments aimed at detecting the effects studied here would facilitate the development of radio-spectroscopic and optical methods for identifying the presence of inhomogeneities of various dimensions in multilayer magnetic and optical structures.

Combined Effects of 2D and 3D Inhomogeneities on the Dynamic Susceptibility of Superlattices

The dynamic susceptibility and the one-dimensional density of states (DOS) of an initially sinusoidal superlattice (SL) with simultaneous presence of two-dimensional (2D) phase inhomogeneities that simulate the deformations of the interfaces between the SL’s layers and three-dimensional (3D) amplitude inhomogeneities of the layer material of the SL were investigated. An analytical expression for the averaged Green’s function of the sinusoidal SL with 2D phase inhomogeneities was obtained in the Bourret approximation. It was shown that the effect of increasing asymmetry of heights of the dynamic susceptibility peaks at the edge of the Brillouin zone of the SL, which was found in [6] at increasing the rms fluctuations of 2D inhomogeneities, also takes place at increasing the correlation wave number of such inhomogeneities. It was also shown that the increase of the rms fluctuations of 3D amplitude inhomogeneities in the superlattice with 2D phase inhomogeneities leads to the suppression of the asymmetry effect and to the decrease of the depth of the DOS gap.

Inverse problem of near-field scattering in multilayer media

The inverse problem of scattering is solved for 3D inhomogeneities of the complex permittivity in multilayer media. The proposed solution involves an analysis of the 2D lateral distributions of the scattered field with the imposed condition of the probing field invariability relative to the receiver. A generalization of the solution beyond the Born approximation is given. Necessary k-space representations of Green functions for a multilayer medium with an arbitrary located source are obtained analytically in closed forms. Based on this solution, methods of multifrequency and multilevel subwavelength tomography are developed; their feasibility is shown for multifrequency tomography in a three-layered absorbing medium and for multilevel tomography with a perfect lens that can enhance the sounding depth. The developed approach is valid not only in electromagnetic theory, but also in similar problems of quantum mechanics and acoustics.

Comparison of acoustic-emission tomography images to an etalon

Criteria for comparing images of acoustic-emission tomography to an etalon via numerical simulation are tested. The results of approbation of metric and correlation criteria for comparing images and the signal-to-noise ratio for 3D inhomogeneities of sinusoidal and gaussoid types are presented. The pixel-by-pixel absolute and relative differences between images are efficient for obtaining the spatial distribution of differences between images and are quite sensitive to the inhomogeneity parameters and the data-collection and tomographic-reconstruction schemes. The comparison of the reconstructed images to a gaussoid-type etalon has shown that the image-correlation coefficient and the signal-to-noise ratio are quite sensitive to the inhomogeneity parameters and the data-collection and tomographic-reconstruction schemes. The integral metric criteria (the mean absolute and rms deviations) are almost insensitive to these parameters. The comparison of the reconstructed images to a sinusoidal etalon characterized by a large constant component has shown that the metric criteria and the centered-data correlation coefficient are sensitive to changes in the inhomogeneity parameters and the data-collection and tomographic-reconstruction schemes.

Temporal coherence after multiple forward scattering through random three-dimensional inhomogeneities in an ocean waveguide

An analytical expression is derived for the temporal coherence of an acoustic field after multiple forward scattering through random three-dimensional (3D) inhomogeneities in an ocean waveguide. This expression makes it possible to predict the coherence time scale of field fluctuations in ocean-acoustic measurements from knowledge of the oceanography. It is used to explain the time scale of acoustic field fluctuations observed at megameter ranges in various deep ocean-acoustic transmission experiments. It is shown that this time scale is nonlinearly related to the much longer coherence time scale of deep ocean internal waves through a multiple forward scattering process. It is also shown that 3D scattering effects become pronounced when the acoustic Fresnel width exceeds the cross-range coherence length of the deep ocean internal waves, which lead to frequency and range-dependent power losses in the forward field that may help to explain historic long range measurements.

High-frequency susceptibility of a superlattice with 2D inhomogeneities

We investigate the high-frequency susceptibility (Green function) of an initially sinusoidal 1D superlattice with 2D phase inhomogeneities that model the deformations of the interfaces between the superlattice layers. For waves propagating along the superlattice axis (the geometry of a photon or magnon crystal), we have found a peculiar behavior of the imaginary part of the Green function that consists in a significant difference between the peaks corresponding to the edges of the band gap in the wave spectrum. The peak corresponding to the lower-frequency band edge remains essentially unchanged as the root-mean-square fluctuation of the 2D inhomogeneities γ2 increases, while the peak corresponding to the higher-frequency band edge broaden and decreases sharply in height until its complete disappearance with increasing γ2. This behavior of the peaks corresponds to a band gap closure mechanism that differs from the traditional one characteristic of 1D and 3D inhomogeneities. These effects can be explained by a peculiarity of the energy conservation laws for the incident and scattered waves for 2D inhomogeneities in a 1D superlattice.

Effects of cross correlations between 1D and 3D inhomogeneities on the high-frequency susceptibility of superlattices

Cross correlations between components of a mixture of one-dimensional (1D) and three-dimensional (3D) inhomogeneities are described by introducing a distribution function taking into account correlations between absolute values of two random variables in the absence of correlations between the variables themselves. This distribution function is used for derivation and analysis of the superlattice correlation function containing a mixture of cross-correlated 1D and 3D inhomogeneities. The effect of such inhomogeneities on the high-frequency susceptibility at the edge of the first Brillouin zone of the superlattice is investigated. It is shown that positive cross correlations partly suppress the effect of a mixture of 1D and 3D inhomogeneities on the wave spectrum: the gap at the boundary of the Brillouin zone increases, and wave damping decreases as compared to the effect produced by a mixture of 1D and 3D inhomogeneities in the absence of cross correlations. Negative cross correlations lead to the opposite effect: the gap decreases and wave damping increases. Cross correlations also lead to the emergence of new resonance effects: a narrow dip or a narrow peak at the center of the band gap (depending on the sign of the correlation factor).

A new scheme for numerical modelling of flow and transport processes in 3D fractured porous media

The objective of this work is to develop a new numerical approach for the three-dimensional modelling of flow and transient solute transport in fractured porous media which would provide an accurate and efficient treatment of 3D complex geometries and inhomogeneities. For this reason, and in order to eliminate as much as possible the number of degrees of freedom, the fracture network, fractures and their intersections, are solved with a coupled 2D–1D model while the porous matrix is solved independently with a 3D model. The interaction between both models is accounted for by a coupling iterative technique. In this way it is possible to improve efficiency and reduce CPU usage by avoiding 3D mesh refinements of the fractures. The approach is based on the discrete-fracture model in which the exact geometry and location of each fracture in the network must be provided as an input. The formulation is based on a multidimensional coupling of the boundary element method-multidomain (BEM-MD) scheme for the flow and boundary element dual reciprocity method-multidomain (BE-DRM-MD) scheme for the transport. Accurate results and high efficiency have been obtained and are reported in this paper.

Effect of the Correlation Properties of One- and Three-Dimensional Inhomogeneities on the High-Frequency Magnetic Susceptibility of Sinusoidal Superlattices

The effect of one-(1D) and three-dimensional (3D) inhomogeneities on the high-frequency magnetic susceptibility at the boundary of the first Brillouin zone of a ferromagnetic superlattice is studied. The study is performed with an earlier developed method of random spatial modulation (RSM) of the superlattice period. In this method, structural inhomogeneities are described in terms of the random-phase model, in which the phase depends on three coordinates in the general case. The frequency spacing Δνm between two peaks in the imaginary part of the averaged Green’s function, which characterizes the gap width in the frequency spectrum at the boundary of the Brillouin zone, is calculated as a function of both the root-mean-square fluctuations γi and the correlation wavenumbers ηi of phase inhomogeneities (i = 1 and 3 for 1D and 3D inhomogeneities, respectively). The function Δνm(γ1, η1) for 1D inhomogeneities is shown to be symmetric with respect to interchanging the variables γ 1 2 and η1, whereas the function Δνm(γ3, η3) for 3D inhomogeneities is strongly asymmetric with respect to interchanging γ 2 3 and η3. This effect is associated with the difference in form between the correlation functions of 1D and 3D inhomogeneities and can be used to determine the dimensionality of inhomogeneities from the results of spectral studies of such superlattices.

How magnetotellurics is able to see through 3D near-surface inhomogeneities?

In order to investigate imaging properties of various magnetotelluric interpretation parameters over complicated models, we carried out numerical model calculations, where the models contained a 3D near-surface (“shallow”) part and a 3D or 2D deep part. Various alternatively defined magnetotelluric responses, all of them based on rotational invariants of the magnetotelluric impedance tensor were considered. Then we calculated correlation coefficients between all these MT responses, and the characteristic geometrical parameters of the subsurface models, considered as a composition of “shallow+deep” elements.