Full Tensor Research Articles

Method for full magnetic gradient tensor detection from a single HTS gradiometer

A new method to measure the full magnetic gradient tensor (FMGT) using a single rotating high-temperature superconducting planar first-order gradiometer is described. Determining the FMGT provides valuable additional information about magnetic sources and their anomalies and, critically, the location of magnetic targets with less ambiguity and with fewer survey lines required. This paper presents both a theoretical description and experimental demonstration of the single sensor system that can, in principle, extract all the magnetic gradient tensor components, with suitable referencing and/or field cancellation procedures. The technique involves rotating the planar gradiometer mounted on an angled plinth about the vertical axis of the sensor package. The technique works by shifting gradient terms to harmonics of the rotating frequency, above the 1/f noise of the device, and allows extraction of all the components in the frequency domain. Additional referencing enables compensation for the non-ideal gradiometer response and provides a more accurate measurement of contaminated gradient components. Laboratory results show tracking of a moving dipole target and these are compared to a modelled response, both with and without field compensation.

Tensorial formulations for improved thixotropic viscoelastic modeling of human blood

Recent work modeling the rheological behavior of human blood indicates that blood has all the hallmark features of a complex material, including shear-thinning, viscoelastic behavior, yield stress, and thixotropy. There is renewed interest in the modeling of human blood with thixo-elasto-visco-plastic rheological models. Previous work [Armstrong and Tussing, Phys. Fluids 32, 094111 (2020)] has led to the development of the enhanced thixotropic viscoelastic model for blood (ethixo-mHAWB; called here, after a minor modification, ETV) that incorporates viscoelasticity to a thixotropic model for the stress contributed by the rouleaux aggregates, in addition to describing using a nonlinear viscoelastic model the stress contributed by the individual red blood cells deforming under the action of the flow. This model has shown superior performance in fitting human blood steady state and transient rheological data from a strain-controlled rheometer [Horner et al., J. Rheol. 62, 577–591 (2018); 63, 799–813 (2019)] as compared to other alternate models. In the present work, we first develop another variant of the ETV model, the enhanced structural stress thixotropic-viscoelastic (ESSTV) model, and the modification patterned following an elastoviscoplastic model developed recently [Varchanis et al., J. Rheol. 63, 609–639 (2019)]. We develop full tensorial stress formulations of the rouleaux stresses for both the above-mentioned models, resulting in the t-ETV and t-ESSTV models. We use steady state and step-ups, and step-downs in shear rate data to independently fit the parameters of all before-mentioned models. We compare predictions against experimental data obtained on small, large, and unidirectional large amplitude oscillatory shear conditions. We find that the full tensor stress formulations t-ETV and t-ESSTV significantly improved the predictive capability of the earlier ETV model.

Density functional theory characterisation of cementite (Fe[formula omitted]C) with substitutional molybdenum (Mo) atoms

The presence of substitutional atoms, other than iron (Fe), in the cementite (Fe3C) phase in steels can have a beneficial influence on different mechanical and thermodynamic properties. For example, the addition of molybdenum (Mo), which tends to partition to cementite and stabilise it, can improve the hardness of the steel at higher temperatures. In order to better understand the effects of Mo as a substitutional element, an energetic, structural, electronic, and mechanical characterisation of cementite containing Mo atoms was performed. Formation enthalpies, densities of states, and the full stiffness tensors where calculated and analysed in terms of preferential occupation sites, stability, ductile/brittle behaviour, and isotropic and directional evolution of the elastic constants.

In-Plane Anisotropy in Biaxial ReS2 Crystals Probed by Nano-Optical Imaging of Waveguide Modes

Near-field imaging has emerged as a reliable probe of the dielectric function of van der Waals crystals. In principle, analyzing the propagation patterns of subwavelength waveguide modes (WMs) allows for extraction of the full dielectric tensor. Yet previous studies have mostly been restricted to high-symmetry materials or narrowband probing. Here, we resolve in-plane anisotropic WMs in thin rhenium disulfide (ReS2) crystals across a wide range of near-infrared frequencies. By tracing the evolution of these modes as a function of crystallographic direction, polarization of the electric field and sample thickness, we have determined the anisotropic dielectric tensor including the elusive out-of-plane response. The excitonic absorption at ~1.5 eV manifests itself as a clear backbending feature in the WM dispersion and a reduction of the quality factors as fully supported by numerical calculations. Our results extend the sensitivity of near-field microscopy towards biaxial anisotropy and provide key insights into the optoelectronic properties of ReS2.

Inverse Problem in Resonant Ultrasound Spectroscopy With Sampling and Optimization: A Comparative Study on Human Cortical Bone.

The Bayesian inference with prior knowledge has been proposed recently to solve the inverse problem in resonant ultrasound spectroscopy. It allows inferring the elastic properties of high damping materials, such as cortical bone with less dependence on the initial guessed values. In this method, the estimation of the stiffness coefficients is expressed as a probabilistic solution to the inverse problem, which can be achieved by sampling or optimization methods. However, the detailed performance comparison of these two strategies applied to high damping materials has not been fully studied. In this work, the full stiffness tensor of 52 transversely isotropic cortical bone specimens was obtained using Markov chain Monte Carlo (MCMC) sampling and particle swarm optimization (PSO), respectively. Results showed that the local probability distributions of stiffness coefficients estimated by the two methods are consistent. Compared with MCMC, the average calculation speed of PSO is ten times faster [614 s ± 59 s (MCMC) versus 53 s ± 22 s (PSO)]. The mean standard error between theoretical and experimental resonant frequencies was slightly smaller for PSO compared with MCMC. In conclusion, PSO, a global optimization strategy, is suitable to solve the inverse problem for high damping materials.

Automatic Calibration of a Geomechanical Model from Sparse Data for Estimating Stress in Deep Geological Formations

Summary In this study, we demonstrate geomechanical modeling with fully automatic parameter calibration to estimate the full geomechanical stress fields of a prospective US carbon dioxide (CO2) storage site, based on sparse measurement data. The goal is to compute full stress tensor field estimates (principal stresses and orientations) that are maximally compatible with observations within the constraints of the model assumptions, thereby extending pointwise, incomplete partial stress measurement to a simulated full formation stress field, as well as a rough assessment of the associated error. We use the Perch site, located in Otsego County, Michigan, USA, as our case study. The input data consist of partial stress tensor information inferred from in-situ borehole tests, geophysical well logs, and processing of seismic data. A static earth model (SEM) of the site was developed, and geomechanical simulation functionality of the open-source MATLAB Reservoir Simulation Toolbox (MRST) was used to model the stress field. Adjoint-based nonlinear optimization was used to adjust boundary conditions and material properties to calibrate simulated results of observations. Results were interpreted through a Bayesian framework. The focus of this paper is to demonstrate how the fully automatic calibration procedure works and discuss the results obtained; it does not attempt a detailed analysis of the stress field in the context of the proposed CO2 storage initiatives. Our work is part of a larger effort to noninvasively determine in-situ stresses in deep formations considered for CO2 storage. Guided by previously published research on geomechanical model calibration, our work presents a novel calibration approach supporting a potentially large number of linear or nonlinear calibration parameters to produce results optimally agreeing with available measurements and thus extend partial pointwise estimates to full tensor fields compatible with the physics of the site.

Quantifying the quadrupolar interaction by 45Sc-NMR spectroscopy of single crystals

Single crystals of the compound [{Sc(H2O)5(μ-OH)}2]Cl4 ⋅ 2H2O were studied by 45Sc-NMR, with the effect of the quadrupolar coupling interaction on the spectra of the spin-7/2 nucleus analysed in the hierarchical framework of perturbation theory. Orientation-dependent spectra acquired at B0 = 17.6 T showed strong second-order effects due to the comparatively large coupling constant of χ = |14.613 ± 0.006| MHz, with an associated asymmetry parameter of ηQ = 0.540 9 ± 0.000 4. By analysing the splittings of the ±3/2 satellites, which in good approximation are subjected to first-order effects only, the full quadrupolar coupling tensor could be determined. The second-order effects caused by this tensor were calculated according to theoretical predictions for all orientations, and subtracted from both the centres of gravity of the satellites, and the central transitions. This allowed extraction of the full chemical shift tensor, with the eigenvalues being δ11 = (5.6 ± 0.9) ppm, δ22 = (12.4 ± 0.9) ppm, and δ33 = (38.5 ± 0.9) ppm. In spectra acquired at a lower magnetic field of B0 = 9.4 T, third-order effects could be detected, and similarly quantified using analytical expressions.

Seismic Source Processes of 25 Earthquakes (Mw>5) in the Gulf of California

ABSTRACT The Gulf of California (GoC) is a complex tectonic boundary that has been instrumented in the past several decades to record broadband seismograms. This volume of data has allowed us to study several source parameters systematically. Before, only a few source parameters of earthquakes greater than magnitude five had been studied in the GoC area. We re-examined the focal mechanisms of several earthquakes in the southern GoC that occurred over the last 20 yr using local–regional distance broadband seismograms. These focal mechanisms were then used as input data to retrieve the time–space history of the rupture for each earthquake. This work contributes to the study of 25 rupture-process models computed with the method proposed by Yagi et al. (1999). To investigate more about the nature of the seismicity in the GoC, we also calculated the non-double-couple component of moment tensors for 45 earthquakes. Previous studies (e.g., Ortega et al., 2013, 2016) have shown that non-double-couple components from moment tensors in this region are associated with complex faulting, suggesting that oblique faults or several parallel faults are interacting simultaneously. Our results show that, at least for moderate earthquakes (5 < M < 6), rupture processes in the GoC show a complex interaction between fault systems. It is revealed on the important contribution of non-double-couple component obtained in the full moment tensor analysis.

Direct Observation of Three-Dimensional Atomic Structure of Twinned Metallic Nanoparticles and Their Catalytic Properties.

We determined a full 3D atomic structure of a dumbbell-shaped Pt nanoparticle formed by a coalescence of two nanoclusters using deep learning assisted atomic electron tomography. Formation of a double twin boundary was clearly observed at the interface, while substantial anisotropy and disorder were also found throughout the nanodumbbell. This suggests that the diffusion of interfacial atoms mainly governed the coalescence process, but other dynamic processes such as surface restructuring and plastic deformation were also involved. A full 3D strain tensor was clearly mapped, which allows direct calculation of the oxygen reduction reaction activity at the surface. Strong tensile strain was found at the protruded region of the nanodumbbell, which results in an improved catalytic activity on {100} facets. This work provides important clues regarding the coalescence mechanism and the relation between the atomic structure and catalytic property at the single-atom level.

Anisotropic elastic parameter estimation from multicomponent ground-motion observations: a theoretical study

SUMMARY We investigate the potential of multicomponent, single-point ground-motion observations (displacement, rotation and strain) to allow the estimation of near-receiver anisotropic elastic parameters. Based on full-space, plane-wave propagation analysis, we demonstrate that in (locally homogeneous) anisotropic media, the wave propagation direction and the velocities of quasi-P and quasi-S waves can—in principle—be determined from three components of displacements and three components of rotations. Mimicking the situation of a borehole setting, we formulate an inverse problem, estimating the full elastic tensor from multidirectional observations. We show that in the presence of noise it is beneficial to observe additionally a longitudinal strain component (e.g. along the borehole), further constraining the predominantly quasi-P related elastic tensor components.

Elastic stability of Ga2O3 : Addressing the β to α phase transition from first principles

The elastic and structural properties of $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ and $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ are investigated from first principles. The full elastic tensors and elastic moduli of both phases at $0\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ are computed in the framework of semilocal density-functional theory. We determine mechanical instabilities of $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ by evaluating the full stiffness tensor under load for a range of hydrostatic pressure values. While a phase transition from the $\ensuremath{\beta}$ to $\ensuremath{\alpha}$ phase is found to be energetically favored at $2.6\phantom{\rule{0.16em}{0ex}}\mathrm{G}\mathrm{Pa}$, we show that the $\ensuremath{\beta}$ phase is mechanically unstable only for much higher pressures $(>30\phantom{\rule{0.16em}{0ex}}\mathrm{G}\mathrm{Pa})$, which agrees well with experimental results. Our employed approach is based on the Born stability criterion, is independent of crystal symmetry, and thus can be readily applied to different materials.

Numerical Modeling of Suprathermal Electron Transport in the Solar Wind: Effects of Whistler Turbulence with a Full Diffusion Tensor

Abstract The electron VDF in the solar wind consists of a Maxwellian core, a suprathermal halo, a field-aligned component strahl, and an energetic superhalo that deviates from the equilibrium. Whistler wave turbulence is thought to resonantly scatter the observed electron velocity distribution. Wave–particle interactions that contribute to Whistler wave turbulence are introduced into a Fokker–Planck kinetic transport equation that describes the interaction between the suprathermal electrons and the Whistler waves. A recent numerical approach for solving the Fokker–Planck kinetic transport equation has been extended to include a full diffusion tensor. Application of the extended numerical approach to the transport of solar wind suprathermal electrons influenced by Whistler wave turbulence is presented. Comparison and analysis of the numerical results with observations and diagonal-only model results are made. The off-diagonal terms in the diffusion tensor act to depress effects caused by the diagonal terms. The role of the diffusion coefficient on the electron heat flux is discussed.

Efficient Dynamical Low-Rank Approximation for the Vlasov-Amp\`{E}Re-Fokker-Planck System

Kinetic equations are difficult to solve numerically due to their high dimensionality. A promising approach for reducing computational cost is the dynamical low-rank algorithm, which decouples the dimensions of the phase space by proposing an ansatz as the sum of separable (rank-1) functions in position and velocity respectively. The fluid asymptotic limit of collisional kinetic equations, obtained in the small-Knudsen number limit, admits a low-rank representation when written as $f = Mg$, where $M$ is the local Maxwellian, and $g$ is low-rank. We apply this decomposition to the Vlasov-Amp\`{e}re-Fokker-Planck equation of plasma dynamics, considering the asymptotic limit of strong collisions and electric field. We implement our proposed algorithm and demonstrate the expected improvement in computation time by comparison to an implementation that evolves the full solution tensor $f$. We also demonstrate that our algorithm can capture dynamics in both the kinetic regime, and in the fluid regime with relatively lower computational effort, thereby efficiently capturing the asymptotic fluid limit.

Analisys of interlaminar stresses in composite laminates by finite difference method

In this work, full stress tensor components regarding stress state for a simmetrical composite laminate under uniform uniaxial extension have been determined. Off-plane stresses are specially meaningful due to the fact that they are responsible for failure mechanisms such as delamination and shear stress cracking. A finite difference scheme has been used to solve internal equilibrium equations subjected to stress-free boundary conditions along boundary lines; moreover symmetry considerations have been made. In such way, we get an improvement in solutions in contrast with results obtained following bidimensional reasoning and using laminate based elements. Off-plane stresses for differents ply-sequences have been evaluated and maximum and minimum values for different fibers orientations were explored.

Joint Nonlinear Inversion of Full Tensor Gravity Gradiometry Data and Its Parallel Algorithm

Geophysical joint inversion is more frequently applied to deep crust probes. For the potential field data, it requires the introduction of large-scale observed data and sensitivity matrices. Massive matrix-vector multiplications occur during iterations, and the obtained data cannot be effectively interpreted by merely using desktop computers. To improve the resolution and the computing ability of inversion, we here propose the parallel joint nonlinear inversion of full tensor gravity gradiometry data. As the inversion is affected by linear searches, it is associated with certain classical computing performance issues. Hence, we addressed the memory and efficiency limitations, which are caused by very large calculation volumes. Also, we performed a quantitative and comprehensive feasibility analysis of parallel computing. Then, we identified the main factor influencing the inversion performance and clarified the correspondence between the cell number and the memory. A parallel inversion solution was proposed via graphics processing unit (GPU) based on the sensitivity matrix compression. The data tests demonstrated that inversion has antinoise property and that it can obtain accurate underground density distributions. Also, the parallel solution was found to be suitable for inverting cells at the million cell scale and greater because of its ability of acceleration and matrix compression. A design pattern was applied for gravity or magnetic anomaly inversion of 100 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times 100\times20$ </tex-math></inline-formula> cells, and the run time was less than 1 min. Overall, we believe that the proposed solution can help implement massive potential field data inversions and promote the application of the parallel technique in other inversion research.

The Advantage Analysis of 3-D Inversion of Airborne Gravity Gradiometry Data With Larger Sampling Interval

Airborne gravity gradiometry is an effective tool for its high efficiency and sensitivity to the interesting buried targets, which has been increasingly introduced in mineral and petroleum exploration. When compared to gravimetry, full tensor gradient (FTG) measurements provide higher resolution and signal-to-noise ratio. In this article, we build and test models with different sampling intervals and compare the performances of individual components or their combinations in minimum structure inversion to evaluate the benefits of FTG combinations. As part of a theoretical study, the singular value spectrum (SVS) and depth-resolution plot (DRP) are examined to determine how much information and resolution different datasets provide in the underdetermined inverse problem. The synthetic examples show that integrating more components in inversion improves the resolution of the recovered model, and the inversion result of gravity or individual component cannot accurately restore the distribution of anomalous bodies. With the increasing sampling interval, joint inversion of FTG data still provides enough information corresponding to the source density distribution, and the limit survey interval is tested through models. In addition, we use a real survey over the Vinton dome as a case study and discover that <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V_{\mathrm {zz}}$ </tex-math></inline-formula> component fails to reconstruct the caprock model at coarse line spacing, whereas FTG combinations recover the acceptable geometry flawlessly. It also reflects the benefit of FTG combinations for inversion processing, which reduces the interference of measured noise on inversion results and allows for longer sampling intervals during the survey, effectively lowering the cost of an airborne survey and improving exploration efficiency

Error Calibration for Full Tensor Magnetic Gradiometer Probe Based on Coordinate Transformation Method

In order to calibrate the zero offset error and triaxial non-orthogonal error of full tensor magnetic gradiometer (FTMG) probe composed of superconducting quantum interference device (SQUID) magnetometers, we propose a new calibration method in this article. With the help of the triaxial Helmholtz coil, we can generate a magnetic field with known parameters. By establishing the objective functions containing the error parameters for the outputs of the SQUIDs and solving them with the least-squares fitting algorithm, the included angle between the SQUID sensor and the Helmholtz coil can be obtained, then all the required error parameters can be calculated by coordinate transformation method. Compared with the traditional method, this method does not need to rotate the SQUID magnetometers-based probe to collect the data set for calibration, thus avoiding the influence of motion induced noise on the calibration results. In order to verify the effectiveness of the proposed method, we adopted the widely used ellipsoid fitting method as a comparison method and conducted field comparison experiments. The results show that the proposed calibration method is better than the traditional ellipsoid fitting calibration method under the same experimental environment. The root mean square errors of five independent magnetic gradient tensor components are reduced to 0.39, 0.35, 0.41, 0.31 and 0.57 nT/m from 1630.55, 756.59, 3097.56, 1051.09 and 1245.64 nT/m by the proposed method.

A Full Tensor Network for Hyperspectral Image Classification

Hyperspectral image (HSI) is widely used in real-world classification tasks since it contains rich spatial and spectral features consisting of hundreds of continuous bands. However, the rich spectral features always result in “dimension disaster” for HSI classification. Some traditional methods adopt the strategy of dimensionality reduction in advance to alleviate the influences of high spectral feature dimension, which usually results in degraded classification accuracy due to the hard coupling of the dimensionality reduction model and the classifier. In this letter, we propose a full tensor network for HSI classification based on Tucker decomposition-based hidden layer and CP decomposition-based classification layer. The proposed network can efficiently extract the high-level structural features directly from the original data and classify HSI in a single network without dimension reduction procedure in advance. Moreover, the proposed model has a simple structure and holds less parameters than the state-of-art classification methods. The experimental results on Pavia University and Salinas datasets show that for training ratio of 5%, the overall accuracy of our model are averaged 3.41% higher than CNN models while the network parameters are averaged 80.44% less, which validate the merits of the proposed method.

Broadband Optical Constants and Nonlinear Properties of SnS2 and SnSe2.

SnS2 and SnSe2 have recently been shown to have a wide range of applications in photonic and optoelectronic devices. However, because of incomplete knowledge about their optical characteristics, the use of SnS2 and SnSe2 in optical engineering remains challenging. Here, we addressed this problem by establishing SnS2 and SnSe2 linear and nonlinear optical properties in the broad (300–3300 nm) spectral range. Coupled with the first-principle calculations, our experimental study unveiled the full dielectric tensor of SnS2 and SnSe2. Furthermore, we established that SnS2 is a promising material for visible high refractive index nanophotonics. Meanwhile, SnSe2 demonstrates a stronger nonlinear response compared with SnS2. Our results create a solid ground for current and next-generation SnS2- and SnSe2-based devices.

A multibranch, multitarget neural network for rapid point-source inversion in a microseismic environment: examples from the Hengill Geothermal Field, Iceland

SUMMARYDespite advanced seismological techniques, automatic source characterization for microseismic earthquakes remains difficult and challenging since current inversion and modelling of high-frequency signals are complex and time consuming. For real-time applications such as induced seismicity monitoring, the application of standard methods is often not fast enough for true complete real-time information on seismic sources. In this paper, we present an alternative approach based on recent advances in deep learning for rapid source-parameter estimation of microseismic earthquakes. The seismic inversion is represented in compact form by two convolutional neural networks, with individual feature extraction, and a fully connected neural network, for feature aggregation, to simultaneously obtain full moment tensor and spatial location of microseismic sources. Specifically, a multibranch neural network algorithm is trained to encapsulate the information about the relationship between seismic waveforms and underlying point-source mechanisms and locations. The learning-based model allows rapid inversion (within a fraction of second) once input data are available. A key advantage of the algorithm is that it can be trained using synthetic seismic data only, so it is directly applicable to scenarios where there are insufficient real data for training. Moreover, we find that the method is robust with respect to perturbations such as observational noise and data incompleteness (missing stations). We apply the new approach on synthesized and example recorded small magnitude (M ≤ 1.6) earthquakes at the Hellisheiði geothermal field in the Hengill area, Iceland. For the examined events, the model achieves excellent performance and shows very good agreement with the inverted solutions determined through standard methodology. In this study, we seek to demonstrate that this approach is viable for microseismicity real-time estimation of source parameters and can be integrated into advanced decision-support tools for controlling induced seismicity.