Assumption Of Anisotropy Research Articles

Weak magnetohydrodynamic turbulence theory revisited

Two recent papers, P. H. Yoon and G. Choe, Phys. Plasmas 28, 082306 (2021) and Yoon et al., Phys. Plasmas 29, 112303 (2022), utilized in the derivation of the kinetic equation for the intensity of turbulent fluctuations the assumption that the wave spectra are isotropic, that is, the ensemble-averaged magnetic field tensorial fluctuation intensity is given by the isotropic diagonal form, ⟨δBiδBj⟩k=⟨δB2⟩kδij. However, it is more appropriate to describe the incompressible magnetohydrodynamic turbulence involving shear Alfvénic waves by modeling the turbulence spectrum as being anisotropic. That is, the tensorial fluctuation intensity should be different in diagonal elements across and along the direction of the wave vector, ⟨δBiδBj⟩k=12 ⟨δB⊥2⟩k(δij−kikj/k2)+⟨δB∥2⟩k(kikj/k2). In the present paper, we thus reformulate the weak magnetohydrodynamic turbulence theory under the assumption of anisotropy and work out the form of nonlinear wave kinetic equation.

An initial investigation of the non-isotropic feature of GNSS tropospheric delay

Tropospheric delay is a significant error source in Global Navigation Satellite Systems (GNSS) positioning. Slant Path Delay (SPD) is commonly derived by multiplying Zenith Tropospheric Delay (ZTD) with a mapping function. However, mapping functions, assuming atmospheric isotropy, restrict the accuracy of derived SPDs. To improve the accuracy, a horizontal gradient correction is introduced to account for azimuth-dependent SPD variations, treating the atmosphere as anisotropic. This study uncovers that, amidst atmospheric dynamics and spatiotemporal changes in moisture content, the SPD deviates from that based on traditional isotropy or anisotropy assumption. It innovatively introduces the concept that SPD exhibits non-isotropy with respect to azimuth angles. Hypothesis validation involves assessing SPD accuracy using three mapping functions at five International GNSS Service (IGS) stations, referencing the SPD with the ray-tracing method. It subsequently evaluates the SPD accuracy with horizontal gradient correction based on Vienna Mapping Function 3 (VMF3) estimation. Lastly, the non-isotropic of SPD is analyzed through the ray-tracing method. The results indicate the smallest residual (1.1–82.7 mm) between the SPDs with VMF3 and those with the ray-tracing. However, introducing horizontal gradient correction yields no significant improvement of SPD accuracy. Considering potential decimeter-level differences in SPD due to non-isotropic tropospheric delay across azimuth angles, a precise grasp and summary of these variations is pivotal for accurate tropospheric delay modeling. This finding provides vital support for future high-precision tropospheric delay modeling.

An optimization method for surface urban heat island footprint extraction based on anisotropy assumption

The footprint (FP) is the main indicator used to quantitatively analyse the surface urban heat island (SUHI) effect. Currently, SUHI FP extraction methods ignore the interference caused by the city shape and are mostly based on the isotropic expansion assumption, resulting in an exaggerated range. Therefore, a new approach for an optimization schema that leverages the assumptions of angle segmentation and anisotropy is proposed herein. This method divides an urban area and its buffer rings into 16 sectors with equal central angles and selects appropriate land surface temperature (LST) curves for an exponential decay fit. The final FP was determined using the SUHI extension distance and the reference rural LST. To verify the effectiveness of this method, SUHI FPs of 27 cities in the central region of the Yangtze River Delta (YRD) were extracted during the summer of 2019, and the results were compared with those derived from traditional methods. The results showed that the FPs calculated using this method were more detailed because they minimized the influence of urban shape, topography, and the surrounding landscape. Moreover, this method played a vital role in revealing the effect of the land use allocation outside urban area on the SUHI effect. This state-of-the-art method is useful for unveiling SUHI spatial distribution patterns and for providing scientific support for land planning for sustainable urban development.

A Linearized Alternating Direction Method of Multipliers Algorithm for Prestack Seismic Inversion in VTI Media Using the Quadratic PP-Reflectivity Approximation

Periodic horizontal thin interlayers, or formations developing horizontally layered fractures in a homogeneous background, are commonly studied as a transverse isotropy with a vertical axis of symmetry (VTI) media. Anisotropy needs to be considered in predicting such special reservoirs, and can be inferred from the amplitude variation with offset (AVO) by the exact or linear reflectivity equations. However, the linear approximation is usually derived based on the assumptions of weak anisotropy and weak contrast, the accuracy suffers when the anisotropy or the contrast of two adjacent media increases. In addition, due to the high nonlinearity of the Graebner equation, the stability and efficiency of the exact inversion are limited. To address these issues, we propose a robust pre-stack seismic inversion for VTI media using quadratic PP-reflectivity approximation. Firstly, by deriving quadratic approximations for phase velocity and polarization, we analyze the advantage of the second-order terms at a higher-contrast interface. Then, based on perturbation theory, we derive a quadratic PP-reflectivity approximation from the exact equation. It consists of first- and second-order terms with isotropic and anisotropic components, and the accuracy is significantly improved even with enhanced anisotropy. Finally, we introduce the Hadamard product operator to linearly characterize the objective function, and develop an improved Alternating Direction Method of Multipliers (ADMM) algorithm to handle the nonlinearity of the quadratic equations. The feasibility and stability of the proposed method are tested on two datasets, that is, the logging curves used as numerical experiments and a field dataset from a shale reservoir.

Probabilistic analysis of pile-reinforced slopes in spatially variable soils with rotated anisotropy

Stabilizing piles have been widely used to remediate landslides and reinforce potentially unstable slopes. Previous investigations on the stability analyses of pile-reinforced slopes, however, were mainly based on deterministic analysis methods, where the spatial variability of soil properties was rarely incorporated. Meanwhile, the assumption of isotropy and horizontal transverse anisotropy in previous studies may bring bias to the slope reliability assessment, and thus the optimization design of piles. This study hence aims at systematically investigating the influence of soil spatially variable anisotropy on statistical characteristics of the factor of safety, failure mechanisms, and probability of failure (Pf) of pile-reinforced slopes. An integrated probabilistic analysis framework is used to obtain an optimal reinforcement scheme of stabilizing piles considering different rotational angles of soil strata. Subset simulation is used to enhance the computational efficiency for reliability analysis. A hypothetical slope and a practical slope are studied as illustrative examples with various parametric studies. Results show that the rotated anisotropy has a significant influence on the performance of pile-reinforced slopes and can largely affect the Pf depending on the strata inclination. For slopes with different rotational angles of strata, the number of critical slip surfaces and the slip band range are different and thereby result in different optimal pile designs.

Potential anisotropic finite-time singularity in the three-dimensional axisymmetric Euler equations

To date, it is not known if smooth initial conditions of the Euler equations with finite energy do or do not blow up in finite time. It is shown that under the assumption of spatial anisotropy, an axisymmetric incompressible and inviscid flow potentially presents a finite-time singularity. The singular flow consists of a quadrupolar structure for the vorticity together with a tangential discontinuity of the swirl velocity. On the discontinuity plane, the velocity field becomes a multivalued singularity. This singularity appears to be generic and robust for a wide number of finite energy initial conditions.

Laboratory characterisation of anisotropic and heterogeneous damage of rock sample using acoustic emission and ultrasonic monitoring technologies

Rock damage characterisation of Gosford sandstone samples under triaxial loading was achieved using an integrated approach, combing passive acoustic emission (AE) and active ultrasonic wave monitoring. The location of AE events is firstly obtained using isotropic wave velocity field measured by continuous ultrasonic wave. Then, passive AE tomography is conducted to progressively-update the anisotropy and heterogenous P-wave velocity field of rock samples. According to the variance in P-wave velocity, damage induced anisotropy and heterogeneity can be identified. The results suggest that the inhomogeneous damage evolution highly dependent on the loading stages and can well reflect the microcrack behaviour. Anisotropic damage variable along the whole loading process is also analysed, by a second order damage tensor with a transversely anisotropy assumption. It is observed that the lateral component of damage is much higher than the axial component. This is mainly due to the dilation behaviour of rock sample. This paper will cast more light on anisotropic and heterogenous damage characterisation using acoustic/ultrasonic lab experiments.

Extremum sensitivity analysis with polynomial Monte Carlo filtering

Global sensitivity analysis is a powerful set of ideas and heuristics for understanding the importance and interplay between uncertain parameters in a computational model. Such a model is characterized by a set of input parameters and an output quantity of interest, where we typically assume that the inputs are independent and their marginal densities are known. If the output quantity is smooth, polynomial chaos can be used to extract Sobol’ indices.In this paper, we build on these well-known ideas by examining two different aspects of this paradigm. First, we study whether sensitivity indices can be computed efficiently if one leverages a polynomial ridge approximation—a polynomial fit over a subspace. Given the assumption of anisotropy in the dependence of a function, we show that sensitivity indices can be computed with a reduced number of model evaluations. Second, we discuss methods for evaluating sensitivities when constrained near output extrema. Methods based on the analysis of skewness are reviewed and a novel type of indices based on Monte Carlo filtering (MCF) – extremum Sobol’ indices – is proposed. We combine these two ideas by showing that these indices can be computed efficiently with ridge approximations, and explore the relationship between MCF-based indices and skewness-based indices empirically.

Prediction of Strain Path Changing Effect on Forming Limits of AA 6111-T4 Based on a Shear Ductile Fracture Criterion

Strain path changing is a phenomenon in the stamping of complex panels or multiple-step stamping processes. In this study, the influence of the strain path changing effect was investigated and assessed for an aluminum alloy of 6111-T4 with a shear ductile fracture criterion. Plastic deformation of the alloy was modeled by an anisotropic Drucker yield function with the assumption of normal anisotropy. Then the shear ductile fracture criterion was calibrated by the fracture strains at uniaxial tension, plane strain tension and equibiaxial tension under proportional loading conditions. The calibrated fracture criterion was utilized to predict forming limit curves (FLCs) of the alloy stretched under bilinear strain paths. The analyzed bilinear strain paths included biaxial tension after uniaxial tension, plane strain tension and equibiaxial tension. The predicted FLCs of bilinear strain paths were compared with experimental results. The comparison showed that the shear ductile fracture criterion could reasonably describe the effect of strain path changing on FLCs, but its accuracy was poor for some bilinear paths, such as uniaxial tension followed by equibiaxial tension and equibiaxial tension followed by plane strain tension. Kinematic hardening is suggested to substitute the isotropic hardening assumption for better prediction of FLCs with strain path changing effect.

3D anisotropic structure of the Japan subduction zone.

How mantle materials flow and how intraslab fabrics align in subduction zones are two essential issues for clarifying material recycling between Earth's interior and surface. Investigating seismic anisotropy is one of a few viable technologies that can directly answer these questions. However, the detailed anisotropic structure of subduction zones is still unclear. Under a general hexagonal symmetry anisotropy assumption, we develop a tomographic method to determine a high-resolution three-dimensional (3D) P wave anisotropic model of the Japan subduction zone by inverting 1,184,018 travel time data of local and teleseismic events. As a result, the 3D anisotropic structure in and around the dipping Pacific slab is firstly revealed. Our results show that slab deformation plays an important role in both mantle flow and intraslab fabric, and the widely observed trench-parallel anisotropy in the forearc is related to the intraslab deformation during the outer-rise yielding of the subducting plate.

Magnetic hysteresis of blocked ferrihydrite nanoparticles

Using minor hysteresis loops in the Stoner–Wohlfarth model allows describing the experimental behavior of the coercive force of minor hysteresis loops in ferrihydrite nanoparticles with a change in the field amplitude. The description allows estimating the parameters of the distribution of the magnetic anisotropy field in nanoparticles. The best agreement of the anisotropy fields estimated by different approaches is achieved for the assumption of uniaxial anisotropy in ferrihydrite nanoparticles.

Influence of the Replacement of the Actual Plastic Orthotropy with Various Approximations of Normal Anisotropy on Residual Stresses and Strains in a Thin Disk Subjected to External Pressure

Plastic anisotropy is very common to metallic materials. This property may significantly affect the performance of structures. However, the actual orthotropic yield criterion is often replaced with a criterion based on the assumption of normal anisotropy. The present paper aims to reveal the influence of this replacement on the distribution of strains and residual strains in a thin hollow disk under plane stress conditions. The boundary-value problem is intentionally formulated such that it is possible to obtain an exact semi-analytical solution without relaxing the boundary conditions. It is assumed that the disk is loaded by external pressure, followed by elastic unloading. The comparative analysis of the distributions of residual strains shows a significant deviation of the distribution resulting from the solutions based on the assumption of normal anisotropy from the distribution found using the actual orthotropic yield criterion. This finding shows that replacing the actual orthotropic yield criterion with the assumption of normal anisotropy may result in very inaccurate predictions. The type of anisotropy accepted is of practical importance because it usually results from such processes as drawing end extrusion with an axis of symmetry.

Reflection and transmission coefficient approximations for P, S1 and S2 waves in triclinic media

SUMMARY The conventional assumptions, in most published approximations of the reflection and transmission (R/T) coefficients of plane waves at a plane interface between two anisotropic half-spaces, confine their applications to weakly anisotropic and/or weak contrast models. We consider the horizontal interface enclosed by two triclinic half-spaces to approximate the R/T coefficients normalized by the vertical energy flux. The homogeneous background medium can be anisotropic with arbitrary symmetry to better simulate the strongly anisotropic media. The second-order approximations are proposed to accommodate the strong contrast interface. We also consider an isotropic background medium under the weak anisotropy assumption. The obtained approximations can be applied to P, S1 and S2 waves, except for the transmission coefficients between the S1 and S2 waves. The S-wave transmission coefficients are insensitive to the model parameter contrasts and predominately rely on the S-wave polarization directions in the half-spaces above and below the interface. The proposed approximations are tested numerically.

Bayesian lithology analysis with seismic-driven likelihood to anisotropic medium: a case study from Northwest Australia

Abstract An isotropic medium is generally assumed for reservoir characterization although it has been reported that velocity anisotropy often has a non-negligible impact. One of the difficulties in incorporating anisotropy is that the exact anisotropy parameters are generally unknown. To overcome the problem, a seismic-driven approach to Bayesian probability analysis is proposed, which defines the likelihood from seismic inversion data. Comparing this approach for lithology prediction to one based on well data, it is found that an isotropic well-data approach does not work well but is improved by taking anisotropy into account. A larger improvement is achieved by the seismic-driven approach which provides a robust result which is insensitive to the anisotropy assumption.

Load resisting mechanism of the mortise-tenon connection with gaps under in-plane forces and moments

Mortise-tenon (MT) connection is a basic structural component connecting beams and columns in a plane in traditional Chinese wooden structures. Much research effort has been made on its behavior and performances, especially on the moment-rotation relationship, while there is not any model on the load resisting mechanism under realistic axial load, shear and bending moment. This paper presents a non-linear analytical model for a MT connection with gaps in traditional wooden structures based on the embedment theory and the assumption of orthogonal anisotropy in wood material. Thefriction-slip-contact mechanism between the mortise and tenon under realistic loadings is analytically studied with consideration of the coupling effects of different deformations on the restoring forces. The stiffness of a hybrid finite element with end springs is then formulated to simulate the presence of a MT connection in a frame member. The performance of this connection in a wooden planar frame in the dynamic analysis under horizontal loads is then studied. The characteristics of the friction-slip-contact behavior in the MT connection under load can be obtained with this model together with detailed information on the energy dissipation mechanism of the connection. The traditional Chinese wooden structures may be concluded to exhibit good seismic resistance capacity with the vibration energy dissipated by friction in the many MT connections throughout the vibration process.

Reflection and transmission approximations for weak contrast orthorhombic media

Subsurface media are in general anisotropic, and this fact should be taken into account for analyzing reflection and transmission (R/T) coefficients. Orthorhombic (ORT) media are commonly regarded as a practical symmetry system to account for polar anisotropy and azimuthal anisotropy. We have focused on the model made up of two welded ORT half-spaces to analyze the R/T coefficients normalized by vertical energy flux. The two half-spaces have azimuthally nonaligned vertical symmetry planes and are parameterized in two local 3D Cartesian coordinate frames, respectively. The vertical coordinate planes in each local frame coincide with the vertical symmetry planes for the corresponding ORT half-spaces. Under the weak contrast assumption for the two half-spaces, this model is taken as the perturbed model in R/T approximations with the perturbation theory. The unperturbed model is also composed of two unperturbed ORT half-spaces with their different vertical symmetry plane orientations inheriting the counterparts for the perturbed half-spaces above and below the interface, respectively. The unperturbed ORT half-spaces above and below the interface have the same model parameters defined in the two local coordinate frames, respectively. With the perturbations respectively evaluated in the local coordinate frames above and below the interface, the azimuth angle that indicates the local frames’ azimuthal difference is decoupled from the model parameter contrasts. Compared with the traditional approximation method with the perturbation theory in a global coordinate frame, the proposed R/T approximations depend on fewer model parameter discontinuities. We also consider the isotropic background medium under the weak anisotropy assumption. Influences of S-wave singularity points are mitigated by introducing pseudowaves for approximations. Numerical tests are implemented to demonstrate the accuracy.

Reflection and transmission responses for layered transversely isotropic media with vertical and horizontal symmetry axes

Reflection and transmission (R/T) responses characterize the energy distributions for incident and generated waves across the subsurface interface. The R/T coefficients are considerably influenced by the local anisotropy, and this implies the significance of the R/T responses analysis for anisotropic media. We have considered the plane interface bounded by two transversely isotropic media with, respectively, vertical and horizontal symmetry axes, and R/T coefficients normalized by the vertical energy flux are obtained in the phase domain. We define two simple anisotropic layered models characterized by fewer independent model parameters. Under the assumption of weak contrast model parameters across the interface, the R/T coefficient approximations are obtained as the perturbations from the simple models’ counterparts. The isotropic background medium is also used to obtain the approximations under an additional weak anisotropy assumption. Compared with approximations degenerated from more general cases, our approximations rely on fewer independent parameters. Numerical tests are implemented to evaluate our approximations.

Reflection and transmission responses in a layered transversely isotropic medium with horizontal symmetry axis

Seismic wave reflection and transmission (R/T) responses characterize the subsurface local property, and the widely spread anisotropy has considerable influences even at small incident angles. We have considered layered transversely isotropic media with horizontal symmetry axes (HTI), and the symmetry axes were not restricted to be aligned. With the assumption of weak contrast across the interface, linear approximations for R/T coefficients normalized by vertical energy flux are derived based on a simple layered HTI model. We also obtain the approximation with the isotropic background medium under an additional weak anisotropy assumption. Numerical tests illustrate the good accuracy of the approximations compared with the exact results.

Dynamic cantilever magnetometry of individual Co nanosheets and applicable conditions of uniaxial magnetic anisotropy assumption

In this work, we investigated individual Co nanosheets by dynamic cantilever magnetometry. For a disk sample, fitting results give consistent magnetic anisotropy from in-plane and out-of-plane magnetization processes. The derived saturation magnetization value is comparable to the bulk value. However, for a rectangular sample, there is a considerable difference between the derived anisotropy constants from the in-plane and out-of-plane. Moreover, the derived saturation magnetization value is much smaller than the bulk value. We conclude that for samples without rotation symmetry, the uniaxial anisotropy assumption is not applicable and a biaxial or more complex magnetic anisotropy should be taken into account in analyzing dynamic cantilever magnetometry measurements.

Calibration method of ductile damage model based on hybrid experimental-numerical analysis of uniaxial tensile and hole-expansion tests

The present study details the calibration method of ductile damage model as a useful and sufficiently accurate procedure for modeling ductile failure in sheet metal forming. This calibration method has been performed through a hybrid experimental-numerical analysis of two characterization tests of the material properties namely the uniaxial tensile and the hole-expansion as a newly added feature of this work. Elastic-plastic finite element models with orthotropic anisotropy assumption and experiments of both characterization tests were carried out. The identification of the parameters related to the anisotropic plastic behavior, the strain-hardening after necking and the ductile damage model has been finally achieved by comparing the experimental and numerical results in terms of true tress-true strain and load-displacement relationships for the uniaxial tensile test as well as the state of the final shape resulted from the hole-expansion test. Finally, a flow chart is proposed in this paper as a practical tool which describes properly the calibration procedure.