Anisotropy measurements and characterization of the Qingshankou shale

Qingshankou shale(Gulong area,China)exhibits strong acoustic anisotropy characteristics,posing significant challenges to its exploration and development.In this study,the five full elastic constants and multipole response law of the Qingshankou shale were studied using experimental measurements.Analyses show that the anisotropy parametersϵandγin the study region are greater than 0.4,whereas the anisotropy parameterδis smaller,generally 0.1.Numerical simulations show that the longitudinal and transverse wave velocities of these strong anisotropic rocks vary significantly with inclination angle,and significant differences in group velocity and phase velocity are also present.Acoustic logging measures the group velocity in dipped boreholes;this differs from the phase velocity to some extent.As the dip angle increases,the longitudinal and SH wave velocities increase accordingly,while the qSV-wave velocity initially increases and then decreases,reaching its maximum value at a dip of approximately 40°.These results provide an effective guide for the correction and modeling of acoustic logging time differences in the region.

Interplay between Micro-Anisotropy and Macro-Isotropy on Evolution of Non-Equilibrium Morphology

Non-equilibrium morphology has received much attention from both scientific and engineering points of view for its intricate pattern selection mechanisms and useful industrial application. Most study of non-equilibrium is about the metal, alloy and other simple system. The complex silicate system is rarely involved. However, silicate is very important in geosciences and ceramic industry. In this paper, two kinds of non-equilibrium crystal morphologies of silicate: dendrite of diopside and spherulite of plagioclase, were introduced. Combining with the other kinds of non-equilibrium morphologies, the characteristics of micro-macro and anisotropy-isotropy of the non-equilibrium morphologies were discussed. Dendrite of diopside is micro- and macro-anisotropic, spherulite of plagioclase is micro-anisotropic, but macro-isotropic, fractal of NH4Cl is also micro-anisotropic, but macro-isotropic, dense-branching morphology (DBM) formed in non-crystalline system is micro-and macro-isotropic. Based on the micro-macro interplay on the pattern formation, it is proposed that the interplay between micro-anisotropy of crystal structure vs macro-isotropy of undercooling in crystal growth system will control the morphological evolution. The nucleation rate related to the anisotropy for the morphological evolution was also discussed. The fact that diopside develops dendrite and plagioclase develop spherulite in our experiment is due to their structural anisotropy difference.

Two-Dimensional Magnetotelluric Forward Research for the Vertical Anisotropy

When we study and process magnetotelluric data, the earth's interior structure is usually equated with isotropic medium in the existing approaches. When the underground structure is complex, there is serious resistivity anisotropy in macroscopic view, and then the traditional processing and interpretation methods often produce wrong results. For that we must establish the study method based on the anisotropy in order to explain the measured data exactly. In this paper, by considering the change of resistivity in three electrical spindle directions, we deduce two-dimensional magnetotelluric variational equation for vertical anisotropy. The study region is divided into many rectangular units, and it is dealt with linear interpolation in each of them. By comparing with former achievements including the results of the isotropic and anisotropic models, it demonstrates the validity of the program. The pseudosection map of vertical anisotropic body shows that we can’t ignore the anisotropy effect and provides a solid foundation for the further inversion study.

Earth’s Serious Anisotropy, Non-Inertiality, Ether, Gain of Free Energy, Revealed, Part 2

The present paper is of historic importance as well as the second part of [1]. In this second part, we detect important details about the orbit of the Earth and about the velocity (of magnitude 217 km/s) of the solar system around the center of the Milky Way galaxy. Some of these details concern the perihelion and aphelion of the orbit of the Earth. For several years we have observed that the return pulses, on the oscilloscope screen, appear to be more energetic than the initial pulses (See Part 1, Figure 2, for which the blue return pulse crests are much higher than the yellow initial crests). The used oscilloscope is and only must be, a storage oscilloscope, in other words, a computerized oscilloscope with a digital memory. The first oscilloscopes like this, came out, only after 1995, a relatively recent time that all wire velocity experiments and measurements were already completely investigated by science. We do astronomy, without receiving images by an astronomical telescope, but instead by sending signals around a loop and making an analysis using the same oscilloscope as in Part 1. We recommend to the reader to study Part 1 as a prerequisite. The Earth surface is accelerating with a centripetal acceleration, due to its rotation, thus it is not an inertial frame. Also, the Earth is evidently anisotropic, due to the same rotation, a second reason for it being a non-inertial rotating frame.

Anisotropy and Empirical Relations for the Estimation of Anisotropy Parameters in Niger Delta Depobelts

The difficulty in achieving well-to-seismic ties due to errors arising from wrong time-to-depth conversions has been as a result of ignoring anisotropy in seismic processing. Anisotropy plays a vital role in the processing and interpretation of seismic data. In this work, an inversion method based on the elastic stiffness tensors was adopted to estimate and quantify anisotropy in two depobelts using petrophysical well logs in Niger delta (Central Swamp and Greater Ughelli). Results show that the estimated delta (δ), epsilon (ε), gamma (γ) and eta (η) exhibit a high degree of anisotropy in the shales than in the sands. The parameters were observed to be higher in the Central Swamp than the Greater Ughelli depobelt. This behavior could be associated with the alternating sequence of massive shale and sand beds geologically observed within this depobelt. This work was also able to derive empirical relations that could be used in estimating these parameters in the depobelts once appropriate information or data for any one parameter is available.

OPTIMAL DESIGN OF A 6-AXIS FORCE TRANSDUCER BASED ON STEWART PLATFORM RELATED TO SENSITIVITY ISOTROPY

The design method of a 6-axis force robot's transducer based on the Stewartplatform is detailed. For this purpose, the sensitivity isotropy evaluation criteria of thetransducer are defined, and by the aid of computer, the relationships between the criteria and theparameters of all the transducers based on the Stewart platform are investigated within thegeometric model of the solution space, which can provide the theoretical background for the optimalconstruction design of the 6-axis force transducer related to the sensitivity isotropy.

Some recent advances in 3D crack and contact analysis of elastic solids with transverse isotropy and multifield coupling

Significant progress has been made in mixed boundary-value problems associated with three-dimensional（3D） crack and contact analyses of advanced materials featuring more complexities compared to the conventional isotropic elastic materials.These include material anisotropy and multifield coupling,two typical characteristics of most current multifunctional materials.In this paper we try to present a state-of-the-art description of 3D exact/analytical solutions derived for crack and contact problems of elastic solids with both transverse isotropy and multifield coupling in the latest decade by the potential theory method in the spirit of V.I.Fabrikant.whose ingenious breakthrough brings new vigor and vitality to the old research subject of classical potential theory.We are particularly interested in crack and contact problems with certain nonlinear features.Emphasis is also placed on the coupling between the temperature field（or the like） and other physical fields（e.g.,elastic,electric,and magnetic fields）.We further highlight the practical significance of 3D contact solutions,in particular in applications related to modern scanning probe microscopes.

Force/Moment Isotropy of 8/4-4 Parallel Six-Axis Force Sensor Based on Performance Atlases

A six-axis force sensor with parallel 8/4-4 structure is introduced and its measurement principle is analyzed.Based on condition numbers of Jacobian matrix spectral norm of the sensor,the relationship between the force and moment isotropy and some structural parameters is deduced.Orthogonal test methods are used to determine the degree of primary and secondary factors that have significant effect on sensor characteristics.Furthermore,the relationship between each performance index and the structural parameters of the sensor is analyzed by the method of the atlas,which lays a foundation for structural optimization design of the force sensor.

Effect of inter-cycle heat treatment in accumulative roll-bonding(ARB)process on planar isotropy of mechanical properties of AA1050 sheets

The accumulative roll-bonding(ARB)process was applied on the strips of aluminum alloy 1050 in two processing conditions:cold ARB and warm ARB.The results of tensile tests and microhardness measurement show that the warm ARB process exhibits the lower tensile strength and microhardness,more homogeneous distribution of the microhardness,higher elongation,and especially superior planar isotropy of the tensile properties in comparison to the cold ARB,because of the intermediate heat treatment as well as the elevated temperature rolling in the warm ARB process.Furthermore,with increasing the cycles of both processes,the planar isotropy decreases progressively.

Complete solutions for elastic fields induced by point load vector in functionally graded material model with transverse isotropy

The paper develops and examines the complete solutions for the elastic field induced by the point load vector in a general functionally graded material(FGM)model with transverse isotropy.The FGMs are approximated with n-layered materials.Each of the n-layered materials is homogeneous and transversely isotropic.The complete solutions of the displacement and stress fields are explicitly expressed in the forms of fifteen classical Hankel transform integrals with ten kernel functions.The ten kernel functions are explicitly expressed in the forms of backward transfer matrices and have clear mathematical properties.The singular terms of the complete solutions are analytically isolated and expressed in exact closed forms in terms of elementary harmonic functions.Numerical results show that the computation of the complete solutions can be achieved with high accuracy and efficiency.

Interaction between transverse isotropy rock slope and supporting structure

In order to study the interaction between transverse isotropy rock mass and supporting structure,the laboratory tests for rock sampled from the slope at expressway project were carried out,and the parameters of elasticity for transverse isotropic rock were determined by the uniaxial compression tests for rock sample with different strike of stratification plane.Then,based on the relationship of stress-stain for transverse isotropic rock mass,the analytical model was established for the interaction between transverse isotropic rock mass and frame beam with pre-stressed anchor cable.Furthermore,the conception of the best anchorage-angle in pre-stressed anchor cable was proposed.At last,the parameters of the interaction between transverse isotropy rock mass and frame beam with pre-stressed anchor cable were investigated by finite element method,and the best anchorage-angle in pre-stressed anchor cable was obtained.The rules of the influence of the directivity of stratification plane on supporting structure were determined.The results show that the analytical model and numerical method on the design of pre-stressed anchor cable with frame beam supporting for transverse isotropy rock slope are reasonable and reliable in practical engineering design.

Three-dimensional surface current loops in broadband responsive negative refractive metamaterial with isotropy

We propose a bulk negative refractive index （NRI） metamaterial composed of periodic array of tightly coupled metallic cross-pairs printed oR the six sides of a cube for applications of superlenses. The structural characteristics of the three-dimensional （3D） metamaterial consist in the high symmetry and the superposition of metallic cross-pairs, which can increase the magnetic inductive coupling between adjacent cross-pairs and realize a broadband and isotropic NRI. The proposed 3D structure is simulated using the CS~ Microwave Studio 2006 to verify the design validity. The simulation results show that the proposed structure can not only realize simultaneously an electric and magnetic response to an incident electromagnetic （EM） wave, but also exhibit a broadband NRI whose relative bandwidth can reach up to 56.7%. In addition, the NRI band is insensitive to tile polarization and the incident angle of the incident EM wave. Therefore, the proposed metamaterial is a good candidate material as three-dimensional broadband isotropic NRI metamaterial.

DESIGN OF 6-AXIS FORCE/TORQUE SENSOR BASED ON STEWART PLATFORM RELATED TO ISOTROPY

A model of the solution space for all the sensor mechanisms based on the Stewart platform is established, which is a novel and useful tool for investigation of the optimal sensor design. A kind of performance evaluation atlases are plotted within the model of the solution space, which clearly show relationships between the condition number of Jacobjan matrix and parameters of all the sensor mechanisms. By using the performance atlases, an optimal design for the sensor mechanism can be achieved. Because the elastic joints are proposed for replacing the spherical joints, the Stewart platform based sensor can be designed as small as possible.

Inhomogeneous material property assignment and orientation definition of transverse isotropy of femur

The finite element method has been increasingly adopted to study the biomechanical behavior of biologic structures. Once the finite element mesh has been generated from CT data set, the assignment of bone tissue’s material properties to each element is a fundamental step in the generation of individualized or subject-specific finite element models. The aim of this work is to simulate the inhomogeneous and anisotropic material properties of femur using the finite element method. A program is developed to read a CT data set as well as the finite element mesh generated from it, and to assign to each element of the mesh the material properties derived from the bone tissue density at the element location. Moreover, for cancellous bone in femoral neck and cortical bone in femoral stem, the principal orientations of transverse isotropy were defined based on the tra-becular structures and the haversian system respectively.

The symmetric space,strong isotropy irreducibility and equigeodesic properties

A smooth curve on a homogeneous manifold G/H is called a Riemannian equigeodesic if it is a homogeneous geodesic for any G-invariant Riemannian metric.The homogeneous manifold G/H is called Riemannian equigeodesic,if for any x∈G/H and any nonzero y∈Tx(G/H),there exists a Riemannian equigeodesic c(t) with c(0)=x and ■(0)=y.These two notions can be naturally transferred to the Finsler setting,which provides the definitions for Finsler equigeodesics and Finsler equigeodesic spaces.We prove two classification theorems for Riemannian equigeodesic spaces and Finsler equigeodesic spaces,respectively.Firstly,a homogeneous manifold G/H with a connected simply connected quasi compact G and a connected H is Riemannian equigeodesic if and only if it can be decomposed as a product of Euclidean factors and compact strongly isotropy irreducible factors.Secondly,a homogeneous manifold G/H with a compact semisimple G is Finsler equigeodesic if and only if it can be locally decomposed as a product,in which each factor is Spin(7)/G2,G2/SU (3) or a symmetric space of compact type.These results imply that the symmetric space and the strongly isotropy irreducible space of compact type can be interpreted by equigeodesic properties.As an application,we classify the homogeneous manifold G/H with a compact semisimple G such that all the G-invariant Finsler metrics on G/H are Berwald.It suggests a new project in homogeneous Finsler geometry,i.e.,to systematically study the homogeneous manifold G/H on which all the G-invariant Finsler metrics satisfy a certain geometric property.

Bending Resistance and Anisotropy of Basalt Fibers Laminate Composite with Bionic Helical Structure

The appendages of mantis shrimp often bear bending loads from different directions during the in the process of preying on prey with its grazing limb.Hence,it has excellent bending resistance and isotropy to confront complex and changeable external load.The outstanding performance owes to the helical Bouligand structure with a certain interlayer corner,which is also widely found in other natural materials.Hence,the bio-inspired materials with basalt fiber are fabricated with outstanding bending resistance,isotropy and toughness.The research shows laminates with 18°interlayer corners exhibit relatively excellent bending resistance and isotropy,and the laminate with 11.25°interlayer corner has best toughness.Compared with traditional composites,average bending strength along different loading direction of bio-inspired materials increased by 28%,and anisotropy decreased by 86%.Besides,the maximum toughness of laminates can increase to 1.7 times of the original.Following the introduction of interlayer corners,the bio-inspired composite tends to be isotropic.To explore the reason for the change of the isotropic performance caused by diverse interlayer corners,the Finite Element Analysis based on classical laminate theory and Tsai–Wu and Tsai–Hill failure criterion.Besides,further experiments and observations are conducted to explore possible reasons.In conclusion,following the introduction of interlayer corners,the bio-inspired composites tend to be isotropic.This bio-inspired composites are expected to be applied to various complex modern engineering fields,such as vehicle,rail transit and aerospace.

8-rank of the class group and isotropy index

Suppose F = Q(√-p1 pt) is an imaginary quadratic number field with distinct primes p1,..., pt,where pi≡ 1(mod 4)(i = 1,..., t- 1) and pt ≡ 3(mod 4). We express the possible values of the 8-rank r8 of the class group of F in terms of a quadratic form Q over F2 which is defined by quartic symbols. In particular,we show that r8 is bounded by the isotropy index of Q.

Geodesic orbit metrics on homogeneous spaces constructed by strongly isotropy irreducible spaces

In this paper,we focus on homogeneous spaces which are constructed from two strongly isotropy irreducible spaces,and prove that any geodesic orbit metric on these spaces is naturally reductive.

Analytical solution for the effective elastic properties of rocks with the tilted penny-shaped cracks in the transversely isotropic background

Seismic prediction of cracks is of great significance in many disciplines,for which the rock physics model is indispensable.However,up to now,multitudinous analytical models focus primarily on the cracked rock with the isotropic background,while the explicit model for the cracked rock with the anisotropic background is rarely investigated in spite of such case being often encountered in the earth.Hence,we first studied dependences of the crack opening displacement tensors on the crack dip angle in the coordinate systems formed by symmetry planes of the crack and the background anisotropy,respectively,by forty groups of numerical experiments.Based on the conclusion from the experiments,the analytical solution was derived for the effective elastic properties of the rock with the inclined penny-shaped cracks in the transversely isotropic background.Further,we comprehensively analyzed,according to the developed model,effects of the crack dip angle,background anisotropy,filling fluid and crack density on the effective elastic properties of the cracked rock.The analysis results indicate that the dip angle and background anisotropy can significantly either enhance or weaken the anisotropy degrees of the P-and SH-wave velocities,whereas they have relatively small effects on the SV-wave velocity anisotropy.Moreover,the filling fluid can increase the stiffness coefficients related to the compressional modulus by reducing crack compliance parameters,while its effects on shear coefficients depend on the crack dip angle.The increasing crack density reduces velocities of the dry rock,and decreasing rates of the velocities are affected by the crack dip angle.By comparing with exact numerical results and experimental data,it was demonstrated that the proposed model can achieve high-precision estimations of stiffness coefficients.Moreover,the assumption of the weakly anisotropic background results in the consistency between the proposed model and Hudson's published theory for the orthorhombic rock.

Phase velocity in 2D TTI media

We derive an expression for phase velocity in 2D tilted transverse isotropy （TTI） media. Snapshots of phase velocity in TTI and transverse isotropy （TI） model media are simulated and analyzed using the derived expression. In addition, the x-component character differences between the modeled phase velocities of the two media models are compared and analyzed.