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.

Magneto-optical Kerr Effect of Mono-layer NiX_(2)(X=Cl,Br,I):A Density Functional Theory Study

The full-potential linearized augmented plane wave plus local orbital method is utilized for exploring the electronic,magnetic,and magneto-optical properties of the NiX_(2)(X=Cl,Br,and I)single layer.The first-principles calculation demonstrates that these compounds are ferromagnetic indirect semiconductors,and the energy band gaps of NiX_(2)for X=Cl,Br,and I are 3.888,3.134,and 2.157 eV,respectively.The magnetic moments of Ni atoms in NiX_(2)monolayer are 1.656,1.588,1.449μB,and their magneto-crystalline anisotropy energies are 0.167,0.029,0.090 meV,respectively.Based on the macro-linear response theory,we systematically studied the influences of the external magnetic field and out-of-plane strain on the magneto-optical Kerr effect(MOKE)spectrum of the NiX_(2)single layer.It is found that,when the external magnetic field is perpendicular to the sample plane,the value of the Kerr rotation angle reaches the maximum,and the single-layer NiI_(2)material has a Kerr rotation angle of 1.89°at the photon energy of 1.986 eV.Besides,the Kerr rotation spectrum of NiCl_(2)and NiBr_(2)monolayers redshift as the out-of-plane strain increases,while NiI_(2)monolayer blueshifts.Accurate computation of the MOKE spectrum of NiX_(2)materials provides an opportunity for applications of 2D magnetic material ranging from sensing to data storing.

Magneto-optical Kerr and Faraday effects in bilayer antiferromagnetic insulators

Control and detection of antiferromagnetic topological materials are challenging since the total magnetization vanishes.Here we investigate the magneto-optical Kerr and Faraday effects in bilayer antiferromagnetic insulator Mn Bi2Te4.We find that by breaking the combined mirror symmetries with either perpendicular electric field or external magnetic moment,Kerr and Faraday effects occur.Under perpendicular electric field,antiferromagnetic topological insulators(AFMTI)show sharp peaks at the interband transition threshold,whereas trivial insulators show small adjacent positive and negative peaks.Gate voltage and Fermi energy can be tuned to reveal the differences between AFMTI and trivial insulators.We find that AFMTI with large antiferromagnetic order can be proposed as a pure magneto-optical rotator due to sizable Kerr(Faraday)angles and vanishing ellipticity.Under external magnetic moment,AFMTI and trivial insulators are significantly different in the magnitude of Kerr and Faraday angles and ellipticity.For the qualitative behaviors,AFMTI shows distinct features of Kerr and Faraday angles when the spin configurations of the system change.These phenomena provide new possibilities to optically detect and manipulate the layered topological antiferromagnets.

TRANSVERSE VELOCITY ESTIMATION BASED ON HIGH-ORDER DOPPLER EFFECT OF MOVING OBJECT

The one-order phase of the echo changes if there is relative radial moving between the object and the radar, i.e. , the Doppler effect. The Doppler effect is widely used in radar signal processing. The transverse motion of the object cannot change the one-order phase of the echo, but the high-order phase. The high-order Doppler effect of the transverse moving target is presented and a new algorithm for obtaining the transverse velocity is given. The scalar velocity of a target moving steadily in any direction can be calculated with one-order and two-order items of the echo phase. The calculating method and simulating results are given. As the transverse speed is 900 km/h, the speed calculation error is less than 0. 06% if SNR of echo signal is higher than 0 dB.

Vertical vibration of a large diameter pipe pile considering transverse inertia effect of pile

Considering the transverse inertia effect of pile, the vertical soil layer is studied. The wave propagations in the outer and inner soil dynamic response of a large diameter pipe pile in viscoelastic are simulated by three-dimensional elastodynamic theory and those in the pile are simulated by Rayleigh-Love rod theory. The vertical and radial displacements of the outer and inner soil are obtained by utilizing Laplace transform technique and differentiation on the governing equations of soils. Then, based on the continuous conditions between the pile and soils, the displacements of the pile are derived. The frequency domain velocity admittance and time domain velocity response of the pile top are also presented. The solution is compared to a classical rod model solution to verify the validity. The influences of the radii and Poisson ratio of pile on the transverse inertia effect of pile are analyzed. The parametric study shows that Poisson ratio and outer radius of pile have significant influence on the transverse inertia effect of large diameter pipe piles, while the inner radius has little effect.

Differential Quadrature Method for Bending Problem of Plates with Transverse Shear Effects

A differential quadrature (DQ) method for orthotropic plates was proposed based on Reddy' s theory of plates with the effects of the higher-order transverse shear deformations. Wang-Bert's DQ approach was also further extended to handle the boundary conditions of plates. The computational convergence was studied, and the numerical results were obtained for different grid spacings and compared with the existing results. The results show that the DQ method is fairly reliable and effective.

Classic analogue of Autler–Townes-splitting transparency using a single magneto-optical ring resonator

We show that an optical transparency can be obtained by using only one single magneto-optical ring resonator. This effect is based on the splitting of counterclockwise and clockwise modes in the ring resonator. Within a proposed resonator-waveguide configuration the superposition between the two degeneracy broken modes produces a transparency window,which can be closed, open, and modified by tuning the applied magnetic field. This phenomenon is an analogue of Autler–Townes splitting, and the magnetic field is equivalent to the strong external pump field. We provide a theoretic analysis on the induced transparency, and numerically demonstrate the effect using full-wave simulation. Feasible implication of this effect and its potential applications are also discussed.

Theoretical research on the transverse spin of structured optical fields inside a waveguide

Structured optical fields inside a waveguide possess the transverse spin, i.e., the spin angular momentum perpendicular to the direction of the waveguide. The physical origin of the transverse spin can be attributed to the presence of an effective rest mass of photons in guided waves, or equivalently, to the existence of a longitudinal field component, such that the transverse and longitudinal fields together form an elliptical polarization plane. In contrary to the traditional viewpoint, the transverse spin of photons in guided waves is also quantized, and its quantization form is related to the ellipticity of the polarization ellipse. The direction of the transverse spin depends on the propagation direction of electromagnetic waves along the waveguide, such a spin-momentum locking may have important applications in spin-dependent unidirectional optical interfaces. By means of a coupling between the transverse spin of guided waves and some physical degrees of freedom, one can develop an optical analogy of spintronics, i.e., spinoptics.

Effective(kinetic freeze-out) temperature, transverse flow velocity, and kinetic freeze-out volume in high energy collisions

The transverse momentum spectra of different types of particles produced in central and peripheral gold–gold(Au–Au)and inelastic proton–proton(pp)collisions at the Relativistic Heavy Ion Collider,as well as in central and peripheral lead-lead(Pb–Pb)and pp collisions at the Large Hadron Collider,are analyzed by the multi-component standard(Boltzmann–Gibbs,Fermi–Dirac,and Bose–Einstein)distributions.The obtained results from the standard distribution give an approximate agreement with the measured experimental data by the STAR,PHENIX,and ALICE Collaborations.The behavior of the effective(kinetic freeze-out)temperature,transverse flow velocity,and kinetic freeze-out volume for particles with different masses is obtained,which observes the early kinetic freezeout of heavier particles as compared to the lighter particles.The parameters of emissions of different particles are observed to be different,which reveals a direct signature of the mass-dependent differential kinetic freeze-out.It is also observed that the peripheral nucleus–nucleus(AA)and pp collisions at the same center-of-mass energy per nucleon pair are in good agreement in terms of the extracted parameters.

Strain Effect of Manganin Transverse Piezoresistive Gauge and Measurement of Dynamic Transverse Stresses

Manganin piezoresistive gauges have been extensively used in dynamic stress measurement for decades.It is noted,however,that when used to measure transverse stresses,considerable strain effect is caused as the consequence of change of electrical resistance resulted from bending of wires in the longitudinal-strain-experiencing sensing element of the gauge,a phenomenon discussed in this paper theoretically as well as experimentally.This effect yields unwanted signals to blend with output piezoresistive signals and is not negligible,hence decreases measurement accuracy sizably if not properly handled.To overcome this drawback,a new type of manganin transverse piezoresistive gauge has been developed by authors of this paper,which can reduce the resistance increment to acceptable low level so as to effectively bring the adverse effect under control.

Determination of the magnetic anisotropy constant of Cu/Fe/SiO_2/Si by a magneto-optical Kerr effect susceptometer

The magneto-optical Kerr effect susceptometry technique is proposed to determine the uniaxial magnetic anisotropy （UMA） constant Ku. The magnetic properties of Cu/Fe/SiO2/Si grown by dc magnetron sputtering were investigated. The in-plane uniaxial magnetic anisotropy was probed by the magneto-optical Kerr effect （MOKE）. The value of UMA, Ku = 2.5 x 103 J/m3, was simulated from the field dependence of ac susceptibility along the hard axis according to the Stoner-Wohlfarth （S-W） model, which is consistent with Ku = 2.7~ 103 J/m3 calculated from the magnetic hysteresis loops. Our results show that the magneto-optical Kerr effect susceptometry can be employed to determine the magnetic anisotropy constant owing to its high sensitivity.

Resonant magneto-optical Kerr effect induced by hybrid plasma modes in ferromagnetic nanovoids

With nanovoids buried in Co films, resonant structures were observed in spectra of polar magneto-optical Kerr effect（MOKE）, where both a narrow bandwidth and high intensity were acquired. Through changing the thickness of Co films and the lattice of voids, different optical modes were introduced. For a very shallow array of voids, the resonant MOKE was induced by Ag plasma edge resonance, for deeper ones, hybrid plasma modes, such as void plasmons in the voids, surface lattice plasmons between the voids, and the co-action of them, etc. resulted in resonant MOKE. We found that resonant MOKE resulted from the void plasmons resonance which possesses the narrowest bandwidth for the lowest absorption of voids. The simulated electromagnetic field（EF） distribution consolidated different effects of these three optical modes on resonant MOKE modulation. Such resonant polar MOKE possesses high sensitivity, which might pave the way to on-chip MO devices.

Transverse effects in photorefractive two-wave mixing

In a biased photorefractive crystal, the process of two one-dimensional waves mixing, i.e., the dynamical evolution of both pump beam and signal beam, is traced by numerically solving the coupled-wave equation. Direct simulations show that the propagation and stability of the two beams are completely determined by the system parameters, such as the external bias field, the intensity and the beam waist of the pump beam. By adjusting these parameters, one can control the state of two Gaussian waves mixing. The numerical results are helpful for performing a two-wave mixing experiment.

Improvement on the magneto-optical Kerr effect of cobalt film with a quadrilayer structure

The magneto-optical Kerr effect of the HfO2/Co/HfO2/A1 multilayer structure is investigated in this work, and an ob- vious cavity enhancement of the Kerr response for the HfO2 semiconductor is found both theoretically and experimentally. Surprisingly, a maximum value of about -3 of the polar Kerr rotation for s-polarized incident light is observed in our experiment. We propose that this improvement on the Kerr effect can be attributed to the multiple reflection and optical interference in the cavity, which can also be proved by simulation using the finite element method.

The subwavelength tuned magneto-optical Kerr effect in L1_0-FePt films with perpendicular magnetic anisotropy

For L10-FePt films with strong perpendicular anisotropy covered by arrays of hexagonal close-packed polystyrene spheres （PSSs）, fine structures are observed in magneto-optical Kerr rotation spectra in the visible spectral range. The reflection minima are found to be located at the same wavelengths as the Kerr rotation peaks. The Kerr rotation enhancement is attributed to the excitation of both the surface plasmon polariton in the dielectric PSS/metal interface and the guide waves （guide mode） in the PSS array. The two-dimensional PSSs/SiO2/FePt system exhibiting a tunable magneto-optical Kerr effect and a high perpendicular magnetic anisotropy will be helpful for designing and fabricating magneto-optics devices.

Effects of Transverse Temperature Gradient on the Rotor Velocity in an Ultrasonic Motor

As a result of the nonlinear effect, acoustic streaming has been widely used for increasing the transport coefficient or driving a rotor, for example, in resonant cavities and non-contact ultrasonic motors. It has been demonstrated by experiments that a temperature gradient transverse to the wave propagating direction can significantly increase the velocity of the streaming flows in resonant cavities. To check whether the transverse temperature gradient can also increase the working velocity of acoustic streaming-driven motors, we investigate this issue by numerically solving the hydrodynamic equations. It is found that the velocity of the rotor only weakly depends on the transverse temperature gradient, e.g., even with a temperature difference of 40℃ between the rotor and the stator, the velocity increases only -8.8%.

Space Charge Effects of Bunched Beam with Nonuniform Distribution in Both Longitudinal and Transverse Directions

The nonlinear space charge effect of bunched beam with nonuniform densitydistribution in both longitudinal and transverse directions is discussed.Some usefulformulae are derived for calculating the potential induced by a cylinder model of spacecharge in the waveguide of a linac with longitudinal density distributions of waterbag(WB) or parabolic (PA) type combining with transverse density distributions ofKapchinskij-Vladimirskij (K-V).waterbag,parabolic and Gaussian (GA) types,resepectively.

Surface Plasmon and Fabry-Perot Enhanced Magneto-Optical Kerr Effect in Graphene Microribbons

A single sheet of graphene exhibits the ability to turn polarization of light by several degrees in modest magnetic fields. Here we demonstrate that giant angle rotation in graphene in the terahertz range can be realized and further increased by the introduction of surface plasmon and constructive Fabry Perot interference with the supporting substrate. The maximum Kerr rotation angle is up to 15° in a single layer of graphene ribbons at 6 TPIz for the applied magnetic field 4 T. Such a magnification in magneto-optical Kerr effect can be realized in a fairly large incident angle.

Transversal effects of high order numerical schemes for compressible fluid flows

Finite volume schemes for the two-dimensional(2D) wave system are taken to demonstrate the role of the genuine dimensionality of Lax-Wendroff flow solvers for compressible fluid flows. When the finite volume schemes are applied, the transversal variation relative to the computational cell interfaces is neglected, and only the normal numerical flux is used, thanks to the Gauss-Green formula. In order to offset such defects, the Lax-Wendroff flow solvers or the generalized Riemann problem(GRP) solvers are adopted by substituting the time evolution of flows into the spatial variation. The numerical results show that even with the same convergence rate, the error by the GRP2D solver is almost one ninth of that by the multistage Runge-Kutta(RK) method.

Study of magnetic and magneto-optical properties of heavily doped bismuth substitute yttrium iron garnet (Bi∶YIG) film

The magnetic and magneto-optical properties of heavily doped Bi∶YIG film were studied. The film was deposited by radio frequency magnetron sputtering method and crystallized by rapid recurrent thermal annealing (RRTA). The results show that the RRTA treated film has good properties both in microwave and optical wave band. The saturation magnetization of the film on different substrates varies from 135.7 to 138.6 kA·m-1. The coercive field of the film on GGG substrate is about 0.32 kA·m-1, while about 0.8-1.43 kA·m-1 on YAG substrate and 1.75 kA·m-1 on Al2O3 substrate. The Faraday angle is about 3-5 (°)·μm-1 when optical wavelength ranges at 450-600 nm. The transmission spectra of the Bi∶YIG films on three substrates has similar change as annealing temperature below 800 ℃. Specially, when annealing temperature is above 800 ℃ a step is observed between 550 and 650 nm wavelength for the film deposited on Al2O3 substrate.Three results are very useful in magneto-optical recording application and integrated microwave devices.