Reply to “Comment on ‘A numerical investigation of the acoustic mode waves in a deviated borehole penetrating a transversely isotropic formation' ”

正We appreciate the comment from Horne,Miller and Wang on the paper‘A numerical investigation of the acoustic mode waves in a deviated borehole penetrating a transversely isotropic formation’by Liu et al.(2015)[1],for the opportunity to consider and clarify the group and phase velocity issue in sonic logging with a deviated borehole penetrating a VTI formation.We re-read the paper by Liu et al.[1]and did some numerical tests and analyses.After discussions we agree that at low     

An acoustic imaging system of migration technique used in borehole

In order to detect the damage of casing boreholes, an acoustic imaging method with a two-dimensional ultrasonic array was presented. Each element of the array independently emits down ultrasonic waves, the echoes received by all elements are sampled and transmitted to a computer on ground surface, where the dynamic migration method is used to form a 2 or 3-dimensional image of the situation in the borehole. The numerical simulation and experiment are conducted that demonstrate a high imaging accuracy with a small number of elements used in array. Since the delay circuits used in the traditional phased array imaging system is not needed in this system, and all data process could be completed in a ground system. the complexity and the volume of system in borehole may be significantly simplified, which is critical to the borehole instrument.     

Coupling of Acoustical Plane p-Wave to a Cased Borehole

Theoretical and numerical study on the coupling acoustic field of the plane p-wave to a cased borehole is carried out. The medium outside the cased borehole is modeled as the porous medium. The scattering field characteristics in the cased borehole are investigated when a plane fast p-wave is incident in tilt to the cased borehole from the porous medium. The scattering fields inside and outside the cased borehole are analyzed and deduced by Biot＇s theory under the boundary conditions on each interface, and they are numerically studied. It is found that the scattering field has strong resonant characteristics and there exists a series of resonant frequencies and peaks. The effects of the frequency, radii of each interface, incident angle, porosity, and other parameters on the resonant acoustic field have been investigated in detail in the fast and slow formations respectively. The resonant characteristics of the scattering field are also analyzed from the physical sense.     

Perturbation Analysis on Guided Waves in a Fluid-Filled Borehole Surrounded by a Cubic Crystal Anisotropic Medium

The perturbation method is employed to analyse the guided waves in a borehole surrounded by a cubic crystal medium for the first time. The cubic crystal medium is regarded as a reference unperturbed isotropic state added to the perturbation. The dispersion characteristics of Stoneley wave, pseudo-Rayleigh wave, flexural wave, and screw wave are investigated in detail. It is found that dispersion of the guided waves excited by monopole and dipole sources does not depend on the azimuth of the source, whereas the dispersion of screw wave excited by quadrupole source is significantly related to the azimuth of the source. Screw waves propagated along different azimuth in the borehole can be split. This is different from screw waves in transversely isotropic media （hexagonal crystal）, which have been widely studied.     

Acousto-electric well logging by eccentric source and extraction of shear wave

The nonaxisymmetric acousto-electric field excited by an eccentric acoustic source in the borehole based on Pride seismoelectric theory is considered. It is shown that the acoustic field inside the borehole, converted electric and magnetic fields and coupled fields outside the borehole are composed of an infinitude of multipole fields with different orders. The numerical results show that both the electromagnetic waves and the seismoelectric field in the borehole, and the three components of both electric field and magnetic field can be detected. Measurements on the borehole axis will be of advantage to determining shear velocity information. The components of the symmetric and nonsymmetric acoustic and electromagnetic fields can be strengthened or weakened by adding or subtracting the two full waveforms logged in some azimuths. It may be a new method of directly measuring the shear wave velocity by using the borehole seismoelectric effect.     

Optimal distance from high power laser diode to cylindrical microlens in a coupling system

In a practical coupling system, a cylindrical microlens is used to collimate the emission of a high power laser diode (LD) in the dimension perpendicular to the junction plane. Using passive alignment, the LD is placed in the focus of the cylindrical microlens generally, regardless of the performance of the multimode optical fiber and the LD. In this paper, a more complete analysis is arrived at by ray-tracing technique, by which the angle 9 of the ray after refraction is computed as a function of the angle θo of the ray before refraction. The focus of the cylindrical microlens is not always the optimal position of the LD. In fact, in order to achieve a higher coupling efficiency, the optimal distance from the LD to the cylindrical microlens is dependent on not only the radius R and the index of refraction n of the cylindrical microlens, but also the divergence angle of the LD in the dimension perpendicular to the junction plane and the numerical aperture (NA) of the multimode optical fiber. The result     

Seismoelectric waves in a borehole excited by an external explosive source

The conversion of energy between seismic and electromagnetic wave fields has been described by Pride’s coupled equations in porous media. In this paper, the seismoelectric field excited by the explosive point source located at the outside of the borehole is studied. The scattering fields inside and outside a borehole are analyzed and deduced under the boundary conditions at the interface between fluid and porous media. The influences of the distance of the point source, multipole components of the eccentric explosive source, and the receiving position along the axis of vertical borehole, on the converted waves inside the borehole are all investigated. When the distance from the acoustic source to the axis of a borehole is far enough, the longitudinal and coseismic longitudinal wave packets dominate the acoustic and electric field, respectively. The three components of both electric field and magnetic field can be detected, and the radial electric field is mainly excited and converted by the dipole component. Owing to the existence of borehole, the electric fields and magnetic fields in the borehole are azimuthal. The distance from the point where the maximum amplitude of the axial components of electric field is recorded, to the origin of coordinate indicates the horizontal distance from the explosive source to the axis of vertical borehole.     

Design of output feedback controller for a unified chaotic system

In this paper, the synchronization of a unified chaotic system is investigated by the use of output feedback controllers; a two-input single-output feedback controller and single-input single-output feedback controller are presented to synchronize the unified chaotic system when the states are not all measurable. Compared with the existing results, the controllers designed in this paper have some advantages such as small feedback gain, simple structure and less conservation. Finally, numerical simulations results are provided to demonstrate the validity and effectiveness of the proposed method.     

On the origin of intrinsic randomness of Rayleigh-B′enard turbulence

It is of broad interest to understand how the evolution of non-equilibrium systems can be triggered and the role played by external perturbations. A famous example is the origin of randomness in the laminar-turbulence transition, which is raised in the pipe flow experiment by Reynolds as a century old unresolved problem. Although there exist different hypotheses, it is widely believed that the randomness is "intrinsic", which, however, remains as an open question to be verified. Simulating the modeled RayleighB′enard convection system by means of the so-called clean numerical simulation(CNS) with negligible numerical noises that are smaller even than thermal fluctuation, we verify that turbulence can be self-excited from the inherent thermal fluctuation without any external disturbances, i.e. out of nothing. This reveals a relationship between microscopic physical uncertainty and macroscopic randomness. It is found that in physics the system nonlinearity functions as a channel for randomness information,and energy as well, to transport microscopic uncertainty toward large scales. Such scenario can generally be helpful to understand the various relevant phenomena. In methodology, compared with direct numerical simulation(DNS), CNS opens a new direction to investigate turbulent flows with largely improved accuracy and reliability.     

Current-driven transformations of a skyrmion tube and a bobber in stepped nanostructures of chiral magnets

Magnetic skyrmion tubes and bobbers are two types of different nanoscale spin configurations that can coexist in nanostructures of chiral magnets.They are then proposed to be utilized as binary bits to build racetrack memory devices.The ability to manipulate the two magnetic objects controllably by current in nanostructures is the prerequisite to realize the device.Here,we demonstrate by numerical simulations that a magnetic bobber and a skyrmion tube can be transformed to each other using spinpolarized current in nanostripes with stepped shape.We also show such stepped nanostructures can be readily applied as the write head for the skyrmion-bobber-based racetrack memory.     

Axial distribution of Gaussian beam limited by a hard-edged aperture

In this letter, the axial distribution of Gaussian beam limited by a hard-edged aperture is studied. We theoretically analyze the axial diffraction of Gaussian beam limited by a hard-edged aperture, and give the simpler formulas of the axial diffraction intensities of Gaussian beam in Fresnel diffraction field and Fraun-hofer diffraction field. The corresponding numerical calculation of axial diffraction intensity distribution of Gaussian beam with different wave waist is provided and the evolution of the diffraction distribution with the wave waist of Gaussian beam is explained. As the especial cases of the truncated Gaussian beam, the Gaussian beam in free space and the parallel light limited by the aperture are discussed too, and the system parameters of the truncated Gaussian beam which can cause it to equal to these cases are given. The theoretical results conform to the numerical analysis.     

Finite-amplitude vibration of a bubble in water

The numerical results obtained by Rayleigh-Plesset （R-P） equation failed to agree with the experimental Mie scattering data of a bubble in water without inappropriately increasing the shear viscosity and decreasing the surface tension coefficient. In this paper, a new equation proposed by the present authors （Qian and Xiao） is solved. Numerical solutions obtained by using the symbolic computation program from both the R-P equation and the Qian-Xiao （Q-X） equation clearly demonstrate that Q-X equation yields best results matching the experimental data （in expansion phase）. The numerical solutions of R-P equation also demonstrate the oscillation of a bubble in water depends strongly upon the surface tension and the shear viscosity coefficients as well as the amplitude of driving pressure, so that the uniqueness of the numerical solutions may be suspected if they are varied arbitrarily in order to fit the experimental data. If the bubble＇s vibration accompanies an energy loss such as the light radiation during the contract phase, the mechanism of the energy loss has to be taken into account. We suggest that by use of the bubble＇s vibration to investigate the state equations of aqueous solutions seem to be possible. We also believe that if one uses this equation instead of R-P equation to deal with the relevant problems such as the ＇phase diagrams for sonoluminescing bubbles＇, etc., some different results may be expected.     

Heat Conductivity in a Two-Dimensional Finite-Size Spin System with Dzyaloshinskii-Moriya Interactions

Heat conductivity is studied by direct numerical simulations in a two-dimensional model with chiral Dzyaloshinskii-Moriya （DM） spin superexchange interactions for various DM strengths and finite sizes. We find that when temperature is not too low, the thermal conductivity can be well described in the semi-classical spin wave picture, and connections of thermal conductivity with the specific heat and the dynamic relaxation time are verified to be suitable. In particular, the transition arising in Sr14-xCaxCu24O41 is related to a magnetic spin glass and qualitatively understood as a kind of Kosterlitz-Thouless transitions. It is shown that the critical temperature is linearly dependent on the spin-spin interactions for the relevant strong DM strength.     

Hydrostatic pressure effect on the electron mobility in a ZnSe/Zn1－xdx Se strained heterojunction

With a memory function approach, this paper investigates the electronic mobility parallel to the interface in a ZnSe/Zn1-xCdxSe strained heterojunction under hydrostatic pressure by considering the intersubband and intrasubband scattering from the optical phonon modes. A triangular potential approximation is adopted to simplify the potential of the conduction band bending in the channel side and the electronic penetrating into the barrier is considered by a finite interface potential in the adopted model. The numerical results with and without strain effect are compared and analysed. Meanwhile, the properties of electronic mobility under pressure versus temperature, Cd concentration and electronic density are also given and discussed, respectively. It shows that the strain effect lowers the mobility of electrons while the hydrostatic pressure effect is more obvious to decrease the mobility. The contribution induced by the longitudinal optical phonons in the channel side is dominant to decide the mobility. Compared with the intrasubband scattering it finds that the effect of intersubband scattering is also important for the studied material.     

A conservative Fourier pseudospectral algorithm for a coupled nonlinear Schrdinger system

We derive a new method for a coupled nonlinear Schrdinger system by using the square of first-order Fourier spectral differentiation matrix D1 instead of traditional second-order Fourier spectral differentiation matrix D2 to approximate the second derivative.We prove the proposed method preserves the charge and energy conservation laws exactly.In numerical tests,we display the accuracy of numerical solution and the role of the nonlinear coupling parameter in cases of soliton collisions.Numerical experiments also exhibit the excellent performance of the method in preserving the charge and energy conservation laws.These numerical results verify that the proposed method is both a charge-preserving and an energy-preserving algorithm.     

Study on diffraction characteristics of a planar diamond waveguide

A numerical simulation is performed to study the far-field diffraction properties of planar diamond waveguides.The far-field intensity distributions of a planar air waveguide and a diamond waveguide with different distances are given by numerical calculations.In the experiment,the diffraction patterns on the screen with different distances are recorded using a He-Ne laser as the light source,wherein the laser beam is coupled with and propagates in the diamond waveguide.The simulation results are found to be consistent with the experimental ones.     

How to identify dislocations in molecular dynamics simulations?

Dislocations are of great importance in revealing the underlying mechanisms of deformed solid crystals.With the development of computational facilities and technologies,the observations of dislocations at atomic level through numerical simulations are permitted.Molecular dynamics(MD)simulation suggests itself as a powerful tool for understanding and visualizing the creation of dislocations as well as the evolution of crystal defects.However,the numerical results from the large-scale MD simulations are not very illuminating by themselves and there exist various techniques for analyzing dislocations and the deformed crystal structures.Thus,it is a big challenge for the beginners in this community to choose a proper method to start their investigations.In this review,we summarized and discussed up to twelve existing structure characterization methods in MD simulations of deformed crystal solids.A comprehensive comparison was made between the advantages and disadvantages of these typical techniques.We also examined some of the recent advances in the dynamics of dislocations related to the hydraulic fracturing.It was found that the dislocation emission has a significant effect on the propagation and bifurcation of the crack tip in the hydraulic fracturing.     

An approximation for the boundary optimal control problem of a heat equation defined in a variable domain

In this paper, we consider a numerical approximation for the boundary optimal control problem with the control constraint governed by a heat equation defined in a variable domain. For this variable domain problem, the boundary of the domain is moving and the shape of theboundary is defined by a known time-dependent function. By making use of the Galerkin finite element method, we first project the original optimal control problem into a semi-discrete optimal control problem governed by a system of ordinary differential equations. Then, based on the aforementioned semi-discrete problem, we apply the control parameterization method to obtain an optimal parameter selection problem governed by a lumped parameter system, which can be solved as a nonlinear optimization problem by a Sequential Quadratic Programming （SQP） algorithm. The numerical simulation is given to illustrate the effectiveness of our numerical approximation for the variable domain problem with the finite element method and the control parameterization method.     

Bubble nonlinear dynamics and stimulated scattering process

A complete understanding of the bubble dynamics is deemed necessary in order to achieve their full potential applications in industry and medicine. For this purpose it is first needed to expand our knowledge of a single bubble behavior under different possible conditions including the frequency and pressure variations of the sound field. In addition, stimulated scattering of sound on a bubble is a special effect in sound field, and its characteristics are associated with bubble oscillation mode. A bubble in liquid can be considered as a representative example of nonlinear dynamical system theory with its resonance, and its dynamics characteristics can be described by the Keller–Miksis equation. The nonlinear dynamics of an acoustically excited gas bubble in water is investigated by using theoretical and numerical analysis methods. Our results show its strongly nonlinear behavior with respect to the pressure amplitude and excitation frequency as the control parameters, and give an intuitive insight into stimulated sound scattering on a bubble. It is seen that the stimulated sound scattering is different from common dynamical behaviors, such as bifurcation and chaos, which is the result of the nonlinear resonance of a bubble under the excitation of a high amplitude acoustic sound wave essentially. The numerical analysis results show that the threshold of stimulated sound scattering is smaller than those of bifurcation and chaos in the common condition.     

Holographic p-wave superfluid with Weyl corrections

In this work,we study the effects of the Weyl corrections on the p-wave superfluid phase transition in terms of an EinsteinMaxwell theory coupled to a complex vector field.In the probe limit,it is observed that the phase structure is significantly modified owing to the presence of the higher order Weyl corrections.The latter,in general,facilitates the emergence of the superfluid phase as the condensate increases with the Weyl coupling measured byγ.Moreover,several features about the phase structure of the holographic superfluid are carefully investigated.In a specific region,the phase transition from the normal phase to the superfluid phase is identified to be the first order,instead of being the second order,as in the cases for many holographic superconductors.By carrying out a numerical scan of model parameters,the boundary dividing these two types of transitions is located and shown to be rather sensitive to the strength of Weyl coupling.Also,a feature known as"Cave of Winds",associated with the emergence of a second superfluid phase,is observed for specific choices of model parameters.However,it becomes less prominent and eventually disappears asγincreases.Furthermore,for temperature in the vicinity of the critical one for vanishing superfluid velocity,denoted by T0,the supercurrent is found to be independent of the Weyl coupling.The calculated ratio,of the condensate with vanishing superfluid velocity to that with maximal superfluid velocity,is in good agreement with that predicted by Ginzburg-Landau theory.While compared with the impact on the phase structure owing to the higher curvature corrections,the findings in our present study demonstrate entirely different characteristics.Further implications are discussed.