Finite-difference time-domain modeling of curved material interfaces by using boundary condition equations method

To deal with the staircase approximation problem in the standard finite-difference time-domain（FDTD） simulation,the two-dimensional boundary condition equations（BCE） method is proposed in this paper.In the BCE method,the standard FDTD algorithm can be used as usual,and the curved surface is treated by adding the boundary condition equations.Thus,while maintaining the simplicity and computational efficiency of the standard FDTD algorithm,the BCE method can solve the staircase approximation problem.The BCE method is validated by analyzing near field and far field scattering properties of the PEC and dielectric cylinders.The results show that the BCE method can maintain a second-order accuracy by eliminating the staircase approximation errors.Moreover,the results of the BCE method show good accuracy for cylinder scattering cases with different permittivities.

A stable staggered-grid finite-difference scheme for acoustic modeling beyond conventional stability limit

Staggered-grid finite-difference(SGFD)schemes have been widely used in acoustic wave modeling for geophysical problems.Many improved methods are proposed to enhance the accuracy of numerical modeling.However,these methods are inevitably limited by the maximum Courant-Friedrichs-Lewy(CFL)numbers,making them unstable when modeling with large time sampling intervals or small grid spacings.To solve this problem,we extend a stable SGFD scheme by controlling SGFD dispersion relations and maximizing the maximum CFL numbers.First,to improve modeling stability,we minimize the error between the FD dispersion relation and the exact relation in the given wave-number region,and make the FD dispersion approach a given function outside the given wave-number area,thus breaking the conventional limits of the maximum CFL number.Second,to obtain high modeling accuracy,we use the SGFD scheme based on the Remez algorithm to compute the FD coefficients.In addition,the hybrid absorbing boundary condition is adopted to suppress boundary reflections and we find a suitable weighting coefficient for the proposed scheme.Theoretical derivation and numerical modeling demonstrate that the proposed scheme can maintain high accuracy in the modeling process and the value of the maximum CFL number of the proposed scheme can exceed that of the conventional SGFD scheme when adopting a small maximum effective wavenumber,indicating that the proposed scheme improves stability during the modeling.

Time-domain dynamic constitutive model suitable for mucky soil site seismic response

Soil nonlinear behavior displays noticeable effects on the site seismic response.This study proposes a new functional expression of the skeleton curve to replace the hyperbolic skeleton curve.By integrating shear modulus and combining the dynamic skeleton curve and the damping degradation coefficient,the constitutive equation of the logarithmic dynamic skeleton can be obtained,which considers the damping effect in a soil dynamics problem.Based on the finite difference method and the multi-transmitting boundary condition,a 1D site seismic response analysis program called Soilresp1D has been developed herein and used to analyze the time-domain seismic response in three types of sites.At the same time,this study also provides numerical simulation results based on the hyperbolic constitutive model and the equivalent linear method.The results verify the rationality of the new soil dynamic constitutive model.It can analyze the mucky soil site nonlinear seismic response,reflecting the deformation characteristics and damping effect of the silty soil.The hysteresis loop area is more extensive,and the residual strain is evident.

Poroelastic finite-difference modeling for ultrasonic waves in digital porous cores

Scattering attenuation in short wavelengths has long been interesting to geophysicists. Ultrasonic coda waves, observed as the tail portion of ultrasonic wavetrains in laboratory ultrasonic measurements, are important for such studies where ultrasonic waves interact with smallscale random heterogeneities on a scale of micrometers, but often ignored as noises because of the contamination of boundary reflections from the side ends of a sample core. Numerical simulations with accurate absorbing boundary can provide insight into the effect of boundary reflections on coda waves in laboratory experiments. The simulation of wave propagation in digital and heterogeneous porous cores really challenges numerical techniques by digital image of poroelastic properties, numerical dispersion at high frequency and strong heterogeneity, and accurate absorbing boundary schemes at grazing incidence. To overcome these difficulties, we present a staggered-grid high-order finite-difference （FD） method of Biot＇s poroelastic equations, with an arbitrary even-order （2L） accuracy to simulate ultrasonic wave propagation in digital porous cores with strong heterogeneity. An unsplit convolutional perfectly matched layer （CPML） absorbing boundary, which improves conventional PML methods at grazing incidence with less memory and better computational efficiency, is employed in the simulation to investigate the influence of boundary reflections on ultra- sonic coda waves. Numerical experiments with saturated poroelastic media demonstrate that the 2L FD scheme with the CPML for ultrasonic wave propagation significantly improves stability conditions at strong heterogeneity and absorbing performance at grazing incidence. The boundary reflections from the artificial boundary surrounding the digital core decay fast with the increase of CPML thick- nesses, almost disappearing at the CPML thickness of 15 grids. Comparisons of the resulting ultrasonic coda Qsc values between the numerical and experimental ultrasonic S waveforms for a cylindrical rock sample demonstrate that the boundary reflection may contribute around one-third of the ultrasonic coda attenuation observed in laboratory experiments.

Uniform stable conformal convolutional perfectly matched layer for enlarged cell technique conformal finite-difference time-domain method

Based on conformal construction of physical model in a three-dimensional Cartesian grid,an integral-based conformal convolutional perfectly matched layer（CPML） is given for solving the truncation problem of the open port when the enlarged cell technique conformal finite-difference time-domain（ECT-CFDTD） method is used to simulate the wave propagation inside a perfect electric conductor（PEC） waveguide.The algorithm has the same numerical stability as the ECT-CFDTD method.For the long-time propagation problems of an evanescent wave in a waveguide,several numerical simulations are performed to analyze the reflection error by sweeping the constitutive parameters of the integral-based conformal CPML.Our numerical results show that the integral-based conformal CPML can be used to efficiently truncate the open port of the waveguide.

Investigation of three-pulse photon echo in thick crystal using finite-difference time-domain method

This paper investigates the phenomenon of three-pulse photon echo in thick rare-earth ions doped crystal whose thickness is far larger than 0.002 cm which is adopted in previous works.The influence of thickness on the three-pulse photon echo＇s amplitude and efficiency is analyzed with the Maxwell-Bloch equations solved by finite-difference timedomain method.We demonstrate that the amplitude of three-pulse echo will increase with the increasing of thickness and the optimum thickness to generate three-pulse photon echo is 0.3 cm for Tm^（3＋）：YAG when the attenuation of the input pulse is taken into account.Meanwhile,we find the expression 0.09 exp（α＇L）,which is previously employed to describe the relationship between echo＇s efficiency and thickness,should be modified as 1.3 · 0.09 exp（2.4 ·α＇L） with the propagation of echo considered.

Finite-difference model of land subsidence caused by cluster loads in Zhengzhou,China

Groundwater exploitation has been regarded as the main reason for land subsidence in China and thus receives considerable attention from the government and the academic community.Recently,building loads have been identified as another important factor of land subsidence,but researches in this sector have lagged.The effect of a single building load on land subsidence was neglected in many cases owing to the narrow scope and the limited depth of the additional stress in stratum.However,due to the superposition of stresses between buildings,the additional stress of cluster loads is greater than that of a single building load under the same condition,so that the land subsidence caused by cluster loads cannot be neglected.Taking Shamen village in the north of Zhengzhou,China,as an example,a finite-difference model based on the Biot consolidation theory to calculate the land subsidence caused by cluster loads was established in this paper.Cluster loads present the characteristics of large-area loads,and the land subsidence caused by cluster loads can have multiple primary consolidation processes due to the stress superposition of different buildings was shown by the simulation results.Pore water migration distances are longer when the cluster loads with high plot ratio are imposed,so that consolidation takes longer time.The higher the plot ratio is,the deeper the effective deformation is,and thus the greater the land subsidence is.A higher plot ratio also increases the contribution that the deeper stratigraphic layers make to land subsidence.Contrary to the calculated results of land subsidence caused by cluster loads and groundwater recession,the percentage of settlement caused by cluster loads in the total settlement was 49.43%and 55.06%at two simulated monitoring points,respectively.These data suggest that the cluster loads can be one of the main causes of land subsidence.

Optical simulation of in-plane-switching blue phase liquid crystal display using the finite-difference time-domain method

The finite-difference time-domain method is used to simulate the optical characteristics of an in-plane switching blue phase liquid crystal display.Compared with the matrix optic methods and the refractive method,the finite-difference timedomain method,which is used to directly solve Maxwell＇s equations,can consider the lateral variation of the refractive index and obtain an accurate convergence effect.The simulation results show that e-rays and o-rays bend in different directions when the in-plane switching blue phase liquid crystal display is driven by the operating voltage.The finitedifference time-domain method should be used when the distribution of the liquid crystal in the liquid crystal display has a large lateral change.

A spherical higher-order finite-difference time-domain algorithm with perfectly matched layer

A higher-order finite-difference time-domain（HO-FDTD） in the spherical coordinate is presented in this paper. The stability and dispersion properties of the proposed scheme are investigated and an air-filled spherical resonator is modeled in order to demonstrate the advantage of this scheme over the finite-difference time-domain（FDTD） and the multiresolution time-domain（MRTD） schemes with respect to memory requirements and CPU time. Moreover, the Berenger＇s perfectly matched layer（PML） is derived for the spherical HO-FDTD grids, and the numerical results validate the efficiency of the PML.

Perfect plane-wave source for a high-order symplectic finite-difference time-domain scheme

The method of splitting a plane-wave finite-difference time-domain （SP-FDTD） algorithm is presented for the initiation of plane-wave source in the total-field / scattered-field （TF/SF） formulation of high-order symplectic finite- difference time-domain （SFDTD） scheme for the first time. By splitting the fields on one-dimensional grid and using the nature of numerical plane-wave in finite-difference time-domain （FDTD）, the identical dispersion relation can be obtained and proved between the one-dimensional and three-dimensional grids. An efficient plane-wave source is simulated on one-dimensional grid and a perfect match can be achieved for a plane-wave propagating at any angle forming an integer grid cell ratio. Numerical simulations show that the method is valid for SFDTD and the residual field in SF region is shrinked down to -300 dB.

An efficient locally one-dimensional finite-difference time-domain method based on the conformal scheme

An efficient conformal locally one-dimensional finite-difference time-domain（LOD-CFDTD） method is presented for solving two-dimensional（2D） electromagnetic（EM） scattering problems. The formulation for the 2D transverse-electric（TE） case is presented and its stability property and numerical dispersion relationship are theoretically investigated. It is shown that the introduction of irregular grids will not damage the numerical stability. Instead of the staircasing approximation, the conformal scheme is only employed to model the curve boundaries, whereas the standard Yee grids are used for the remaining regions. As the irregular grids account for a very small percentage of the total space grids, the conformal scheme has little effect on the numerical dispersion. Moreover, the proposed method, which requires fewer arithmetic operations than the alternating-direction-implicit（ADI） CFDTD method, leads to a further reduction of the CPU time. With the total-field/scattered-field（TF/SF） boundary and the perfectly matched layer（PML）, the radar cross section（RCS） of two2 D structures is calculated. The numerical examples verify the accuracy and efficiency of the proposed method.

MODELING OF CONTROLLED THERMO-MECHANICAL PROCESSING OF TUBES FOR ENHANCED MANUFACTURING AND PERFORMANCE

An integrated mathematical model to simulate seamless tube rolling processes has been developed at The Timken Company. The model is capable of simulating the thermal, deformation and microstructure evolution in the piercing, elongating and reducing/sizing and the austenite decomposition in the mill annealing and cooling operations. Finite difference schemes are employed to model cooling, reducing/sizing and stretch reducing, and finite-element schemes are employed to simulate piercing and elongating. The model predicts the thermal history, deformation, rolling load, torque, recrystallization and grain growth in hot tube rolling, austenite decomposition in cooling or annealing, and the final structure-properties. In this paper mathematical models which are employed to describe the thermal, deformation and microstructure evolution along with the modeling results are presented. The developed 'tube rolling mill in the computer' provides a powerful tool for engineers for product and process development, process control, process optimization and quality control.

Hybrid sub-gridding ADE–FDTD method of modeling periodic metallic nanoparticle arrays

In this paper, a modified sub-gridding scheme that hybridizes the conventional finite-difference time-domain（FDTD）method and the unconditionally stable locally one-dimensional（LOD） FDTD is developed for analyzing the periodic metallic nanoparticle arrays. The dispersion of the metal, caused by the evanescent wave propagating along the metal-dielectric interface, is expressed by the Drude model and solved with a generalized auxiliary differential equation（ADE） technique.In the sub-gridding scheme, the ADE–FDTD is applied to the global coarse grids while the ADE–LOD–FDTD is applied to the local fine grids. The time step sizes in the fine-grid region and coarse-grid region can be synchronized, and thus obviating the temporal interpolation of the fields in the time-marching process. Numerical examples about extraordinary optical transmission through the periodic metallic nanoparticle array are provided to show the accuracy and efficiency of the proposed method.

Finite-difference calculation of traveltimes based on rectangular grid

To the most of velocity fields, the traveltimes of the first break that seismic waves propagate along rays can be computed on a 2-D or 3-D numerical grid by finite-difference extrapolation. Under ensuring accuracy, to improve calculating efficiency and adaptability, the calculation method of first-arrival traveltime of finite-difference is de- rived based on any rectangular grid and a local plane wavefront approximation. In addition, head waves and scat- tering waves are properly treated and shadow and caustic zones cannot be encountered, which appear in traditional ray-tracing. The testes of two simple models and the complex Marmousi model show that the method has higher accuracy and adaptability to complex structure with strong vertical and lateral velocity variation, and Kirchhoff prestack depth migration based on this method can basically achieve the position imaging effects of wave equation prestack depth migration in major structures and targets. Because of not taking account of the later arrivals energy, the effect of its amplitude preservation is worse than that by wave equation method, but its computing efficiency is higher than that by total Green′s function method and wave equation method.

Modeling and Sliding Mode Control with Boundary Layer for Unmanned Coaxial Rotor Ducted Fan Helicopter

The structure and modeling of a novel unmanned coaxial rotor ducted fan helicopter(RDFH)are introduced,and then,based on the helicopter air dynamics and kinematics principles,a nonlinear model of the coaxial rotor ducted fan helicopter is developed and implemented on the basis of the wind tunnel experiment.After that,the helicopter′s stability and coupling characteristics of manipulation are analyzed through time-domain.Finally,a sliding mode controller(SMC)with boundary layers is developed on a hardware in the loop platform using digital signal processor(DSP)as the flight control computer.The results show that the RDFH′s tracking ability performs well under the use of proposed controller.

Receiver function imaging in strongly laterally heterogeneous crust:Synthetic modeling of BOLIVAR data

We resolve a large （-20 km） discrepancy in Moho depth determined from PdS receiver functions （RFs） and from active source seismic profiling in the complex Caribbean-South American plate boundary zone in eastern Venezuela. As part of the BOLIVAR experiment 20 broadband stations were deployed along an active source profile to record teleseisms. Using the extremely heterogeneous crustal model obtained from active source data, we generated 2D finite-difference elastic wave synthetics and from them calculated receiver functions and CCP stacks. We compare the observations with synthetic sections that have been spatially sampled at 0.25 km to 40 km. The densely sampled synthetics show that several events in the field data that were originally interpreted as the Moho are multiple reflections within sedimentary basins. Where the Moho has the steepest dip under the plate boundary the CCP stacks fail to image the Moho well, regardless of the density of spatial sampling. A suitable spatial sampling criterion for clearly imaging the lower crust and Moho is to overlap Fresnel zones by 50% at Moho depth, which for the 1 Hz receiver functions examined here, requires an instrument spacing of 15-20 km, with the actual field data density ranging from 20 km to 100 km.

Time-Domain Protection for Transmission Lines Connected to Wind Power Plant based on Model Matching and Hausdorff Distance

The system impedance instability,high-order harmonics,and frequency offset are main fault characteristics of wind power system.Moreover,the measurement angle of faulty phase is affected by rotation speed frequency component,which causes traditional directional protections based on angle comparison between voltage and current to operate incorrectly.In this paper,a time-domain protection for connected to wind power plant based on model matching is proposed,which compares the calculated current and the measured current to identify internal faults and external faults.Under external faults,the calculated current and measured current waveform are quite similar because the protected transmission lines is equivalent to a lumped parameter model and the model itself is not damaged.However,the similarity of calculated current and measured current is quite low,due to destroyed integrity of model under internal faults.Additionally,Hausdorff distance is introduced to obtain the similarity of the calculated current and measured current.Since the proposed protection scheme is applied in time domain,it is independent from current frequency offsets of wind energy system,high-order harmonics,and system impedance variations.Comprehensive case studies are undertaken through Power Systems Computer Aided Design(PSCAD),while simulation results verify the accuracy and efficiency of the proposed approach in fault identification.

Unconditionally stable Crank-Nicolson algorithm with enhanced absorption for rotationally symmetric multi-scale problems in anisotropic magnetized plasma

Large calculation error can be formed by directly employing the conventional Yee’s grid to curve surfaces.In order to alleviate such condition,unconditionally stable CrankNicolson Douglas-Gunn(CNDG)algorithm with is proposed for rotationally symmetric multi-scale problems in anisotropic magnetized plasma.Within the CNDG algorithm,an alternative scheme for the simulation of anisotropic plasma is proposed in body-of-revolution domains.Convolutional perfectly matched layer(CPML)formulation is proposed to efficiently solve the open region problems.Numerical example is carried out for the illustration of effectiveness including the efficiency,resources,and absorption.Through the results,it can be concluded that the proposed scheme shows considerable performance during the simulation.

Far-infrared conductivity of CuS nanoparticles measured by terahertz time-domain spectroscopy

This paper reports that terahertz time-domain spectroscopy is used to measure the optical properties of CuS nanoparticles in composite samples. The complex conductivity of pure CuS nanoparticles is extracted by applying the Bruggeman effective medium theory. The experimental data are consistent with the Drude-Smith model of conductivity in the range of 0.2 1.5 THz. The results demonstrate that carriers become localized with a backscattering behaviour in small-size nanostructures. In addition, the time constant for the carrier scattering is obtained and is only 64.3 fs due to increased electron interaction with interfaces and grain boundaries.

Inversion of time-domain airborne EM data with IP effect based on Pearson correlation constraints

Due to the induced polarization(IP)eff ect,the sign reversal often occurs in timedomain airborne electromagnetic(AEM)data.The inversions that do not consider IP eff ect cannot recover the true umderground electrical structures.In view of the fact that there are many parameters of airborne induced polarization data in time domain,and the sensitivity diff erence between parameters is large,which brings challenges to the stability and accuracy of the inversion.In this paper,we propose an inversion mehtod for time-domain AEM data with IP effect based on the Pearson correlation constraints.This method uses the Pearson correlation coeffi cient in statistics to characterize the correlation between the resistivity and the chargeability and constructs the Pearson correlation constraints for inverting the objective function to reduce the non uniqueness of inversion.To verify the eff ectiveness of this method,we perform both Occam’s inversion and Pearson correlation constrained inversion on the synthetic data.The experiments show that the Pearson correlation constrained inverison is more accurate and stable than the Occam’s inversion.Finally,we carried out the inversion to a survey dataset with and without IP eff ect.The results show that the data misfit and the continuity of the inverted section are greatly improved when the IP eff ect is considered.