Converted-wave Seismology in Anisotropic Media Revisited, Part II: Application to Parameter Estimation

In transversely isotropic media with a vertical symmetry axis （VTI）, the converted-wave （C-wave） moveout over intermediate-to-far offsets is determined by four parameters. These are the C-wave stacking velocity Vc2 , the vertical and effective velocity ratios γ0 and γeff, and the anisotropic parameter χeff. We refer to the four parameters as the C-wave stacking velocity model. The purpose of C-wave velocity analysis is to determine this stacking velocity model. The C-wave stacking velocity model Vc2, γ0, γeff, and χeff can be determined from P-and C-wave reflection moveout data. However, error propagation is a severe problem in C-wave reflection-moveout inversion. The current short-spread stacking velocity as deduced from hyperbolic moveout does not provide sufficient accuracy to yield meaningful inverted values for the anisotropic parameters. The non-hyperbolic moveout over intermediate-offsets （x/z from 1.0 to 1.5） is no longer negligible and can be quantified using a background γ. Non-hyperbolic analysis with a γ correction over the intermediate offsets can yield Vc2 with errors less than 1% for noise free data. The procedure is very robust, allowing initial guesses of γ with up to 20% errors. It is also applicable for vertically inhomogeneous anisotropic media. This improved accuracy makes it possible to estimate anisotropic parameters using 4C seismic data. Two practical work flows are presented for this purpose： the double-scanning flow and the single-scanning flow. Applications to synthetic and real data show that the two flows yield results with similar accuracy but the single-scanning flow is more efficient than the double-scanning flow.

A speed-flow relationship model of highway traffic flow

In the view that the generally used speed-flow relationship model is insufficient in the traffic analysis under over-saturated conditions, this paper first establishes the theoretical models of speed flow relationship for each highway class based upon a large number of traffic data collected from the field. Then by analyzing the traffic flow dissipation mechanism under peak hour over-saturated traffic conditions, the speed flow relationship model structures for each highway class are reviewed under different traffic load conditions. Through curve-fitting of large numbers of observed data, functional equations of general speed-flow relationship models for each highway class under any traffic load conditions are established. The practical model parameters for each highway class under different design speeds are also put forward. This model is successful in solving the speed-forecasting problem of the traffic flow under peak hour over-saturated conditions. This provides the theoretical bases for the development of projects related to highway network planning, economic analysis, etc.

A fast explicit finite difference method for determination of wellhead injection pressure

A fast explicit finite difference method (FEFDM),derived from the differential equations of one-dimensional steady pipe flow,was presented for calculation of wellhead injection pressure.Recalculation with a traditional numerical method of the same equations corroborates well the reliability and rate of FEFDM.Moreover,a flow rate estimate method was developed for the project whose injection rate has not been clearly determined.A wellhead pressure regime determined by this method was successfully applied to the trial injection operations in Shihezi formation of Shenhua CCS Project,which is a good practice verification of FEFDM.At last,this method was used to evaluate the effect of friction and acceleration terms on the flow equation on the wellhead pressure.The result shows that for deep wellbore,the friction term can be omitted when flow rate is low and in a wide range of velocity the acceleration term can always be deleted.It is also shown that with flow rate increasing,the friction term can no longer be neglected.

Contributions to Hom-Schunck optical flow equations-part I： Stability and rate of convergence of classical algorithm

Globally exponential stability （which implies convergence and uniqueness） of their classical iterative algorithm is established using methods of heat equations and energy integral after embedding the discrete iteration into a continuous flow. The stability condition depends explicitly on smoothness of the image sequence, size of image domain, value of the regularization parameter, and finally discretization step. Specifically, as the discretization step approaches to zero, stability holds unconditionally. The analysis also clarifies relations among the iterative algorithm, the original variation formulation and the PDE system. The proper regularity of solution and natural images is briefly surveyed and discussed. Experimental results validate the theoretical claims both on convergence and exponential stability.

A Mathematical Model for Pulsating Flow of Ionic Fluid under an Axial Electric Field： EMF Effect on Blood Flow

The present work introduces a mathematical model for ionic fluid that flows under the effect of both pulsating pressure and axial electromagnetic field. The fluid is treated as a Newtonian fluid applying Navier-Stokes equation. The fluid is considered as a neutral mixture of positive and negative ions. The effect of axial electric field is investigated to determine velocity profiles. Hydroelectric equation of the flow is deduced under dc and ac external electric field. Hence the effect of applied frequency （0-1 GHz） and amplitude （10-350 V/m） is illustrated. The ultimate goal is to approach the problem of EMF field interaction with blood flow. The applied pressure waveform is represented as such to simulate the systolic-diastolic behavior. Simulation was carried out using Maple software using blood plasma parameters; hence velocity profiles under various conditions are reported.

Interaction between Topographic Conditions and Entrainment Rate in Numerical Simulations of Debris Flow

Debris flow simulations are useful for predicting the sediment supplied to watersheds from upstream areas. However, the topographic conditions upstream are more complicated than those downstream and the relationship between the topographic conditions and debris flow initiation is not well understood. This study compared the use of several entrainment rate equations in numerical simulations of debris flows to examine the effect of topographic conditions on the flow. One-dimensional numerical simulations were performed based on the shallow water equations and three entrainment rate equations were tested. These entrainment rate equations were based on the same idea that erosion and the deposition of debris flows occur via the difference between the equilibrium and current conditions of debris flows, while they differed in the expression of the concentration, channel angle, and sediment amount. The comparison was performed using a straight channel with various channel angles and a channel with a periodically undulating surface. The three entrainment rate equations gave different amounts of channel bed degradation and hydrographs for a straight channel with a channel angle greater than 21° when water was supplied from upstream at a steady rate. The difference was caused by the expression of the entrainment rate equations. For channels with little undulation, the numerical simulations gave results almost identical to those for straight channels with the same channel angle. However, for channels with large undulations, the hydrographs differed from those for straight channels with the same channel angle when the channel angle was less than 21°. Rapid erosion occurred and the hydrograph showed a significant peak, especially in cases using the entrainment equation expressed by channel angle. This was caused by the effects of the steep undulating sections, since the effect increased with the magnitude of the undulation, suggesting that a debris flow in an upstream area develops differently according to the topographic conditions. These results also inferred that numerical simulations of debris flow can differ depending on the spatial resolution of the simulation domain, as the resolution determines the reproducibility of the undulations.

Experimental study on hydrodynamic effect of orientation micro-pored surfaces

The orientation of the dimple increases the flow distance in the dimple and produces fluid cumulative effect in the dimple length direction, which leads to obvious hydrodynamic effect as a result. In order to investigate the hydrodynamic effect of orientation dimples, a series of experiments was carried out on a ring-on-ring test. Multi-pored faces were tested with different dimple inclination angles and slender ratios. Film thickness and frictional torque were measured under different conditions of load and rotation speed. Experimental results showed that the orientation dimple could produce obvious dynamic effect by change of the flow direction and the increasing dimple orientation leads to increase of the load capability. The hydrodynamic effect strongly depends on dimple orientation parameters such as inclination angle and slender ratio. A larger load capability can be available by increasing dimple orientation and rotation speed. Experimental results agreed well with the theory that orientation micro-pores can significantly improve hydrodynamic performance of surfaces.

Evolution of Unsteady Flow near Rotor Tip during Stall Inception

Previously the features of circumferential propagation of self-induced tip leakage flow unsteadiness for a low speed isolated axial compressor rotor in the authors' laboratory were discovered and investigated via numerical simulation,which only occurs below a critical stable flow point that is close to but not yet at the stall limit.Further in this paper,the detailed investigation on evolution of tip leakage flow during the throttling process into spike rotating stall was conducted by adopting the valve-throttling model.During this process,the development of the circumferential propagation of tip leakage flow unsteadiness was especially focused on.According to the unsteady characteristics of pressure signals,the evolvement of compressor flow field can be classified into four stages.As compressor throttled,the oscillation frequency of self-induced unsteady tip leakage flow decreased gradually,and thus resulted in the decrease of its circumferential propagation speed.The circumferential propagation of self-induced tip leakage flow unsteadiness is closely related with rotating instability.When the forward spillage of tip leakage flow at the leading edge occurred,the spike type rotating stall was initiated.Its flow struc-tures were given in the paper.

An in-plane low-noise accelerometer fabricated with an improved process flow

We present a bulk micromachined in-plane capacitive accelerometer fabricated with an improved process flow,by etching only one-fifth of the wafer thickness at the back of the silicon while forming the bar-structure electrode for the sensing capacitor.The improved flow greatly lowers the footing effect during deep reactive ion etching(DRIE),and increases the proof mass by 54% compared to the traditional way,resulting in both improved device quality and a higher yield rate.Acceleration in the X direction is sensed capacitively by varying the overlapped area of a differential capacitor pair,which eliminates the nonlinear behavior by fixing the parallel-plate gap.The damping coefficient of the sensing motion is low due to the slide-film damping.A large proof mass is made using DRIE,which also ensures that dimensions of the spring beams in the Y and Z directions can be made large to lower cross axis coupling and increase the pull-in voltage.The theoretical Brownian noise floor is 0.47 μg/Hz1/2 at room temperature and atmospheric pressure.The tested frequency response of a prototype complies with the low damping design scheme.Output data for input acceleration from ?1 g to 1 g are recorded by a digital multimeter and show very good linearity.The tested random bias of the prototype is 130 μg at an averaging time of around 6 s.

Convergence proof of the DSMC method and the Gas-Kinetic Unified Algorithm for the Boltzmann equation

This paper investigates the convergence proof of the Direct Simulation Monte Carlo(DSMC) method and the Gas-Kinetic Unified Algorithm in simulating the Boltzmann equation.It can be shown that the particle velocity distribution function obtained by the DSMC method converges to a modified form of the Boltzmann equation,which is the equation of the gas-kinetic unified algorithm to directly solve the molecular velocity distribution function.Their convergence is derived through mathematical treatment.The collision frequency is presented using various molecular models and the local equilibrium distribution function is obtained by Enskog expansion using the converged equation of the DSMC method.These two expressions agree with those used in the unified algorithm.Numerical validation of the converging consistency between these two approaches is illustrated by simulating the pressure driven Poiseuille flow in the slip transition flow regime and the two-dimensional and three-dimensional flows around a circular cylinder and spherical-cone reentry body covering the whole flow regimes from low speed micro-channel flow to high speed non-equilibrium aerothermodynamics.

Multi-spacecraft observations of earthward flow bursts

On the basis of the plasma, electric and magnetic fields jointly observed by Cluster and the Double Star TC-I spacecraft in the Earth＇s magnetotail, we have investigated the earthward flow bursts by introducing the momentum equation in the X-direction in the ideal conditions of magneto hydrodynamics （MHD）. One earthward flow burst with a peak in excess of 500 km/s was selected, when the four spacecraft of Cluster were located around -16 RE and TC-1 was located around -10 RE in the X-direction. The inter-spacecraft distances in Y and Z directions were smaller than the statistical spatial scales of the bursty bulk flows. When the Y components of E and -VxB were compared, there was no clear breakdown of the frozen-in condition during the earthward flow burst. With the measured plasma and magnetic parameters from two spacecraft at different positions in the magnetotail, the X component of the pressure gradient was calculated. Magnetic tension was calculated using the mag- netic field measured at four points, which could be compared with the assumed constant in the past research with single satel- lite. When the pressure gradient and the magnetic tension were put into the MHD momentum equation, some samples of the earthward flow bursts were accelerated and some were decelerated. The braking process of the earthward flow burst was more complicated than what the past results had shown. The accelerated samples accounted for about one third of the whole earth- ward flow bursts and discontinuously located among the decelerated elements. The original single earthward flow burst event might be split into several short flow bursts when it was moving to the Earth. Our results may partly illustrate that the duration of fast flows during three phases of substorm becomes short near the Earth. The results are consistent with the past results that fast flows intrude to places earthward the typical braking region.

Investigation of the unstable flow phenomenon in a pump turbine

Instability of pump turbine with S-shaped curve is characterized by large fluctuations of rotational speed during the transient processes.For investigating this phenomenon,a numerical model based on the dynamic sliding mesh method(DSSM)is presented and used to numerically solve the 3D transient flow which is characterized by the variable rotation speed of runner.The method is validated by comparison with measured data for a load rejection process in a prototype pump turbine.The results show that the calculated rotation speed agrees well with the experimental data.Based on the validated model,simulations were performed for the runaway process using an artificially assumed operating condition under which the unstable rotation speed is expected to appear.The results confirm that the instability of runner rotational speed can be effectively captured with the proposed method.Presented results include the time history profiles of unit flow rate and unit rotating speed.The internal flow characteristics in a typical unstable period are discussed in detail and the mechanism of the unstable hydraulic phenomenon is explained.Overall,the results suggest that the method presented here can be a viable alternative to predict the dynamic characteristics of pump turbines during transient processes.

Mixed Convective Viscoelastic Nanofluid Flow Past a Porous Media with Soret–Dufour Effects

The present study is carried out to see the thermal-diffusion(Dufour) and diffusion-thermo(Soret) effects on the mixed convection boundary layer flow of viscoelastic nanofluid flow over a vertical stretching surface in a porous medium. Optimal homotopy analysis method(OHAM) is best candidate to handle highly nonlinear system of differential equations obtained from boundary layer partial differential equations via appropriate transformations. Graphical illustrations depicting different physical arising parameters against velocity, temperature and concentration distributions with required discussion have also been added. Numerically calculated values of skin friction coefficient, local Nusselt and Sherwood numbers are given in the form of table and well argued. It is found that nanofluid velocity increases with increase in mixed convective and viscoelastic parameters but it decreases with the increasing values of porosity parameter. Also, it is observed that Dufour number has opposite behavior on temperature and concentration profiles.

Mathematical modeling of micropolar fluid flow through an overlapping arterial stenosis

In this study a mathematical model for two-dimensional pulsatile blood flow through overlapping constricted tapered vessels is presented. In order to establish resemblance to the in vivo conditions, an improved shape of the time-variant overlapping stenosis in the elastic tapered artery subject to pulsatile pressure gradient is considered. Because it contains a suspension of all erythrocytes, the flowing blood is represented by micropolar fluid. By applying a suitable coordinate transformation, tapered cosine-shaped artery turned into non-tapered rectangular and a rigid artery. The governing nonlinear partial differential equations under the imposed realistic boundary conditions are solved using the finite difference method. The effects of vessel tapering on flow characteristics consid- ering their dependencies with time are investigated. The results show that by increasing the taper angle the axial velocity and volumetric flow rate increase and the microrota- tional velocity and resistive impedance reduce. It has been shown that the results are in agreement with similar data from the literature.