A class of fully third-order accurate projection methods for solving the incompressible Navier-Stokes equations

In this paper, a fully third-order accurate projection method for solving the incompressible Navier-Stokes equations is proposed. To construct the scheme, a continuous projection procedure is firstly presented. We then derive a sufficient condition for the continuous projection equations to be temporally third-order accurate approximations of the original Navier-Stokes equations by means of the localtruncation-error-analysis technique. The continuous projection equations are discretized temporally and spatially to third-order accuracy on the staggered grids, resulting in a fully third-order discrete projection scheme. The possibility to design higher-order projection methods is thus demonstrated in the present paper. A heuristic stability analysis is performed on this projection method showing the probability of its being stable. The stability of the present scheme is further verified through numerical tests. The third-order accuracy of the present projection method is validated by several numerical test cases.

Jacobi-Sobolev Orthogonal Polynomialsand Spectral Methods for Elliptic Boundary Value Problems

Generalized Jacobi polynomials with indexes α,β∈ R are introduced and some basic properties are established. As examples of applications,the second- and fourth-order elliptic boundary value problems with Dirichlet or Robin boundary conditions are considered,and the generalized Jacobi spectral schemes are proposed. For the diagonalization of discrete systems,the Jacobi-Sobolev orthogonal basis functions are constructed,which allow the exact solutions and the approximate solutions to be represented in the forms of infinite and truncated Jacobi series. Error estimates are obtained and numerical results are provided to illustrate the effectiveness and the spectral accuracy.

Design and calibration of a high-sensitivity and high-accuracy polarimeter based on liquid crystal variable retarders

Polarimetry plays an important role in the measurement of solar magnetic fields. We devel- oped a high-sensitivity and high-accuracy polarimeter （HHP） based on nematic liquid crystal variable retarders （LCVRs）, which has a compact setup and no mechanical moving parts. The system design and calibration methods are discussed in detail. The azimuth error of the transmission axis of the polarizer as well as the fast axes of the two LCVRs and the quarter-wave plate were determined using dedicated procedures. Linearly and circularly polarized light were employed to evaluate the performance of the HHP. The experimental results indicate that a polarimetric sensitivity of better than 5.7 × 10-3 can be achieved by using a single short-exposure image, while an accuracy on the order of 10-5 can be reached by using a large number of short-exposure images. This makes the HHP a high-performance system that can be used with a ground-based solar telescope for high-precision solar magnetic field investigations.

A hyperbolic Lindstedt-Poincare method for homoclinic motion of a kind of strongly nonlinear autonomous oscillators

A hyperbolic Lindstedt-Poincare method is presented to determine the homoclinic solutions of a kind of nonlinear oscillators, in which critical value of the homoclinic bifurcation parameter can be determined. The generalized Lienard oscillator is studied in detail, and the present method＇s predictions are compared with those of Runge-Kutta method to illustrate its accuracy.

Optical fiber positioning based on four-quadrant detector with Gaussian fitting method

With the development of large-scale spectral surveys, fiber positioning technology has been developing rapidly. Because of the performance advantages of a four-quadrant（4Q） detector, a fiber positioning and real-time monitoring system based on the 4Q detector is proposed. The detection accuracy of this system is directly determined by the precision of the center of the spot. A Gaussian fitting algorithm based on the 4Q detector is studied and applied in the fiber positioning process to improve the calculated accuracy of the spot center. The relationship between the center position of the incident spot and the detector output signal is deduced. An experimental platform is built to complete the simulated experiment. Then we use the Gaussian fitting method to process experimental data, compare the fitting value with the theoretical one and calculate the corresponding error.

Surface and Texture Properties of Tb-Doped Ceria-Zirconia Solid Solution Prepared by Sol-Gel Method

The three-way catalysts （TWCs） promoters Ce0.6Zr0.4- x TbxO2-y were prepared by sol-gel method. BET surface areas analysis indicated that an increase of the dopant Tb content from x = 0.05 to x = 0.15 favors an increase of surface area from 66.8 to 80.4 m^2· g^-1 compared with the undoped sample Ce0 .6oZr0.40O2 65.1 m^2·g^- 1 after calcination at 650℃. Transmission electron microscopy （TEM） observation indicated that the doped samples have a higher thermal stability. The XRD and Raman spectra confirmed that the Ce0.6Zr0.4-xTbxO2-y cubic solid solution is formed. XPS analysis revealed that Ce and Tb mainly existed in the form of Ce^4＋ and Tb^3 ＋ , and Zr existed in the form of Zr^4＋ on the surface of the samples. The doped samples were homogenous in composition ; the introduction of Tb into the CeO2-ZrO2 promoters resuited in the formation of a solid solution, and the concentration of surface lattice oxygen was increased.

Construction of n-sided polygonal spline element using area coordinates and B-net method

In general, triangular and quadrilateral elements are commonly applied in two-dimensional finite element methods. If they are used to compute polycrystalline materials, the cost of computation can be quite significant. Polygonal elements can do well in simulation of the materials behavior and provide greater flexibility for the meshing of complex geometries. Hence, the study on the polygonal element is a very useful and necessary part in the finite element method. In this paper, an n-sided polygonal element based on quadratic spline interpolant, denoted by PS2 element, is presented using the triangular area coordinates and the B-net method. The PS2 element is conforming and can exactly model the quadratic field. It is valid for both convex and non-convex polygonal element, and insensitive to mesh distortions. In addition, no mapping or coordinate transformation is required and thus no Jacobian matrix and its inverse are evaluated. Some appropriate examples are employed to evaluate the performance of the proposed element.

Multi-train modeling and simulation integrated with traction power supply solver using simplified Newton–Raphson method

Multi-train modeling and simulation plays a vital role in railway electrification during operation and planning phase. Study of peak power demand and energy consumed by each traction substation needs to be deter- mined to verify that electrical energy flowing in its railway power feeding system is appropriate or not. Gauss-Seidel, conventional Newton-Raphson, and current injection methods are well-known and widely accepted as a tool for electrical power network solver in DC railway power supply study. In this paper, a simplified Newton-Raphson method has been proposed. The proposed method employs a set of current-balance equations at each electrical node instead of the conventional power-balance equation used in the conventional Newton-Raphson method. This concept can remarkably reduce execution time and computing complexity for multi-train simulation. To evaluate its use, Sukhumvit line of Bangkok transit system （BTS） of Thai- land with 21.6-km line length and 22 passenger stopping stations is set as a test system. The multi-train simulation integrated with the proposed power network solver is developed to simulate 1-h operation service of selected 5-min headway. From the obtained results, the proposed method is more efficient with approximately 18 % faster than the conventional Newton-Raphson method and just over 6 % faster than the current injection method.

A hybrid vertex-centered finite volume/element method for viscous incompressible flows on non-staggered unstructured meshes

This paper proposes a hybrid vertex-centered fi- nite volume/finite element method for solution of the two di- mensional （2D） incompressible Navier-Stokes equations on unstructured grids. An incremental pressure fractional step method is adopted to handle the velocity-pressure coupling. The velocity and the pressure are collocated at the node of the vertex-centered control volume which is formed by join- ing the centroid of cells sharing the common vertex. For the temporal integration of the momentum equations, an im- plicit second-order scheme is utilized to enhance the com- putational stability and eliminate the time step limit due to the diffusion term. The momentum equations are discretized by the vertex-centered finite volume method （FVM） and the pressure Poisson equation is solved by the Galerkin finite el- ement method （FEM）. The momentum interpolation is used to damp out the spurious pressure wiggles. The test case with analytical solutions demonstrates second-order accuracy of the current hybrid scheme in time and space for both veloc- ity and pressure. The classic test cases, the lid-driven cavity flow, the skew cavity flow and the backward-facing step flow, show that numerical results are in good agreement with the published benchmark solutions.

A meshfree-based local Galerkin method with condensation of degree of freedom for elastic dynamic analysis

Condensation technique of degree of freedom is first proposed to improve the computational efficiency of meshfree method with Galerkin weak form for elastic dy- namic analysis. In the present method, scattered nodes with- out connectivity are divided into several subsets by cells with arbitrary shape. Local discrete equation is established over each cell by using moving Kriging interpolation, in which the nodes that located in the cell are used for approxima- tion. Then local discrete equations can be simplified by con- densation of degree of freedom, which transfers equations of inner nodes to equations of boundary nodes based on cells. The global dynamic system equations are obtained by as- sembling all local discrete equations and are solved by using the standard implicit Newmark＇s time integration scheme. In the scheme of present method, the calculation of each cell is carried out by meshfree method, and local search is imple- mented in interpolation. Numerical examples show that the present method has high computational efficiency and good accuracy in solving elastic dynamic problems.

Short-term solar flare prediction using multi-model integration method

A multi-model integration method is proposed to develop a multi-source and heterogeneous model for short-term solar flare prediction. Different prediction models are constructed on the basis of extracted predictors from a pool of observation databases. The outputs of the base models are normal- ized first because these established models extract predictors from many data resources using different prediction methods. Then weighted integration of the base models is used to develop a multi-model integrated model （MIM）. The weight set that single models assign is optimized by a genetic algorithm. Seven base models and data from Solar and Heliospheric Observatory/Michelson Doppler Imager lon- gitudinal magnetograms are used to construct the MIM, and then its performance is evaluated by cross validation. Experimental results showed that the MIM outperforms any individual model in nearly every data group, and the richer the diversity of the base models, the better the performance of the MIM. Thus, integrating more diversified models, such as an expert system, a statistical model and a physical model, will greatly improve the performance of the MIM.

Pseudo-beam method for compressive buckling characteristics analysis of space inflatable load-carrying structures

This paper extends Le van＇s work to the case of nonlinear problem and the complicated configuration. The wrinkling stress distribution and the pressure effects are also included in our analysis. Pseudo-beam method is presented based on the inflatable beam theory to model the inflatable structures as a set of inflatable beam elements with a prestressed state. In this method, the discretized nonlinear equations are given based upon the virtual work principle with a 3-node Timoshenko＇s beam model. Finite element simulation is performed by using a 3-node BEAM189 element incorporating ANSYS nonlinear program. The pressure effect is equivalent included in our method by modifying beam element cross-section parameters related to pressure. A benchmark example, the bending case of an inflatable cantilever beam, is performed to verify the accuracy of our proposed method. The comparisons reveal that the numerical results obtained with our method are close to open published analytical and membrane finite element results. The method is then used to evaluate the whole buckling and the loadcarrying characteristics of an inflatable support frame subjected to a compression force. The wrinkling stress and region characteristics are also shown in the end. This method gives better convergence characteristics, and requires much less computation time. It is very effective to deal with the whole load-carrying ability analytical problems for large scale inflatable structures with complex configuration.

Two 8-node quadrilateral spline elements by B-net method

Isoparametric quadrilateral elements are widely used in the finite element method, but the accuracy of the isoparametric quadrilateral elements will drop obviously deteriorate due to mesh distortions. Spline functions have some properties of simplicity and conformality. Two 8-node quadrilateral elements have been developed using the trian- gular area coordinates and the B-net method, which can ex- actly model the quadratic field for both convex and concave quadrangles. Some appropriate examples are employed to evaluate the performance of the proposed elements. The nu- merical results show that the two spline elements can obtain solutions which are highly accurate and insensitive to mesh distortions.

Comparison of two earthquake early warning location methods

According to earthquake catalog records of Fujian Seismic Network, the Tnow method and the fourstation continuous location method put forward by Jin Xing are inspected by using P-wave arrival information of the first four stations in each earthquake. It shows that the fourstation continuous location method can locate more seismic events than the Tnow method. By analyzing the results, it is concluded that the reason for this is that the Tnow method makes use of information from stations without being triggered, while some stations failed to be reflected in earthquake catalog because of discontinuous records or unclear records of seismic phases. For seismic events whose location results can be given, there is no obvious difference in location results of the two methods and positioning deviation of most seismic events is also not significant. For earthquakes outside the network, the positioning deviation may amplify as the epicentral distance enlarges, which may relate to the situation that the seismic stations are centered on one side of epicenter and the opening angle between seismic stations used for location and epicenter is small.

Preparation of BaCe_(0.5)Zr_(0.4)Y_(0.1)O_(3-α) by Sol-Gel Method and Its Electrical Properties

A precursor of BaCe0.5Zr0.4Y0. 1O3-α electrolytes was synthesized by the sol-gel method and sintered at temperature which were 150 - 250 ℃ lower than by solid state reaction. The AC impedance spectrums of electrolytes were measured by AUTOLAB PGSTA30 electrochemical measuring device at different temperatures. The conductivities of the electrolytes are 1.62×10^-4 - 6.43×10^-3, 2.52×10^-5 - 3.73×10^-3S·cm^-1 in the temperature range of 350-800℃. The activity energies are 0.54 and 0.84 eV. At the same time BaCe0.9Y0.1O3-α was prepared by direct solid state reaction. The conductivity of BaCe0.9Y0.1O3-α is 1 × 10^-4- 4×10^-3 S·cm^-1 and the activation energy is 0.50 eV at the same condition. The results show that conduction of electrolyte prepared by sol-gel method is higher than the one by solid state reaction. As far as BaCe0.9Y0.1O3-α concerned, its conductivity of the Zr-substituted specimens is decreased.

Texture invariant estimation of equivalent number of looks based on log-cumulants in polarimetric radar imagery

A novel estimation of the equivalent number of looks (ENL) is proposed in statistical modeling of multilook polarimetric synthetic aperture radar (PolSAR) images for the product model, which is based on the log-determinant moments (LDM). The LDM estimators discovered by looking at certain log-cumulants of the intensities of different polarization channels and the multilook polarimetric covariance matrix, which can be used for both the Gaussian model and all product models. This estimator has analytic expressions, and uses the full covariance matrix and intensities as input, which makes more statistical information available. Experiments based on simulated data and real data are performed. The comparisons among the widely used methods of equivalent number of looks (ENL) estimation for the product model such as K and G0 distributions show that the performance of the LDM estimator is outstanding. The performance of estimators for the real data of San Francisco and Flevoland is analyzed and the results are according to those of simulated data. Finally, it can be concluded that the LDM estimator is well robust to each product model with low computational complexity and high accuracy. © 1990-2011 Beijing Institute of Aerospace Information.

A high-contrast imaging polarimeter with a stepped-transmission filter based coronagraph

The light reflected from planets is polarized mainly due to Rayleigh scattering, but starlight is normally unpolarized. Thus it provides an approach to enhance the imaging contrast by inducing the imaging polarimetry technique. In this paper, we propose a high-contrast imaging polarimeter that is op- timized for the direct imaging of exoplanets, combined with our recently developed stepped-transmission filter based coronagraph. Here we present the design and calibration method of the polarimetry system and the associated test of its high-contrast performance. In this polarimetry system, two liquid crystal variable retarders （LCVRs） act as a polarization modulator, which can extract the polarized signal. We show that our polarimeter can achieve a measurement accuracy of about 0.2% at a visible wavelength （632.8 nm） with linearly polarized light. Finally, the whole system demonstrates that a contrast of 10 9 at 5A/D is achievable, which can be used for direct imaging of Jupiter-like planets with a space telescope.

基于Test Method 1311法重结晶α-半水石膏重金属元素的浸出特性研究

以脱硫石膏及其常压盐溶液法重结晶得到的α-半水石膏为研究对象,采用改进的Tessier流程和Test Method 1311法研究两种石膏晶体重金属元素的赋存形态和浸出特性,并对其进行环境效应评价。结果表明:重结晶过程能够释放脱硫石膏中的重金属元素并使其赋存形态改变;重结晶后石膏晶体中的重金属组分短期内可达到释放平衡,其中Cr、Pb、Ni元素的最大浸出量明显低于对应的脱硫石膏,As元素的浸出量几乎不变;α-半水石膏的环境友好性优于脱硫石膏,但仍具有污染环境的潜在风险。

Discrimination of background events in the PolarLight X-ray polarimeter

PolarLight is a space-borne X-ray polarimeter that measures the X-ray polarization via electron tracking in an ionization chamber.It is a collimated instrument and thus suffers from the background on the whole detector plane.The majority of background events are induced by high energy charged particles and show ionization morphologies distinct from those produced by X-rays of interest.Comparing on-source and off-source observations,we find that the two datasets display different distributions on image properties.The boundaries between the source and background distributions are obtained and can be used for background discrimination.Such a means can remove over 70%of the background events measured with PolarLight.This approaches the theoretical upper limit of the background fraction that is removable and justifies its effectiveness.For observations with the Crab nebula,the background contamination decreases from 25%to 8%after discrimination,indicative of a polarimetric sensitivity of around 0.2 Crab for PolarLight.This work also provides insights into future X-ray polarimetric telescopes.

Microwave absorption properties regulation and bandwidth formula of oriented Y_(2)Fe_(17)N_(3-δ)@SiO_(2)/PU composite synthesized by reduction-diffusion method

As concepts closely related to microwave absorption properties,impedance matching and phase matching were rarely combined with material parameters to regulate properties and explore related mechanisms.In this work,reduction–diffusion method was innovatively applied to synthesize rare earth alloy Y_(2)Fe_(17).In order to regulate the electromagnetic parameters of absorbers,the Y_(2)Fe_(17)N_(3-δ)particles were coated with silica(Y_(2)Fe_(17)N_(3-δ)@SiO_(2))and absorbers with different volume fractions were prepared.The relationship between impedance matching,matching thickness,and the strongest reflection loss peak(RLmin)was presented obviously.Compared to the microwave absorption properties of Y_(2)Fe_(17)N_(3-δ)/PU absorber,Y_(2)Fe_(17)N_(3-δ)@SiO_(2)/PU absorbers are more conducive to the realization of microwave absorption material standards which are thin thickness,light weight,strong absorbing intensity,and broad bandwidth.Based on microwave frequency bands,the microwave absorption properties of the absorbers were analyzed and the related parameters were listed.As an important parameter related to perfect matching,reflection factor(√ε_(r)/μ_(r))was discussed combined with microwave amplitude attenuation.According to the origin and mathematical model of bandwidth,the formula of EAB(RL<-10 dB)was derived and simplified.The calculated bandwidths agreed well with experimental results.