Synthesis of Vanadium Nitride by a One Step Method

Vanadium nitrides were prepared via one step method of carbothermal reduction and nitridation of vanadium trioxide. Thermalgravimetric analysis （TGA） and X-ray diffraction were used to determine the reaction paths of vanadium carbide, namely the following sequential reaction： V2O3→V8C7 in higher temperature stage, the rule of vanadium nitride synthesized was established, and defined conditions of temperature for the production of the carbides and nitrides were determined. Vanadium oxycarbide may consist in the front process of carbothermal reduction of vanadium trioxide. In one step method for vanadium nitride by carbothermal reduction and nitridation of vanadium trioxide, the nitridation process is simultaneous with the carbothermal reduction. A one-step mechanism of the carbothermal reduction with simultaneous nitridation leaded to a lower terminal temperature in nitridation process for vanadium nitride produced, compared with that of carbothermal reduction process without nitridation. The grain size and shape of vanadium nitride were uniform, and had the shape of a cube. The one step method combined vacuum carborization and nitridation （namely two step method） into one process. It simplified the technological process and decreased the costs.

Modified precise time step integration method of structural dynamic analysis

The precise time step integration method proposed for linear time-invariant homogeneous dynamic systems can provide precise numerical results that approach an exact solution at the integration points. However, difficulty arises when the algorithm is used for non-homogeneous dynamic systems, due to the inverse matrix calculation and the simulation accuracy of the applied loading. By combining the Gaussian quadrature method and state space theory with the calculation technique of matrix exponential function in the precise time step integration method, a new modified precise time step integration method （e.g., an algorithm with an arbitrary order of accuracy） is proposed. In the new method, no inverse matrix calculation or simulation of the applied loading is needed, and the computing efficiency is improved. In particular, the proposed method is independent of the quality of the matrix H. If the matrix H is singular or nearly singular, the advantage of the method is remarkable. The numerical stability of the proposed algorithm is discussed and a numerical example is given to demonstrate the validity and efficiency of the algorithm.

FULL DISCRETE NONLINEAR GALERKIN METHOD FOR THE NAVIER-STOKES EQUATIONS

This paper deals with the inertial manifold and the approximate inertialmanifold concepts of the Navier-Stokes equations with nonhomogeneous boundary conditions and inertial algorithm. Furtheremore,we provide the error estimates of the approximate solutions of the Navier-Stokes Equations.

NUMERICAL ANALYSIS AND EXPERI-MENT OF UNSTEADY THERMAL FIELD OF ROTOR PLATE FOR EDDY CURRENT RETARDER

The physical model based on heat transfer theory and virtual boundary method for analyzing unsteady thermal field of rotor plate for eddy current retarder used in automobile is established and boundary conditions are also defined. The finite element governing equation is derived by Galerkin method. The time differential item is discrete based on Galerkin format that is stable at any condition. And a new style of varying time step method is used in iteration process. The thermal field on the rotor plate at the radial and axle directions is analyzed and varying temperature at appointed points on two side-surfaces is measured. The testing and analytical data are uniform approximately. Finite element method can be used for estimating thermal field of the rotor plate at initial design stage of eddy current retarder.

Excited response of granular ores in vibrating field

The dynamical theory was utilized to probe into the law of the excited response of granular ores generated by the exciting action of exciter and the influence of wave propagation in vibrating field. The exciter with double axes was presented as an example, and the principle of exciter and its mathematical expression of the excitation force were given. The granular ores have viscidity and damping speciality, on the basis of which the motion equation of excited response of ores was established and the approximate expression of mode displacement by harmonic excitation and the steady effect solution of coordinate response were deduced. Utilizing the step by step integration method, the recursion relation matrix of displacement, velocity and acceleration of the excited response of ores were obtained, and the computational flow chart and a computational example were given. The results show that the excited response can change the dynamical character and the flowing characteristic of granular ores.

On Improving the Written English Level of Middle School Students

This paper is an attempt to improve the studen the written English level. There are three parts in this passage. Part one: Analyze the types of mistakes. Part two is "six - step" method in written English. Part three is conclusion.

Modeling of seasonal soil cold storage using natural cold energy

To reduce energy consumption on summer air conditioning,a novel seasonal soil cold storage mode using natural energy is presented and two-dimensional transient heat transfer model of U-tube is developed. The three processes of cold storage in winter,shut-down in transition season and cold extraction in summer are simulated by using sensitive heat capacity method with variable time step. The changing of U-tube outlet water temperature in different periods,daily cold storage and cold extraction are estimated. The temperature field of the U-tube and soil around the tube is investigated. Simulations show that seasonal soil cold storage using natural cold energy is feasible in the north to Changchun,which provides theoretical support for seasonal soil cold storage application.

ON THE ERROR ESTIMATES OF A NEW OPERATE SPLITTING METHOD FOR THE NAVIER-STOKES EQUATIONS

In this paper, a new operator splitting scheme is introduced for the numerical solution of the incompressible Navier-Stokes equations. Under some mild regularity assumptions on the PDE solution, the stability of the scheme is presented, and error estimates for the velocity and the pressure of the proposed operator splitting scheme are given.

The Modified Upwind Finite Difference Fractional Steps Method for Compressible Two-phase Displacement Problem

For compressible two-phase displacement problem,the modified upwind finite difference fractionalsteps schemes are put forward.Some techniques,such as calculus of variations,commutative law of multiplicationof difference operators,decomposition of high order difference operators,the theory of prior estimates and tech-niques are used.Optimal order estimates in L^2 norm are derived for the error in the approximate solution.Thismethod has already been applied to the numerical simulation of seawater intrusion and migration-accumulationof oil resources.

New Numerical Methods for the Coupled Nonlinear Schrdinger Equations

In this paper, three numerical schemes with high accuracy for the coupled Schrodinger equations are studied. The conserwtive properties of the schemes are obtained and the plane wave solution is analysised. The split step Runge-Kutta scheme is conditionally stable by linearized analyzed. The split step compact scheme and the split step spectral method are unconditionally stable. The trunction error of the schemes are discussed. The fusion of two solitions colliding with different β is shown in the figures. The numerical experments demonstrate that our algorithms are effective and reliable.

First attempt to overcome the disaster of Dirac sea in imaginary time step method

Efforts have been made to solve the Dirac equation with axially deformed scalar and vector WoodsSaxon potentials in the coordinate space with the imaginary time step method. The results of the singleparticle energies thus obtained are consistent with those calculated with the basis expansion method, which demonstrates the feasibility of the imaginary time step method for the relativistic static problems.

AViscosity-Splitting Method for the Navier-Stokes/ Darcy Problem

In this report,we give a viscosity splitting method for the Navier-Stokes/Darcy problem.In this method,the Navier-Stokes/Darcy equation is solved in three steps.In the first step,an explicit/implicit formulation is used to solve the nonlinear problem.We introduce an artificial diffusion term qDu in our scheme whose purpose is to enlarge the time stepping and enhance numerical stability,especially for small viscosity parameter n,by choosing suitable parameter q.In the second step,we solve the Stokes equation for velocity and pressure.In the third step,we solve the Darcy equation for the piezometric head in the porous media domain.We use the numerical solutions at last time level to give the interface condition to decouple the Navier-Stokes equation and the Darcy’s equation.The stability analysis,under some condition △t≤k0,k0>0,is given.The error estimates prove our method has an optimal convergence rates.Finally,some numerical results are presented to show the performance of our algorithm.

High Order Compact Schemes in Projection Methods for Incompressible Viscous Flows

Within the projection schemes for the incompressible Navier-Stokes equations(namely"pressure-correction"method),we consider the simplest method(of order one in time)which takes into account the pressure in both steps of the splitting scheme.For this scheme,we construct,analyze and implement a new high order compact spatial approximation on nonstaggered grids.This approach yields a fourth order accuracy in space with an optimal treatment of the boundary conditions(without error on the velocity)which could be extended to more general splitting.We prove the unconditional stability of the associated Cauchy problem via von Neumann analysis.Then we carry out a normal mode analysis so as to obtain more precise results about the behavior of the numerical solutions.Finally we present detailed numerical tests for the Stokes and the Navier-Stokes equations(including the driven cavity benchmark)to illustrate the theoretical results.

A MEMBRANE ELEMENT MODEL WITH BENDING MODIFICATION FOR ONE STEP INVERSE METHOD

A membrane element model with bending modification based on element moment equilibrium is proposed for the first time by the authors, who apply the element model in one step inverse method and simulate the forming process of a flower-shaped box using the membrane element model with and without this modification. The numerical results are compared with those of the incremental method to verify the validity of the element model developed in this paper.

Elaboration of ZnO nanowires by solution based method,characterization and solar cell applications

ZnO nanowires（NWs）layers have been synthesized using a two-step chemical solution method on ITO glass substrates coated with ZnO seeds at different immersing times.The structures,morphology and optical properties of the synthesized ZnO NWs have been investigated.The prepared ZnO NWs have an obvious polycrystalline hexangular wurtzite structure and are preferentially oriented along the c-axis（002）.FESEM micrographs showed that the prepared ZnO NWs are close to being vertically grown and more densely at higher immersing times.Poly[2-methoxy-5（2-′-ethyl-hexyloxy）-1,4-phenylenevinylene],MEH-PPV,was used as an active layer to prepare three samples of MEH-PPV/ZnO solar cell based on ZnO NWs that were prepared at different immersing times.A maximum power conversion efficiency of 0.812%was achieved for MEH-PPV/ZnO solar cell prepared at a higher immersing time.The improved efficiency may be attributed to the enhancement of both open-circuit voltage and fill factor.

Comparison of two projection methods for modeling incompressible flows in MPM

Material point method（MPM）was originally introduced for large deformation problems in solid mechanics applications.Later,it has been successfully applied to solve a wide range of material behaviors.However,previous research has indicated that MPM exhibits numerical instabilities when resolving incompressible flow problems.We study Chorin＇s projection method in MPM algorithm to simulate material incompressibility.Two projection-type schemes,non-incremental projection and incremental projection,are investigated for their accuracy and stability within MPM.Numerical examples show that the non-incremental projection scheme provides stable results in single phase MPM framework.Further,it avoids artificial pressure oscillations and small time steps that are present in the explicit MPM approach.

AN EXPONENTIAL WAVE INTEGRATOR PSEUDOSPECTRAL METHOD FOR THE SYMMETRIC REGULARIZED-LONG-WAVE EQUATION

An efficient and accurate exponential wave integrator Fourier pseudospectral （EWI-FP） method is proposed and analyzed for solving the symmetric regularized-long-wave （SRLW） equation, which is used for modeling the weakly nonlinear ion acoustic and space-charge waves. The numerical method here is based on a Gautschi-type exponential wave integrator for temporal approximation and the Fourier pseudospectral method for spatial discretization. The scheme is fully explicit and efficient due to the fast Fourier transform. Numerical analysis of the proposed EWI-FP method is carried out and rigorous error estimates are established without CFL-type condition by means of the mathematical induction. The error bound shows that EWI-FP has second order accuracy in time and spectral accuracy in space. Numerical results are reported to confirm the theoretical studies and indicate that the error bound here is optimal.

Honeycomb-like g-C_(3)N_(4)/CeO_(2)-x nanosheets obtained via one step hydrothermal-roasting for efficient and stable Cr(Ⅵ) photo-reduction

Graphitic carbon nitride(g-C_(3)N_(4))-based materials are regarded as one of the most potential photocatalysts for utilizing solar energy.In this work,we reported a facile one step in-situ hydrothermal-roasting method for preparing honeycomb-like g-C_(3)N_(4)/CeO_(2) nanosheets with abundant oxygen vacancies(g-C_(3)N_(4)/CeO_(2)-x).The hydrothermal-roasting and incomplete-sealed state can(i)generate an in-situ reducing atmosphere(CO,N2,NH3) to tune the concentration of oxygen vacancies in CeO_(2);(ii) beneficial to prevent continuous growth of g-C_(3)N_(4) and results in honeycomb-like g-C_(3)N_(4)/CeO_(2)-x hybrid nanosheets.What is more,the g-C_(3)N_(4)/CeO_(2)-x photocatalyst exhibited extended photoresponse range,increased specific surface area and obviously enhanced separation efficiency of photogenerated electron-hole pairs.As a proof-of-concept application,the optimized g-C_(3)N_(4)/CeO_(2)-xnanosheets could achieve 98% removal efficiency for Cr(Ⅵ) under visible light irradiation(λ≥420 nm)within 2.5 h,which is significantly better than those of pure g-C_(3)N_(4) and CeO_(2).This work provides a new idea for more rationally designing and constructing g-C_(3)N_(4)-based catalysts for efficient extended photochemical application.

Investigation into improving the efficiency and accuracy of CFD/DEM simulations

The Euler-Lagrange approach combined with a discrete element method has frequently been applied to elucidate the hydrodynamic behavior of dense fluid-solid flows in fluidized beds. In this work, the efficiency and accuracy of this model are investigated. Parameter studies are performed; in these studies, the stiffness coefficient, the fluid time step and the processor number are varied under conditions with different numbers of particles and different particle diameters. The obtained results are compared with measurements to derive the optimum parameters for CFD/DEM simulations. The results suggest that the application of higher stiffness coefficients slightly improves the simulation accuracy. However, the average computing time increases exponentially. At larger fluid time steps, the results show that the average computation time is independent of the applied fluid time step whereas the simulation accuracy decreases greatly with increasing the fluid time step. The use of smaller time steps leads to negligible improvements in the simulation accuracy but results in an exponential rise in the average computing time. The parallelization accelerates the DEM simulations if the critical number for the domain decomposition is not reached. Above this number, the performance is no longer proportional to the number of processors. The critical number for the domain decomposition depends on the number of particles. An increase in solid contents results in a shift of the critical decomposition number to higher numbers of CPUs.

AN OPERATOR-SPLITTING ALGORITHM FOR ADVECTION-DIFFUSION-REACTION EQUATION

An operator-splitting algorithm for three-dimensional advection-diffusion-reaction equation is presented.The method of characteristics is adopted for the pure advection operator, the explicit difference scheme is used for diffusion,and a prediction-correction scheme is em- ployed for reaction.The condition for stability of the algorithm is analysed.Severall inear and nonlinear examples are illustrated to test the convergence and accuracy of the numerical proce- dure,and satisfactory agreements between computed and analytical solutions are achieved.Due to its simplicity,stability,and validity for both one-and two-dimensional problems,the success- ful algorithm can be used to numerical simulations of viscous fluid flows,the transport of pollu- tants and sedimentations in reservoirs,lakes,rivers,estuaries and other environments,cooling- problems in heat or nuclear power plants,etc.