THE UPWIND FINITE DIFFERENCE FRACTIONAL STEPS METHOD FOR NONLINEAR COUPLED SYSTEM OF DYNAMICS OF FLUIDS IN POROUS MEDIA

For nonlinear coupled system of multilayer dynamics of fluids in porous media, the second order and first order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward, trod two-dimensional and three-dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates, are adopted. Optimal order estimates in L2 norm are derived to determine the error in the second order approximate solution. This method has already been applied to the numerical simulation of migration-accumulation of oil resources.

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.

Improved finite difference method for pressure distribution of aerostatic bearing

An improved finite difference method （FDM）is described to solve existing problems such as low efficiency and poor convergence performance in the traditional method adopted to derive the pressure distribution of aerostatic bearings. A detailed theoretical analysis of the pressure distribution of the orifice-compensated aerostatic journal bearing is presented. The nonlinear dimensionless Reynolds equation of the aerostatic journal bearing is solved by the finite difference method. Based on the principle of flow equilibrium, a new iterative algorithm named the variable step size successive approximation method is presented to adjust the pressure at the orifice in the iterative process and enhance the efficiency and convergence performance of the algorithm. A general program is developed to analyze the pressure distribution of the aerostatic journal bearing by Matlab tool. The results show that the improved finite difference method is highly effective, reliable, stable, and convergent. Even when very thin gas film thicknesses （less than 2 Win）are considered, the improved calculation method still yields a result and converges fast.

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.

Gradient Step Method to Predict the Ozone Solubility in Water

In this work it presents a strategy to obtain the ozone solubility in water by gradient step method. In this methodology, the ozone in mixture with oxygen is bubbling in a reactor with distilled water at 21℃ and pH 7. The ozone concentration on gas phase is continually increased after the saturation is reached. The method proposed is faster than conventional method （isocratic method）. The solubility from the gradient method is compared with that values obtained from correlations founded in the literature.

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.

Iterative Methods for Parametric Linear Systems with Linear Functions

This paper mainly proposes a new C-XSC （C- for eXtended Scientific Computing） software for the symmetric single step method and relaxation method for computing an enclosure for the solution set and compares the methods with others＇ and then makes some modifications and finally, examples illustrating the applicability of the proposed methods are given.

Distribution of Oxytocin Hypothamic-Picuitary-Ovary Axis in Guangxi Local Buffalo

To study the association of oxytocin (OT)'s distribution in hypothalamatic,pituitary and ovary,and understand how the OT secrete releasing in hypothalamus,pituitary and ovaries,the paraffin section immunohistochemistry SuperPicTureTM two step method was used to detect the distribution of OT in hypothalamatic-pituitary-ovary axis of five femal Guangxi local buffalo. The test results could provide morphology according to study the OT's synthesis and mechanism of action,and could play reference and directions part in breeding Guangxi local buffalo. The test results display:oxytocin immuno reactive (OT-IR) neuronsw eremainly distributed arcuate nucleus,supraoptic nucleus and paraventricular nucleus,and OT-IR neurons was also found in ventromedial nucleus,ventrolateralis nucleus,suprachiasmaticus nucleus,dorsomedial nucleus,mamillary body,anterior hypothalamic nucleus and so on. The OT immunoactive production was found in pituitary and few OT-IR nerve fibers extended to post pituitary from hypophyseal stalk and medium eminence. In ovaries,OT immunoactive productions were only distributed in germinal epithelium cells,granulosa cells and lutein cells. The OT was first discovered in singulorum link of hypothalamatic-pituitary-ovary axis of Guangxi local buffalo. The OT immunoactive neurons were first discovered in every main nucleus of Guangxi local buffalo hypothalamus,especially distributed in arcuate nucleus,supraoptic nucleus and paraventricular nucleus.

Modified One Step Isolation of RNA,DNA and Protein from Plant Tissues

[Objective] The aim of this study was to extract RNA,DNA and protein from plants by using modified one step method.[Method]CTAB was used for the modifying of Biozol-based one step extraction method,which was then used for the isolation of RNA,DNA and protein from the roots of maize（Zea mays L.）,soybean（Glycine max L.）,alfalfa（Medicago sativa L.）and cucumber（Cucumis sativus L.）.And the heme oxygenase-1 gene（HO-1）and calcium-dependent protein kinase-1 gene（CDPK1）,as well as HO-1 protein were identified.[Result]The result of UV spectrophotometer determination and agarose gel electrophoresis analysis showed that the purity of obtained RNA and DNA sample was relatively high;HO-1 and CDPK1 gene exhibited the positive signals checked by RT-PCR;the extracted protein could be used for western blotting analysis;the whole isolation procedure cost 3 h.[Conclusion]This method can be used as a good reference for researcher and will offer a better value with a wide range of applications.

An improvement to the simulation of phase-change heat-transfer during soil freezing and thawing

A new variable time step method,which is called the backwards calculating time step method,is presented in this paper.It allows numerical simulation of soil freezing and thawing while avoiding "phase change missing and overflowing".A sensitive heat capacity model is introduced through which the calculation errors are analyzed.Then the equation using the self-adjusted time step is presented and solved using finite differences.Through this equation,the time needed for a space cell to reach the phase change point temperature is calculated.Using this time allows the time step to be adjusted so that errors caused by "phase change missing and overflowing" are successfully eliminated.Above all,the obvious features of this method are an accelerated rate for adjusting the time step and simplifing the computations.An actual example proves that this method can accurately calculate the temperature fields during soil freezing and thawing.It is an improvement over traditional methods and can be widely used on complicated multi-dimensional phase change problems.

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.

Combinations of nonstandard finite difference schemes and composition methods with complex time steps for population models

We propose an efficient numerical method for two population models, based on the nonstandard finite difference （NSFD） schemes and composition methods with complex time steps. The NSFD scheme is able to give positive numerical solutions that satisfy the conservation law, which is a key property for biological population models. The accuracy is improved by using the composition methods with complex time steps. Numerical tests on the plankton nutrient model and whooping cough model are presented to show the efficiency and advantage of the proposed numerical method.

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.

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.

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.