Analytic equation of state for solids with multi-exponential potential based on analytic mean field potential approach and applied to the epsilon phase of solid oxygen

The thermodynamic properties of the ε phase of solid oxygen are studied by using the analytic mean field approach （AMFP）. Analytic expressions for the Helmholtz free energy, internal energy and equation of state of solid oxygen have been derived based on the multi-exponential potential. The formulism for the case of double-exponential （DE） model is applied to the ε phase of solid oxygen. Its four potential parameters are determined through fitting the experimental compression data of the ε phase of solid oxygen. Numerical results of the pressure dependence of the volume calculated by using the AMFP are in good agreement with the original experimental data. This suggests that the AMFP is a useful approach to study the thermodynamic properties of the ε phase of solid oxygen. Furthermore, we predict the variation of the volume, lattice parameters and intermolecular distances with pressure, and some thermodynamic quantities versus volume, at several higher temperatures.

Analytical Solutions to the D-Dimensional Schrodinger Equation with the Eckart Potential

The analytical solutions to the Schrodinger equation with the Eckart potential in arbitrary dimension D is investigated by using the Nikiforov-Uvarov method, and the centrifugal term is treated approximatively with the scheme of Greene and Aldrich. The discrete spectrum is obtained and the wavefunetion is expressed in terms of the Jacobi polynomial or the hypergeometric function. Some special cases of the Eckart potential are discussed for D=3, and the resulting energy equation agrees well with that obtained by other methods.

ANALYTICAL SOLUTIONS FOR EQUATIONS OF UNSTEADY FLOW OF NON-NEWTONIAN FLUIDS IN TUBE

This paper presents analytieal solutions to the partial differential equations for unsteady flow of the second-order fluid and Maxwell fluid in tube by using the integral transform method. It can be used to analyse the behaviour of axial velocity and shear stress for unsteady flow of nun-Newtonian visco-elastie fluids in tube, and to provide a theoretical base for the projection of pipe-line engineering.

THE STABILITY AND CONVERGENCE OF THE FINITE ANALYTIC METHOD FOR THE NUMERICAL SOLUTION OF CONVECTIVE DIFFUSION EQUATION

In this paper we make a close study of the finite analytic method by means of the maximum principles in differential equations and give the proof of the stability and convergence of the finite analytic method.

MATHEMATIC MODEL AND ANALYTIC SOLUTION FOR CYLINDER SUBJECT TO UNEVEN PRESSURES

According to the inverse solution of elasticity mechanics, a stress function is constructed which meets the space biharmonic equation, this stress functions is about cubic function pressure on the inner and outer surfaces of cylinder. When borderline condition that is predigested according to the Saint-Venant＇s theory is joined, an equation suit is constructed which meets both the biharmonic equations and the boundary conditions. Furthermore, its analytic solution is deduced with Matlab. When this theory is applied to hydraulic bulging rollers, the experimental results inosculate with the theoretic calculation. Simultaneously, the limit along the axis invariable direction is given and the famous Lame solution can be induced from this limit. The above work paves the way for mathematic model building of hollow cylinder and for the analytic solution of hollow cvlinder with randomly uneven pressure.

THE SOLUTIONS OF STEADY－STATE CONVECTION EQUATIONS IN THE SPACES THAT POSSESS RESTORI NGNUCLEUS

In this paper ,in the space that possesses restoring nucleus, we obtain analyticsolutions in the series form for the steady-state convection diffusion equation The solutions have the following characteristics: (1) they ave given in the accurate form:(2)they can be calculated in the explicit way, without solving the eguations;(3) the error of the approximate solution will be monotonically decreased under the meaning of the norm of the spaces when a cardinal term is added in the procedure of numerical solution .Finally, we calculated the example in [2] the result shows that our solution is more accurate than that in [2].

RESEARCH ON DEEP COAL SEAM MINING FLOOR STARTA WATER BURSTING INFLUENCED FACTORS BASED ON ANALYTIC HIERACHY PROCESS

Deep coal seam mining floor strata water bursting is a complicate nonlinear system, whose factors are coupling and influencing themselves. It built the analytic structure model for deep coal seam mining floor strata water bursting, the judgment matrix was found by the expert scoring method, the contribution weights of the influenced factors were given out by the equation analytic process. The thirteen controlling factors and five main controlling factors were put award by analyzing weights, so the result was basically conform to the field practice. The expert scoring method and analytic process can convert the objective fact to the subjective cognition, so it is a method that can turn the qualitative into the quantitative. This can be relative objectively and precisely to study the question of many factors and grey box.

Development of component stiffness equations for thread-fixed one-side bolt connections to an enclosed rectangular hollow section column under tension

The derivation and validation of analytical equations for predicting the tensile initial stiffness of threadfixed one-side bolts(TOBs),connected to enclosed rectangular hollow section(RHS)columns,is presented in this paper.Two unknown stiffness components are considered:the TOBs connection and the enclosed RHS face.First,the trapezoidal thread of TOB,as an equivalent cantilevered beam subjected to uniformly distributed loads,is analyzed to determine the associated deformations.Based on the findings,the thread-shank serial-parallel stiffness model of TOB connection is proposed.For analysis of the tensile stiffness of the enclosed RHS face due to two bolt forces,the four sidewalls are treated as rotation constraints,thus reducing the problem to a two-dimensional plate analysis.According to the load superposition method,the deflection of the face plate is resolved into three components under various boundary and load conditions.Referring to the plate deflection theory of Timoshenko,the analytical solutions for the three deflections are derived in terms of the variables of bolt spacing,RHS thickness,height to width ratio,etc.Finally,the validity of the above stiffness equations is verified by a series of finite element(FE)models of T-stub substructures.The proposed component stiffness equations are an effective supplement to the component-based method.

New empirical model to evaluate groundwater flow into circular tunnel using multiple regression analysis

There are various analytical, empirical and numerical methods to calculate groundwater inflow into tun- nels excavated in rocky media. Analytical methods have been widely applied in prediction of groundwa- ter inflow to tunnels due to their simplicity and practical base theory. Investigations show that the real amount of water infiltrating into jointed tunnels is much less than calculated amount using analytical methods and obtained results are very dependent on tunnel＇s geometry and environmental situations. In this study, using multiple regression analysis, a new empirical model for estimation of groundwater seepage into circular tunnels was introduced. Our data was acquired from field surveys and laboratory analysis of core samples. New regression variables were defined after perusing single and two variables relationship between groundwater seepage and other variables. Finally, an appropriate model for estima- tion of leakage was obtained using the stepwise algorithm. Statistics like R, R2, R2e and the histogram of residual values in the model represent a good reputation and fitness for this model to estimate the groundwater seepage into tunnels. The new experimental model was used for the test data and results were satisfactory. Therefore, multiple regression analysis is an effective and efficient way to estimate the groundwater seeoage into tunnels.

On the relevance of analytical film thickness EHD equations for isothermal point contacts: Qualitative or quantitative predictions?

Thin film and elastohydrodynamic lubrication regimes are rather young domains of tribology and they are still facing unresolved issues.As they rely upon a full separation of the moving surfaces by a thin (or very thin) fluid film,the knowledge of its thickness is of paramount importance,as for instance to developing lubricated mechanisms with long lasting and efficient designs.As a consequence,a large collection of formulae for point contacts have been proposed in the last 40 years.However,their accuracy and validity have rarely been investigated.The purpose of this paper is to offer an evaluation of the most widespread analytical formulae and to define whether they can be used as qualitative or quantitative predictions.The methodology is based on comparisons with a numerical model for two configurations,circular and elliptical,considering both central and minimum film thicknesses.

ANALYTIC SOLUTIONS OF NONLINEAR WAVE EQUATIONS IN THE ATMOSPHERE

In this paper,starting with the nonlinear equations of atmospheric motion and using a relatively simple method,we have obtained the periodic solutions to the nonlinear inertia waves,internal gravity waves and Rossby waves.These solutions represent the characteristics of nonlinear waves in the atmosphere.A preliminary analysis reveals that as for the inertia waves and internal gravity waves with finite amplitudes, the larger the amplitudes are,the faster the waves propagate,but for the Rossby waves with finite ampli- tudes,the larger the amplitudes and wavelengths are,the slower the waves move.The practical senses of the solutions are also discussed in this paper. This paper gives a new way to study the nonlinear waves.This result has certain significance for the weather forecasting and the study of atmospheric turbulence.

Study on Effect of Time Factor on Tree Growth

According to the data of analytic trees,an empirical equation of tree growth was constructed,with annual growth as variable and time and annual precipitation as independent variables. Through arithmetical operation including derivation of function and so on,the effect of precipitation on tree growth was studied through the rejection of effect of time factor.

Capacity Allocation of Renewable Energy Sources Considering Complementarity

The outputs of renewable energy sources(RESs)are inherently variable and uncertain,such as wind power(WP)and photovoltaic(PV).However,the outputs of various types of RESs in different regions are complementary.If the capacity of RESs could be properly allocated during system planning,variability of the total output could be reduced.Consequently,system reliability and renewable energy(RE)consumption could be improved.This paper proposes an analytical model for optimal complementary capacity allocation of RESs to decrease variability of the total output.The model considers the capacity ratio of RESs as decision variables and the coefficient of variation(CV)of the total output as the objective function.The proposed approach transforms the single-level optimization model into a bilevel optimization model and derives an analytical equation that can directly calculate the optimal complementary capacity ratio(OCCR)of system RESs.Case studies on wind and solar farms in Xinjiang and Qinghai,China,are performed to verify the effectiveness of the proposed analytical allocation method.

Analytical modeling and simulation of germanium single gate silicon on insulator TFET

This paper proposes a new two dimensional（2D） analytical model for a germanium（Ge） single gate silicon-on-insulator tunnel field effect transistor（SG SOI TFET）. The parabolic approximation technique is used to solve the 2D Poisson equation with suitable boundary conditions and analytical expressions are derived for the surfacepotential,theelectricfieldalongthechannelandtheverticalelectricfield.Thedeviceoutputtunnellingcurrent is derived further by using the electric fields. The results show that Ge based TFETs have significant improvements inon-currentcharacteristics.Theeffectivenessoftheproposedmodelhasbeenverifiedbycomparingtheanalytical model results with the technology computer aided design（TCAD） simulation results and also comparing them with results from a silicon based TFET.