Determination of Material Parameters of EVA Foam under Uniaxial Compressive Testing Using Hyperelastic Models

The objective of this research was to determine the mechanical parameter from EVA foam and also investigate its behavior by using Blatz-Ko,Neo-Hookean,Mooney model and experimental test.The physical characteristic of EVA foam was also evaluated by scanning electron microscopy(SEM).The results show that Blatz-Ko and Neo-Hookean model can fit the curve at 5%and 8%strain,respectively.The Mooney model can fit the curve at 50%strain.The modulus of rigidity evaluated from Mooney model is 0.0814±0.0027 MPa.The structure of EVA foam from SEM image shows that EVA structure is a closed cell with homogeneous porous structure.From the result,it is found that Mooney model can adjust the data better than other models.This model can be applied for mechanical response prediction of EVA foam and also for reference value in engineering application.

A Microcomputer Fitted Method for Determination of the True ODF of Hexagonal Materials according to the Maximum-Entropy Estimate

A method which is especially suitable for microcomputer calculation of the true orientation distribution function (ODF) according to the maximum-entropy estimate is proposed for hexagonal system polycrystalline materials with physical symmetry.The resultant computational software system has been also designed and first carried out in a microcomputer PANAFACOM-U1200 being on line with the X-ray diffractometer D/max-3A.The simu- lated calculation shows that the method is concisely pragmatic and easily popularized,while the results obtained are trust worthy.

ON CONSTRUCTION OF HIGH ORDER EXPONENTIALLY FITTED METHODS BASED ON PARAMETERIZED RATIONAL APPROXIMATIONS TO exp

By the discussion of the formula and properties of (4,4) parametric form rational approximation to function exp(q), the fourth order derivative one_step exponentially fitted method and the third order derivative hybrid one_step exponentially fitted method are presented, their order p satisfying 6≤p≤8. The necessary and sufficient conditions for the two methods to be A_ stable are given. Finally, for the fourth order derivative method, the error bound and the necessary and sufficient conditions for it to be median are discussed.

Methods of de-noising the low frequency electromagnetic data

The quality of the low frequency electromagnetic data is affected by the spike and the trend noises.Failure in removal of the spikes and the trends reduces the credibility of data explanation.Based on the analyses of the causes and characteristics of these noises,this paper presents the results of a preset statistics stacking method(PSSM)and a piecewise linear fitting method(PLFM)in de-noising the spikes and trends,respectively.The magnitudes of the spikes are either higher or lower than the normal values,which leads to distortion of the useful signal.Comparisons have been performed in removing of the spikes among the average,the statistics and the PSSM methods,and the results indicate that only the PSSM can remove the spikes successfully.On the other hand,the spectrums of the linear and nonlinear trends mainly lie in the low frequency band and can change the calculated resistivity significantly.No influence of the trends is observed when the frequency is higher than a certain threshold value.The PLSM can remove effectively both the linear and nonlinear trends with errors around 1% in the power spectrum.The proposed methods present an effective way for de-noising the spike and the trend noises in the low frequency electromagnetic data,and establish a research basis for de-noising the low frequency noises.

A Numerical Method for Nonlinear Singularly Perturbed Multi-Point Boundary Value Problem

We consider a uniform finite difference method for nonlinear singularly perturbed multi-point boundary value problem on Shishkin mesh. The problem is discretized using integral identities, interpolating quadrature rules, exponential basis functions and remainder terms in integral form. We show that this method is the first order convergent in the discrete maximum norm for original problem (independent of the perturbation parameter ε). To illustrate the theoretical results, we solve test problem and we also give the error distributions in the solution in Table 1 and Figures 1-3.

Effect of thickness of antimony selenide film on its photoelectric properties and microstructure

Antimony selenide(Sb2Se3) films are widely used in phase change memory and solar cells due to their stable switching effect and excellent photovoltaic properties. These properties of the films are affected by the film thickness. A method combining the advantages of Levenberg–Marquardt method and spectral fitting method(LM–SFM) is presented to study the dependence of refractive index(RI), absorption coefficient, optical band gap, Wemple–Di Domenico parameters, dielectric constant and optical electronegativity of the Sb2Se3films on their thickness. The results show that the RI and absorption coefficient of the Sb2Se3films increase with the increase of film thickness, while the optical band gap decreases with the increase of film thickness. Finally, the reasons why the optical and electrical properties of the film change with its thickness are explained by x-ray diffractometer(XRD), energy dispersive x-ray spectrometer(EDS), Mott–Davis state density model and Raman microstructure analysis.

Formula for calculating spatial similarity degrees between point clouds on multi-scale maps taking map scale change as the only independent variable

The degree of spatial similarity plays an important role in map generalization, yet there has been no quantitative research into it. To fill this gap, this study first defines map scale change and spatial similarity degree/relation in multi-scale map spaces and then proposes a model for calculating the degree of spatial similarity between a point cloud at one scale and its gener- alized counterpart at another scale. After validation, the new model features 16 points with map scale change as the x coordinate and the degree of spatial similarity as the y coordinate. Finally, using an application for curve fitting, the model achieves an empirical formula that can calculate the degree of spatial similarity using map scale change as the sole independent variable, and vice versa. This formula can be used to automate algorithms for point feature generalization and to determine when to terminate them during the generalization.

Dynamic Coupling Correlation of Gas Film in Dry Gas Seal with Spiral Groove

In working state, the dynamic performance of dry gas seal, generated by the rotating end face with spiral grooves, is determined by the open force of gas film and leakage flow rate. Generally, the open force and the leakage flow rate can be obtained by finite element method, computational fluid dynamics method and experimental measurement method. However, it will take much time to carry out the above measurements and calculations. In this paper, the approximate model of parallel grooves based on the narrow groove theory is used to establish the dynamic equations of the gas film for the purpose of obtaining the dynamic parameters of gas film. The nonlinear differential equations of gas film model are solved by Runge-Kutta method and shooting method. The numerical values of the pressure profiles, leakage flux and opening force on the seal surface are integrated, and then compared to experimental data for the reliability of the numerical simulation. The results show that the numerical simulation curves are in good agreement with experimental values. Furthermore, the opening force and the leakage flux are proved to be strongly correlated with the operating parameters. Then, the function-coupling method is introduced to analyze the numerical results to obtain the correlation formulae of the opening force and leakage flux respectively with the operating parameters, i.e., the inlet pressure and the rotating speed. This study intends to provide an effective way to predict the aerodynamic performance for designing and optimizing the groove styles in dry gas seal rapidly and accurately.

Wavemotionsarounddifferentsubmergedstructures

Wave motions around different types of submerged structures are investigated by a numerical method, theboundary fitted coordinate method. The types of submerged structures include a submerged horizontal plate, submerged breakwaters (rectangular and trapezoidal) and a step-type structure (topography) . Water level fluctuations, wave height distributions, velocity fields and wave energies around submerged structures are studied comprehensively.

Trends in gravity changes from 2009 to 2013 derived from ground-based gravimetry and GRACE data in North China

North China is a key region for studying geophysical progress. In this study, ground-based and Gravity Recovery and Climate Experiment（GRACE） gravity data from 2009 to 2013 are used to calculate the gravity change rate（GCR） using the polynomial fitting method. In general, the study area was divided into the Shanxi rift, Jing-Jin-Ji（Beijing-Tianjin-Hebei Province）, and Bohai Bay Basin（BBB） regions. Results of the distribution of the GCR determined from ground-based gravimetry show that the GCR appears to be ＂negativepositive-negative＂ from west to east, which indicates that different geophysical mechanisms are involved in the tectonic activities of these regions. However, GRACE solutions are conducted over a larger spatial scale and are able to show a difference between southern and northern areas and a mass redistribution of land water storage.

A full-dimensional analytical potential energy surface for the F+CH_4→HF+CH_3 reaction

A full-dimensional analytical potential energy surface （APES） for the F ＋ CH4 →HF ＋ CH3 reaction is developed based on 7127 ab initio energy points at the unrestricted coupled-cluster with single, double, and perturbative triple excitations. The correlation-consistent polarized triple-split valence basis set is used. The APES is represented with a many-body expansion containing 239 parameters determined by the least square fitting method. The two-body terms of the APES are fitted by potential energy curves with multi-reference configuration interaction, which can describe the diatomic molecules （CH, H2, HF, and CF） accurately. It is found that the APES can reproduce the geometry and vibrational frequencies of the saddle point better than those available in the literature. The rate constants based on the present APES support the experimental results of Moore et al. [Int. J. Chem. Kin. 26, 813 （1994）]. The analytical first-order derivation of energy is also provided, making the present APES convenient and efficient for investigating the title reaction with quasiclassical trajectory calculations.

Precise Determination of Period of a Torsion Pendulum in Measurement of Gravitational Constant

The period of a torsion pendulum would vary under the disturbances of environmental noise factors. In order to subtract the period of the pendulum from external influence, we employ the correlation method to determine the period with a high precision. Theoretical analysis shows that the relative precision is improved to be proportional to 1/m^3/2 with the number of the period m, compared with the conventional statistical mean that is proportional to 1/m^1/2, which is significant for the determination of gravitational constant with the swing time method.

Upward Transition Probabilities B(E2)↑ Properties Study of Even-Even ^104-114Ru Nuclei

In this research work, the upward transition probabilities for the transition levels, 0+ → 2+, 2+ → 4+, 4+ → 6+ and 6+ → 8+ levels of even-even neutron rich 104-114Ru isotopes have been calculated by using the Global Best Fit (GBF) method. In addition, the associated parameters such as, Quadrupole moment and Deformation parameter of even-even 104-114Ru have been calculated. The dependency of these nuclear parameters shows the nuclear magic number tendency.

On the Convergence of a Crank-Nicolson Fitted Finite Volume Method for Pricing European Options under Regime-Switching Kou’s Jump-Diffusion Models

In this paper,we construct and analyze a Crank-Nicolson fitted finite volume scheme for pricing European options under regime-switching Kou’s jumpdiffusion model which is governed by a system of partial integro-differential equations(PIDEs).We show that this scheme is consistent,stable and monotone as the mesh sizes in space and time approach zero,hence it ensures the convergence to the solution of continuous problem.Finally,numerical experiments are performed to demonstrate the efficiency,accuracy and robustness of the proposed method.

An Improved Power Flow Method to Cope with Non-smooth Constraints of Integrated Energy Systems

Integrated energy system applications can significantly improve energy efficiency.In this paper,we establish an integrated energy system containing heat,electricity and gas.The existing power flow(PF)calculation method applied to integrated energy systems(IESs)does not consider non-smooth constraints,such as the piecewise pipeline friction coefficient and generator buses reactive power limits,etc.Mixed integer nonlinear programming(MINLP)is conventionally used to deal with piecewise pipeline friction coefficients in gas network parts,but it is both complex and inefficient.Hence,we develop a piecewise linear function-based fitting method that can reduce the number of integer variables and enhanced the computational efficiency.In the electric network part,if the reactive power of the PV bus violates limits,it will be converted into a PQ bus,which is a non-differentiable and non-smooth constraint.Mixed complementarity problems are conventionally introduced to represent the PV-PQ buses type switching relationship and are addressed by the Newton-Raphson(NR)method.However,the above method is sensitive to the initial point.Here,we introduce a robust projected Levenberg-Marquardt(PLM)algorithm to cope with this issue.We demonstrate the advantages of our method and validate it both in a small-scale system and largescale network test cases.

A Fitted Numerov Method for Singularly Perturbed Parabolic Partial Differential Equation with a Small Negative Shift Arising in Control Theory

In this paper,a fitted Numerov method is constructed for a class of singularly perturbed one-dimensional parabolic partial differential equations with a small negative shift in the temporal variable.Similar boundary value problems are associated with a furnace used to process a metal sheet in control theory.Here,the study focuses on the effect of shift on the boundary layer behavior of the solution via finite difference approach.When the shift parameter is smaller than the perturbation parameter,the shifted term is expanded in Taylor series and an exponentially fitted tridiagonal finite difference scheme is developed.The proposed finite difference scheme is unconditionally stable.When the shift parameter is larger than the perturbation parameter,a special type of mesh is used for the temporal variable so that the shift lies on the nodal points and an exponentially fitted scheme is developed.This scheme is also unconditionally stable.The applicability of the proposed methods is demonstrated by means of two examples.

Conservative and Finite Volume Methods for the Convection-Dominated Pricing Problem

This work presents a comparison study of different numerical methods to solve Black-Scholes-type partial differential equations(PDE)in the convectiondominated case,i.e.,for European options,if the ratio of the risk-free interest rate and the squared volatility-known in fluid dynamics as P´eclet number-is high.For Asian options,additional similar problems arise when the"spatial"variable,the stock price,is close to zero.Here we focus on three methods:the exponentially fitted scheme,a modification of Wang’s finite volume method specially designed for the Black-Scholes equation,and the Kurganov-Tadmor scheme for a general convection-diffusion equation,that is applied for the first time to option pricing problems.Special emphasis is put in the Kurganov-Tadmor because its flexibility allows the simulation of a great variety of types of options and it exhibits quadratic convergence.For the reduction technique proposed by Wilmott,a put-call parity is presented based on the similarity reduction and the put-call parity expression for Asian options.Finally,we present experiments and comparisons with different(non)linear Black-Scholes PDEs.

EXPONENTIAL FITTED METHODS FOR THE NUMEMCAL SOLUTION OF THE SCHRDINGER EQUATION

A new sixth-order Runge-Kutta type method is developed for the numericalintegration of the radial Schrodinger equation and of the coupled differential equa-tions of the Schrodinger type. The formula developed contains certain free pa-rameters which allows it to be fitted automatically to exponential functions. Wegive a comparative error analysis with other sixth order exponentially fitted meth-ods. The theoretical and numerical results indicate that the new method is moreaccurate than the other exponentially fitted methods.

General strategy for evaluating the d-band center shift and ethanol oxidation reaction pathway towards Pt-based electrocatalysts

The catalytic performance of Pt-based catalysts depends sensitively on their d-band centers.Nevertheless,there are still huge challenges to evaluate their d-band centers from experimental technologies,and modulate them to analyze their selectivity in ethanol oxidation reaction(EOR).Here,Pt1Au1alloy supported on the commercial carbon material(Pt_(1)Au_(1)/C)is employed as a typical example to investigate its d-band center shift of surface Pt,and as electrocatalysts to study its selectivity towards EOR.Significantly,a highly reliable in situ Fourier-transform infrared spectroscopy CO-probe strategy is developed to characterize the d-band center shift of surface Pt.The modified electronic effect and site effect of Pt_(1)Au_(1)/C dictated the adsorption configuration of intermediate species and the OH species coverage,thereby influencing its selectivity.More importantly,we developed a universal cyclic voltammetry peak differentiation fitting method as an electrochemical analysis technique to investigate CO_(2)selectivity,which is potentially extendable to other Pt-based electrocatalysts.

WAVE TRANSMISSION AND REFIECTION DUE TO A THIN VERTICAL BARRIER

WT5”BZ]A numerical method, the boundary fitted coordinate method (BFC), was used to investigate the transmission and reflection of water waves due to a rigid thin vertical barrier descending from the water surface to a depth, i.e., a curtain-wall type breakwater. A comparison between the present computed results and previous experimental and analytical results was carried out which verifies the prediction of the BFC method. Wave transmission and reflection due to the barrier were computed, and the transmission and refiection coefficients were given in a figure. [WT5”HZ]