Effective electroelastic constants for three-phase confocal elliptical cylinder model in piezoelectric quasicrystal composites

A three-phase confocal elliptical cylinder model is proposed to analyze micromechanics of one-dimensional hexagonal piezoelectric quasicrystal （PQC） compos- ites. Exact solutions of the phonon, phason, and electric fields are obtained by using the conformal mapping combined with the Laurent expansion technique when the model is subject to far-field anti-plane mechanical and in-plane electric loadings. The effective elec- troelastic constants of several different composites made up of PQC, quasicrystal （QC）, and piezoelectric （PE） materials are predicted by the generalized self-consistent method. Numerical examples are conducted to show the effects of the volume fraction and the cross-sectional shape of inclusion （or fiber） on the effective electroelastic constants of these composites. Compared with other micromechanical methods, the generalized self- consistent and Mori-Tanaka methods can predict the effective electroelastic constants of the composites consistently.

Elastic Constants of Superconducting MgB2 from Molecular Dynamics Simulations with Shell Model

The elastic constants of superconducting MgB2 are calculated using a molecular dynamics method (MD)with shell model. The lattice parameters, five independent elastic constants, equations of state (EOS), Debye temperature, and bulk modulus of MgB2 are obtained. Meanwhile, the dependence of the bulk modulus B, the lattice parameters a and c, and the unit cell volume V on the applied pressure are presented. It is demonstrated that the method introduced here can well reproduce the experimental results with a reasonable accuracy.

Simplest Method for Calculating the Lowest Achievable Uncertainty of Model at Measurements of Fundamental Physical Constants

The CODATA procedure for calculating the recommended relative uncertainty of the measured fundamental physical constants is complex and is based on the use of powerful computers and modern mathematical statistical methods. In addition, the expert’s opinion caused by accumulated knowledge, life experience and intuition of researchers is applied at each stage of the calculations. In this article, the author continues to advocate a theoretically grounded information method as the most effective tool for testing and achieving the minimum possible relative uncertainty for any measurements of experimental physics and engineering. The introduced fundamental limit characterizing discrepancy between a model and the observed object cannot be overcome by any improvement of instruments, methods of measurement and the model’s computerization. Examples are given.

Modeling of Orientation-Dependent Photoelastic Constants in Cubic Crystal System

Euler’s rotation theorem and tensor rotation technique are applied to develop a generalized mathematical model for determining photoelastic constants in arbitrary orientation of cubic crystal system. Two times rotations are utilized in the model relating to crystallographic coordinates with Cartesian coordinates. The symmetry of photoelastic constants is found to have strong dependence with rotation angle. Using the model, one can determine photoelastic constants in any orientation by selecting appropriate rotation angle. The outcome of this study helps to characterize spatial variation of residual strain in crystalline as well as polycrystalline materials having cubic structure using the experimental technique known as scanning infrared polariscope.

Solution of rate constants in pharmacokinetics local model of nuclear medicine

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Effects of initial δ phase(Ni_3Nb) on hot tensile deformation behaviors and material constants of Ni-based superalloy

Effects of initial δ phase（Ni_3Nb） on the hot tensile deformation behaviors and material constants of a Ni-based superalloy were investigated over wide ranges of strain rate and deformation temperature. It is found that the true stress-true strain curves exhibit peak stress at a small strain, and the peak stress increases with the increase of initial δ phase. After the peak stress, initial δ phase promotes the dynamic softening behaviors, resulting in the decreased flow stress. An improved Arrhenius constitutive model is proposed to consider the synthetical effects of initial δ phase, deformation temperature, strain rate, and strain on hot deformation behaviors. In the improved model, material constants are expressed as the functions of the content of initial δ phase and strain. A good agreement between the predicted and measured results indicates that the improved Arrhenius constitutive model can well describe hot deformation behaviors of the studied Ni-based superalloy.

Development of a modified Mooney-Rivlin constitutive model for rubber to investigate the effects of aging and marine corrosion on seismic isolated bearings

In this study, aging and marine corrosion tests of a large number of rubber material and rubber bearings have been carried out. The constitutive Mooney-Rivlin model parameters for a rubber isolated bearing have been determined. By applying the least-square method to the experimental data, the relationships between the aging time and the marine corrosion time with the constants in the constitutive model for a rubber beating have been derived. Next, the Mooney-Rivlin model has been modified accordingly. Further, using the modified Mooney-Rivlin model and the Abaqus software, the performance of the rubber isolated bearings has been simulated. The simulation results have been compared to the experimental results so as to verify the accuracy of the modified model. The comparison shows that the maximum errors for the vertical and horizontal stiffnesses are 16.8% and 0.49%, respectively. Since these errors are considered acceptable, the accuracy of the modified constitutive model can be considered verified. The results of this study can provide theoretical support for the performance study on rubber isolated bearings under the complex ocean environment and the life-cycle performance evaluation of bridges and other offshore structures.

RUIN PROBABILITY IN A SEMI-MARKOV RISK MODEL WITH CONSTANT INTEREST FORCE AND HEAVY-TAILED CLAIMS

In the present paper, we consider a kind of semi-Markov risk model （SMRM） with constant interest force and heavy-tailed claims~ in which the claim rates and sizes are conditionally independent, both fluctuating according to the state of the risk business. First, we derive a matrix integro-differential equation satisfied by the survival probabilities. Second, we analyze the asymptotic behaviors of ruin probabilities in a two-state SMRM with special claim amounts. It is shown that the asymptotic behaviors of ruin probabilities depend only on the state 2 with heavy-tailed claim amounts, not on the state 1 with exponential claim sizes.

A model for estimating the rate constant between CO_2-CO gas and molten slag containing iron oxides using optical basicity

A simple model for estimating the rate constant between CO2-CO gas and molten slag containing iron oxides was developed using optical basicity only. In this model, the temperature dependence of the rate constant can be described by the Arrhenius law, and the activation energy can be expressed with a linear function of the slag＇s optical basicity. The model was applied to some molten slag systems, such as FeO, FeO-CaO, FeO-SiO2, FeO-Na2O, FeO-CaO-SiO2, FeO-SiO2-P2O5, FeO-SiOE-Na2O, and FeO-CaO-SiOE-P2O5. A comparison between the predicted results and measured data showed that the model worked well.

Study on geometric models of non-numerically controlled machining revolving cutter with constant pitch

This paper presents a new approach of designing the revolving cutter with constant pitch, and provides geometric models. The corresponding models in the non-numerically controlled manufacturing, such as designing the helical groove, grinding wheel, relative feeding motion, and calculating the helical angle of the cutting edge, are introduced. The examples are given to testify that the design approach is simple and readily realized in machining the revolving cutter with constant pitch. The effective design and manufacture method provides general references for non-NC machining revolving cutter with constant pitch and reducing the equipments input.

Prediction of Henry's constant in polymer solutions using PCOR equation of state coupled with an activity coefficient model

In this paper,the polymer chain of rotator(PCOR) equation of state(EOS) was used together with an EOS/G^E mixing rule(MHV1) and the Wilson's equation as an excess-Gibbs-energy model in the proposed approach to extend the capability and improve the accuracy of the PCOR EOS for predicting the Henry's constant of solutions containing polymers.The results of the proposed method compared with two equation of state(van der Waals and GC-Flory) and three activity coefficient models(UNIFAC,UNIFAC-FV and Entropic-FV) indicated that the PCOR EOS/Wilson's equation provided more accurate results.The interaction parameters of Wilson's equation were fitted with Henry's constant experimental data and the property parameters of PCOR,a and b,were fitted with experimental volume data(Tait equation).As a result,the present work provided a simple and useful model for prediction of Henry's constant for polymer solutions.

Does the EVA valuation model explain the market value of equity better under changing required return than constant required return?

Through the Economic-Value-Added(EVA)valuation model,the expected market value of equity can be determined by adding the book value of equity with the present value of expected EVAs under the assumption of constant required return and constant return on equity.The equation of EVA valuation model has taken its shape under the assumption of constant required return and constant return on equity.However,a large body of empirical evidence indicates that required rate of return never remain constant.The EVA-valuation model formulated under constant required return cannot be implemented under the scenario of changing required return.In this study,we explored whether the EVA valuation model could be implemented under changing required return by making any changes in the model and found that it could be implemented under the scenario of changing required return by replacing the book value of the equity of the existing model with the present value of required earnings or normal market earnings.We further examined whether the explanatory ability of the EVA valuation model under the assumption of changing required return is better than that of the valuation model under the assumption of constant required return.Relative information content analyses were conducted by considering sample of the intrinsic value of equities determined by valuation models and the market value of equities of 69 large-cap,88 mid-cap,and 79 small-cap companies.The results showed that the EVA-based valuation model with changing normal market return outperformed the EVA-based valuation model with constant required return.

Macroscopic Elastic Constants of Pure Metal Based on the Interactions between Microscopic Particles

The research activities of the calculation of the elastic constants of metal are mainly focused on the elastic constants of crystal at the micro level. To the calculation of the macroscopic elastic constants of metal, although molecular dynamics method and quasicontinuum method can be used, but there are shortcomings in them, such as a large amount of computation and that the spatial scale of the study model is limited. Therefore, with a pure metal thin plate composed of a single layer of microscopic particles as research object, a new mechanical model is established after the interactions between microscopic particles of the thin plate are applied on the continuum mechanics model of the thin plate. According to this model, the calculation formulas for the microscopic elastic constants, which are the elastic constants of any triangle region in the model, are obtained. After the concept of the ideal micro structure is presented, the calculation formulas for the macroscopic elastic constants, the elastic modulus and the Poisson’s ratio of pure metal are obtained, where the Poisson＇s ratio is the constant that is equal to 1？3. As an example, the elastic constants and the elastic modulus of pure copper are solved, where c11 is 175.811 GPa, c12 is 58.604 GPa, c33 is 58.604 GPa and E is 156.277 GPa, the rationality and the correctness of the model are verified. The model presented fully embodies the discreteness of the microstructure of solid, is a development to the continuum model, and is more suitable to reality, more simplified and more new to the study of the macroscopic elastic constants of pure metal.

Modeling and Analysis of Transitional Tube with Constant Sectional Area along Derivative Central Route

Firstly, sample square-circular transition tube along straight central route was modeled on CATIA software. The parameters are as follows： let the tube length is L, and the constant cross section area is S, and S = πR^2 = a2, in which R stands for the circle radius on one end, and a the square side length on the other end; set up the coordinate system with OX axis on the central route in which the origin O is on centroid of the square end and assume the cross section size at x as the square shaped with all four comers filleted in radius r which is proportional to x, that is, the linear slope of r is R/L, thus, both values r and square side length ax can be attained on the constant cross section area assumption. Secondly, some sample polygonal-circular transition tubes along straight, circular and helical central route were implemented similarly. Thirdly, numerical analysis of stress and displacement of these tubes were carried out on MSC/PATRAN software which are important to the distribution of turbulent flow and the layout of these transitional tube structures.

A Mean-variance Problem in the Constant Elasticity of Variance(CEV) Model

In this paper, we focus on a constant elasticity of variance （CEV） modeland want to find its optimal strategies for a mean-variance problem under two constrainedcontrols： reinsurance/new business and investment （no-shorting）. First, aLagrange multiplier is introduced to simplify the mean-variance problem and thecorresponding Hamilton-Jacobi-Bellman （HJB） equation is established. Via a powertransformation technique and variable change method, the optimal strategies withthe Lagrange multiplier are obtained. Final, based on the Lagrange duality theorem,the optimal strategies and optimal value for the original problem （i.e., the efficientstrategies and efficient frontier） are derived explicitly.

High Accuracy When Measuring Physical Constants: From the Perspective of the Information-Theoretic Approach

The practical value of high-precision models of the studied physical phenomena and technological processes is a decisive factor in science and technology. Currently, numerous methods and criteria for optimizing models have been proposed. However, the classification of measurement uncertainties due to the number of variables taken into account and their qualitative choice is still not given sufficient attention. The goal is to develop a new criterion suitable for any groups of experimental data obtained as a result of applying various measurement methods. Using the “information-theoretic method”, we propose two procedures for analyzing experimental results using a quantitative indicator to calculate the relative uncertainty of the measurement model, which, in turn, determines the legitimacy of the declared value of a physical constant. The presented procedure is used to analyze the results of measurements of the Boltzmann constant, Planck constant, Hubble constant and gravitational constant.

An improved constant volume cycle model for performance analysis and shape design of PDRE nozzle

An improved constant volume cycle （CVC） model is developed to analyze the nozzle effects on the thrust and specific impulse of pulse detonation rocket engine （PDRE）. Theoretically, this model shows that the thrust coefficient/specific impulse of PDRE is a function of the nozzle contraction/expansion ratio and the operating frequency. The relationship between the nozzle contraction ratio and the operation frequency is obtained by introducing the duty ratio, by which the key problem in the theoretical design can be solved. Therefore, the performance of PDRE can be accessed to guide the preliminary shape design of nozzle conveniently and quickly. The higher the operating frequency of PDRE is, the smaller the nozzle contraction ratio should be. Besides, the lower the ambient pressure is, the larger the expansion ratio of the nozzle should be. When the ambient pressure is 1.013 × 105 Pa, the optimal expansion ratio will be less than 2.26. When the ambient pressure is reduced to vacuum, the extremum of the optimal thrust coefficient is 2.236 9, and the extremum of the specific impulse is 321.01 s. The results of the improved model are verified by numerical simulation.

Moments of Discounted Dividend Payments in the Sparre Andersen Model with a Constant Dividend Barrier

We consider the Sparre Andersen risk process in the presence of a constant dividend barrier, and propose a new expected discounted penalty function which is different from that of Gerber and Shiu. We find that iteration mothed can be used to compute the values of expected discounted dividends until ruin and the new penalty function. Applying the new function and the recursion method proposed in Section 5, we obtain the arbitrary moments of discounted dividend payments until ruin.

Effects of heavy metal ions Cu^(2+)/Pb^(2+)/Zn^(2+)on kinetic rate constants of struvite crystallization

Struvite(MAP)crystallization technology is widely used to treat ammonia nitrogen in waste effluents of its simple operation and good removal efficiency.However,the presence of heavy metal ions in the waste effluents causes problems such as slow crystallization rate and small crystal size,limiting the recovery rate and economic value of the MAP.The present study was conducted to investigate the effects of concentrations of three heavy metal ions(Cu^(2+),Zn^(2+),and Pb^(2+))on the crystal morphology,crystal size,average growth rate,and crystallization kinetics of MAP.A relationship was established between the kinetic rate constant Ktcalculated by the chemical gradient model and the concentrations of heavy metal ions.The results showed that low concentrations of heavy metal ions in the solution created pits on the MAP surface,and high level of heavy metal ions generated flocs on the MAP surface,which were composed of metal hydroxides,thus inhibiting crystal growth.The crystal size,average growth rate,MAP crystallization rate,and kinetic rate constant Ktdecreased with the increase in heavy metal ion concentration.Moreover,the Ktdemonstrated a linear relationship with the heavy metal concentration ln(C/C~*),which provided a reference for the optimization of the MAP crystallization process in the presence of heavy metal ions.

Determining Angstrom Constants for Estimating Solar Radiation in Malawi

This paper discusses a procedure that was adopted for the development of a linear regression model for estimating solar radiation in Malawi. By making use of sunshine-hours data recorded at six selected meteorological stations in the country, namely: Salima, Makoka, Karonga, Bolero, Chileka and Mzimba over the period 1991-1995, a set of Angstrom constants were obtained and averaged in order to develop the linear regression model. This model has potential for generating ground observation data of solar radiation at any given location in the country using sunshine hours as the only required input. The Gunn-Bellan Spherical Pyranometer and the Campbell Stokes Sunshine Recorder were respectively used in the measurement of incident radiation (Ib) in J·cm–2/day (converted to MJ·m–2·day–1) and sunshine hours. An Angstrom model of monthly average Clearness Index with normalized sunshine duration was then developed for each of the six meteorological stations. The resulting linear regression model was applied in estimating monthly average daily solar radiation. Regression analysis between computed and measured radiation data was applied to assess the reliability of the generated Angstrom constants. The results generally show a high degree of agreement between the two variables, with correlation coefficients ranging from 0.63 to 0.90. Angstrom constants obtained at the six meteorological stations were thereafter averaged in order to develop a linear regression model for estimating solar radiation in Malawi. Solar radiation values obtained using this model were noted to be in good agreement with those developed for each of the six meteorological stations.