Operator Semi-group of Density Evolution Equation for a Repairable Redundant System with Two Same Components

For a repairable redundant system consisting of two same components with exponential lifetime and general repair time distribution, the probability densities of the system in some state at time t were determined by a group of ordinary and partial differential equations, called density evolution equations. It was proved that the time dependent solution of the density evolution equations uniquely exists and strongly converges to its steady state density solution by a semi group method. In this proof, it is not necessary to suppose that the repair rate function is bounded. The technique of the proof is valuable for many density evolution equations.

C_0-Semigroup Method of the Density Evolution Equation for M/M/∞ Model

In this paper, the existence, uniqueness, and asymptotic behavior of the solution of the density evolution equation for M/M/∞ model was studied by the semigroup theory of linear operators.

CO_2 Density-Raman Shift Relation Derived from Synthetic Inclusions in Fused Silica Capillaries and Its Application

The densities of CO2 inclusions in minerals are commonly used to determine the crystallizing conditions of the host minerals. However, conventional microthermometry is difficult to apply for inclusions of small size （〈 5-10 μm） or low density. Raman analysis is an alternative method for determining CO2 density, provided that the CO2 density-Raman shift relation is known. This study aims to establish this CO2 density-Raman shift relation by using CO2 inclusions synthesized in fused silica capillaries. By using this newly-developed synthetic technique, we formed pure CO2 inclusions, and their densities were determined by microthermometry. The Raman analysis showed that the relation between CO2 density （D in g/cm^3） and the separations （△ in cm^-1） between the two main bands （i.e. Fermi diad bands） in CO2 Raman spectra can be represented by a cubic equation： D （g/cm^3）=0.74203（-0.019^3＋5.90332△^2-610.79472△＋21050.30165）-3.54278 （r^2=0.99920）. Our calculated D value for a given A is between those obtained from two previously-reported equations, which were derived from different experimental methods. An example was given in this study to demonstrate that the densities of natural CO2 inclusions that could not be derived from microthermometry could be determined by using our method.

Correlation of the mean activity coefficient of aqueous electrolyte solutions using an equation of state

Accurate calculation of thermodynamic properties of electrolyte solution is essential in the design and optimization of many processes in chemical industries. A new electrolyte equation of state is developed for aqueous electrolyte solutions. The Carnahan-Starling repulsive model and an attractive term based on square-well potential are adopted to represent the short range interaction of ionic and molecular species in the new electrolyte EOS. The long range interaction of ionic species is expressed by a simplified version of Mean Spherical Approximation theory （MSA）. The new equation of state also contains a Born term for charging free energy of ions. Three adjustable parameters of new eEOS per each electrolyte solution are size parameter, square-well potential depth and square-well potential interaction range. The new eEOS is applied for correlation of mean activity coefficient and prediction of osmotic coefficient of various strong aqueous electrolyte solutions at 25℃ and 0.1 MPa. In addition, the extension of the new eEOS for correlation of mean activity coefficient and solution density of a few aqueous electrolytes at temperature range of 0 to 100℃ is carried out.

Travelling Waves for a Density Dependent Diffusion Nagumo Equation over the Real Line

We consider the density dependent diffusion Nagumo equation, where the diffusion coefficient is a simple power function. This equation is used in modelling electrical pulse propagation in nerve axons and in population genetics (amongst other areas). In the present paper, the δ-expansion method is applied to a travelling wave reduction of the problem, so that we may obtain globally valid perturbation solutions (in the sense that the perturbation solutions are valid over the entire infinite domain, not just locally; hence the results are a generalization of the local solutions considered recently in the literature). The resulting boundary value problem is solved on the real line subject to conditions at z →±∞. Whenever a perturbative method is applied, it is important to discuss the accuracy and convergence properties of the resulting perturbation expansions. We compare our results with those of two different numerical methods (designed for initial and boundary value problems, respectively) and deduce that the perturbation expansions agree with the numerical results after a reasonable number of iterations. Finally, we are able to discuss the influence of the wave speed c and the asymptotic concentration value α on the obtained solutions. Upon recasting the density dependent diffusion Nagumo equation as a two-dimensional dynamical system, we are also able to discuss the influence of the nonlinear density dependence (which is governed by a power-law parameter m) on oscillations of the travelling wave solutions.

Evolution of Generalized Sizing for Evaluation of Converter Fed Machines

Based on the concept of the converter fed machines (CFMs), an optimal machine design can be considered as the best match of the machine topology, the power electronic converter and the performance specifications. To evaluate power production potentials of machines with various topologies with different waveforms of back emf and current, the generalized sizing equations and the power density equation are needed to evaluate the main dimensions and the power of such machines. In this paper. a general approach is presented to develop and to discuss these equations. Sample applications of the generalized sizing and power density equations are utilized to evaluate the induction machine and the double-salient permanent magnet (DSPM) machine.