The latent fingerprint in mass transport of polycrystalline materials

Herein, a systematic investigation was carried out to reach a rational understanding and to provide information concerning the possible causes for a significant influence of pressure variation in the underlying processes of mass transport in polycrystalline materials. The authors focused their research in solid-state diffusion, a part of the subject “Mass Transport in Solids”. Theories on diffusion are the subject by itself which exists as a latent fingerprint in every text of higher learning in interdisciplinary science. In this research, authors prepared sandwich samples of titanium alloy and stainless steel using nickel as an intermediate metal. The samples were processed at three different levels of bonding pressure (3, 4 and 5 MPa) while bonding temperature and bonding time was maintained at 750 °C and 1 h, respectively, throughout the experiments. It was observed that the net flux of atomic diffusion of nickel atoms into Ti-alloy at TiA/Ni interface increased by ~63 % with the rise in the bonding pressure from 3 to 4 MPa, but decreased by ~40 % with the rise in the bonding pressure from 4 to 5 MPa. At the same time, the net flux of atomic diffusion of nickel atoms into stainless steel at Ni/SS interface increased by ~19 % with the rise in the bonding pressure from 3 to 4 MPa, but increased by ~17 % with the rise in the bonding pressure from 4 to 5 MPa. Here authors showed that the pressure variations have different effects at the TiA/Ni interface and Ni/SS interface, and tried to explain the explicit mechanisms operating behind them. In general for sandwich samples processed irrespective of bonding pressure chosen, the net flux of Ni-atoms diffused into SS is greater than that of the net flux of Ni-atoms diffused in Ti-alloy matrix by four orders of magnitude. The calculated diffusivity of Ni-atoms into Ti-alloy reaches its highest value of ~5.083 × 10^?19 m²/s for the sandwich sample processed using 4-MPa bonding-pressure, whereas the diffusivity of Ni-atoms into SS reaches its peak value of ~1.615 × 10^?14 m²/s for the sample bonded using 5-MPa bonding-pressure.     

Bivariate Birnbaum–Saunders distribution and associated inference

Univariate Birnbaum–Saunders distribution has been used quite effectively to model positively skewed data, especially lifetime data and crack growth data. In this paper, we introduce bivariate Birnbaum–Saunders distribution which is an absolutely continuous distribution whose marginals are univariate Birnbaum–Saunders distributions. Different properties of this bivariate Birnbaum–Saunders distribution are then discussed. This new family has five unknown parameters and it is shown that the maximum likelihood estimators can be obtained by solving two non-linear equations. We also propose simple modified moment estimators for the unknown parameters which are explicit and can therefore be used effectively as an initial guess for the computation of the maximum likelihood estimators. We then present the asymptotic distributions of the maximum likelihood estimators and use them to construct confidence intervals for the parameters. We also discuss likelihood ratio tests for some hypotheses of interest. Monte Carlo simulations are then carried out to examine the performance of the proposed estimators. Finally, a numerical data analysis is performed in order to illustrate all the methods of inference discussed here.     

Possibility of Love wave propagation in a porous layer under the effect of linearly varying directional rigidities

The present paper investigates the Love wave propagation in an anisotropic porous layer under the effect of rigid boundary. Effect of initial stresses on the propagation of Love waves in a fluid saturated, anisotropic, porous layer having linear variation in directional rigidities lying in contact over a pre-stressed, inhomogeneous elastic half-space has also been considered. The dispersion equation of phase velocity has been derived and the influence of medium characteristic such as porosity, rigid boundary, initial stress, anisotropy and inhomogeneity over it has been discussed. The velocities of Love waves have been calculated numerically as a function of KH (where K is the wave number and H is the thickness of the layer) and are presented in a number of graphs.     

Bivariate generalized exponential distribution

Recently it has been observed that the generalized exponential distribution can be used quite effectively to analyze lifetime data in one dimension. The main aim of this paper is to define a bivariate generalized exponential distribution so that the marginals have generalized exponential distributions. It is observed that the joint probability density function, the joint cumulative distribution function and the joint survival distribution function can be expressed in compact forms. Several properties of this distribution have been discussed. We suggest to use the EM algorithm to compute the maximum likelihood estimators of the unknown parameters and also obtain the observed and expected Fisher information matrices. One data set has been re-analyzed and it is observed that the bivariate generalized exponential distribution provides a better fit than the bivariate exponential distribution.