Validation of the S‐CLSVOF method with the density‐scaled balanced continuum surface force model in multiphase systems coupled with thermocapillary flows

Three numerical methods, namely, volume of fluid (VOF), simple coupled volume of fluid with level set (S‐CLSVOF), and S‐CLSVOF with the density‐scaled balanced continuum surface force (CSF) model, have been incorporated into OpenFOAM source code and were validated for their accuracy for three cases: (i) an isothermal static case, (ii) isothermal dynamic cases, and (iii) non‐isothermal dynamic cases with thermocapillary flow including dynamic interface deformation. Results have shown that the S‐CLSVOF method gives accurate results in the test cases with mild computation conditions, and the S‐CLSVOF technique with the density‐scaled balanced CSF model leads to accurate results in the cases of large interface deformations and large density and viscosity ratios. These show that these high accuracy methods would be appropriate to obtain accurate predictions in multiphase flow systems with thermocapillary flows. Copyright © 2016 John Wiley & Sons, Ltd.     

The likelihood ratio tests for the dimensionality of regression coefficients

In this paper we give a unified derivation of the likelihood ratio (LR) statistics for testing the hypothesis on the dimensionality of regression coefficients under a usual MANOVA model. We also derive the LR statistics under a general MANOVA model and study their asymptotic null and nonnull distributions. Further it is shown that the test statistic used by Bartlett [4] for testing the hypothesis that the last p?k canonical correlations are all zero is the LR statistic.     

Gravitational Effects on Mixing and Growth Morphology of an In0.5Ga0.5 System

A mixing experiment of multicomponents melts was performed using a uniform temperature furnace in the Second International Microgravity Laboratories (IML-2) mission. Growth morphologies and Ga concentration profiles were analyzed for the samples with the compositional ratio of 0.5 In–0.5 Ga–1.0 Sb grown under microgravity and on earth. The sample with free surface grown under microgravity was nearly spherical in shape, except some parts with projections. Ga was dispersed homogeneously in the bulk because the mixing was enhanced by Marangoni convection due to the concentration gradient. On the other hand, the sample grown on earth was a double cylindrical shape with different diameters, and Ga concentration decreased from top to bottom, showing clearly the effect of gravity. Many needle crystals were formed in both space and earth samples due to rapid cooling. The average size of the needle crystals grown in space was larger than that of the earth sample.