On thermodynamically consistent Stefan problems with variable surface energy

A thermodynamically consistent two-phase Stefan problem with temperature-dependent surface tension and with or without kinetic undercooling is studied. It is shown that these problems generate local semiflows in well-defined state manifolds. If a solution does not exhibit singularities, it is proved that it exists globally in time and converges towards an equilibrium of the problem. In addition, stability and instability of equilibria is studied. In particular, it is shown that multiple spheres of the same radius are unstable if surface heat capacity is small; however, if kinetic undercooling is absent, they are stable if surface heat capacity is sufficiently large.Comment: To appear in Arch. Ration. Mech. Anal. The final publication is available at Springer via http://dx.doi.org/10.1007/s00205-015-0938-y. arXiv admin note: substantial text overlap with arXiv:1101.376

Qualitative behavior of solutions for thermodynamically consistent Stefan problems with surface tension

The qualitative behavior of a thermodynamically consistent two-phase Stefan problem with surface tension and with or without kinetic undercooling is studied. It is shown that these problems generate local semiflows in well-defined state manifolds. If a solution does not exhibit singularities in a sense made precise below, it is proved that it exists globally in time and its orbit is relatively compact. In addition, stability and instability of equilibria is studied. In particular, it is shown that multiple spheres of the same radius are unstable, reminiscent of the onset of Ostwald ripening.Comment: 56 pages. Expanded introduction, added references. This revised version is published in Arch. Ration. Mech. Anal. (207) (2013), 611-66

Comparison of the third molar maturity index (I3M) between left and right lower third molars to assess the age of majority: a multi-ethnic study sample.

The diagnostic accuracy of the I3M to assess the legal age of 18 years has already been tested in several specific-population samples. The left lower third molar has been extensively used for discriminating between minors and adults. This research aimed to compare the usefulness of lower third molar maturity indexes, from both left and right side (I3ML and I3MR), in samples originating from four distinct continents in order to examine possible differences in their accuracy values. For this purpose, a sample of 10,181 orthopantomograms (OPGs), from Europe, Africa, Asia and America, was analysed and previously scored in other studies. The samples included healthy subjects with no systemic disorders with both third molars and clear depicted root apices. Wilcoxon Signed Rank test for left and right asymmetry did not show any significant differences. Data about sensitivity, specificity, predictive values, likelihood ratio and accuracy were pooled together and showed similar results for I3ML and I3MR, respectively. In addition, all these quantities were high when only the I3MR was considered to discriminate between adults and minors. The present referable database was the first to pool third molar measurements using panoramic radiographs of subjects coming from different continents. The results highlighted that both I3ML and I3MR are reliable indicators for assessing the legal age of 18 years old in those jurisdictions where this legal threshold has been set as the age of majority