On the Bragg, Leibfried, and Modified Leibfried Numbers

The Bragg, Leibfried, and modified Leibfried numbers are defined in the context of a theory of dislocation-mediated melting, and their values are determined from the properties of the dislocation ensemble at the melting temperature. The approximate numerical coincidence of the Bragg and modified Leibfried numbers is explained. The parameter K in the definition of the modified Leibfried number is shown to be the natural logarithm of the effective coordination number. Our analysis reveals that the Bragg number can be considered an elemental constant, in contrast to the Leibfried and modified Leibfried numbers.Comment: 5 pages, LaTe

Covariant Thermodynamics and ``Realistic'' Friedmann Model

We discuss a cosmological Friedmann model modified by inclusion of off-shell matter which has an equation of state $p,\rho \propto T^5,$ $p=1/4\rho .$ Such matter is shown to have energy density comparable with that of non-interacting radiation at temperatures of the order of the Hagedorn temperature, $\sim 10^{12}$ K, indicating the possibility of a phase transition. It is argued that the $T^5$-phase, or an admixture, lies below the high-temperature $T^4$-phase