The $alpha$-$gamma$ transition in cerium has been studied in both zero and finite temperature by Gutzwiller density functional theory. We find that the first order transition between $alpha$ and $gamma$ phases persists to the zero temperature with ne
gative pressure. By further including the entropy contributed by both electronic quasi-particles and lattice vibration, we obtain the total free energy at given volume and temperature, from which we obtain the $alpha$-$gamma$ transition from the first principle calculation. We also computed the phase diagram and pressure versus volume isotherms of cerium at finite temperature and pressure, finding excellent agreement with the experiments. Our calculation indicate that both the electronic entropy and lattice vibration entropy plays important role in the $alpha$-$gamma$ transition.
We perform rescaled range analysis upon the signals measured by Dual Particle Dynamical Analyzer in gas-liquid two-phase turbulent jets. A novel rescaled range analysis is proposed to investigate these unevenly sampled signals. The Hurst exponents of
velocity and other passive scalars in the bulk of spray are obtained to be 0.59$pm $0.02 and the fractal dimension is hence 1.41$pm $ 0.02, which are in remarkable agreement with and much more precise than previous results. These scaling exponents are found to be independent of the configuration and dimensions of the nozzle and the fluid flows. Therefore, such type of systems form a universality class with invariant scaling properties.
