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.
The transformation media concept based on the form-invariant Maxwells equations under coordinate transformations has opened up new possibilities to manipulate the electromagnetic fields. In this paper we report on applying the finite-embedded coordin
ate transformation method to design electromagnetic beam modulating devices both in the Cartesian coordinates and in the cylindrical coordinates. By designing the material constitutive tensors of the transformation optical structures through different kinds of coordinate transformations, either the beam width of an incident Gaussian plane wave could be modulated by a slab, or the wave propagating direction of an omni-directional source could be modulated through a cylindrical shell. We present the design procedures and the full wave electromagnetic simulations that clearly confirm the performance of the proposed beam modulating devices.
