Total energy differences between SiC polytypes revisited

The total energy differences between various SiC polytypes (3C, 6H, 4H, 2H, 15R and 9R) were calculated using the full-potential linear muffin-tin orbital method using the Perdew-Wang-(91) generalized gradient approximation to the exchange-correlation functional in the density functional method. Numerical convergence versus k-point sampling and basis set completeness are demonstrated to be better than 1 meV/atom. The parameters of several generalized anisotropic next-nearest-neighbor Ising models are extracted and their significance and consequences for epitaxial growth are discussed.Comment: 8 pages, 3 figures, Latex, uses epsfig and revte

Edge covering with budget constrains

We study two related problems: finding a set of k vertices and minimum number of edges (kmin) and finding a graph with at least m' edges and minimum number of vertices (mvms). Goldschmidt and Hochbaum \cite{GH97} show that the mvms problem is NP-hard and they give a 3-approximation algorithm for the problem. We improve \cite{GH97} by giving a ratio of 2. A 2(1+\epsilon)-approximation for the problem follows from the work of Carnes and Shmoys \cite{CS08}. We improve the approximation ratio to 2. algorithm for the problem. We show that the natural LP for \kmin has an integrality gap of 2-o(1). We improve the NP-completeness of \cite{GH97} by proving the pronlem are APX-hard unless a well-known instance of the dense k-subgraph admits a constant ratio. The best approximation guarantee known for this instance of dense k-subgraph is O(n^{2/9}) \cite{BCCFV}. We show that for any constant \rho>1, an approximation guarantee of \rho for the \kmin problem implies a \rho(1+o(1)) approximation for \mwms. Finally, we define we give an exact algorithm for the density version of kmin.Comment: 17 page

Non-relativistic radiation mediated shock breakouts: I. Exact bolometric planar breakout solutions

The problem of a non-steady planar radiation mediated shock (RMS) breaking out from a surface with a power-law density profile, \rho\propto x^n, is numerically solved in the approximation of diffusion with constant opacity. For an appropriate choice of time, length and energy scales, determined by the breakout opacity, velocity and density, the solution is universal, i.e. depends only on the density power law index n. The resulting luminosity depends weakly on the value of n. An approximate analytic solution, based on the self-similar hydrodynamic solutions and on the steady RMS solutions, is constructed and shown to agree with the numerical solutions as long as the shock is far from the surface, \tau>> c/v_{sh}. Approximate analytic expressions, calibrated based on the exact solutions, are provided, that describe the escaping luminosity as a function of time. These results can be used to calculate the bolometric properties of the bursts of radiation produced during supernova (SN) shock breakouts. For completeness, we also use the exact breakout solutions to provide an analytic approximation for the maximum surface temperature for fast (v_{sh}>~0.1) non-thermal breakouts, and show that it is few times smaller than inferred based on steady-state RMS solutions

Assessing the Performance of Recent Density Functionals for Bulk Solids

We assess the performance of recent density functionals for the exchange-correlation energy of a nonmolecular solid, by applying accurate calculations with the GAUSSIAN, BAND, and VASP codes to a test set of 24 solid metals and non-metals. The functionals tested are the modified Perdew-Burke-Ernzerhof generalized gradient approximation (PBEsol GGA), the second-order GGA (SOGGA), and the Armiento-Mattsson 2005 (AM05) GGA. For completeness, we also test more-standard functionals: the local density approximation, the original PBE GGA, and the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA. We find that the recent density functionals for solids reach a high accuracy for bulk properties (lattice constant and bulk modulus). For the cohesive energy, PBE is better than PBEsol overall, as expected, but PBEsol is actually better for the alkali metals and alkali halides. For fair comparison of calculated and experimental results, we consider the zero-point phonon and finite-temperature effects ignored by many workers. We show how Gaussian basis sets and inaccurate experimental reference data may affect the rating of the quality of the functionals. The results show that PBEsol and AM05 perform somewhat differently from each other for alkali metal, alkaline earth metal and alkali halide crystals (where the maximum value of the reduced density gradient is about 2), but perform very similarly for most of the other solids (where it is often about 1). Our explanation for this is consistent with the importance of exchange-correlation nonlocality in regions of core-valence overlap.Comment: 32 pages, single pdf fil

The Cumulant Expansion for the Anderson Lattice with Finite U: The Completeness Problem

``Completeness'' (i.e. probability conservation) is not usually satisfied in the cumulant expansion of the Anderson lattice when a reduced state space is employed for $U\to \infty$. To understand this result, the well known ``Chain'' approximation is first calculated for finite $U$, followed by taking $U\to \infty$. Completeness is recovered by this procedure, but this result hides a serious inconsistency that causes completeness failure in the reduced space calculation. Completeness is satisfied and the inconsistency is removed by choosing an adequate family of diagrams. The main result of this work is that using a reduced space of relevant states is as good as using the whole space.Comment: Latex 22 pages, 6 figures with postscript files attached, accepted for publication in the Int. J. of Mod. Phys. B (1998). Subject field : Strongly Correlated System

The Behaviour of the Green Function for the BFKL Pomeron with Running Coupling

We analyse here in LO the physical properties of the Green function solution for the BFKL equation. We show that the solution obeys the orthonormality conditions in the physical region and fulfills the completeness requirements. The unintegrated gluon density is shown to consists of a set of few poles with parameters which could be determined by comparison with the DIS data of high precision