Exact Failure Frequency Calculations for Extended Systems

This paper shows how the steady-state availability and failure frequency can be calculated in a single pass for very large systems, when the availability is expressed as a product of matrices. We apply the general procedure to $k$-out-of-$n$:G and linear consecutive $k$-out-of-$n$:F systems, and to a simple ladder network in which each edge and node may fail. We also give the associated generating functions when the components have identical availabilities and failure rates. For large systems, the failure rate of the whole system is asymptotically proportional to its size. This paves the way to ready-to-use formulae for various architectures, as well as proof that the differential operator approach to failure frequency calculations is very useful and straightforward

Exact two-terminal reliability of some directed networks

The calculation of network reliability in a probabilistic context has long been an issue of practical and academic importance. Conventional approaches (determination of bounds, sums of disjoint products algorithms, Monte Carlo evaluations, studies of the reliability polynomials, etc.) only provide approximations when the network's size increases, even when nodes do not fail and all edges have the same reliability p. We consider here a directed, generic graph of arbitrary size mimicking real-life long-haul communication networks, and give the exact, analytical solution for the two-terminal reliability. This solution involves a product of transfer matrices, in which individual reliabilities of edges and nodes are taken into account. The special case of identical edge and node reliabilities (p and rho, respectively) is addressed. We consider a case study based on a commonly-used configuration, and assess the influence of the edges being directed (or not) on various measures of network performance. While the two-terminal reliability, the failure frequency and the failure rate of the connection are quite similar, the locations of complex zeros of the two-terminal reliability polynomials exhibit strong differences, and various structure transitions at specific values of rho. The present work could be extended to provide a catalog of exactly solvable networks in terms of reliability, which could be useful as building blocks for new and improved bounds, as well as benchmarks, in the general case

Vertex corrections in localized and extended systems

Within many-body perturbation theory we apply vertex corrections to various closed-shell atoms and to jellium, using a local approximation for the vertex consistent with starting the many-body perturbation theory from a DFT-LDA Green's function. The vertex appears in two places -- in the screened Coulomb interaction, W, and in the self-energy, \Sigma -- and we obtain a systematic discrimination of these two effects by turning the vertex in \Sigma on and off. We also make comparisons to standard GW results within the usual random-phase approximation (RPA), which omits the vertex from both. When a vertex is included for closed-shell atoms, both ground-state and excited-state properties demonstrate only limited improvements over standard GW. For jellium we observe marked improvement in the quasiparticle band width when the vertex is included only in W, whereas turning on the vertex in \Sigma leads to an unphysical quasiparticle dispersion and work function. A simple analysis suggests why implementation of the vertex only in W is a valid way to improve quasiparticle energy calculations, while the vertex in \Sigma is unphysical, and points the way to development of improved vertices for ab initio electronic structure calculations.Comment: 8 Pages, 6 Figures. Updated with quasiparticle neon results, extended conclusions and references section. Minor changes: Updated references, minor improvement

Dynamical Screening Effects in Correlated Electron Materials -- A Progress Report on Combined Many-Body Perturbation and Dynamical Mean Field Theory: "GW+DMFT"

We give a summary of recent progress in the field of electronic structure calculations for materials with strong electronic Coulomb correlations. The discussion focuses on developments beyond the by now well established combination of density functional and dynamical mean field theory dubbed "LDA+DMFT". It is organized around the description of dynamical screening effects in the solid. Indeed, screening in the solid gives rise to dynamical local Coulomb interactions U(w) (Aryasetiawan et al 2004 Phys. Rev. B 70 195104), and this frequency-dependence leads to effects that cannot be neglected in a truly first principles description. We review the recently introduced extension of LDA+DMFT to dynamical local Coulomb interactions "LDA+U(w)+DMFT" (Casula et al. Phys. Rev. B 85 035115 (2012), Werner et al. Nature Phys. 8 331 (2012)). A reliable description of dynamical screening effects is also a central ingredient of the "GW+DMFT" scheme (Biermann et al. Phys. Rev. Lett. 90 086402 (2003)), a combination of many-body perturbation theory in Hedin's GW approximation and dynamical mean field theory. Recently, the first GW+DMFT calculations including dynamical screening effects for real materials have been achieved, with applications to SrVO3 (Tomczak et al. Europhys. Lett. 100 67001 (2012); Phys. Rev. B 90 165138 (2014)) and adatom systems on surfaces (Hansmann et al. Phys. Rev. Lett. 110 166401 (2013)). We review these and comment on further perspectives in the field. This review is an attempt to put elements of the original works (Refs. 1-11) into the broad perspective of the development of truly first principles techniques for correlated electron materials.Comment: 40 pages, 12 figures. First published as "Highlight of the Month" (June 2013), of the Psi-k Network on "Ab initio calculation of complex processes in materials", see http://www.psi-k.org/newsletters/News_117/Highlight_117.pd

Localization and Absorption of Light in 2D Composite Metal-Dielectric Films at the Percolation Threshold

We study in this paper the localization of light and the dielectric properties of thin metal-dielectric composites at the percolation threshold and around a resonant frequency where the conductivities of the two components are of the same order. In particular, the effect of the loss in metallic components are examined. To this end, such systems are modelized as random $L-C$ networks, and the local field distribution as well as the effective conductivity are determined by using two different methods for comparison: an exact resolution of Kirchoff equations, and a real space renormalization group method. The latter method is found to give the general behavior of the effective conductivity but fails to determine the local field distribution. It is also found that the localization still persists for vanishing losses. This result seems to be in agreement with the anomalous absorption observed experimentally for such systems.Comment: 14 page latex, 3 ps figures. submitte