7,575 research outputs found

    Asymmetric dynamics and critical behavior in the Bak-Sneppen model

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    We investigate, using mean-field theory and simulation, the effect of asymmetry on the critical behavior and probability density of Bak-Sneppen models. Two kinds of anisotropy are investigated: (i) different numbers of sites to the left and right of the central (minimum) site are updated and (ii) sites to the left and right of the central site are renewed in different ways. Of particular interest is the crossover from symmetric to asymmetric scaling for weakly asymmetric dynamics, and the collapse of data with different numbers of updated sites but the same degree of asymmetry. All non-symmetric rules studied fall, independent of the degree of asymmetry, in the same universality class. Conversely, symmetric variants reproduce the exponents of the original model. Our results confirm the existence of two symmetry-based universality classes for extremal dynamics.Comment: 14 pages, 8 figures, 1 tabl

    Vacuum Decay in CFT and the Riemann-Hilbert problem

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    We study vacuum stability in 1+1 dimensional Conformal Field Theories with external background fields. We show that the vacuum decay rate is given by a non-local two-form. This two-form is a boundary term that must be added to the effective in/out Lagrangian. The two-form is expressed in terms of a Riemann-Hilbert decomposition for background gauge fields, and its novel "functional" version in the gravitational case.Comment: 16 pages, 3 figure

    Preliminary EoS for core-collapse supernova simulations with the QMC model

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    In this work we present the preliminary results of a complete equation of state (EoS) for core-collapse supernova simulations. We treat uniform matter made of nucleons using the the quark-meson coupling (QMC) model. We show a table with a variety of thermodynamic quantities, which covers the proton fraction range Yp=00.65Y_{p}=0-0.65 with the linear grid spacing ΔYp=0.01 \Delta Y_{p}=0.01 (6666 points) and the density range ρB=10141016\rho_{B}=10^{14}-10^{16}g.cm3^{-3} with the logarithmic grid spacing Δlog10(ρB/[\Delta log_{10}(\rho_{B}/[g.cm3])=0.1^{-3}])=0.1 (2121 points). This preliminary study is performed at zero temperature and our results are compared with the widely used EoS already available in the literature

    On the Combinatorial Complexity of Approximating Polytopes

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    Approximating convex bodies succinctly by convex polytopes is a fundamental problem in discrete geometry. A convex body KK of diameter diam(K)\mathrm{diam}(K) is given in Euclidean dd-dimensional space, where dd is a constant. Given an error parameter ε>0\varepsilon > 0, the objective is to determine a polytope of minimum combinatorial complexity whose Hausdorff distance from KK is at most εdiam(K)\varepsilon \cdot \mathrm{diam}(K). By combinatorial complexity we mean the total number of faces of all dimensions of the polytope. A well-known result by Dudley implies that O(1/ε(d1)/2)O(1/\varepsilon^{(d-1)/2}) facets suffice, and a dual result by Bronshteyn and Ivanov similarly bounds the number of vertices, but neither result bounds the total combinatorial complexity. We show that there exists an approximating polytope whose total combinatorial complexity is O~(1/ε(d1)/2)\tilde{O}(1/\varepsilon^{(d-1)/2}), where O~\tilde{O} conceals a polylogarithmic factor in 1/ε1/\varepsilon. This is a significant improvement upon the best known bound, which is roughly O(1/εd2)O(1/\varepsilon^{d-2}). Our result is based on a novel combination of both old and new ideas. First, we employ Macbeath regions, a classical structure from the theory of convexity. The construction of our approximating polytope employs a new stratified placement of these regions. Second, in order to analyze the combinatorial complexity of the approximating polytope, we present a tight analysis of a width-based variant of B\'{a}r\'{a}ny and Larman's economical cap covering. Finally, we use a deterministic adaptation of the witness-collector technique (developed recently by Devillers et al.) in the context of our stratified construction.Comment: In Proceedings of the 32nd International Symposium Computational Geometry (SoCG 2016) and accepted to SoCG 2016 special issue of Discrete and Computational Geometr

    Anderson localization on the Falicov-Kimball model with Coulomb disorder

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    The role of Coulomb disorder is analysed in the Anderson-Falicov-Kimball model. Phase diagrams of correlated and disordered electron systems are calculated within dynamical mean-field theory applied to the Bethe lattice, in which metal-insulator transitions led by structural and Coulomb disorders and correlation can be identified. Metallic, Mott insulator, and Anderson insulator phases, as well as the crossover between them are studied in this perspective. We show that Coulomb disorder has a relevant role in the phase-transition behavior as the system is led towards the insulator regime
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