7,575 research outputs found
Asymmetric dynamics and critical behavior in the Bak-Sneppen model
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
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
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 with the linear grid spacing
( points) and the density range g.cm with
the logarithmic grid spacing g.cm
( 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
Approximating convex bodies succinctly by convex polytopes is a fundamental
problem in discrete geometry. A convex body of diameter
is given in Euclidean -dimensional space, where is a constant. Given an
error parameter , the objective is to determine a polytope of
minimum combinatorial complexity whose Hausdorff distance from is at most
. By combinatorial complexity we mean the
total number of faces of all dimensions of the polytope. A well-known result by
Dudley implies that 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
, where conceals a
polylogarithmic factor in . This is a significant improvement
upon the best known bound, which is roughly .
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
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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