43,107 research outputs found
Condensation of degrees emerging through a first-order phase transition in classical random graphs
Due to their conceptual and mathematical simplicity, Erd\"os-R\'enyi or
classical random graphs remain as a fundamental paradigm to model complex
interacting systems in several areas. Although condensation phenomena have been
widely considered in complex network theory, the condensation of degrees has
hitherto eluded a careful study. Here we show that the degree statistics of the
classical random graph model undergoes a first-order phase transition between a
Poisson-like distribution and a condensed phase, the latter characterized by a
large fraction of nodes having degrees in a limited sector of their
configuration space. The mechanism underlying the first-order transition is
discussed in light of standard concepts in statistical physics. We uncover the
phase diagram characterizing the ensemble space of the model and we evaluate
the rate function governing the probability to observe a condensed state, which
shows that condensation of degrees is a rare statistical event akin to similar
condensation phenomena recently observed in several other systems. Monte Carlo
simulations confirm the exactness of our theoretical results.Comment: 8 pages, 6 figure
Level compressibility for the Anderson model on regular random graphs and the eigenvalue statistics in the extended phase
We calculate the level compressibility of the energy levels
inside for the Anderson model on infinitely large random regular
graphs with on-site potentials distributed uniformly in . We show
that approaches the limit
for a broad interval of the disorder strength within the extended phase,
including the region of close to the critical point for the Anderson
transition. These results strongly suggest that the energy levels follow the
Wigner-Dyson statistics in the extended phase, consistent with earlier
analytical predictions for the Anderson model on an Erd\"os-R\'enyi random
graph. Our results are obtained from the accurate numerical solution of an
exact set of equations valid for infinitely large regular random graphs.Comment: 7 pages, 3 figure
Tame and wild theorem for the category of filtered by standard modules for a quasi-hereditary algebra
We introduce the notion of interlaced weak ditalgebras and apply reduction
procedures to their module categories to prove the tame-wild dichotomy for the
category of filtered by standard modules for a
quasi-hereditary algebra. Moreover, in the tame case, we show that given a
fixed dimension , for every -dimensional indecomposable module , with the only possible exception of those lying in a finite
number of isomorphism classes, the module coincides with its
Auslander-Reiten translate in . Our results are based on a
theorem by Koenig, K\"ulshammer, and Ovsienko relating with
the module category of some special type of ditalgebra.Comment: 51 page
Integral field observations of the blue compact galaxy Haro14. Star formation and feedback in dwarf galaxies
(Abridged) Low-luminosity, gas-rich blue compact galaxies (BCG) are ideal
laboratories to investigate many aspects of the star formation in galaxies. We
study the morphology, stellar content, kinematics, and the nebular excitation
and ionization mechanism in the BCG Haro 14 by means of integral field
observations with VIMOS in the VLT. From these data we build maps in continuum
and in the brighter emission lines, produce line-ratio maps, and obtain the
velocity and velocity dispersion fields. We also generate the integrated
spectrum of the major HII regions and young stellar clusters identified in the
maps to determine reliable physical parameters and oxygen abundances. We find
as follows: i) the current star formation in Haro 14 is spatially extended with
the major HII regions placed along a linear structure, elongated in the
north-south direction, and in a horseshoe-like curvilinear feature that extends
about 760 pc eastward; the continuum emission is more concentrated and peaks
close to the galaxy center; ii) two different episodes of star formation are
present: the recent starburst, with ages 6 Myrs and the intermediate-age
clusters, with ages between 10 and 30 Myrs; these stellar components rest on a
several Gyr old underlying host galaxy; iii) the H/H pattern is
inhomogeneous, with excess color values varying from E(B-V)=0.04 up to
E(B-V)=1.09; iv) shocks play a significant role in the galaxy; and v) the
velocity field displays a complicated pattern with regions of material moving
toward us in the east and north galaxy areas. The morphology of Haro 14, its
irregular velocity field, and the presence of shocks speak in favor of a
scenario of triggered star formation. Ages of the knots are consistent with the
ongoing burst being triggered by the collective action of stellar winds and
supernovae originated in the central clusters.Comment: 18 pages, 17 figures. Accepted for publication in A&
Higher Order Approximation to the Hill Problem Dynamics about the Libration Points
An analytical solution to the Hill problem Hamiltonian expanded about the
libration points has been obtained by means of perturbation techniques. In
order to compute the higher orders of the perturbation solution that are needed
to capture all the relevant periodic orbits originated from the libration
points within a reasonable accuracy, the normalization is approached in complex
variables. The validity of the solution extends to energy values considerably
far away from that of the libration points and, therefore, can be used in the
computation of Halo orbits as an alternative to the classical
Lindstedt-Poincar\'e approach. Furthermore, the theory correctly predicts the
existence of the two-lane bridge of periodic orbits linking the families of
planar and vertical Lyapunov orbits.Comment: 28 pages, 8 figure
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