73 research outputs found
Finite-size scaling analysis of the critical behavior of a general epidemic process in 2D
AbstractWe investigate the critical behavior of a stochastic lattice model describing a General Epidemic Process. By means of a Monte Carlo procedure, we simulate the model on a regular square lattice and follow the spreading of an epidemic process with immunization. A finite size scaling analysis is employed to determine the critical point as well as some critical exponents. We show that the usual scaling analysis of the order parameter moment ratio does not provide an accurate estimate of the critical point. Precise estimates of the critical quantities are obtained from data of the order parameter variation rate and its fluctuations. Our numerical results corroborate that this model belongs to the dynamic isotropic percolation universality class. We also check the validity of the hyperscaling relation and present data collapse curves which reinforce the accuracy of the estimated critical parameters
Convergence of the critical attractor of dissipative maps: Log-periodic oscillations, fractality and nonextensivity
For a family of logistic-like maps, we investigate the rate of convergence to
the critical attractor when an ensemble of initial conditions is uniformly
spread over the entire phase space. We found that the phase space volume
occupied by the ensemble W(t) depicts a power-law decay with log-periodic
oscillations reflecting the multifractal character of the critical attractor.
We explore the parametric dependence of the power-law exponent and the
amplitude of the log-periodic oscillations with the attractor's fractal
dimension governed by the inflexion of the map near its extremal point.
Further, we investigate the temporal evolution of W(t) for the circle map whose
critical attractor is dense. In this case, we found W(t) to exhibit a rich
pattern with a slow logarithmic decay of the lower bounds. These results are
discussed in the context of nonextensive Tsallis entropies.Comment: 8 pages and 8 fig
Universal renormalization-group dynamics at the onset of chaos in logistic maps and nonextensive statistical mechanics
We uncover the dynamics at the chaos threshold of the logistic
map and find it consists of trajectories made of intertwined power laws that
reproduce the entire period-doubling cascade that occurs for . We corroborate this structure analytically via the Feigenbaum
renormalization group (RG) transformation and find that the sensitivity to
initial conditions has precisely the form of a -exponential, of which we
determine the -index and the -generalized Lyapunov coefficient . Our results are an unequivocal validation of the applicability of the
non-extensive generalization of Boltzmann-Gibbs (BG) statistical mechanics to
critical points of nonlinear maps.Comment: Revtex, 3 figures. Updated references and some general presentation
improvements. To appear published as a Rapid communication of PR
Two-dimensional maps at the edge of chaos: Numerical results for the Henon map
The mixing properties (or sensitivity to initial conditions) of
two-dimensional Henon map have been explored numerically at the edge of chaos.
Three independent methods, which have been developed and used so far for the
one-dimensional maps, have been used to accomplish this task. These methods are
(i)measure of the divergence of initially nearby orbits, (ii)analysis of the
multifractal spectrum and (iii)computation of nonextensive entropy increase
rates. The obtained results strongly agree with those of the one-dimensional
cases and constitute the first verification of this scenario in two-dimensional
maps. This obviously makes the idea of weak chaos even more robust.Comment: 4 pages, 3 figure
A recent appreciation of the singular dynamics at the edge of chaos
We study the dynamics of iterates at the transition to chaos in the logistic
map and find that it is constituted by an infinite family of Mori's -phase
transitions. Starting from Feigenbaum's function for the diameters
ratio, we determine the atypical weak sensitivity to initial conditions associated to each -phase transition and find that it obeys the form
suggested by the Tsallis statistics. The specific values of the variable at
which the -phase transitions take place are identified with the specific
values for the Tsallis entropic index in the corresponding . We
describe too the bifurcation gap induced by external noise and show that its
properties exhibit the characteristic elements of glassy dynamics close to
vitrification in supercooled liquids, e.g. two-step relaxation, aging and a
relationship between relaxation time and entropy.Comment: Proceedings of: Verhulst 200 on Chaos, Brussels 16-18 September 2004,
Springer Verlag, in pres
Nonextensive Entropies derived from Form Invariance of Pseudoadditivity
The form invariance of pseudoadditivity is shown to determine the structure
of nonextensive entropies. Nonextensive entropy is defined as the appropriate
expectation value of nonextensive information content, similar to the
definition of Shannon entropy. Information content in a nonextensive system is
obtained uniquely from generalized axioms by replacing the usual additivity
with pseudoadditivity. The satisfaction of the form invariance of the
pseudoadditivity of nonextensive entropy and its information content is found
to require the normalization of nonextensive entropies. The proposed principle
requires the same normalization as that derived in [A.K. Rajagopal and S. Abe,
Phys. Rev. Lett. {\bf 83}, 1711 (1999)], but is simpler and establishes a basis
for the systematic definition of various entropies in nonextensive systems.Comment: 16 pages, accepted for publication in Physical Review
Charging Effects and Quantum Crossover in Granular Superconductors
The effects of the charging energy in the superconducting transition of
granular materials or Josephson junction arrays is investigated using a
pseudospin one model. Within a mean-field renormalization-group approach, we
obtain the phase diagram as a function of temperature and charging energy. In
contrast to early treatments, we find no sign of a reentrant transition in
agreement with more recent studies. A crossover line is identified in the
non-superconducting side of the phase diagram and along which we expect to
observe anomalies in the transport and thermodynamic properties. We also study
a charge ordering phase, which can appear for large nearest neighbor Coulomb
interaction, and show that it leads to first-order transitions at low
temperatures. We argue that, in the presence of charge ordering, a non
monotonic behavior with decreasing temperature is possible with a maximum in
the resistance just before entering the superconducting phase.Comment: 15 pages plus 4 fig. appended, Revtex, INPE/LAS-00
Spatial correlations in vote statistics: a diffusive field model for decision-making
We study the statistics of turnout rates and results of the French elections
since 1992. We find that the distribution of turnout rates across towns is
surprisingly stable over time. The spatial correlation of the turnout rates, or
of the fraction of winning votes, is found to decay logarithmically with the
distance between towns. Based on these empirical observations and on the
analogy with a two-dimensional random diffusion equation, we propose that
individual decisions can be rationalised in terms of an underlying "cultural"
field, that locally biases the decision of the population of a given region, on
top of an idiosyncratic, town-dependent field, with short range correlations.
Using symmetry considerations and a set of plausible assumptions, we suggest
that this cultural field obeys a random diffusion equation.Comment: 18 pages, 5 figures; added sociophysics references
Guillain-Barré syndrome related to Zika virus infection: A systematic review and meta-analysis of the clinical and electrophysiological phenotype
BACKGROUND: The Zika virus (ZIKV) has been associated with Guillain-Barré syndrome (GBS) in epidemiological studies. Whether ZIKV-associated GBS is related to a specific clinical or electrophysiological phenotype has not been established. To this end, we performed a systematic review and meta-analysis of all published s
Bias driven coherent carrier dynamics in a two-dimensional aperiodic potential
We study the dynamics of an electron wave-packet in a two-dimensional square
lattice with an aperiodic site potential in the presence of an external uniform
electric field. The aperiodicity is described by at lattice sites
, with being a rational number, and and
tunable parameters, controlling the aperiodicity. Using an exact
diagonalization procedure and a finite-size scaling analysis, we show that in
the weakly aperiodic regime (), a phase of extended states
emerges in the center of the band at zero field giving support to a macroscopic
conductivity in the thermodynamic limit. Turning on the field gives rise to
Bloch oscillations of the electron wave-packet. The spectral density of these
oscillations may display a double peak structure signaling the spatial
anisotropy of the potential landscape. The frequency of the oscillations can be
understood using a semi-classical approach.Comment: 16 pages, to appear in Phys. Lett.
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