1,794 research outputs found
Finite-size scaling of the stochastic susceptible-infected-recovered model
The critical behavior of the stochastic susceptible-infected-recovered model
on a square lattice is obtained by numerical simulations and finite-size
scaling. The order parameter as well as the distribution in the number of
recovered individuals is determined as a function of the infection rate for
several values of the system size. The analysis around criticality is obtained
by exploring the close relationship between the present model and standard
percolation theory. The quantity UP, equal to the ratio U between the second
moment and the squared first moment of the size distribution multiplied by the
order parameter P, is shown to have, for a square system, a universal value
1.0167(1) that is the same as for site and bond percolation, confirming further
that the SIR model is also in the percolation class
Nonlinear evolution of r-modes: the role of differential rotation
Recent work has shown that differential rotation, producing large scale
drifts of fluid elements along stellar latitudes, is an unavoidable feature of
r-modes in the nonlinear theory. We investigate the role of this differential
rotation in the evolution of the l=2 r-mode instability of a newly born, hot,
rapidly rotating neutron star. It is shown that the amplitude of the r-mode
saturates a few hundred seconds after the mode instability sets in. The
saturation amplitude depends on the amount of differential rotation at the time
the instability becomes active and can take values much smaller than unity. It
is also shown that, independently of the saturation amplitude of the mode, the
star spins down to rotation rates that are comparable to the inferred initial
rotation rates of the fastest pulsars associated with supernova remnants.
Finally, it is shown that, when the drift of fluid elements at the time the
instability sets in is significant, most of the initial angular momentum of the
star is transferred to the r-mode and, consequently, almost none is carried
away by gravitational radiation.Comment: 10 pages, 5 figure
Self-organized patterns of coexistence out of a predator-prey cellular automaton
We present a stochastic approach to modeling the dynamics of coexistence of
prey and predator populations. It is assumed that the space of coexistence is
explicitly subdivided in a grid of cells. Each cell can be occupied by only one
individual of each species or can be empty. The system evolves in time
according to a probabilistic cellular automaton composed by a set of local
rules which describe interactions between species individuals and mimic the
process of birth, death and predation. By performing computational simulations,
we found that, depending on the values of the parameters of the model, the
following states can be reached: a prey absorbing state and active states of
two types. In one of them both species coexist in a stationary regime with
population densities constant in time. The other kind of active state is
characterized by local coupled time oscillations of prey and predator
populations. We focus on the self-organized structures arising from
spatio-temporal dynamics of the coexistence. We identify distinct spatial
patterns of prey and predators and verify that they are intimally connected to
the time coexistence behavior of the species. The occurrence of a prey
percolating cluster on the spatial patterns of the active states is also
examined.Comment: 19 pages, 11 figure
The fluctuation-dissipation theorem and the linear Glauber model
We obtain exact expressions for the two-time autocorrelation and response
functions of the -dimensional linear Glauber model. Although this linear
model does not obey detailed balance in dimensions , we show that the
usual form of the fluctuation-dissipation ratio still holds in the stationary
regime. In the transient regime, we show the occurence of aging, with a special
limit of the fluctuation-dissipation ratio, , for a quench at
the critical point.Comment: Accepted for publication (Physical Review E
Kinetic Ising System in an Oscillating External Field: Stochastic Resonance and Residence-Time Distributions
Experimental, analytical, and numerical results suggest that the mechanism by
which a uniaxial single-domain ferromagnet switches after sudden field reversal
depends on the field magnitude and the system size. Here we report new results
on how these distinct decay mechanisms influence hysteresis in a
two-dimensional nearest-neighbor kinetic Ising model. We present theoretical
predictions supported by numerical simulations for the frequency dependence of
the probability distributions for the hysteresis-loop area and the
period-averaged magnetization, and for the residence-time distributions. The
latter suggest evidence of stochastic resonance for small systems in moderately
weak oscillating fields.Comment: Includes updated results for Fig.2 and minor text revisions to the
abstract and text for clarit
Continuous partial trends and low-frequency oscillations of time series
International audienceThis paper presents a recent methodology developed for the analysis of the slow evolution of geophysical time series. The method is based on least-squares fitting of continuous line segments to the data, subject to flexible conditions, and is able to objectively locate the times of significant change in the series tendencies. The time distribution of these breakpoints may be an important set of parameters for the analysis of the long term evolution of some geophysical data, simplifying the intercomparison between datasets and offering a new way for the analysis of time varying spatially distributed data. Several application examples, using data that is important in the context of global warming studies, are presented and briefly discussed
Quasi-stationary distributions for the Domany-Kinzel stochastic cellular automaton
We construct the {\it quasi-stationary} (QS) probability distribution for the
Domany-Kinzel stochastic cellular automaton (DKCA), a discrete-time Markov
process with an absorbing state. QS distributions are derived at both the one-
and two-site levels. We characterize the distribuitions by their mean, and
various moment ratios, and analyze the lifetime of the QS state, and the
relaxation time to attain this state. Of particular interest are the scaling
properties of the QS state along the critical line separating the active and
absorbing phases. These exhibit a high degree of similarity to the contact
process and the Malthus-Verhulst process (the closest continuous-time analogs
of the DKCA), which extends to the scaling form of the QS distribution.Comment: 15 pages, 9 figures, submited to PR
New methods to reconstruct and the energy of gamma-ray air showers with high accuracy in large wide-field observatories
Novel methods to reconstruct the slant depth of the maximum of the
longitudinal profile (\Xmax) of high-energy showers initiated by gamma-rays as
well as their energy () are presented. The methods were developed for
gamma rays with energies ranging from a few hundred GeV to TeV. An
estimator of \Xmax is obtained, event-by-event, from its correlation with the
distribution of the arrival time of the particles at the ground, or the signal
at the ground for lower energies. An estimator of is obtained,
event-by-event, using a parametrization that has as inputs the total measured
energy at the ground, the amount of energy contained in a region near to the
shower core and the estimated \Xmax.
Resolutions about and about for,
respectively, \Xmax and at energies are obtained,
considering vertical showers. The obtained results are auspicious and can lead
to the opening of new physics avenues for large wide field-of-view gamma-ray
observatories. The dependence of the resolutions with experimental conditions
is discussed.Comment: 11 pages; 15 figures, to appear in EPJ
Mean-field analysis of the majority-vote model broken-ergodicity steady state
We study analytically a variant of the one-dimensional majority-vote model in
which the individual retains its opinion in case there is a tie among the
neighbors' opinions. The individuals are fixed in the sites of a ring of size
and can interact with their nearest neighbors only. The interesting feature
of this model is that it exhibits an infinity of spatially heterogeneous
absorbing configurations for whose statistical properties we
probe analytically using a mean-field framework based on the decomposition of
the -site joint probability distribution into the -contiguous-site joint
distributions, the so-called -site approximation. To describe the
broken-ergodicity steady state of the model we solve analytically the
mean-field dynamic equations for arbitrary time in the cases n=3 and 4. The
asymptotic limit reveals the mapping between the statistical
properties of the random initial configurations and those of the final
absorbing configurations. For the pair approximation () we derive that
mapping using a trick that avoids solving the full dynamics. Most remarkably,
we find that the predictions of the 4-site approximation reduce to those of the
3-site in the case of expectations involving three contiguous sites. In
addition, those expectations fit the Monte Carlo data perfectly and so we
conjecture that they are in fact the exact expectations for the one-dimensional
majority-vote model
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