235 research outputs found
Some Open Points in Nonextensive Statistical Mechanics
We present and discuss a list of some interesting points that are currently
open in nonextensive statistical mechanics. Their analytical, numerical,
experimental or observational advancement would naturally be very welcome.Comment: 30 pages including 6 figures. Invited paper to appear in the
International Journal of Bifurcation and Chao
Universal fluctuations in the support of the random walk
A random walk starts from the origin of a d-dimensional lattice. The
occupation number n(x,t) equals unity if after t steps site x has been visited
by the walk, and zero otherwise. We study translationally invariant sums M(t)
of observables defined locally on the field of occupation numbers. Examples are
the number S(t) of visited sites; the area E(t) of the (appropriately defined)
surface of the set of visited sites; and, in dimension d=3, the Euler index of
this surface. In d > 3, the averages (t) all increase linearly with t as
t-->infinity. We show that in d=3, to leading order in an asymptotic expansion
in t, the deviations from average Delta M(t)= M(t)-(t) are, up to a
normalization, all identical to a single "universal" random variable. This
result resembles an earlier one in dimension d=2; we show that this
universality breaks down for d>3.Comment: 17 pages, LaTeX, 2 figures include
Global analysis of gene expression associated with chlorophyll retention in soybean seeds.
Edição Especial contendo os Anais do XVIII Congresso Brasileiro de Sementes, Florianópolis, set. 2013
Restricted random walk model as a new testing ground for the applicability of q-statistics
We present exact results obtained from Master Equations for the probability
function P(y,T) of sums of the positions x_t of a discrete
random walker restricted to the set of integers between -L and L. We study the
asymptotic properties for large values of L and T. For a set of position
dependent transition probabilities the functional form of P(y,T) is with very
high precision represented by q-Gaussians when T assumes a certain value
. The domain of y values for which the q-Gaussian apply
diverges with L. The fit to a q-Gaussian remains of very high quality even when
the exponent of the transition probability g(x)=|x/L|^a+p with 0<p<<1 is
different from 1, all though weak, but essential, deviation from the q-Gaussian
does occur for . To assess the role of correlations we compare the T
dependence of P(y,T) for the restricted random walker case with the equivalent
dependence for a sum y of uncorrelated variables x each distributed according
to 1/g(x).Comment: 5 pages, 7 figs, EPL (2011), in pres
A note on q-Gaussians and non-Gaussians in statistical mechanics
The sum of sufficiently strongly correlated random variables will not in
general be Gaussian distributed in the limit N\to\infty. We revisit examples of
sums x that have recently been put forward as instances of variables obeying a
q-Gaussian law, that is, one of type (cst)\times[1-(1-q)x^2]^{1/(1-q)}. We show
by explicit calculation that the probability distributions in the examples are
actually analytically different from q-Gaussians, in spite of numerically
resembling them very closely. Although q-Gaussians exhibit many interesting
properties, the examples investigated do not support the idea that they play a
special role as limit distributions of correlated sums.Comment: 17 pages including 3 figures. Introduction and references expande
Selfsimilar solutions in a sector for a quasilinear parabolic equation
We study a two-point free boundary problem in a sector for a quasilinear
parabolic equation. The boundary conditions are assumed to be spatially and
temporally "self-similar" in a special way. We prove the existence, uniqueness
and asymptotic stability of an expanding solution which is self-similar at
discrete times. We also study the existence and uniqueness of a shrinking
solution which is self-similar at discrete times.Comment: 23 page
Spontaneous symmetry breaking in a two-lane model for bidirectional overtaking traffic
First we consider a unidirectional flux \omega_bar of vehicles each of which
is characterized by its `natural' velocity v drawn from a distribution P(v).
The traffic flow is modeled as a collection of straight `world lines' in the
time-space plane, with overtaking events represented by a fixed queuing time
tau imposed on the overtaking vehicle. This geometrical model exhibits platoon
formation and allows, among many other things, for the calculation of the
effective average velocity w=\phi(v) of a vehicle of natural velocity v.
Secondly, we extend the model to two opposite lanes, A and B. We argue that the
queuing time \tau in one lane is determined by the traffic density in the
opposite lane. On the basis of reasonable additional assumptions we establish a
set of equations that couple the two lanes and can be solved numerically. It
appears that above a critical value \omega_bar_c of the control parameter
\omega_bar the symmetry between the lanes is spontaneously broken: there is a
slow lane where long platoons form behind the slowest vehicles, and a fast lane
where overtaking is easy due to the wide spacing between the platoons in the
opposite direction. A variant of the model is studied in which the spatial
vehicle density \rho_bar rather than the flux \omega_bar is the control
parameter. Unequal fluxes \omega_bar_A and \omega_bar_B in the two lanes are
also considered. The symmetry breaking phenomenon exhibited by this model, even
though no doubt hard to observe in pure form in real-life traffic, nevertheless
indicates a tendency of such traffic.Comment: 50 pages, 16 figures; extra references adde
Surface critical behavior of two-dimensional dilute Ising models
Ising models with nearest-neighbor ferromagnetic random couplings on a square
lattice with a (1,1) surface are studied, using Monte Carlo techniques and
star-tiangle transformation method. In particular, the critical exponent of the
surface magnetization is found to be close to that of the perfect model,
beta_s=1/2. The crossover from surface to bulk critical properties is
discussed.Comment: 6 pages in RevTex, 3 ps figures, to appear in Journal of Stat. Phy
Quantitative features of multifractal subtleties in time series
Based on the Multifractal Detrended Fluctuation Analysis (MFDFA) and on the
Wavelet Transform Modulus Maxima (WTMM) methods we investigate the origin of
multifractality in the time series. Series fluctuating according to a qGaussian
distribution, both uncorrelated and correlated in time, are used. For the
uncorrelated series at the border (q=5/3) between the Gaussian and the Levy
basins of attraction asymptotically we find a phase-like transition between
monofractal and bifractal characteristics. This indicates that these may solely
be the specific nonlinear temporal correlations that organize the series into a
genuine multifractal hierarchy. For analyzing various features of
multifractality due to such correlations, we use the model series generated
from the binomial cascade as well as empirical series. Then, within the
temporal ranges of well developed power-law correlations we find a fast
convergence in all multifractal measures. Besides of its practical significance
this fact may reflect another manifestation of a conjectured q-generalized
Central Limit Theorem
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