349 research outputs found
On the fractal structure of the rescaled evolution set of Carlitz sequences of polynomials
AbstractSelf-similarity properties of the coefficient patterns of the so-called m-Carlitz sequences of polynomials are considered. These properties are coded in an associated fractal set – the rescaled evolution set. We extend previous results on linear cellular automata with states in a finite field. Applications are given for the sequence of Legendre polynomials and sequences associated with the zero Bessel function
Ergodicity properties of -adic -rational dynamical systems with unique fixed point
We consider a family of -rational functions given on the set of
-adic field . Each such function has a unique fixed point. We study
ergodicity properties of the dynamical systems generated by -rational
functions. For each such function we describe all possible invariant spheres.
We characterize ergodicity of each -adic dynamical system with respect to
Haar measure reduced on each invariant sphere. In particular, we found an
invariant spheres on which the dynamical system is ergodic and on all other
invariant spheres the dynamical systems are not ergodic
Optimal box-covering algorithm for fractal dimension of complex networks
The self-similarity of complex networks is typically investigated through
computational algorithms the primary task of which is to cover the structure
with a minimal number of boxes. Here we introduce a box-covering algorithm that
not only outperforms previous ones, but also finds optimal solutions. For the
two benchmark cases tested, namely, the E. Coli and the WWW networks, our
results show that the improvement can be rather substantial, reaching up to 15%
in the case of the WWW network.Comment: 5 pages, 6 figure
Wavelet transforms in a critical interface model for Barkhausen noise
We discuss the application of wavelet transforms to a critical interface
model, which is known to provide a good description of Barkhausen noise in soft
ferromagnets. The two-dimensional version of the model (one-dimensional
interface) is considered, mainly in the adiabatic limit of very slow driving.
On length scales shorter than a crossover length (which grows with the strength
of surface tension), the effective interface roughness exponent is
, close to the expected value for the universality class of the
quenched Edwards-Wilkinson model. We find that the waiting times between
avalanches are fully uncorrelated, as the wavelet transform of their
autocorrelations scales as white noise. Similarly, detrended size-size
correlations give a white-noise wavelet transform. Consideration of finite
driving rates, still deep within the intermittent regime, shows the wavelet
transform of correlations scaling as for intermediate frequencies.
This behavior is ascribed to intra-avalanche correlations.Comment: RevTeX, 10 pages, 9 .eps figures; Physical Review E, to be publishe
Controlling surface statistical properties using bias voltage: Atomic force microscopy and stochastic analysis
The effect of bias voltages on the statistical properties of rough surfaces
has been studied using atomic force microscopy technique and its stochastic
analysis. We have characterized the complexity of the height fluctuation of a
rough surface by the stochastic parameters such as roughness exponent, level
crossing, and drift and diffusion coefficients as a function of the applied
bias voltage. It is shown that these statistical as well as microstructural
parameters can also explain the macroscopic property of a surface. Furthermore,
the tip convolution effect on the stochastic parameters has been examined.Comment: 8 pages, 11 figures
Long-range correlation and multifractality in Bach's Inventions pitches
We show that it can be considered some of Bach pitches series as a stochastic
process with scaling behavior. Using multifractal deterend fluctuation analysis
(MF-DFA) method, frequency series of Bach pitches have been analyzed. In this
view we find same second moment exponents (after double profiling) in ranges
(1.7-1.8) in his works. Comparing MF-DFA results of original series to those
for shuffled and surrogate series we can distinguish multifractality due to
long-range correlations and a broad probability density function. Finally we
determine the scaling exponents and singularity spectrum. We conclude fat tail
has more effect in its multifractality nature than long-range correlations.Comment: 18 page, 6 figures, to appear in JSTA
Long range correlation in cosmic microwave background radiation
We investigate the statistical anisotropy and Gaussianity of temperature
fluctuations of Cosmic Microwave Background radiation (CMB) data from {\it
Wilkinson Microwave Anisotropy Probe} survey, using the multifractal detrended
fluctuation analysis, rescaled range and scaled windowed variance methods. The
multifractal detrended fluctuation analysis shows that CMB fluctuations has a
long range correlation function with a multifractal behavior. By comparing the
shuffled and surrogate series of CMB data, we conclude that the multifractality
nature of temperature fluctuation of CMB is mainly due to the long-range
correlations and the map is consistent with a Gaussian distribution.Comment: 10 pages, 7 figures, V2: Added comments, references and major
correction
Fast Estimation of the Vascular Cooling in RFA Based on Numerical Simulation
We present a novel technique to predict the outcome of an RF ablation, including the vascular cooling effect. The main idea is to separate the problem into a patient independent part, which has to be performed only once for every applicator model and generator setting, and a patient dependent part, which can be performed very fast. The patient independent part fills a look-up table of the cooling effects of blood vessels, depending on the vessel radius and the distance of the RF applicator from the vessel, using a numerical simulation of the ablation process. The patient dependent part, on the other hand, only consists of a number of table look-up processes. The paper presents this main idea, along with the required steps for its implementation. First results of the computation and the related ex-vivo evaluation are presented and discussed. The paper concludes with future extensions and improvements of the approach
The shape of invasion perclation clusters in random and correlated media
The shape of two-dimensional invasion percolation clusters are studied
numerically for both non-trapping (NTIP) and trapping (TIP) invasion
percolation processes. Two different anisotropy quantifiers, the anisotropy
parameter and the asphericity are used for probing the degree of anisotropy of
clusters. We observe that in spite of the difference in scaling properties of
NTIP and TIP, there is no difference in the values of anisotropy quantifiers of
these processes. Furthermore, we find that in completely random media, the
invasion percolation clusters are on average slightly less isotropic than
standard percolation clusters. Introducing isotropic long-range correlations
into the media reduces the isotropy of the invasion percolation clusters. The
effect is more pronounced for the case of persisting long-range correlations.
The implication of boundary conditions on the shape of clusters is another
subject of interest. Compared to the case of free boundary conditions, IP
clusters of conventional rectangular geometry turn out to be more isotropic.
Moreover, we see that in conventional rectangular geometry the NTIP clusters
are more isotropic than TIP clusters
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