1,918 research outputs found
A nonextensive entropy approach to solar wind intermittency
The probability distributions (PDFs) of the differences of any physical
variable in the intermittent, turbulent interplanetary medium are scale
dependent. Strong non-Gaussianity of solar wind fluctuations applies for short
time-lag spacecraft observations, corresponding to small-scale spatial
separations, whereas for large scales the differences turn into a Gaussian
normal distribution. These characteristics were hitherto described in the
context of the log-normal, the Castaing distribution or the shell model. On the
other hand, a possible explanation for nonlocality in turbulence is offered
within the context of nonextensive entropy generalization by a recently
introduced bi-kappa distribution, generating through a convolution of a
negative-kappa core and positive-kappa halo pronounced non-Gaussian structures.
The PDFs of solar wind scalar field differences are computed from WIND and ACE
data for different time lags and compared with the characteristics of the
theoretical bi-kappa functional, well representing the overall scale dependence
of the spatial solar wind intermittency. The observed PDF characteristics for
increased spatial scales are manifest in the theoretical distribution
functional by enhancing the only tuning parameter , measuring the
degree of nonextensivity where the large-scale Gaussian is approached for
. The nonextensive approach assures for experimental studies
of solar wind intermittency independence from influence of a priori model
assumptions. It is argued that the intermittency of the turbulent fluctuations
should be related physically to the nonextensive character of the
interplanetary medium counting for nonlocal interactions via the entropy
generalization.Comment: 17 pages, 7 figures, accepted for publication in Astrophys.
Intermittency of Superpositions of Ornstein-Uhlenbeck Type Processes
The phenomenon of intermittency has been widely discussed in physics
literature. This paper provides a model of intermittency based on L\'evy driven
Ornstein-Uhlenbeck (OU) type processes. Discrete superpositions of these
processes can be constructed to incorporate non-Gaussian marginal distributions
and long or short range dependence. While the partial sums of finite
superpositions of OU type processes obey the central limit theorem, we show
that the partial sums of a large class of infinite long range dependent
superpositions are intermittent. We discuss the property of intermittency and
behavior of the cumulants for the superpositions of OU type processes
Non stationary multifractality in stock returns
We perform an extensive empirical analysis of scaling properties of equity
returns, suggesting that financial data show time varying multifractal
properties. This is obtained by comparing empirical observations of the
weighted generalised Hurst exponent (wGHE) with time series simulated via
Multifractal Random Walk (MRW) by Bacry \textit{et al.} [\textit{E.Bacry,
J.Delour and J.Muzy, Phys.Rev.E \,{\bf 64} 026103, 2001}]. While dynamical wGHE
computed on synthetic MRW series is consistent with a scenario where
multifractality is constant over time, fluctuations in the dynamical wGHE
observed in empirical data are not in agreement with a MRW with constant
intermittency parameter. We test these hypotheses of constant multifractality
considering different specifications of MRW model with fatter tails: in all
cases considered, although the thickness of the tails accounts for most of
anomalous fluctuations of multifractality, still cannot fully explain the
observed fluctuations.Comment: 27 pages, 10 figure
Assessing Relative Volatility/Intermittency/Energy Dissipation
We introduce the notion of relative volatility/intermittency and demonstrate
how relative volatility statistics can be used to estimate consistently the
temporal variation of volatility/intermittency when the data of interest are
generated by a non-semimartingale, or a Brownian semistationary process in
particular. This estimation method is motivated by the assessment of relative
energy dissipation in empirical data of turbulence, but it is also applicable
in other areas. We develop a probabilistic asymptotic theory for realised
relative power variations of Brownian semistationary processes, and introduce
inference methods based on the theory. We also discuss how to extend the
asymptotic theory to other classes of processes exhibiting stochastic
volatility/intermittency. As an empirical application, we study relative energy
dissipation in data of atmospheric turbulence.Comment: 25 pages, 4 figures, v3: major revision, this version contains an
application to electricity prices that was omitted from the published versio
Analysis of chaotic motion and its shape dependence in a generalized piecewise linear map
We analyse the chaotic motion and its shape dependence in a piecewise linear
map using Fujisaka's characteristic function method. The map is a
generalization of the one introduced by R. Artuso. Exact expressions for
diffusion coefficient are obtained giving previously obtained results as
special cases. Fluctuation spectrum relating to probability density function is
obtained in a parametric form. We also give limiting forms of the above
quantities. Dependence of diffusion coefficient and probability density
function on the shape of the map is examined.Comment: 4 pages,4 figure
About coherent structures in random shell models for passive scalar advection
A study of anomalous scaling in models of passive scalar advection in terms
of singular coherent structures is proposed. The stochastic dynamical system
considered is a shell model reformulation of Kraichnan model. We extend the
method introduced in \cite{DDG99} to the calculation of self-similar instantons
and we show how such objects, being the most singular events, are appropriate
to capture asymptotic scaling properties of the scalar field. Preliminary
results concerning the statistical weight of fluctuations around these optimal
configurations are also presented.Comment: 4 pages, 2 postscript figures, submitted to PR
Conditional Lagrangian acceleration statistics in turbulent flows with Gaussian distributed velocities
The random intensity of noise approach to one-dimensional
Laval-Dubrulle-Nazarenko type model having deductive support from the
three-dimensional Navier-Stokes equation is used to describe Lagrangian
acceleration statistics of a fluid particle in developed turbulent flows.
Intensity of additive noise and cross correlation between multiplicative and
additive noises entering a nonlinear Langevin equation are assumed to depend on
random velocity fluctuations in an exponential way. We use exact analytic
result for the acceleration probability density function obtained as a
stationary solution of the associated Fokker-Planck equation. We give a
complete quantitative description of the available experimental data on
conditional and unconditional acceleration statistics within the framework of a
single model with a single set of fit parameters. The acceleration distribution
and variance conditioned on Lagrangian velocity fluctuations, and the marginal
distribution calculated by using independent Gaussian velocity statistics are
found to be in a good agreement with the recent high-Reynolds-number Lagrangian
experimental data. The fitted conditional mean acceleration is very small, that
is in agreement with DNS, and increases for higher velocities but it departs
from the experimental data, which exhibit anisotropy of the studied flow.Comment: RevTeX4, twocolumn, 9 pages, 7 figures; revised version, to appear in
Phys. Rev.
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