7,059 research outputs found
Spectrum of Fractal Interpolation Functions
In this paper we compute the Fourier spectrum of the Fractal Interpolation
Functions FIFs as introduced by Michael Barnsley. We show that there is an
analytical way to compute them. In this paper we attempt to solve the inverse
problem of FIF by using the spectru
Weakly Self Affine Functions and Applications in Signal Processing
International audienceWe study a class of functions, called weakly self afire functions, which are a generalization of Fractal Interpolation Functions where the concentrate ratios are allowed to envolve in scale. We show how to compute the milifractal spectrum of such functions, and mention an application to the multifractal segmentation of signals
Synthetic Turbulence, Fractal Interpolation and Large-Eddy Simulation
Fractal Interpolation has been proposed in the literature as an efficient way
to construct closure models for the numerical solution of coarse-grained
Navier-Stokes equations. It is based on synthetically generating a
scale-invariant subgrid-scale field and analytically evaluating its effects on
large resolved scales. In this paper, we propose an extension of previous work
by developing a multiaffine fractal interpolation scheme and demonstrate that
it preserves not only the fractal dimension but also the higher-order structure
functions and the non-Gaussian probability density function of the velocity
increments. Extensive a-priori analyses of atmospheric boundary layer
measurements further reveal that this Multiaffine closure model has the
potential for satisfactory performance in large-eddy simulations. The
pertinence of this newly proposed methodology in the case of passive scalars is
also discussed
Energy Dissipation in Fractal-Forced Flow
The rate of energy dissipation in solutions of the body-forced 3-d
incompressible Navier-Stokes equations is rigorously estimated with a focus on
its dependence on the nature of the driving force. For square integrable body
forces the high Reynolds number (low viscosity) upper bound on the dissipation
is independent of the viscosity, consistent with the existence of a
conventional turbulent energy cascade. On the other hand when the body force is
not square integrable, i.e., when the Fourier spectrum of the force decays
sufficiently slowly at high wavenumbers, there is significant direct driving at
a broad range of spatial scales. Then the upper limit for the dissipation rate
may diverge at high Reynolds numbers, consistent with recent experimental and
computational studies of "fractal-forced'' turbulence.Comment: 14 page
Anomalous diffusion in the dynamics of complex processes
Anomalous diffusion, process in which the mean-squared displacement of system
states is a non-linear function of time, is usually identified in real
stochastic processes by comparing experimental and theoretical displacements at
relatively small time intervals. This paper proposes an interpolation
expression for the identification of anomalous diffusion in complex signals for
the cases when the dynamics of the system under study reaches a steady state
(large time intervals). This interpolation expression uses the chaotic
difference moment (transient structural function) of the second order as an
average characteristic of displacements. A general procedure for identifying
anomalous diffusion and calculating its parameters in real stochastic signals,
which includes the removal of the regular (low-frequency) components from the
source signal and the fitting of the chaotic part of the experimental
difference moment of the second order to the interpolation expression, is
presented. The procedure was applied to the analysis of the dynamics of
magnetoencephalograms, blinking fluorescence of quantum dots, and X-ray
emission from accreting objects. For all three applications, the interpolation
was able to adequately describe the chaotic part of the experimental difference
moment, which implies that anomalous diffusion manifests itself in these
natural signals. The results of this study make it possible to broaden the
range of complex natural processes in which anomalous diffusion can be
identified. The relation between the interpolation expression and a diffusion
model, which is derived in the paper, allows one to simulate the chaotic
processes in the open complex systems with anomalous diffusion.Comment: 47 pages, 15 figures; Submitted to Physical Review
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