14,059 research outputs found
Analysis of the geomagnetic activity of the D(st) index and self-affine fractals using wavelet transforms
The geomagnetic activity of the D(st) index is analyzed using wavelet transforms and it is shown that the D(st) index possesses properties associated with self-affine fractals. For example, the power spectral density obeys a power-law dependence on frequency, and therefore the D(st) index can be viewed as a self-affine fractal dynamic process. In fact, the behaviour of the D(st) index, with a Hurst exponent H≈0.5 (power-law exponent β≈2) at high frequency, is similar to that of Brownian motion. Therefore, the dynamical invariants of the D(st) index may be described by a potential Brownian motion model. Characterization of the geomagnetic activity has been studied by analysing the geomagnetic field using a wavelet covariance technique. The wavelet covariance exponent provides a direct effective measure of the strength of persistence of the D(st) index. One of the advantages of wavelet analysis is that many inherent problems encountered in Fourier transform methods, such as windowing and detrending, are not necessary
Possibility between earthquake and explosion seismogram differentiation by discrete stochastic non-Markov processes and local Hurst exponent analysis
The basic purpose of the paper is to draw the attention of researchers to new
possibilities of differentiation of similar signals having different nature.
One of examples of such kind of signals is presented by seismograms containing
recordings of earthquakes (EQ's) and technogenic explosions (TE's). We propose
here a discrete stochastic model for possible solution of a problem of strong
EQ's forecasting and differentiation of TE's from the weak EQ's. Theoretical
analysis is performed by two independent methods: with the use of statistical
theory of discrete non-Markov stochastic processes (Phys. Rev. E62,6178 (2000))
and the local Hurst exponent. Time recordings of seismic signals of the first
four dynamic orthogonal collective variables, six various plane of phase
portrait of four dimensional phase space of orthogonal variables and the local
Hurst exponent have been calculated for the dynamic analysis of the earth
states. The approaches, permitting to obtain an algorithm of strong EQ's
forecasting and to differentiate TE's from weak EQ's, have been developed.Comment: REVTEX +12 ps and jpg figures. Accepted for publication in Phys. Rev.
E, December 200
The Harmonic Measure for critical Potts clusters
We present a technique, which we call "etching," which we use to study the
harmonic measure of Fortuin-Kasteleyn clusters in the Q-state Potts model for
Q=1-4. The harmonic measure is the probability distribution of random walkers
diffusing onto the perimeter of a cluster. We use etching to study regions of
clusters which are extremely unlikely to be hit by random walkers, having
hitting probabilities down to 10^(-4600). We find good agreement between the
theoretical predictions of Duplantier and our numerical results for the
generalized dimension D(q), including regions of small and negative q.Comment: 20 pages, 10 figure
Application of Fractal and Wavelets in Microcalcification Detection
Breast cancer has been recognized as one or the most frequent, malignant tumors in women, clustered microcalcifications in mammogram images has been widely recognized as an early sign of breast cancer. This work is devote to review the application of Fractal and Wavelets in microcalcifications detection
The effect of forcing on the spatial structure and spectra of chaotically advected passive scalars
The stationary distribution of passive tracers chaotically advected by a
two-dimensional large-scale flow is investigated. The tracer field is force by
resetting the value of the tracer in certain localised regions. This problem is
mathematically equivalent to advection in open flows and results in a fractal
tracer structure. The spectral exponent of the tracer field is different from
that for a passive tracer with the usual additive forcing (the so called
Batchelor spectrum) and is related to the fractal dimension of the set of
points that have never visited the forcing regions. We illustrate this
behaviour by considering a time-periodic flow whose effect is equivalent to a
simple two-dimensional area-preserving map. We also show that similar structure
in the tracer field is found when the flow is aperiodic in time.Comment: 7 pages, 9 figure
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