The regular and chaotic dynamics of structures in fluid flows

Rabinovich, M. I.; Sushchik, M. M.

doi:10.3367/ufnr.0160.199001a.0003

Cited by 42 publications

(19 citation statements)

References 97 publications

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“…The structural function of amplitude fluctuations of the received signal for a small time delay τ can be described by the well-known relationship [8]:…”

Section: Multifractal Analysis Of the Received Signalsmentioning

confidence: 99%

“…whereN = r 3−D N is the measure of space occupied by small-scale electron-density irregularities, D N is the fractal dimension of this space [8], and ϕ 2 = p 3 − D N . The small-scale ionospheric turbulence spectrum corresponding to structural function (10) will have the form (cf.…”

Section: Local Structure Of the Isotropic Small-scale Ionospheric Turmentioning

confidence: 99%

“…where T is the time interval of a signal-amplitude record, ϕ A (q) is the scaling index for the approximation of the experimentally measured structural function of the qth-order amplitude fluctuations, and D A (α q ) is the fractal dimension of amplitude fluctuations of the received signals, which is determined on the set q of structural functions from the obvious parametric dependence [8] …”

Section: Multifractal Analysis Of the Received Signalsmentioning

confidence: 99%

“…Correspondingly, for the global (averaged over the entire temporal interval T of the signal amplitude record) structural function of amplitude fluctuations, we have (see [1,8])…”

Section: Local Structure Of the Isotropic Small-scale Ionospheric Turmentioning

confidence: 99%

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On fractal properties of small-scale ionospheric irregularities

Alimov

Vybornov

Rakhlin

2007

Radiophys Quantum Electron

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UDC 621.371We consider the problem of relating the local structure of small-scale ionospheric turbulence to the measured frequency-spectrum indices and fractal dimensions of amplitude records of the signals received on the Earth during remote sensing of the ionosphere onboard the satellites. It is shown that knowledge of these parameters permits one to determine the true values of the local-spectrum indices of the electron-density fluctuations for isotropic small-scale turbulence of the ionosphere both under natural conditions and during its modification by high-power short-wave radiation as well as to specify fractal dimensions of space filled by small-scale irregularities of the turbulent structures in the ionosphere. We show the necessity of detailed experimental studies of the fractal properties of small-scale ionospheric irregularities of both natural and artificial origin by using a multifractal analysis in combination with the synchronous correlation processing of received signals during remote sensing of the ionosphere. This will give important information on the local structure of small-scale ionospheric turbulence inaccessible for studies within the framework of the classical method of radio scintillation.

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“…The structural function of amplitude fluctuations of the received signal for a small time delay τ can be described by the well-known relationship [8]:…”

Section: Multifractal Analysis Of the Received Signalsmentioning

confidence: 99%

Section: Local Structure Of the Isotropic Small-scale Ionospheric Turmentioning

confidence: 99%

Section: Multifractal Analysis Of the Received Signalsmentioning

confidence: 99%

“…Correspondingly, for the global (averaged over the entire temporal interval T of the signal amplitude record) structural function of amplitude fluctuations, we have (see [1,8])…”

Section: Local Structure Of the Isotropic Small-scale Ionospheric Turmentioning

confidence: 99%

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On fractal properties of small-scale ionospheric irregularities

Alimov

Vybornov

Rakhlin

2007

Radiophys Quantum Electron

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“…Different aspects of intermittency (and, first of all, the pronounced spatial inhomogeneity of turbulence) are manifested in a multifractal analysis of the fluctuation structure of the wave processes in a turbulent medium. The multifractal structure of intermittency, which is inherent in developed hydrodynamic turbulence, has intensely been studied in a number of papers (see, e.g., [5,6] and references cited therein). However, the multifractal structure of the intermittency of turbulent electron-density fluctuations in the ionospheric plasma has not been studied so far.…”

Section: Introductionmentioning

confidence: 99%

On the fractal structure of small-scale traveling ionospheric disturbances

Alimov

Vybornov

Rakhlin

2008

Radiophys Quantum El

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We present the results of the studies of fractal properties of the small-scale inhomogeneities of traveling ionospheric disturbances in special experiments on radio-raying of the midlatitude ionosphere by signals from orbital satellites in [2004][2005][2006]. Along with the conventional correlation processing of the received signals, we performed their multifractal analysis, as well as fractal processing of signals by the correlation-integral method. Important information on fractal properties of the small-scale turbulence for the least studied part of the upper-ionosphere inhomogeneity spectrum in the interval of characteristic scales l ≈ 1−10 km is obtained. In particular, it is noted that the fractal structure of these inhomogeneities can be originated from the nonlinear "destruction" of several large-scale sinusoidal structures in a quasistable traveling disturbance. It is also noted that the multifractal spectra of amplitude fluctuations of the received signals obtained in the experiments in different years, in different time of the day, and in different seasons of the observations are quite similar. This is evidence that intermittency is a universal property of the plasma turbulence, at least for the midlatitude upper ionosphere.

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Formation of new types of inhomogeneous spatial structures in the chemical reaction in imperfect systems

Krasilnikov

Савотченко

2004

Int J of Quantum Chemistry

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ABSTRACT:Taking the system imperfection and the inhomogeneity of the diffusion processes into account derives the extension of a simple chemical reaction model proposed by Schlogl. The Fick equation modification makes the breakdown of the ideality of diffusion. It leads to high-order spatial derivatives of a concentration in an evolution equation. The system imperfection is also taken into account by the excess Gibbs function of a regular solution. It leads to modification of the chemical potential as well as to the dependence of a diffusion coefficient on a reagent concentration. The formation of the spatial inhomogeneous structures being stable during the chemical reaction under definite conditions is due to the breakdown of an ideal system. Certain spatial inhomogeneous structures can exist only in the imperfection system and do not appear in an ideal system. Three new types of spatial inhomogeneous structures appear: periodic, quasi-periodic, and nonperiodic structures. The functions characterizing concentration contain two terms. Note that in the ideal systems, the quasi-periodic and nonperiodic structures cannot exist. This means that such a new spatial structure formation is due to the system imperfection. The parameters characterizing the system imperfection represent the coefficients at nonlinear terms and a high-order spatial derivative in the evolution equation. This permits consideration of a system deviation from the ideal as a significantly nonlinear phenomenon. The conditions of spatial structure stability are determined mainly by parameters that describe the system imperfection.

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The regular and chaotic dynamics of structures in fluid flows

Cited by 42 publications

References 97 publications

On fractal properties of small-scale ionospheric irregularities

On fractal properties of small-scale ionospheric irregularities

On the fractal structure of small-scale traveling ionospheric disturbances

Formation of new types of inhomogeneous spatial structures in the chemical reaction in imperfect systems

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