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Proceedings Paper

Possible background of fractal models
Author(s): Victor Ol'khov
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Paper Abstract

We present a simple statistical model that has no fractal nature, but certain set of measurements of such model might lead to the conclusion, that it is a fratal. We regard plain model and show how usual fractal dimension D of measured trajectory might take any value 1<EQD<EQ2. We regard the system which statistical behavior is described by a set of Hamiltonians (by two Hamiltonians in the simplest case). Similar multi-Hamiltonian models are known, for example. If one uses the simplest assumption on probability P of realization for different Hamiltonians, for example PequalsN-(alpha ) where N is a number of measurements during fixed time interval T, then it can be shown, that the measured trajectory might be treated as a fractal with dimensions Dequals2-(alpha ), 0<EQ(alpha) <EQ1 Dequals1, (alpha) >1. Such results permit us to suggest multi-Hamiltonians models to describe the effects of random media (rain, clouds and turbulence) in the Wave Propagation problems.

Paper Details

Date Published: 29 June 1994
PDF: 11 pages
Proc. SPIE 2222, Atmospheric Propagation and Remote Sensing III, (29 June 1994); doi: 10.1117/12.177964
Show Author Affiliations
Victor Ol'khov, P.N. Lebedev Physical Institute (Russia)


Published in SPIE Proceedings Vol. 2222:
Atmospheric Propagation and Remote Sensing III
Walter A. Flood; Walter B. Miller, Editor(s)

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