29 June 1994 Possible background of fractal models
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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.
© (1994) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Victor Ol'khov, "Possible background of fractal models", Proc. SPIE 2222, Atmospheric Propagation and Remote Sensing III, (29 June 1994); doi: 10.1117/12.177964; https://doi.org/10.1117/12.177964
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