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Fractal Parametrization of the One-Dimensional Singular Physical Objects


O.V. Gorshkova, A.E. Chalykh, М.K. Gerasimov, V.V. Matveev

The analysis of the periodic, survey and monographic literature devoted to examination of structure of physical objects has shown, that exists enough a major class of objects which we have spotted as «stochastic one-dimensional objects in two-dimensional and three-dimensional spaces». They are characterised by the various physical nature - from metal whiskers to organic soaps, but have the similar structural organisation. In this connection there was a necessity of working out of a procedure of their fractal parametrization. On the developed procedure values of differential and integral fractal dimensionality for objects of the similar structural organisation, but the various nature have been discovered: carbon nanotubes, short moustaches of oxide of copper, a fibril of lithium soap, threadlike particles of dioxide of silicon and a cuprene particle. The interval of alteration of fractal dimensionalities for carbon nanotubes is the widest. It can be caused various requirements of deriving of nanotubes in a case with short moustaches of oxide of copper temperature effect in the gas cabinet of a microscope on geometrical perfor-mances of samples is observed. At heating linear objects gain more twisting structure that is accompanied by accretion of fractal dimensionality. For the fibrils gained from lubrications of lithium soap legitimacy of alteration of values of fractal dimensionality depending on cooling conditions is revealed. Values of fractal dimensionality for threadlike particles of dioxide of silicon and cuprene particles lay in similar intervals. The image processing of objects of the various nature, but similar on a geometrical arrangement, has allowed to reveal a generality of fractal performances. Besides, it was possible to instal dependences of values of fractal dimensionality, and it is investigatory also morphology, from requirements of deriving of systems. For clearing up of connection of fractal performances of the one-dimensional stochastic objects with an angle of conjugation of two elementary linear sites numerical modelling has been made.
June 24, 2020
May 29, 2020

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