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Journal Electromagnetic Waves and Electronic Systems №5 for 2014 г.
Article in number:
On problem of electromagnetic waves propagation in fractals medium
Keywords: electromagnetic wave fractal set fractional integro-differentiation skin layer surface impedance
Authors:
A.A. Trenkin - Ph. D. (Phys.-Math.), Leading Research Scientist, State Corporation on Atomic Energy «Rosatom» Federal State Unitary Entity «Russian Federal Nuclear Center - All-Russian Scientific and Research Institute of Experimental Physics». E-mail: trenkin@ntc.vniief.ru
Abstract:
Diffusion-wave equation of fractional order and its particular solutions applicably to a problem of electromagnetic waves (EMW) propagation in fractal media is obtained based on analogues of Maxwell's equations with fractional time derivatives. Propagation of plane electromagnetic waves in fractal conductive medium is considered. This problem is interpreted as propagation of EMW in the fractal layered structure, representing one dimensional Cantor set. Generalized expression for the skin layer is obtained. It is shown that with increasing frequency electromagnetic wave decays slower than in a continuous medium. An expression for a surface impedance is obtained. The problem of propagation of electromagnetic waves in the fractal dielectric medium is considered; expressions for the skin layer and the surface impedance are obtained. Frequency shift of EMW is established during its propagation in a fractal medium: the value of the spectral shift increases with increasing distance from the source. It is shown that the medium has a positive dispersion, and the magnitude of the spectral shift is determined by the characteristics of the medium. The problem of identifying the electromagnetic earthquake precursors to develop appropriate methods and means of the earthquake-s forecast is noted as one of the possible practical applications of these results. Since in most cases the process of earthquake formation reveals the fractal nature of the dynamics of structural modification of geophysical medium, the latter, according to the results, should influence the specificity of electromagnetic wave propagation mode and their characteristics. Monitoring of amplitude-frequency characteristics of EMW in seismic regions allow obtaining information about the current structural state of the geophysical medium and develop forecast about its evolution.
Pages: 71-76
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