Universal Journal of Mechanical Engineering Vol. 6(4), pp. 76 - 95
DOI: 10.13189/ujme.2018.060403
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Expansion of Wave Rays and Fronts in Media with Inhomogeneous Structure


Anatoli Chigarev 1,*, Ju. Chigarev 2
1 Department Theoretical Mechanics and Mechatronics, Belarusian National Technical University, Belarus
2 West Pomeranian University of Technology, Szczecin, Poland

ABSTRACT

In the article on the principles of Fermet, Huygens obtaine the differential equations in the form of Hamilton, which describe the ray trajectories and wave fronts in inhomogeneous media. Established that the vector of Poynting-Umov's determining the direction of energy propagation in inhomogeneous medium is coincident with the vector tangent to the ray. In the second part of the article established that the equations of the theory of rays' propagation in inhomogeneous media have the form of equations of nonlinear dynamics and describe the emergence of deterministic chaos in the geometry of rays for a wide variety of types of heterogeneous structures. In this case, the rays behave randomly and their description you must go to the description based on the theory of random functions and fields. In the third part of the paper is considered a model which is equivalent to the random medium and the calculation of the coordinates of the ray (the mathematical expectation and correlation functions). Understanding of these characteristics gives information about the behavior of the trajectories of the rays for these models of media. The description of the behavior of rays on the basis of the equations of statistical mechanics is discussed in the article for functions of Markov's type.

KEYWORDS
Ray, Inhomogeneous Media, Deterministic Chaos, Correlation Function, Probabilistic, Energy, Stochastic

Cite this paper
Anatoli Chigarev , Ju. Chigarev . "Expansion of Wave Rays and Fronts in Media with Inhomogeneous Structure." Universal Journal of Mechanical Engineering 6.4 (2018) 76 - 95. doi: 10.13189/ujme.2018.060403.