Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Nonlinear Rays and Fronts Dynamics in Stochastically Inhomogeneous Media and in Media with Deterministic Structure

  • Anatoly V. ChigarevEmail author
  • Yury V. Chigarev
Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_107-1

Synonyms

Definitions

The behavior of rays’ trajectories in stochastically inhomogeneous media is governed by nonlinear dynamic equations which describe the emergence of deterministic chaos in the geometry of rays and fronts for a wide variety of types of heterogeneous structures.

Preliminary Remarks

In the entry “Rays Propagation in Inhomogeneous Media”, it has been shown that the approach based on the construction of rays is effective for solving the problems of the wave kinematics by geometrical methods for inhomogeneous isotropic media, including the cases of transmission and reflection of waves at the interface of two media, through lens, etc. Below the peculiarities of rays and fronts propagation in the stochastically inhomogeneous media and media with deterministic structure will be discussed.

Rays’ Propagation in Stochastically Inhomogeneous Media

Models of randomly inhomogeneous media allow one to take into account the fact...

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References

  1. Abdullaev SS, Zaslavsky GM (1981) Nonlinear dynamics of rays in inhomogeneous media. J Exp Theor Phys 80(2):525–536MathSciNetGoogle Scholar
  2. Borisov AV, Burenin AA, Polenov VS, Chigarev AV (2015) A wave dynamics of inhomogeneous and nonlinear media with application to geomechanics and biomechanics. Universum, SmolenskGoogle Scholar
  3. Chigarev AV (2000) A stochastic and regular dynamics of inhomogeneous media. Technoprint, MinskGoogle Scholar
  4. Chigarev AV, Chigarev YV (1978) A possibility of a instability of rays in inhomogeneous media. Sov Phys Acoust 24(6):765–771Google Scholar
  5. Chigarev AV, Chigarev YV (2018) Expansion of wave rays and fronts in media with inhomogeneous structure. Univ J Mech Eng 6(4):76–95. https://doi.org/10.13189/ujme.2018.060403CrossRefGoogle Scholar
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  7. Van Kampen NG (1988) Stochastic processes in physics and chemistry. Amsterdam, North-HollandGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Theoretical and Material MechanicsBelarusian National Technical UniversityMinskBelarus
  2. 2.Department of Theoretical Mechanics and Theory of Mechanisms and MashinesBelarusian State Agrarian Technical UniversityMinskBelarus

Section editors and affiliations

  • Marina V. Shitikova
    • 1
  1. 1.Research Center on Dynamics of Solids and Structures, Voronezh State Technical UniversityVoronezhRussia