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Mechanistic Model of Generalized Non-antisymmetrical Electrodynamics

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Dynamical Processes in Generalized Continua and Structures

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 103))

Abstract

In this work, the methods of continuum mechanics are transferred to the four-dimensional continuum, in which the normalized four-dimensional vector-potential of the electromagnetic field is playing the role of 4D-displacement. Classical electrodynamics is presented as a theory of elasticity of 4D-medium with anti-symmetric stress tensor, where Faraday equations are the equations of compatibility, and Ampere equations are the equations of equilibrium. It is shown, that for the considered continuum, the tensor of the fourth rank modules in defining ratios formally allows not only anti-symmetric structure. Uncertain symmetry of electromagnetic “stresses” allows to build a version of the non-anti-symmetric electrodynamics and to predict new effects of the interaction of electromagnetic field with spatially-isotropic material: dynamic, thermal and striction.

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References

  1. Maxwell, J.C.: On physical lines of force. Phil. Mag. 90, 11–23 (1861)

    Article  Google Scholar 

  2. Maxwell, J. C.: On Faraday’s lines of force. Trans. Camb. Philos. Soc. 10 Part I, 27–65 (1864)

    Google Scholar 

  3. Maxwell, J.C.: A dynamical theory of the electromagnetic field. Philos. Trans. R. Soc. Lond. 155, 459–512 (1865)

    Article  Google Scholar 

  4. Eringen, A.C.: A unified continuum theory of electrodynamics of liquid a unified continuum theory of electrodynamics of liquid crystals. Int. J. Eng. Sc. 35(12/13), 1137–1157 (1997)

    Article  MathSciNet  Google Scholar 

  5. Maugin, G.A.: Further comments on the equivalence of Abraham’s, Minkowski’s, and others’ electrodynamics. Can. J. Phys. 58, 1163–1170 (1980)

    Article  MathSciNet  Google Scholar 

  6. Eringen, A.C., Maugin, G.A.: Electrodynamics of continua, 2. Springer, NY (1990)

    Google Scholar 

  7. Maugin G.A.: On the universality of the thermomechanics of forces driving singular sets. Arch. Appl. Mech.70 31–45, Springer (2000)

    Google Scholar 

  8. Fomethe, A., Maugin, G.A.: Material forces in thermoelastic ferromagnets. Continuum Mech. Thermodyn. 8, 275–292 (1996)

    Article  MathSciNet  Google Scholar 

  9. Epstein, M., Maugin, G. A.: Thermoelastic material forces: definition and geometric aspects. C.R. Acad. Sci. Paris II-320, 63–68 (1995)

    Google Scholar 

  10. Hernandezjr, W.: Elasticity theory in general Phys. Rev.v. 1(415), 1013–1018 (1970) (Google Scholar)

    Google Scholar 

  11. Lurie, S. A., Belov, P.A.: Mathematical models of continuum mechanics and physical fields, Izd-vo VTs, Moscow, (2000) [in Russian] (Google Scholar)

    Google Scholar 

  12. Lurie, S. A., Belov, P.A.: A variational model for nonholonomic media. Mekh. Komp. Mater. Konstr. 7(2), 266–276 (2001) [J. Comp. Mech. Design (Engl. Transl.)] (Google Scholar)

    Google Scholar 

  13. Belov, P.A., Gorshkov, A.G., Lurie, S.A.: Variational model of nonholonomic 4d-media. Mech. Solids 41(6), 22–35 (2006)

    Google Scholar 

  14. Belov, P.A., Lurie, S.A.: Models of deformation of solids and their analogs in field theory. Mech. Solids 43(3), 128–136 (1998) (Google Scholar)

    Google Scholar 

  15. Belov, P.A., Lurie, S.A.: Ideal nonsymmetric 4d-medium as a model of invertible dynamic thermoelasticity. Mech. Solids 47(5), 580–590 (2012)

    Article  Google Scholar 

  16. Belov, P.A., Lurie, S.A.: Theory of 4D-media with stationary dislocations. Mech. Solids 43(4), 545–557 (2008)

    Google Scholar 

  17. Lurie, S.A., Belov, P.A.: Theory of space-time dissipative elasticity and scale effects. Nanoscale Syst. Math. Model. Theory Appl. 2, 66–178 (2013)

    MATH  Google Scholar 

  18. Gusev, A., Lurie, S.: Theory of spacetime. Elast. Int. J. Mod. Phys. 26(05), 50032 (2012)

    MathSciNet  Google Scholar 

  19. Gusev, A., Lurie, S.: Wave-relaxation duality of heat propagation in fermi-pasta-ulam chains. Mod. Phys. Lett. B 26(22), 1250145 (2013)

    Article  Google Scholar 

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Acknowledgements

The authors are deeply grateful to Professor Dmitriy Indeitsev for professional criticism and extremely useful discussions of our research.

This work was partially supported by the grants RFBR 18-29-10085-mk, 18-01-00553-a, RFBR 18-08-00643-a, MK-1336.2017.8 and funding of IAM RAS program.

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Authors and Affiliations

  1. Institute of Applied Mechanics of Russian Academy of Science, Moscow, Russia

    S. A. Lurie & P. A. Belov

  2. Dorodnicyn Computing Centre of FRC CSC RAS, Moscow, Russia

    S. A. Lurie

  3. Moscow Aviation Institute, Moscow, Russia

    S. A. Lurie & Y. O. Solyaev

Authors
  1. S. A. Lurie
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  2. P. A. Belov
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  3. Y. O. Solyaev
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Corresponding author

Correspondence to S. A. Lurie .

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Editors and Affiliations

  1. Lehrstuhl Technische Mechanik, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Sachsen-Anhalt, Germany

    Holm Altenbach

  2. Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia

    Alexander Belyaev

  3. Faculty of Civil and Environmental Engineering, Gdańsk University of Technology, Gdańsk, Poland

    Victor A. Eremeyev

  4. Department of Theoretical Mechanics, Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia

    Anton Krivtsov

  5. Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia

    Alexey V. Porubov

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Lurie, S.A., Belov, P.A., Solyaev, Y.O. (2019). Mechanistic Model of Generalized Non-antisymmetrical Electrodynamics. In: Altenbach, H., Belyaev, A., Eremeyev, V., Krivtsov, A., Porubov, A. (eds) Dynamical Processes in Generalized Continua and Structures. Advanced Structured Materials, vol 103. Springer, Cham. https://doi.org/10.1007/978-3-030-11665-1_21

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  • DOI: https://doi.org/10.1007/978-3-030-11665-1_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-11664-4

  • Online ISBN: 978-3-030-11665-1

  • eBook Packages: EngineeringEngineering (R0)

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