Dynamic Materials in Electrodynamics of Moving Dielectrics

  • Konstantin A. Lurie
Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 15)


The theory of DM receives a tensor form in this chapter. An ideal embodiment for it is found to be the Maxwell-Minkowski electrodynamics of moving bodies. Among other things, it rigorously explains the classification of DM into activated and kinetic introduced before in Chapter  1 Also, the DM, as spatial-temporal entities, receive the sense of conceptually relativistic formations, though they certainly do not necessarily require relativistic material velocities. Laminates, this time activated and kinetic, are given further investigation, particularly, from the viewpoint of the energy transformation and performance.


  1. 1.
    Einstein, A.: Zur Elektrodynamik bewegter Körper. Ann. Phys. 17, 891 (1905)CrossRefzbMATHGoogle Scholar
  2. 2.
    Lamb, H.: On group velocity. Proc. Lond. Math. Soc. 1, 473–479 (1904)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Lurie, K.A.: The problem of effective parameters of a mixture of two isotropic dielectrics distributed in space-time and the conservation law for wave impedance in one-dimensional wave propagation. Proc. R. Soc. Lond. A 454, 1767–1779 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Lurie, K.A.: Bounds for the electromagnetic material properties of a spatio-temporal dielectric polycrystal with respect to one-dimensional wave propagation. Proc. R. Soc. Lond. A 456, 1547–1557 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Lurie, K.A., Weekes, S.L.: Effective and averaged energy densities in one-dimensional wave propagation through spatio-temporal dielectric laminates with negative effective values of ε and μ. In: Agarwal, R., O’Regan, D. (eds.) Nonlinear Analysis and Applications: to V. Lakshmikantham on his 80th Birthday, pp. 767–789. Kluwer, Boston (2004)Google Scholar
  6. 6.
    Minkowski, H.: Nachr. Ges. Wiss. Göttingen, S. 53 (1908); also: Raum und Zeit, Phys. Z., Bd. 10, S. 104 (1909)Google Scholar
  7. 7.
    Mandelstam, L.I.: Group velocity in crystalline arrays. Zh. Eksp. Teor. Fiz. 15, 475–478 (1945)Google Scholar
  8. 8.
    Mandelstam, L.I.: Complete Collected Works. Akad. Nauk SSSR, Moscow 2, 334 (1947)Google Scholar
  9. 9.
    Mandelstam, L.I.: Complete Collected Works. Akad. Nauk SSSR, Moscow 5, 419 (1950)Google Scholar
  10. 10.
    Nezlin, M.V.: Negative-energy waves and the anomalous Doppler effect. Sov. Phys. Usp. 19(11), 946–954 (1976)CrossRefGoogle Scholar
  11. 11.
    Rashevsky, P.K.: Riemannian Geometry and Tensor Analysis (in Russian). Nauka, Moscow (1967)Google Scholar
  12. 12.
    Sommerfeld, A.: Elektrodynamik. Geest & Portig, Leipzig (1964)zbMATHGoogle Scholar
  13. 13.
    Sturrock, P.A.: In what sense do slow wave carry negative energy? J. Appl. Phys. 31, 2052–2056 (1960)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Veselago, V.G.: The electrodynamics of substances with simultaneously negative values of eps and mu. Sov. Phys. Usp. 10, 509 (1968). Usp. Fiz. Nauk 92, 517–526 (1967)Google Scholar
  15. 15.
    Weekes, S.L.: A stable scheme for the numerical computation of long wave propagation in temporal laminates. J. Comput. Phys. 176, 345–362 (2002)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Konstantin A. Lurie
    • 1
  1. 1.Department of Mathematical SciencesWorcester Polytechnic InstituteWorcesterUSA

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