G-Closures of a Set of Isotropic Dielectrics with Respect to One-Dimensional Wave Propagation

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


This chapter is about G-closures (i.e., the sets of invariant properties) of the regular mixtures of two isotropic dielectrics distributed in 1D + time. It begins with the conservation law of the wave impedance through one-dimensional wave propagation along a DM-polycrystal. This is a kinetic laminate assembled in 1D + time of fragments of the same dielectric brought into a relative longitudinal motion. This conservation law is then extended to any regular assembly of two arbitrary (activated or kinetic) dielectrics in 1D + time. G-closure of any number of such dielectrics can be characterized on the basis of this law. Some special features of dynamic G-closures are discussed through the comparison with similar results known in the static conditions.


  1. 1.
    Dykhne, A.M.: Conductivity of a two-dimensional two-phase systems. Sov. Phys. JETP 32, 63–65 (1971)Google Scholar
  2. 2.
    Lurie, K.A.: A stable spatio-temporal G-closure and G m-closure of a set of isotropic dielectrics with respect to one-dimensional wave propagation. Wave Motion 40, 95–110 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Lurie, K.A., Cherkaev, A.V.: Exact estimates of conductivity of composites formed by two isotropically conducting media taken in prescribed proportion. Proc. R. Soc. Edinburgh A 99(1–2), 71–87 (1984)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Lurie, K.A., Cherkaev, A.V.: G-closure of a set of anisotropically conducting media in the two-dimensional case. J. Optim. Theory Appl. 42, 283–304 (1984); Corrig. 53, 319 (1987)Google Scholar
  5. 5.
    Lurie, K.A., Fedorov, A.V., Cherkaev, A.V.: On the existence of solutions to some problems of optimal design for bars and plates. Ioffe Institute Technical Report 668, Leningrad, p. 43 (1980); also J. Optim. Theory Appl. 42, 247–282 (1984)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

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

Personalised recommendations