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

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

Abstract

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.

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© Springer International Publishing AG 2017

Authors and Affiliations

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

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