G-CLOSURES OF MATERIAL SETS IN SPACE-TIME AND PERSPECTIVES OF DYNAMICCONTROL IN THE COEFFICIENTS OF LINEAR HYPERBOLIC-EQUATIONS

The paper is focused on the concept of material mixing in dynamics. Th is concept introduces the spatio-temporal composites, i.e. material mi crostructures assembled and maintained in space-time. The knowledge of the relevant sets of effective material parameters (G-closures) is cr ucial for the purpose of material optimization arising in dynamics of moving media, particularly acoustics and hydroacoustics, as well as in the high-frequency electronic engineering. The analysis is based on c ovariant description of the mixing problem in terms of relativistic eq uations acting in Minkowski space. The specific characterization of a. G-closure is given for a special, case of a dielectric composite in o ne-dimensional electromagnetic wave propagation. If such composite is assembled in space-time from two dielectrics with the same ratio epsil on/mu of permittivity epsilon to permeability mu and different otherwi se then the ratio epsilon(0)/mu(0) of the relevant effective parameter s will preserve the same value. This is a conservation law for the wav e impedance of the medium with respect to one-dimensional wave propaga tion.