Some new advances in the theory of dynamic materials

In this paper, we present some recent advances in the theory of dynamic materials or spatio-temporal composites. We discuss the technique used to determine the set of invariant characteristics of material mixtures in one spatial dimension and time, in the context of electrodynamics of moving dielectrics, versus the relevant results in traditional electrostatics. Energy transformation in spatio-temporal laminates is discussed. We also present some results on dynamic materials with a rectangular microstructure. Some special features of dynamic materials demonstrated through material design are given as well. Among them, we mention the possibility to eliminate the cut-off frequency in the waveguides with activated dielectric filling.