Title: Homogenization of space-time composites.

Abstract:

Space-time composites are composite materials whose microstructure exists not
only in space but also in time. This novel notion was relatively recently put
forward by Konstantine Lurie with a series of papers where he examined the
propagation of electromagnetic waves through such a media.

The mathematical difference between stationary and space-time composites is
that the former is described by the elliptic system with rapidly varying
coefficients, while the later - by the hyperbolic system of Maxwell's
equations. In this talk we examine the homogenization theorem for Maxwell's
system formulated by the formal similarity between the elliptic and hyperbolic
systems.

The present work done with my graduate student Hansun To attempts to justify
the homogenization procedure for Maxwell's equations.  We succeed in the case
of a uniformly moving media. In the case of genuine space-time structures we
encounter new difficulties not present in the elliptic case.  For the
uniformly moving media we apply Milton's W-transformation to automate the
computation of the effective behavior of a moving laminate.