2023 108 P

Dispersion Relations for Space-Time Laminates

By: Paulina Svensson

Department: Mathematics

Faculty Advisor: Dr. Ornella Mattei

A standard spatial laminate is a one-dimensional element made of alternating segments of, say, two materials. A space-time laminate is a space laminate in which the property pattern moves at a speed c_m, called the modulation speed. Like any composite material, when a space laminate is impinged by time-harmonic waves, certain frequencies are filtered out, in the sense that a wave with a specific frequency may evanesce as it travels through the laminate. In such a case we say that that frequency belongs to a band gap; otherwise, it belongs to a passing band. The relation that provides the band gaps of a laminate is called the dispersion relation. For a spatial laminate, it was found that the density of the gaps exhibits universal features, independently of the specific laminate composition. Here we prove a similar argument for space-time laminates.