Appears in collection : Herglotz-Nevanlinna Functions and their Applications to Dispersive Systems and Composite Materials / Fonctions de Herglotz-Nevanlinna et leurs applications aux systèmes dispersifs et aux matériaux composites

In collaboration with Graeme W. Milton (University of Utah) and Mihai Putinar (University of California at Santa Barbara). In this talk, we will discuss bounds on the quasistatic response of lossy two-phase materials when subject to applied electromagnetic fields (or antiplane elastic fields), that can have any variation in time, not necessarily a fixed frequency one. Interestingly enough, appropriate choices of the applied field can directly provide the volume fractions of the phases from measurements at specific times and, for specially tailored boundary conditions, this occurs at any time. We also show how time varying boundary conditions, not oscillating at a single frequency, can be designed to exactly retrieve the response at a single frequency.