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Waves Seminar

October 29, 2020 - 10:30am

Speaker: Ornella Mattei

Abstract: Field patterns are a new type of wave propagating in one-dimensional linear media with moduli that vary both in space and time. Specifically, the geometry of these space-time materials is commensurate with the slope of the characteristic lines so that a disturbance does not generate a complicate cascade of subsequent disturbances, but rather concentrates on a periodic space-time pattern, that we call field pattern. Field patterns present spectacularly novel features. One of the most interesting ones is the appearance of a wave generated from an instantaneous source, whose amplitude, unlike a conventional wake, does not tend to zero away from the wave front. Furthermore, very interestingly, the band structure associated with these special space-time geometries is infinitely degenerate: associated with each point on the dispersion diagram is an infinite space of Bloch functions, a basis for which are generalized functions each concentrated on a field pattern.