MetaMAT’s 3rd webinar S3 - 01.11.2022 - Presentation - Ornella Mattei скачать в хорошем качестве

MetaMAT’s 3rd webinar S3 - 01.11.2022 - Presentation - Ornella Mattei

Seminar 3rd S3, Tuesday 1st November 2022, 14:00 (London Time) Title: Time-modulated composites: some recent results on field-pattern materials Speaker: Ornella Mattei (Department of Mathematics, San Francisco State University, USA) Abstract: Field patterns are a new type of wave propagating in one-dimensional linear media with moduli that vary both in space and time [1, 2, 3]. 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, when the parameters of the material are suitably chosen, so that the condition of PT-symmetry is unbroken, the wavefront propagates maintaining the same amplitude. This is particularly remarkable if one observes that, due to the instantaneous time modulation, energy is not conserved but it increases exponentially in time. In this talk, we will explain how stable modes that do not blow up in time, even though the associated energy does, can be generated by suitably designing the spatial geometry of the composite, which must be related to the periodicity of the time modulation as well as the material properties. We will start from the classical results for the one-dimensional case, obtained in [1, 2, 3] in collaboration with Graeme W. Milton. Then, we will extend such design concepts to the two dimensional case and show the most recent results obtained in collaboration with Vincenzo Gulizzi. 1. O. Mattei and G. Milton (2017) Field patterns: A new type of wave with infinitely degenerate band structure. EPL (Europhysics Letters), 120(5) 2. O. Mattei and G. Milton (2017) Field patterns without blow up. New Journal of Physics, 19(9) 3. G. Milton and O. Mattei (2017) Field patterns: a new mathematical object. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473(2198) 4. O. Mattei, V. Gulizzi. On the effects of suitably designed space microstructures in the propagation of waves in time modulated composites, In preparation. Follow us on: www.meta-mat.org