LMA - Laboratoire de Mécanique et d’Acoustique

G. Milton - Field Patterns and a new sort of wave / Séminaire Fédération Fabri de Peiresc

Amphithéâtre François Canac, LMA

Le 12 septembre 2017 à 11h00

Graeme Milton
Distinguished Professor, Department of Mathematics / University of Utah

Field pattern materials are space-time composites with Parity-Time (P-T) symmetry in which the spatial distribution of the constituents changes in time in such a special manner to give rise to a new type of waves, which we call field pattern waves (FP—waves). Specifically, due to the special periodic space—time geometry of these materials, when an instantaneous disturbance propagates through the system, the branching of the characteristic lines at the space—time interfaces between phases does not lead to a chaotic cascade of disturbances but concentrates on an orderly pattern of disturbances : this is the field pattern. An instantaneous disturbance creates a wave with the novel property that the wake behind the wavefront does not decay away from the wavefront. By applying Bloch—Floquet theory we find that the dispersion diagrams associated with these field pattern materials are 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, paramaterized by a variable that we call the launch parameter. The dynamics separates into independent dynamics on the different field patterns, each with the same dispersion relation. (Ornella Mattei and Graeme Milton)

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