Abstract

Wave formation and propagation in complex media involves extreme phenomena such as branching and rogue-type waves as well as partial synchronization in the form of chimeras. We present results from disordered media where singular wave events may appear. We first address wave propagation in optical metamaterial-type units with disorder and strong scattering. We show that theory and experiments agree that coalescing waves due to strong disorder lead to singular waves. The experimental work is on silica layers where the intensity of the impinging laser light is used to tune from the linear to the nonlinear regimes [1]. The second, mathematically related problem, involves electric current patterns in doped graphene and the onset of branching. We find theoretically and also numerically a scaling relationship that connects statistically the location of where the first branches occur to the disordered properties of the medium [2]. We show further that the patterns of the occurrence of branches in graphene may be detected through machine learning. Specifically we use recurrent neural networks and show that after initial training and while using partial information on the electron flow, the network is able to predict quite accurately the location and properties of the branches. We propose that machine learning may be used for experimental data reconstruction in graphene and related problems [3]. Finally, we switch to a medium made of SQUIDS that form a nonlinear superconducting metamaterial [4]. In this system a wave pattern with stable yet partially coherent features termed “chimeras” has been predicted to form; we describe their basic properties and address the issue of chimera predictability through machine learning algorithms [3].

[1] M. Mattheakis, I. J. Pitsios, G. P. Tsironis and S. Tzortzakis, Extreme events in complex linear and nonlinear photonic media, Chaos, Solitons and Fractals, 84, 73 (2016). [2] M. Mattheakis, G. P. Tsironis and E. Kaxiras, Emergence and dynamical properties of stochastic branching in electronic flows in disordered Dirac solids, arXiv:1801.08217v1. [3] G. Neofotistos et al, in preparation [4] N. Lazarides and G. P. Tsironis, Superconducting metamaterials, arXiv :1712.01323v1.