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Rare events, freak waves, and branching

- Porteur : Kuhl Ulrich

- Collaborateurs LPMC : Legrand Olivier, Mortessagne Fabrice

- Collaborateurs extérieurs : Stöckmann H.-J. (AG Quantenchaos, Marburg, Germany), Kaplan L. (Quantum chaos group, Tulane University, New Orleans, USA), Heller E. (Harvard University, Cambridge, USA), Fleischmann R. and Geisel T. (Max Planck Institute in Göttingen, Germany)

- Description :

Waves propagating through an inhomogeneous medium produce patterns irregular in space and time. Assuming a random superposition of plane waves, already a century ago Lord Rayleigh predicted an exponential probability distribution for the intensity of the waves P(I), where I is proportional to the square of the height. However, Rayleigh’s law considerably underestimates the probability for extraordinarily high waves in the sea. Reliable knowledge of the probability of these freak events is clearly of uttermost practical importance. The common explanation is based on non-linearity, but images of the electron flow through a point contact, which exhibited an intricate branched structure, suggested that deviations from a random behavior might already be present and significant in the linear regime. To explain their findings the authors assumed the formation of caustics in potentials due to charged impurities. We want to investigate this problem not using water waves but micro- and acoustic waves. In running microwave experiments we were able to observe freak events. The transmission is measured between a fixed antenna mounted in the bottom plate close to the boundary at the center of one of the short sided and a movable antenna in the top plate which can be positioned arbitrarily in the scattering setup. We studied both the stationary wave fields and the transient transport of microwaves through an arrangement of randomly distributed scatterers. For the very high intensities, the probability exceeds by several orders of magnitude the expectation from multiple scattering theory, caused by spatially localized “hot spots” showing up erratically in small frequency windows [1]. Recently we observed branching patterns while using weaker scattering [2], which corresponds more to the situation found in the ocean and in the electron flow in two dimensions.

[1] R. Höhmann, U. Kuhl, H.-J. Stöckmann, L. Kaplan, and E. J. Heller. “Freak waves in the linear regime : A microwave study.” Phys. Rev. Lett. 104, 093901, 2010.
[2] S. Barkhofen, J. J. Metzger, R. Fleischmann, U. Kuhl, and H.-J. Stöckmann. “Experimental observation of a fundamental length scale of waves in random media.” Phys. Rev. Lett. 111, 164102, 2013.

PNG - 238.9 ko


MOSAIQ, Physique Mésoscopique