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Crisis at the Origin of Deterministic Rogue Waves

Crisis at the Origin of Deterministic Rogue Waves. PPME, Universite de la Nouvelle Caledonie C. Metayer , A. Serres , J. Tredicce INLN, UMR 6618 UNS-CNRS France S. Barland , M. Giudici CEILAP - CITEDEF – Argentina A. Hnilo, M. Kovalski Univ. Politecn. Cataluna, Spain

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Crisis at the Origin of Deterministic Rogue Waves

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  1. Crisis at the Origin of Deterministic Rogue Waves PPME, Universite de la Nouvelle Caledonie C. Metayer, A. Serres, J. Tredicce INLN, UMR 6618 UNS-CNRS France S. Barland, M. Giudici CEILAP - CITEDEF – Argentina A. Hnilo, M. Kovalski Univ. Politecn. Cataluna, Spain Masoller, C. Univ. Fed Pernambuco, Recife, PE Brazil W. Barbosa, F. MenezesD’Aguiar, J. Rios Leite, Rosero E.

  2. Are rogue waves just tales of fishermen into an Irish Pub?

  3. Or are rogue waves a common feature of a complex dynamical systems? • This fact is in contradiction with the Gaussian models used to describe fluctuations of the wave height in the sea*. * M. S. Longuet-Higgins, Phil. Trans. Roy. Soc. A 249 321 (1957). S. Aberg and G. Lindgren, Height distribution of stochastic Lagrange ocean waves, Prob. Eng. Mech. 23, 359 (2008) HOWEVER……

  4. Ferry rescue after freak wave in Irish Sea

  5. The freighter Riverdance was hit by a giant wave during severe gales in the Irish Sea…..

  6. But….What is the definition of a rogue wave? • Old Recipe: Take the 1/3 biggest amplitude waves; calculate their average value; multiply by 2….whatever amplitude exceeds such value is a rogue wave!!! • Or another Recipe: Take the probability distribution; calculate s ; multiply by 4; whatever….; and if you want a BIG BIG rogue wave…multiply by 8

  7. In the WEB:It isprobablysufficient to saythatanywaveso large thatitisunexpectedbased on current conditions canbecounted as a rogue. There are very few photographs of rogue waves. For centuries, the best evidence for their existence wasanecdotal -- the countless stories told by sailorswhohadsurvived one.

  8. How was that “Opticians” got interested on Rogue Waves? • A “NONLINEAR OPTICS PHYSICIST” WENT TO THE IRISH PUB….and then some papers appear in Nature or other “GO..O..D” Journals D. R. Solli, C. Ropers et al, Optical rogue waves, Nature 450 1054 (2007). B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev and J. M. Dudley, The Peregrine soliton in nonlinear fibre optics Nature Phys. 6, 790 (2010). A. Montina, U. Bortolozzo, S. Residori, F.T. Arecchi, Phys. Rev. Lett. 103, 173901 (2009)

  9. For us, the story begins with.. • “Critical slowing down at a bifurcation” JRT, Lippi ; Mandel; and B. Charasse ; A. Chevalier; B. Picque: American Journal of Physics Vol 72  Jun 2004 • Cited by a series of papers on Anticipating Critical Transitions Scheffer, M.et al. SCIENCE  338  (2012) Dakos,V. et al. PLOS ONE  7 (2012) Scheffer, M.; et al. NATURE  461 (2009)

  10. Our Experiments o, …. 1) Mode Locked Ti:Sa laser Hnilo et al. (Opt. Lett. November 2011) 2) Semiconductor Laser with Injected Signal Bonatto et al. (PRL, July 2011); Zamora-Munt et al. (PRA, March 2013). 3) Laser with saturable absorber Hnilo et al. (Journal of Optics, June 2013).

  11. Probability distribution of maxima

  12. OurAlreadyPublishedConclusions • 1) Extreme Events are rarebutthey can be much more probable than in Gaussianmodelswhenthedynamicalbehavioris “Deterministically” Chaotic • 2) Thereis “chaos” withoutroguewaves and chaos withroguewaves

  13. Somequestions: • How? What is the dynamical process the laser use to generate “extreme events”? • Can we predict deterministic extreme events in optical systems? • Can we control them?

  14. How? a) Intermittency …. P Gaspard and X Wang, PNAS 1988 Nicolis et al., Journal of Statistical physics 1995 b) By abrupt expansion of a chaoticattractor??

  15. Bifurcation Diagrams

  16. Experimental results

  17. Laser with Modulated parameter Rememberingveryold « times »: H.G. Solari J, E. Eschenazi, R. Gilmoreet al., Opt. Commun. 64, 49 (1987) on “Crisis of chaotic attractors” Two ingredients: 1) chaos 2) Enough low dissipation in order to have “generalized” multistability (several stable dynamical solutions for the same parameter values)

  18. Crisis of chaotic attractors

  19. Externalcrisis in a laser withmopdulatedparameter

  20. Then extreme events appear after an external crisis

  21. Predicting “Roguewaves”? In a deterministic system, the time of “prediction” equals the inverse of the maximum positive Lyapunov exponent But in the laser with injected signal, the prediction time is much larger, and just looking one variable: the intensity

  22. Conclusions • Externalcrisisproduce abrupt expansion of chaoticattractors and are at the origin of someextremeevents • Deterministicextremeeventscouldbepredictedwith « some » anticipation • I still do not know if we are able to control deterministicextremeevents BUT

  23. I am always looking for the rogue waves in New Caledonia

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