Crisis at the Origin of Deterministic Rogue Waves - PowerPoint PPT Presentation


Title: Crisis at the Origin of Deterministic Rogue Waves


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. Menezes DAguiar,
  • J. Rios Leite, Rosero E.

2
  • According to fishermen tales from a pub in
    Ireland, rogue waves like solid walls of water,
    higher than 30 meters, are more or less common
    phenomena in deep ocean waters.

3
Is it true? Are rogue waves so common?
  • 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!!!
  • More Recent Recipe Take the probability
    distribution calculate s multiply by 4
    whatever.
  • and if you want a BIG BIG rogue wavemultiply by
    8

7
  • In the WEBIt is probably sufficient to say that
    any wave so large that it is unexpected based on
    current conditions can be counted as a rogue.
  • There are very few photographs of rogue waves.
    For centuries, the best evidence for their
    existence was anecdotal -- the countless stories
    told by sailors who had survived one.

8
Some Bibliography about Rogue Waves
  • Osborne, A.R. et al. Phys. Lett. A 275, 386
    (2000) and PRL 96, 014503 (2006).
  • Clauss, G.F. Appl. Ocean Res. 24, 147 (2002)
    Dramas of the sea episodic waves and their
    impact on offshore structures.
  • Kharif, C. and Pelinovsky E. EJ of
    Mechan.B/Fluids 22, 603 (2003).
  • Petrova, P. and Guedes Soares C. Appl. Ocean
    Res. 30, 144 (2008).
  • Dyachenko, A. and Zakharov, V.E. JETP lett. 81,
    255 (2005).

9
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)

10
Our First Experiments.
  • 1) Mode Locked TiSa laser
  • Hnilo et al. (Opt. Lett. November 2011)
  • 2) Semiconductor Laser with Injected Signal
  • Bonatto et al. (PRL, July 2011)
  • 3) Laser with saturable absorber (Journal of
    Optics, submitted)

11
Laser with Injected Signal
12
Probability distribution of maxima
13
(No Transcript)
14
(No Transcript)
15
Our Already Published Conclusions
  • 1) Extreme Events are rare but they can be much
    more probable than in Gaussian models when the
    dynamical behavior is Deterministically
    Chaotic
  • 2) There is chaos without rogue waves and chaos
    with rogue waves

16
Some questions
  • 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?

17
How?
  • a) Intermittency .
  • P Gaspard and X Wang, PNAS 1988
  • Nicolis et al., Journal of Statistical physics
    1995
  • b) By abrupt expansion of a chaotic attractor??

18
Bifurcation Diagrams
19
Experimental results
20
Laser with Modulated parameter
  • Remembering very old  times 
  • H.G. Solari J, E. Eschenazi, R. Gilmore et 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)

21
Crisis of chaotic attractors
22
External crisis in a laser with mopdulated
parameter
23
Then extreme events appear after an external
crisis
24
Predicting Rogue waves?
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
25
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27
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28
Conclusions
  • External crisis produce abrupt expansion of
    chaotic attractors and are at the origin of some
    extreme events
  • Deterministic extreme events could be predicted
    with  some  anticipation
  • I still do not know if we are able to control
    deterministic extreme events
  • BUT

29
I am always looking for the rogue waves in New
Caledonia
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Laser with saturable absorber in Q-switch regime
(to be subm. to special issue)
  • With Alejandro Hnilo and Marcelo Kovalski,
  • CEILAP, Villa Martelli, Argentina

53
Relevance of Spatial Effects
54
Theoretical results without spatial effects
55
Number of rogue waves in parameter space in LIS
(from J. Zamora)
56
Some bibliography to take into account
  • V. Balakrishnan, C. Nicolis, and G. Nicolis
    Extreme Value Distributions in Chaotic Dynamics
    J. of Stat.Phys. 80, 307 1995
  • C. Nicolis,V. Balakrishnan, and G. Nicolis
    Extreme Events in Deterministic Dynamical
    Systems PRL 97, 210602 (2006)
  • P. Gaspard and X.J. Wang Sporadicity between
    periodic and chaotic dynamical behaviors Proc.
    Nat. Acad. Sci. USA 85, 4591 (1988).

57
Perspectives
  • 1) Experiment of laser with modulation in solid
    state laser (at CEILAP). Why solid state and not
    semiconductor at INLN?
  • 2) Experiments laser with injection large Fresnel
    number (if INLN agree)
  • 3) large fresnel number edge emitter lasers
    (UFPE)
  • 4) laser with feedback (UPC) theory
  • 5) Numerical work at UNC

58
(No Transcript)
59
Conclusions
  • Rogue waves appearsometimes very often!!!!
  • Origin deterministic (at least in our
    experiments)
  • Different types of chaos without and with rogue
    waves
  • Simple models allow heuristic interpretation for
    the generation of rogue waves

60
Université de Nice Sophia Antipolis - CNRS
I N L N
I hope you enjoyed the presentation
  • If not, please .do not kill me!!
  • If Yes,
  • Thank you

61
Mode Locked TiSa Laser
. LB pump focusing lens R laser rod (L4mm)
M mirrors P1, 2 pair of fused silica prisms to
introduce negative GVD. The observations are done
with a fast photodiode (100 ps risetime) and a
350 MHz, 5 Gs/s digital oscilloscope with a
memory of 16 MB.
62
Results
63
Two chaotic regimes
P2
P1
64
Statistics of pulse amplitude
  • (a) Experimental, regime P2, 2?AI394 9978
    pulses, 237 are above the 2?AI value and 206 are
    above the 4? value. Note the L-shape. Optical
    rogue waves are hence observed.
  • (b) Experimental, regime P1, 2?AI 417.6, 4?
    256 3747 pulses, the highest one has amplitude
    234? 2?AI and 4?.

65
Model based on a five dim. map
  • (c) Numerical, regime P2, 2?AI 56.8 4? 3?104
    pulses, 147 are above the 2?AI and 4?.
  • (d) Numerical, regime P1, 2?AI 50.22, 4?
    48.25 104 pulses, the highest one is 27

66
Theoretical results
(dE/dt) k ( 1 ia ) (N - 1)E I w E
Einj (dN/dt) g ( m N N E 2 )
67
About Physical Origin (PRA to be published)
68
(No Transcript)
69
Crisis
70
(No Transcript)
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Crisis at the Origin of Deterministic Rogue Waves

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Title: Crisis at the Origin of Deterministic Rogue Waves


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. Menezes DAguiar,
  • J. Rios Leite, Rosero E.

2
  • According to fishermen tales from a pub in
    Ireland, rogue waves like solid walls of water,
    higher than 30 meters, are more or less common
    phenomena in deep ocean waters.

3
Is it true? Are rogue waves so common?
  • 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!!!
  • More Recent Recipe Take the probability
    distribution calculate s multiply by 4
    whatever.
  • and if you want a BIG BIG rogue wavemultiply by
    8

7
  • In the WEBIt is probably sufficient to say that
    any wave so large that it is unexpected based on
    current conditions can be counted as a rogue.
  • There are very few photographs of rogue waves.
    For centuries, the best evidence for their
    existence was anecdotal -- the countless stories
    told by sailors who had survived one.

8
Some Bibliography about Rogue Waves
  • Osborne, A.R. et al. Phys. Lett. A 275, 386
    (2000) and PRL 96, 014503 (2006).
  • Clauss, G.F. Appl. Ocean Res. 24, 147 (2002)
    Dramas of the sea episodic waves and their
    impact on offshore structures.
  • Kharif, C. and Pelinovsky E. EJ of
    Mechan.B/Fluids 22, 603 (2003).
  • Petrova, P. and Guedes Soares C. Appl. Ocean
    Res. 30, 144 (2008).
  • Dyachenko, A. and Zakharov, V.E. JETP lett. 81,
    255 (2005).

9
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)

10
Our First Experiments.
  • 1) Mode Locked TiSa laser
  • Hnilo et al. (Opt. Lett. November 2011)
  • 2) Semiconductor Laser with Injected Signal
  • Bonatto et al. (PRL, July 2011)
  • 3) Laser with saturable absorber (Journal of
    Optics, submitted)

11
Laser with Injected Signal
12
Probability distribution of maxima
13
(No Transcript)
14
(No Transcript)
15
Our Already Published Conclusions
  • 1) Extreme Events are rare but they can be much
    more probable than in Gaussian models when the
    dynamical behavior is Deterministically
    Chaotic
  • 2) There is chaos without rogue waves and chaos
    with rogue waves

16
Some questions
  • 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?

17
How?
  • a) Intermittency .
  • P Gaspard and X Wang, PNAS 1988
  • Nicolis et al., Journal of Statistical physics
    1995
  • b) By abrupt expansion of a chaotic attractor??

18
Bifurcation Diagrams
19
Experimental results
20
Laser with Modulated parameter
  • Remembering very old  times 
  • H.G. Solari J, E. Eschenazi, R. Gilmore et 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)

21
Crisis of chaotic attractors
22
External crisis in a laser with mopdulated
parameter
23
Then extreme events appear after an external
crisis
24
Predicting Rogue waves?
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
25
(No Transcript)
26
(No Transcript)
27
(No Transcript)
28
Conclusions
  • External crisis produce abrupt expansion of
    chaotic attractors and are at the origin of some
    extreme events
  • Deterministic extreme events could be predicted
    with  some  anticipation
  • I still do not know if we are able to control
    deterministic extreme events
  • BUT

29
I am always looking for the rogue waves in New
Caledonia
30
(No Transcript)
31
(No Transcript)
32
(No Transcript)
33
(No Transcript)
34
(No Transcript)
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(No Transcript)
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(No Transcript)
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(No Transcript)
50
(No Transcript)
51
(No Transcript)
52
Laser with saturable absorber in Q-switch regime
(to be subm. to special issue)
  • With Alejandro Hnilo and Marcelo Kovalski,
  • CEILAP, Villa Martelli, Argentina

53
Relevance of Spatial Effects
54
Theoretical results without spatial effects
55
Number of rogue waves in parameter space in LIS
(from J. Zamora)
56
Some bibliography to take into account
  • V. Balakrishnan, C. Nicolis, and G. Nicolis
    Extreme Value Distributions in Chaotic Dynamics
    J. of Stat.Phys. 80, 307 1995
  • C. Nicolis,V. Balakrishnan, and G. Nicolis
    Extreme Events in Deterministic Dynamical
    Systems PRL 97, 210602 (2006)
  • P. Gaspard and X.J. Wang Sporadicity between
    periodic and chaotic dynamical behaviors Proc.
    Nat. Acad. Sci. USA 85, 4591 (1988).

57
Perspectives
  • 1) Experiment of laser with modulation in solid
    state laser (at CEILAP). Why solid state and not
    semiconductor at INLN?
  • 2) Experiments laser with injection large Fresnel
    number (if INLN agree)
  • 3) large fresnel number edge emitter lasers
    (UFPE)
  • 4) laser with feedback (UPC) theory
  • 5) Numerical work at UNC

58
(No Transcript)
59
Conclusions
  • Rogue waves appearsometimes very often!!!!
  • Origin deterministic (at least in our
    experiments)
  • Different types of chaos without and with rogue
    waves
  • Simple models allow heuristic interpretation for
    the generation of rogue waves

60
Université de Nice Sophia Antipolis - CNRS
I N L N
I hope you enjoyed the presentation
  • If not, please .do not kill me!!
  • If Yes,
  • Thank you

61
Mode Locked TiSa Laser
. LB pump focusing lens R laser rod (L4mm)
M mirrors P1, 2 pair of fused silica prisms to
introduce negative GVD. The observations are done
with a fast photodiode (100 ps risetime) and a
350 MHz, 5 Gs/s digital oscilloscope with a
memory of 16 MB.
62
Results
63
Two chaotic regimes
P2
P1
64
Statistics of pulse amplitude
  • (a) Experimental, regime P2, 2?AI394 9978
    pulses, 237 are above the 2?AI value and 206 are
    above the 4? value. Note the L-shape. Optical
    rogue waves are hence observed.
  • (b) Experimental, regime P1, 2?AI 417.6, 4?
    256 3747 pulses, the highest one has amplitude
    234? 2?AI and 4?.

65
Model based on a five dim. map
  • (c) Numerical, regime P2, 2?AI 56.8 4? 3?104
    pulses, 147 are above the 2?AI and 4?.
  • (d) Numerical, regime P1, 2?AI 50.22, 4?
    48.25 104 pulses, the highest one is 27

66
Theoretical results
(dE/dt) k ( 1 ia ) (N - 1)E I w E
Einj (dN/dt) g ( m N N E 2 )
67
About Physical Origin (PRA to be published)
68
(No Transcript)
69
Crisis
70
(No Transcript)
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