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Contents
Part I. Data Analysis
Violin sounds are chaoticMasanori Shiro, Yoshito Hirata, Kazuyuki Aihara . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Quasiperiodic to Chaotic Transition in a DC PlasmaSudeshna Lahiri, Dola Roy Chowdhury, A.N.S Iyengar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Characterising time series dynamics with complex networksMichael Small, Ruoxi Xiang, Jie Zhang, Xiaoke Xu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Acoustic target Identification with chaos based waveforms.Frederic Rachford, Thomas Carroll . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Consequences of violated simultaneity on the concept of causalityLinda Sommerlade, Jens Timmer, Bjorn Schelter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Arbitray order Hilbert spectral analysis : a new tool to analyze the scaling complexityof time series, application to turbulence dataFrancois Schmitt, Yongxiang Huang, Zhiming Lu, Yulu Liu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Chaotic Oscillator from a PMSM model using DSPLuis Nestor Coria, Konstantin E Starkov, Arturo Sotelo, Ivan Contreras, Ramon Ramirez, Paul
Valle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Detection of unstable periodic orbits in biological time seriesBibudhananda Biswal, Chandan Dasgupta, Maria Hasse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
On the unique reconstruction of a signal from its recurrence plotAloys Sipers, Paul Borm, Ralf Peeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Embeddings with SymmetryDaniel Cross, Robert Gilmore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Biological Algorithm for Data ReconstructionRobert Gilmore, Daniel Cross, Ryan Michaluk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Reduction of the complexity of an open cavity air-flow by catching the spatial floworganization within a few dynamical modesLuc Pastur, Francois Lusseyran, Jeremy Basley, Nathalie Delprat . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Probing nonlinearity through a measure inspired in the Autocorrelation functionDavid Carlo Almeida Barbato . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Numerical Design of Robust Estimators for Box-Photochemistry SystemMark Pinsky, Hyun Cho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
II Contents
Part II. Electronic Networks
Design of OPCL coupling for arbitrary lag synchronization in chaotic oscillatorsProdyot Kumar Roy, Sourav Kumar Bhowmick, Ioan Grosu, Syamal Kumar Dana . . . . . . . . . . . . . 19
Experimental study of Chaos in Parallel-Connected DC-DC Boost Converter withMutually-Coupled Output Filter-InductorsAmmar Natsheh, J. Gordon Kettleborough, Awni Jayyousi, Moh’d Mothafar . . . . . . . . . . . . . . . . . . 20
Synchronization transitions in coupled time-delay electronic circuitsD V Senthilkumar, K Srinivasan, K Murali, M Lakshmanan, J Kurths . . . . . . . . . . . . . . . . . . . . . . . 21
SNAs IN A QUASIPERIODICALLY FORCED SERIES LCR CIRCUITAppadurai Arulgnanam, Kathamuthu Thamilmaran, Muthiah Daniel . . . . . . . . . . . . . . . . . . . . . . . . . 22
Experiments in noise-enhanced propagation and related phenomena: fault-tolerantbehavior and other propertiesRoberto R. Deza, Mauro F. Calabria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Experimental realization of synchronization in enviromentally coupled systemsAmit Sharma, Manish Dev Shrimali . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Torus doubling via Strange Nonchaotic Attractor in quasiperiodically forced ChuacircuitThamilmaran kathamuthu, Suresh Kumarasamy, Syamal Kumar Dana . . . . . . . . . . . . . . . . . . . . . . . 25
Observation of chaos in small networks of Boolean-like logic circuitsDaniel Gauthier, Hugo Cavalcante, Seth Cohen, Rui Zhang, Zheng Gao, Joshua Socolar, Daniel
Lathrop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Part III. Quantum Chaos
Quantum-Resonance Ratchets: Experimental Realizations and Prediction of StrongerEffectsItzhack Dana . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Chaos and the Quantum: Conditional Probabilities and Bell InequalitiesWm. C. McHarris . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Part IV. Elasticity and Fracture
Is the wave turbulence observed in elastic plates related to ”weak turbulence” ?Nicolas Mordant, Pablo Cobelli, Philippe Petitjeans, Agnes Maurel, Vincent Pagneux . . . . . . . . . . . 33
Experimental studies of defect dynamics in complex (dusty) plasmasCeline Durniak, Dmitry Samsonov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Modal interactions in thin structures: some experiments on non-linear vibrations ofspherical shells and percussion musical instrumentsOlivier Thomas, Cyril Touze . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Contents III
Part V. Neuronal Dynamics
Synchronization of uncoupled excitable sytems induced by white and coloured noiseRiccardo Meucci, Samuel Zambrano, Ines P. Marino, Jesus M Seoane, Miguel A. F. Sanjuan,
Stefano Euzzor, Andrea Geltrude, Tito F. Arecchi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Chaos may facilitate decision making in the brainYoshito Hirata, Yoshiya Matsuzaka, Hajime Mushiake, Kazuyuki Aihara . . . . . . . . . . . . . . . . . . . . . . 40
NONTRIVIAL EFFECTS OF NOISE IN EXCITABLE ELECTRONIC CIRCUITSGuillermo V. Savino, Roberto R. Deza, Carlos Formigli . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Complex networks in the evaluation of brain injury therapy.Inmaculada Leyva, Nazaret Castellanos, Javier M. Buldu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
Part VI. Chemical Dynamics
Some Natural Geological Systems Possibly Related to the Liesegang PhenomenonRabih Sultan, Abdel-Fattah Abdel-Rahman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Strong Field Double Ionization: Insights from Nonlinear DynamicsFrancois Mauger, Cristel Chandre, Turgay Uzer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Pattern formation and chaotic dynamics in a three-way catalytic reactor with cross-flowMartin Kohout, Otto Hadac, Jaromir Havlica, Igor Schreiber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Time series analysis of an pH oscillatory chemical reactionIgor Schreiber, Daniel Bakes, Lenka Schreiberova, Marcus Hauser . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
Part VII. Dynamos
Kinematic dynamo threshold in time dependent velocity fields.Miguel Lopez, Javier Burguete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Large scale fluctuations and dynamics of the Bullard - von Karman dynamoNicolas PLIHON, Gautier VERHILLE, Mickael BOURGOIN, Romain VOLK, Jean-Francois
PINTON . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Soft iron impellers: Induction mechanism and dynamoGautier Verhille, Nicolas Plihon, Mickael Bourgoin, Philippe Odier, Jean-Francois Pinton . . . . . . 53
Part VIII. Cardiac Dynamics
Statistical monitoring of atrial fibrillation ?Guillaume Attuel, Patrick Attuel, Nicolas Derval, Leon Glass, Jean-Michel Haissaguerre . . . . . . . . 57
Part IX. Granular Materials
IV Contents
Transition Dynamics of Structural Motifs in a Granular Contact NetworkDavid Walker, Antoinette Tordesillas, Gary Froyland, Robert Behringer . . . . . . . . . . . . . . . . . . . . . . 61
Interaction of a bouncing ball with a sinusoidally vibrating tableElbert Macau, Marcus V. Carneiro, Joaquim J. Barroso . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Bouncing trimer, bouncing droplet: bouncing modesstephane dorbolo, nicolas vandewalle, denis terwagne, francois ludewig, tristan gilet . . . . . . . . . . . . 63
Part X. Optical Systems
Temporally nonlocal electro-optic phase dynamics for 10 Gb/s chaos communicationsLaurent Larger, Roman Lavrov, Maxime Jacquot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Experimental signature unveiling the new route to amplitude death in delay-coupleddiode lasers systemPramod Kumar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Feedback Bandpass filter effects in the dynamics of an optoelectronic wavelengthnonlinear delay systemMaxime jacquot, Romain Martinenghi, Yanne Kouomou Chembo, Laurent Larger . . . . . . . . . . . . . . 69
Experimental Evidence of Microwave Envelope Chaos using an Integro-DifferentialOptoelectronic SystemYanne Chembo, Kirill Volyanskiy, Maxime Jacquot, Laurent Larger . . . . . . . . . . . . . . . . . . . . . . . . . . 70
Synchronization and mixed mode oscillations in a network of coupled light emittingdiodesMarzena Ciszak, Sora F. Abdalah, Kais Al-Naimee, Francesco Marino, Riccardo Meucci, Tito F.
Arecchi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Bursting dynamics in a two-mode semiconductor laser with optical injection: experi-mental results and theoretical analysisStephen O’Brien, Simon Osborne, David Bitauld, Andreas Amann . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
Front dynamics in periodic modulated mediaFlorence Haudin, Ricardo Gabriel Elias, Rene Gabriel Rojas, Umberto Bortolozzo, Marcel Gabriel
Clerc, Stefania Residori . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Adaptive synchronization of a network of chaotic oscillatorsBhargava Ravoori, Adam Cohen, Francesco Sorrentino, Thomas Murphy, Edward Ott, Rajarshi Roy 74
Hybrid chaos based communication system - A chaotically masked electronic messagetransduced to an optical carrier for transmissionJoshua Toomey, Deborah Kane, Aleksandar Davidovic, Elanor Huntington . . . . . . . . . . . . . . . . . . . . 75
Joint polarization and spatial mode coding in isotropic two-line CO2 laserRiccardo Meucci, Kais Al Naimee, Sora Abdalah, Tito Arecchi, Sergio De Nicola . . . . . . . . . . . . . . . 76
IDENTIFICATION OF MULTIPLE FOLDING MECHANISMS OF CHAOS GEN-ERATION BY TOPOLOGICAL ANALYSIS APPLIED TO A HIGHLY DISSIPA-TIVE SYSTEMJuan Carlos Martın, Javier Used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Contents V
Cavity Solitons Laser and Localized Vortex SolitonsPatrice Genevet, Stephane Barland, Massimo Giudici, Jorge Tredicce . . . . . . . . . . . . . . . . . . . . . . . . 78
Influence of Bragg-gratings-induced third-order dispersion on the optical power spec-trum of Raman fiber lasersPierre Suret, Nicolas Dalloz, Stephane Randoux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Anomalous Thermalization of Nonlinear Wave SystemsStephane Randoux, Antonio Picozzi, Hans Jauslin, Pierre Suret . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Part XI. Other
A non-ordinary route to chaos and complexity .Ued Maluf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
A Matched Filter for Chaos: The Missing Piece for Chaos CommunicationsNed Corron, Mark Stahl, Jonathan Blakely . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Complexity of the Particle Dynamics in Time-Dependent Focusing BilliardsAlexander Loskutov, Alexei Ryabov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Gottwald-Melbourne test for chaos of nonlinear fluctuations in complex laboratoryplasmasDola Roychowdhury, Sudeshna Lahiri, A.N.Sekar Iyengar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Modified Extended Active Control for Tracking Control and Synchronization ofChaotic and Hyperchaotic SystemsA. N. Njah . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Experimental study of dislocation avalanches during unstable plastic deformationMikhail Lebyodkin, Nikolay Kobelev, Youcef Bougherira, Denis Entemeyer, Claude Fressengeas,
Tatiana Lebedkina, Ivan Shashkov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Experimental Transition to Chaos in Low-Temperature PlasmaDan-Gheorghe Dimitriu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Nonlinear Dusty Plasma InstabilitiesMaxime Mikikian, Marjorie Cavarroc, Lenaıc Couedel, Yves Tessier, Laıfa Boufendi, Olivier Vallee 90
Influence of pulse power to dynamics of laser droplet generationBlaz Krese, Edvard Govekar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Dynamics of multi-arm pendulums excited parametricallyJose Carlos Sartorelli, Walter Lacarbonara . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
The first ”lost” international conference on non linearJean-Marc GINOUX, Loıc PETITGIRARD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Instabilities in Coupled Huygens PendulaJose R Rios Leite, Josue S Fonseca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Comparative Analysis of Chaos-based and Conventional Pseudo-noise Sequences forSpread Spectrum ApplicationsAngel A. M. Gonzalez, Marcio Eisencraft, Clodoaldo A. M. Lima . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
VI Contents
A new experimental probe for investigating the spatiotemporal dynamics of relativisticelectrons in storage ringsSerge Bielawski, Christophe Szwaj, Clement Evain, Marc Le Parquier, Masahito Hosaka, Miho
Shimada, Masahiro Adachi, Heishun Zen, Masahiro Katoh, Yoshifumi Takashima, Shin-ichiKimura, Toshiharu Takahasahi, Naoto Yamamoto, Takanori Tanikawa . . . . . . . . . . . . . . . . . . . . . . . . 96
Pulse splitting effects in short wavelength seeded Free-Electron LasersNicolas Joly, Marie Labat, Serge Bielawski, Christophe Szwaj, Christelle Bruni, Marie-Emmanuelle
Couprie . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Detachment regimes in laser droplet generationAndrej Jeromen, Edvard Govekar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Part XII. Geophysics
Spectral analysis of interannual bed level variations at a beach in Duck, North Car-olina, USA.Magar Vanesa, Reeve Dominic, Lefranc Marc, Hoyle Rebecca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Tidal instability in exoplanetary systemsDavid Cebron, Rim Fares, Michael Le Bars, Pierre Maubert, Claire Moutou, Patrice Le Gal . . . . 102
Modeling of volcanomagnetic dynamics by recurrent orthogonal least-squares learningsystemStanislaw Jankowski, Gilda Currenti, Rosalba Napoli, Zbigniew Szymanski, Luigi Fortuna, Ciro
Del Negro, Marek Dwulit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Part XIII. Dynamics and Systems Biology
Physics of Age-Related Macular DegenerationFereydoon Family . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Dynamical overlap of protein interaction networks: A method to predict proteinfunctionsIrene Sendina-Nadal, Yanay Ofran, Juan Antonio Almendral, Daqing Li, Inmaculada Leyva, Javier
M. Buldu, Shlomo Havlin, Stefano Boccaletti . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Dynamics of the interactions between the cell cycle and stress responses in yeastsMarco Thiel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Direct observation of spontaneous veins formation and thickness oscillations in Physarumpolycephalum
Paul Dely, Christophe Szwaj, Serge Bielawski, Olivier Hugon, Olivier Jacquin, Eric Lacot,Toshiyuki Nakagaki . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
Robustness of circadian clocks to daylight fluctuations: hints from an unicellular algaBenjamin Pfeuty, Quentin Thommen, Pierre-Emmanuel Morant, Florence Corellou, Francois-Yves
Bouget, Marc Lefranc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Part XIV. Ecological Systems
Contents VII
Hyperbolic extremes and species dynamics in polychaete populationsBenjamin Quiroz-Martinez, Francois G. Schmitt, Jean-Claude Dauvin, Jean-Marie Dewarumez . . 115
ANALYZING A COMPLEX SYSTEMJean - Marc GINOUX, Bruno ROSSETTO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Part XV. Fluid Dynamics
Plasma Confinement in Tokamaks with Robust TorusRicardo Egydio de Carvalho, Caroline G. L. Martins, Ibere L. Caldas, Marisa Roberto . . . . . . . . . 119
Turbulent flows in rotating spherical layers - dynamical behavior vs. meridional spatialstructure: experiment.Dmitry Zhilenko . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
Turbulent flows in rotating spherical layers: dynamical behavior vs. meridional spatialstructure. DNS.Olga Krivonosova . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Pattern formation on sandy bottom: front propagation into sand ripples under theaction of regular surface waves.Julie Lebunetel-Levaslot, Armelle Jarno-Druaux, Alexander Ezersky, Francois Marin . . . . . . . . . . . 122
Complex flows inside drops under acoustical and mechanical vibrationsPhilippe Brunet, Michael Baudoin, Farzam Zoueshtiagh, Virginia Palero, Julia Lobera . . . . . . . . . . 123
Stability analysis of turbulent boundary layer flows with adverse pressure gradientJean-Philippe LAVAL, Matthieu MARQUILLIE, Uwe EHRENSTEIN . . . . . . . . . . . . . . . . . . . . . . . . 124
Instabilities of conducting fluid flows in cylindrical shells under external forcingJavier Burguete, Montserrat Miranda-Galceran . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Pattern formation of buble periodically emerging at a liquid free surfaceHARUNORI YOSHIKAWA, Christian Mathis, Philippe Maıssa, Germain Rousseaux . . . . . . . . . . . 126
Droplet traffic at a junction: dynamics of path selectionAxelle Amon, David Sessoms, Laurent Courbin, Pascal Panizza . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
Part XVI. Dynamical Networks
Synchronization of time-delayed diffusively coupled systems: An experimental casestudy with Hindmarsh-Rose oscillatorsErik Steur, Patrick Neefs, Henk Nijmeijer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
The stability of adaptive synchronization of chaotic systemsAdam Cohen, Bhargava Ravoori, Francesco Sorrentino, Thomas Murphy, Edward Ott, Rajarshi Roy 132
Dynamics and augmentation patterns in adaptive networksCasey Schneider-Mizell, Jack Parent, Eshel Ben-Jacob, Leonard Sander, Michal Zochowski . . . . . . 133
Non-Linear Kalman Filtering Techniques for Estimation and Prediction of Rat SleepDynamicsMadineh Sedigh-Sarvestani, Steven L. Weinstein, Steven J. Schiff, Bruce J. Gluckman . . . . . . . . . 134
VIII Contents
Part XVII. Extreme Events
Rare and extreme events in temporal and spatial optical systemsEric LOUVERGNEAUX, Arnaud MUSSOT, Alexandre KUDLINKSI, Mikhail KOLOBOV, Marc
DOUAY, Majid TAKI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
Part XVIII. Nanosystems
Stability of low-friction surface sliding of nanocrystal with rectangular symmetry andapplication to graphite flakes on graphite and W on NaF(001)Astrid S. de Wijn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
Part I
Data Analysis
Violin sounds are chaotic
Masanori Shiro, Yoshito Hirata, & Kazuyuki Aihara
Ce602 Institute of Industrial Science, the University of Tokyo, 4-6-1 KOMABA MEGURO-KU, TOKYO153-8505, JAPAN
Among sounds of many instruments, sounds of strings have one of the most complicated patterns. Forexample, the sounds of a violin show complicated twisted orbits. Since these orbits looked like a strangeattractor, we wondered whether or not the sounds of violin are of deterministic chaos, which is a questionwe will answer in this talk.
Until now, many physicists have tried to model the sounds of strings. Although a number of researcheshave constructed mathematical models of strings, there are few researches that have analyzed real dataobserved from string instruments such as violins. Here, we make clear the nonlinear properties of violinsounds using methods of nonlinear time series analysis.
Although there are many definitions of deterministic chaos, their common requirement is sensitivedependence on initial conditions. As for an index of sensitive dependence on initial conditions, the maximalLyapunov exponent is often used. We estimated the maximal Lyapunov exponent using the method ofKantz and found that it is positive. The positive maximal Lyapunov exponent is a sign of deterministicchaos.
However, there are some concerns that random time series may also exhibit a positive maximalLyapunov exponent. To eliminate these concerns, we used 4 different surrogate tests with the Waylandstatistic as a test statistic. The results show that violin sounds are nonlinear and have determinism beyondpseudo-periodicity. Our results show that violin sounds are likely to be of deterministic chaos.
Quasiperiodic to Chaotic Transition in a DC Plasma
Sudeshna Lahiri1, Dola Roy Chowdhury2, & A.N.S Iyengar3
1 Dinabandhu Mahavidyalaya, Bongaon, North 24 Pargan, Pin: 7432352 Techno India, EM4/1, Sector V, Salt Lake, Kolkata - 913 Plasma Physics Division, Saha Institute of Nuclear Physics,1/AF Bidhan nagar, Kolkata 700064
sudeshna [email protected]
The temporal dynamics in the fluctuations of the plasma floating potentials (measured using a Lang-muir probe)from cylindrical dc argon plasma at an intermediate gas pressure of 0.056 mbar and at therange of discharge voltage (300- 700 volts) are investigated to probe the nature of the complex plasmadynamics. Over several regions of the discharge voltage, the floating potential fluctuation time seriesdata has been indicative of periodic oscillations, and irregular fluctuations. In the present experiment,the characteristics of these non-linear oscillations have been observed to be different on the two sides ofthe Paschen minimum. In our case, as the control parameter (discharge voltage) is increased, the Fourierspectrum of the data shows signs of transition from quasi periodicity to turbulent oscillations which is incontrast to what has been observed by Jaman et al [1]. The floating potential has been measured both inthe forward and reverse direction of the setting voltage. Over this voltage range a signature of hysteresishas been noticed when the voltage is reduced from the higher to the lower side. Both amplitude andfrequency bifurcation study has been carried out. A number of effective methods have been proposedto identify the dynamics underlying the time series which are based on characteristics such as Hurstexponent, the largest Lyapunov exponent and correlation dimension calculation. The Hurst exponentdecreases from about 1 to about 0.7 as we go from the quasi-periodic to chaotic state whereas the largestLyapunov exponent shows an opposite trend. The exponent of the power spectrum also shows an increasefrom about 1.8 in the quasi periodic state to about 3 in the turbulent phase. The phase diagram alsoshows indication of transition from periodic to turbulent state. We have developed a numerical modelof the plasma device using the neBEM toolkit [2]. Electric field has been estimated solving the Poissonequation. We are in the process of developing a suitable particle model to simulate the behavior of thesignal fluctuations. Preliminary results have been presented.
Reference: 1. Md. Nurujjaman, et al, ‘Parametric Investigation of nonlinear fluctuations in a dc glowdischarge plasma’, Chaos 17, 043121(2007)
2. S. Mukhopadhyay et al, ‘Computation of 3D MEMS electrostatics using a nearly exact BEM solver’,Engineering Analysis with Boundary Elements, Vol 30, Issue 8, 687 - 696 (2006)
Characterising time series dynamics with complex networks
Michael Small, Ruoxi Xiang, Jie Zhang, & Xiaoke Xu
Department of Electronic and Information Engineering, Hong Kong Polytechnic University
The application of complex network structure for the analysis of time series has recently led toseveral new approaches to quantify dynamical behaviour in nonlinear systems. In general these methodsconstruct some sort of network from the time series by mapping dynamical states in the underlyingsystem to individual nodes and drawing links between similar nodes. In particular, one of these methods*has shown considerable promise by providing a classification for dynamical behaviour. By measuring therelative frequency of occurrence of different motifs this method has been shown to be able to differentiatebetween low-dimensional chaos (one positive Lyapunov exponent), hyper chaos, periodic, quasi-periodicand noise periodic dynamics.
By applying this method to nonlinear time series models we show how this method can be extended toshort and noisy time series, and can be used to both evaluate and qualitatively describe the performanceof these models. We build nonlinear models (we use a radial basis model structure, but the choice isarbitrary) from time series data and then evaluate features of the complex networks structures for timeseries simulations produced by these models and for the original data. In cases were the original data wassufficient to make a meaningful assessment of the network structure we can determine which models arequalitatively good models. In cases were the original data is insufficient we can use the performance ofthe models as a surrogate and make a meaningful estimate of the various possible alternatives.
We apply the method to a short ecological time series and an ensemble of long time series of sustainedmusical tones. For the ecological time series (annual populations of Canadian Lynx) we find the previouspronouncements of chaos in this system are premature. For the tone data (pure tones on a standardB[ clarinet) we show strong evidence for bounded aperiodic dynamics which is not consistent with low-dimensional chaos. Further support for this conclusion can be obtained from surrogate time series methodsand some of the more usual nonlinear time series measures. We also observe that (for the clarinet data)the models with the ”right” dynamics are also the models that sound ”right”.
*X. Xu, J. Zhang and M. Small. ”Superfamily phenomena and motifs of networks induced from timeseries.” Proceedings of the National Academy of Sciences of the United States of America 105 (2008):19601-1960
Acoustic target Identification with chaos based waveforms.
Frederic Rachford & Thomas Carroll
Naval Research Laboratory, Code 6362, Washington, DC 20375
We propose a method of distinguishing two known targets using their their acoustic signatures incross correlation with selected chaos based waveforms. Initially acoustic chirp waveforms were digitallygenerated, broadcast from a tweeter and scattered off several similarly sized objects for a number of objectorientations. A microphone aligned with the tweeter received the scattered waveforms and the waveformswere digitized with an oscilloscope. The digitized waveforms received from two distinct objects were sortedinto angular windows. A computer program generated a large number of test waveforms with the sameband width (20%) and center frequency (3.3 or 5 KHz) as the original chirp. Two methods both derivedfrom chaotic time series were employed to generate the test waveforms. In one case constant amplitudewaveforms were assembled from concatenated sinusoids whose periods were specified by the time series. Inthe other case the time series its self was run through a band pass filter. The time series were generated bytaking the modulus of a six parameter chaotic map. The shift register parameters were randomly variedand the generated test waveforms were selected to maximize the averaged cross correlation of the returnfrom one target, while minimizing the averaged cross correlation of the other and vis versa. Contrastratios, ratios of the cross correlations, were then calculated for each target for return waveforms withineach angular window. Waveforms that maximized the difference in contrast between the two targets wereretained and optimized via a standard downhill simplex routine. Using these optimized waveforms wecan distinguish between targets for orientations within our orientation windows.
Consequences of violated simultaneity on the concept ofcausality
Linda Sommerlade1,2,3, Jens Timmer1,2,3,4, & Bjorn Schelter1,2,3
1 Department of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany2 Bernstein Center for Computational Neuroscience, University of Freiburg, Hansastr. 9A, 79104 Freiburg,
Germany3 FDM, Freiburg Center for Data Analysis and Modeling, University of Freiburg, Eckerstr. 1, 79104 Freiburg,
Germany4 Freiburg Institute for Advanced Studies, Albertstr. 19, 79104 Freiburg, Germany
Inferring causal interaction structures in networks of dynamical processes is of particular interest inneurosciences. Since simultaneity of measurements cannot be guaranteed, we investigate its implicationsfor causality, in particular Granger-causality based partial directed coherence, applied to linear and non-linear systems. We present three situations in which the naıve application of partial directed coherenceleads to misleading results. We discuss possible solutions to this end. We also address the question howGranger-causality can be applied to measured data in this context.
Arbitray order Hilbert spectral analysis : a new tool to analyzethe scaling complexity of time series, application to turbulencedata
Francois Schmitt1, Yongxiang Huang1,2, Zhiming Lu2, & Yulu Liu2
1 Laboratory of Oceanology and Geosciences, CNRS-University of Lille 1, France2 Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, China
Empirical Mode Decomposition (EMD) is an analysis technique introduced by Norden Huang in1998; it was imagined to decompose a complex time series into a sum of modes, each one being narrrowbanded. This method is fully data-driven, and is suitable for nonlinear and nonstationary time series.Since its introduction this method has been applied in more than 1000 papers, in many fields of naturalsciences including oceanic and atmospheric sciences, climate studies, mechanical engineering, biomedicaland biological sciences, among others. It has been completed by Hilbert Spectral Analaysis (HSA), amethod involving Hilbert transform to characterize time series fluctuations in an amplitude-frequencyspace.
Here we generalize this approach in order to characterize the scaling intermittency of complex timeseries in an amplitude-frequency space. The new method is a arbitrary order Hilbert spectral analysis. Asa first step the method is applied to fractional Brownian motion, and then to homogeneous turbulencedata and chaotic and nonlinear signals.
We show that Hilbert spectral analysis can be used to recover the Kolmogorov -5/3 inertial range; weobtain a 2D amplitude-frequency representation of the pdf p(A, ω) of turbulent fluctuations with scalingtrend. We obtain multifractal scaling exponents in amplitude-frequency space and show that they areclose to the ones in real space, despite the quite different approaches used in both cases. We find that thenew methodology provides a better estimator than the classical structure functions.
We then investigate the effect of a periodic component on both structure functions and the Hilbertapproach, and find that the former one is strongly influenced by the periodic component, whereas thelatter can constrain such effect in an amplitude-frequency space. This shows the usefulness of this newmethod for general scaling processes and especially for time series possessing energetic large scales.
This new approach is able to characterize the multi-scale properties of the fluctuations of nonlineartime series. It is likely to have many different applications for data analysis of nonlinear, chaotic andcomplex time series.
Refs:Huang Y., F. G. Schmitt, Z. Lu, Y. Liu, EPL 84, 40010, 2008Huang Y., F. G. Schmitt, Z. Lu, Y. Liu, EPL 86, 40010, 2009Schmitt FG, Y Huang, Z. Lu, Y. Liu, N. Fernandez, Journal of Marine Systems 77, 473-481, 2009Huang Y., F. G. Schmitt, Z. Lu, Y. Liu, Journal of Hydrology 373, 103-111, 2009
Chaotic Oscillator from a PMSM model using DSP
Luis Nestor Coria1,2, Konstantin E Starkov2, Arturo Sotelo1, Ivan Contreras1, Ramon Ramirez1, &Paul Valle1
1 Instituto Tecnologico de Tijuana. Blvd. Industrial s/n, Mesa de Otay, Tijuana, BC, Mexico.2 CITEDI-IPN. Av. del Parque 1310, Mesa de Otay, Tijuana, BC, Mexico.
Dynamical properties of chaotic systems suggest complexity for a physical implementation. This pa-per presents a chaotic oscillator using the TMS320C6713 DSP. The implemented chaotic oscillator corre-sponds to a scaled version of the model of a permanent-magnet synchronous motor (PMSM) that presentschaos for some values of its parameters, this model was presented and discussed in [1] and is given bythe following equations:
x = 20(−bx+ 200yz);y = 20(−y − 200xz + cz);z = 20(a(y − z) + 200ξxy).
Traditionally, a chaotic oscillator is implemented with analog components, but this has changed becauseof many benefits provided by a DSP [2]. Time series of all state variables of the chaotic oscillator withDSP were obtained and three different metods were applied in order to establish its chaotic properties.We found: 1) The largest positive Lyapunov exponent; 2) Poincare map; and 3) Fourier Transform.Chaotic signals can be used in data encription [3], [4], and generate chaos like behavior in some physicalapplication where it is desired [5], and so on. This work was supported by SEP-CONACYT project 78890and DGEST project TIJ-IET-2009-217, MEXICO.
References
1. Z. Jing, C. Yuc, and G. Chen, “Complex dynamics in a permanent-magnet synchronous,” Chaos, Solitons andFractals, vol. 22(4), pp. 831–848, 2004.
2. P. Lapsley, DSP Processor Fundamentals. IEEE Press, 1997.3. H. Xiao and W. Zeng, “A hard disk encryption system realized by the digital signal processor,” International
Conference on Computational Intelligence and Security, vol. 2, pp. 312–314, 2009.4. R. Saravanan, T. Sivaramakrishnan, and K. Ramamoorthy, “A new approach on discrete chaotic cryptography
using TMS320C6713 digital signal processors,” International Journal of Applied Engineering Research, vol. 2,no. 3, pp. 545–556, 2007.
5. S. Ye, K. Chau, and N. Shuangxia, “Chaoization of a single-phase induction motor for washing machines,” inIndustry Applications Conference, 2006. 41st IAS Annual Meeting., IEEE. IEEE, 2006, pp. 855 – 860.
Detection of unstable periodic orbits in biological time series
Bibudhananda Biswal1, Chandan Dasgupta2, & Maria Hasse3
1 S. V. College, University of Delhi, India2 Department of Physics, Indian Institute of Science, India3 University of Stuttgart, Germany
Analysis of chaos control experiments on epileptic brain slices suggest presence of low dimensionalchaos in such systems. These claims have been further validated through detection of statistically signif-icant unstable periodic orbits in the time series analysis of the EEG data. The reliability of such timeseries analysis methods depend crucially on the nature and size of data. We present new results on thevalidity of these methods for short, noisy and non-stationary data.
On the unique reconstruction of a signal from its recurrence plot
Aloys Sipers1, Paul Borm1, & Ralf Peeters2
1 Centre of Research Life Sciences, Zuyd University,The Netherlands2 Maastricht University, The Netherlands
Recurrence plots are two-dimensional representations of high-dimensional trajectories of dynamicalsystems. Patterns in recurrence plot carry information on the underlying trajectories and can be studiedand analyzed for detection and classification purposes. From the literature it is known that a recurrenceplot determines its underlying trajectory up to isometry. Here we consider trajectories that are obtainedfrom a one-dimensional signal with the time-delay embedding method. We address the question to whichextent a recurrence plot determines the underlying signal. First we show that a recurrence plot determinesthe power spectrum of this signal. Then we provide conditions on the embedding dimension and thetime-delay which imply uniqueness of the underlying signal (up to a sign factor). A worked examplefrom EEG analysis illustrates how this theory allows one to understand the limitations that apply tothe interpretation of a recurrence plot. We consider a measured EEG signal containing a so-called Murhythm, i.e. exhibiting an m-shaped morphology with frequencies between 8 Hz and 12 Hz. We show thatfor some values of the embedding dimension and time-delay, another signal with a different morphologycan be constructed which yields the same recurrence plot. This induces ambiguity in the interpretation ofthe associated recurrence plot. We also show how to avoid this phenomenon by appropriately choosing theembedding dimension and time-delay parameters to guarantee uniqueness of the corresponding patternin the recurrence plot.
Embeddings with Symmetry
Daniel Cross & Robert Gilmore
Department of Physics, 3141 Chestnut St, Philadelphia, PA 19104
A dynamical system may be reconstructed from scalar data taken along some trajectory of the system.A reconstruction is considered successful if it produces a system diffeomorphic to the original. However,if the original dynamical system is symmetric, it is natural to search for reconstructions that preservethis symmetry. These generally do not exist. It is possible to show that a differential reconstruction ofany nonlinear dynamical system preserves at most a two-fold symmetry and that this is always a paritysymmetry. Implications for embeddings of the Lorenz system will be discussed in detail.
Biological Algorithm for Data Reconstruction
Robert Gilmore, Daniel Cross, & Ryan Michaluk
Department of Physics, 3141 Chestnut St, Philadelphia, PA 19104
We present a simple algorithm inspired by Genome sequencing which “reconstructs” a single longtrajectory of a dynamical system from many short trajectories1. Such a procedure would be useful insituations where many data sets are available but each is insufficiently long to apply a meaningful analysisdirectly2. We apply the algorithm to numerical data taken from the Rossler and Lorenz dynamicalsystems and to experimental data taken from the Belousov-Zhabotinskii chemical reaction. Topologicalinformation was reliably extracted from each system and geometrical and dynamical measures werecomputed.
1. C. Komalapriya, M. Thiel, M. C. Romano, N. Marwan, U. Schwarz, and J. Kurths, Phys. Rev. E78, 066217 (2008).
2. D. J. Cross, R. Michaluk, and R. Gilmore, Phys. Rev. E, in press (2010).
Reduction of the complexity of an open cavity air-flow bycatching the spatial flow organization within a few dynamicalmodes
Luc Pastur1,2, Francois Lusseyran1, Jeremy Basley1,2, & Nathalie Delprat1,3
1 LIMSI-CNRS2 Universite Paris Sud 113 Universite Pierre et Marie Curie
Most open systems in fluid dynamics potentially own an infinite number of degrees of freedom, whichmakes questionable approaches in terms of dynamical system analysis. However, in many situations, theflow complexity actually reduces to very coherent features together with few characteristic structures inspace and time, suggesting that the actual number of degrees of freedom is small. The resulting floworganization, therefore, can often be considered as the projection of the full dynamics over some centralvariety, whose dimension is small, such that a few modes may be selected as relevant with respect tothe long-time dynamics (associated to vanishing or close to imaginary eigenvalues), all the other modesbeing slaved to them. In a very recent work, Schmid and Sesterhenn (2008) have shown how to computemodes relevant with respect to the non-linear state evolution of such systems. The method is empiric, themode computation being directly done based on successive, time-resolved, realizations of some observable(velocity field, pressure, etc), without any explicit knowledge of the evolution-operator (which may be bythe Navier-Stokes equation). The resulting modes of the decomposition are called ”dynamical modes” bySchmid and Sesterhenn because they are the eigen-modes of some operator-evolution in the functionalspace of the observable acting on the fully non-linear state. In the limit of infinite horizon time, beyondtransient phenomena, when the dynamics evolves on an attractor, the dynamical modes reduce to theKoopman modes, which are well-estimated by the discrete (time) Fourier transformed (spatial) modes, asshown by Rowley et al (2009). Based on this assumption, we have identified the dynamical modes char-acteristic of an experimental cavity air-flow. The cavity is rectangular and the flow incompressible (lowMach number limit), which is an academic configuration for studying self-oscillating flows. Such flows areknown to exhibit narrow-banded power spectra, due to the enhancement of self-sustaining oscillations.In such strongly organized flows, dynamical or Koopman modes provide an efficient way for reducingthe flow complexity, for they catch the spatial structures characteristic of the flow with respect to itsspace-time dynamics.
Bibliography
Schmid and Sesterhenn (2008), Schmid P. and Sesterhenn J., (2008) ”Dynamic mode decompositionof numerical and experimental data”, Sixty-First Annual Meeting of the APS Division of Fluid Dynamics,San Antonio, Texas, USA.
Rowley et al (2009), Rowley C. W., Mezic I., Bagheri S.,Schlatter P. and Henningson D. S. (2009)”Spectral analysis of nonlinear flows”, Journal of Fluid Mechanics, pp. 1-13
Probing nonlinearity through a measure inspired in theAutocorrelation function
David Carlo Almeida Barbato
R. Dr. Bento Teobaldo Ferraz 271 - Bl. II - Barra Funda 01140-070 - Sao Paulo, SP - Brasil
In this work, we propose a kind of generalization of the Autocorrelation function (ACF). This newmeasure was designed aiming the search for dependencies between points of the series other than thelinear ones.
The main idea concerned in the development of this tool is to avoid on the measurement process theuse of the series average value. Instead of multiply the demeaned values of the series, the ratios betweenfirst differences of the values are taken.
Even though this seens to be similar to the standard ACF of the first differenced series, some deviationsfrom that occur. We believe them can help in discriminating some nonlinear features of series.
Numerical Design of Robust Estimators forBox-Photochemistry System
Mark Pinsky & Hyun Cho
Department of Mathematics and Statistics, University of Nevada.Reno. Reno NV 89557, USA
Various uncertainties jeopardize numerical forecasts of various atmospheric-chemistry models whichstimulate efforts to improve the accuracy of numerical forecasts by integrating limited observations andsimulations. This paper presents a numerical approach to the design of feedback controlled robust estima-tors for multidimensional nonlinear models that are frequently used to describe photochemical reactions.Parameters of feedback control, which deliver robust tracking of directly immeasurable system states, arefound via off-line minimization of error function assessing mismatches between trial and actual systemtrajectories. This assures efficient online simulation of complex estimator system. Extensive numericaltests show that these estimators provide rapid and robust tracking of solutions to photochemistry sys-tems. These systems accumulate significant uncertainties in their parameters and initial values under themost conservative assumption that a concentration of single reacting specie is only measurable. We alsoassure our approach using the Lyapunov function method and consider its application to the problem ofnoise removal if available data is corrupted by noise.
Part II
Electronic Networks
Design of OPCL coupling for arbitrary lag synchronization inchaotic oscillators
Prodyot Kumar Roy1, Sourav Kumar Bhowmick2, Ioan Grosu3, & Syamal Kumar Dana2
1 Department of Physics, Presidency College, Kolkata 700073, India2 Central Instrumentation, Indian Institute of Chemical Biology, Kolkata 700032, India3 Faculty of Bioengineering, University of Medicine and Pharmacy, Gr.T.Popa, Iasi, Romania
AbstractWe discuss the method of arbitrary lag synchronization (ALS) in chaotic oscillators under unidirec-
tional OPCL coupling. By ALS, we mean that any arbitrary lag time can be set between the driver andslave oscillators. The added advantage is that, one can precisely control the synchronization. LS is alreadyreported in time-delayed systems by others [1] under unidirectional delay coupling. The limitation of suchmethods is their restriction on the amount of time lag. Recently, instead of using simple linear couplingother approaches [2, 3] are reported which increases the lag time for LS [2] or anticipating synchroniza-tion [3]. Although these methods enhance the lag time to an extent yet it remains restricted. In contrast,our proposed OPCL delay coupling is free from such limitation. One delay variable is introduced in thecoupling term used in [4], which helps one target any ALS between the two-coupled chaotic oscillators.The delay time may be of the order of mean characteristic time scale of the system or even its multiples.Further, the method allows flexibility in controlling the lag time. We elaborate the method with numericalexamples of Rossler system, a Sprott system and also with a neuron model namely the Hindmarsh-Rosemodel. Finally, we present experimental evidence of ALS in electronic circuit.
References:[1] D.V.Senthilkumar and M.Lakshmanan, Phys. Rev. E 71, 016211 (2005); S. Sivaprakasam, P. S.
Spencer, P. Rees, K. A. Shore, Optics letters 27(14), 1250 (2002). [2] K.Pyragas, T.Pyragiene, Phy.Rev.E78, 046217 (2008). [3] J.N. Blakely, M.W. Pruitt, N.J. Corron, Chaos 18, 013117 (2008). G.Ambika andR.E.Amritkar, Phys. Rev. E 79, 056206 (2009) [4] I.Grosu, E.Padmanaban, P.K.Roy and S.K.Dana,Phy.Rev.Lett. 100, 0234102 (2008); I.Grosu, R.Banerjee, P.K.Roy and S.K.Dana, Phy.Rev.E 80, 016212(2009).
Experimental study of Chaos in Parallel-Connected DC-DCBoost Converter with Mutually-Coupled OutputFilter-Inductors
Ammar Natsheh1, J. Gordon Kettleborough2, Awni Jayyousi1, & Moh’d Mothafar3
1 Department of Electronic and Communication Engineering, Faculty of Engineering, Al-Ahliyya AmmanUniversity, Post Code 19328 Amman, Jordan
2 Department of Electronic and Electrical Engineering , Loughborough University, Loughborough,Leicestershire, LE11 3TU, UK
3 Department of Electrical Engineering, Jordan University of Science and Technology, P.O. Box 3030, Irbid22110, Jordan
ammar [email protected]
An experimental study is presented of a modular peak current-mode controlled DC-DC boost con-verter. The parallel-input/parallel-output converter consists of two identical boost circuits and operatesin the continuous conduction current mode. [1] investigated the small signal and transient behaviourof two-module DC-DC boost converter with mutually coupled inductors but chaotic behaviour was notaddressed. This device is capable of demonstrating chaotic behaviour [2] arising as a result of period-doubling bifurcations as the main control parameter, reference current, is changed. Chaotic behaviour isundesirable since it results in increased losses together with acoustic noise, and may cause catastrophicfailure of the unit. Mathematically, this controller is described by piece-wise linear differential equationsunder external periodic forcing [3]. To prevent chaos in it, Delayed current feedback control illustratesthe effectiveness and robustness of the chaos control scheme [4]. Experimental results and FORTRANsimulations show good agreement. The effect of chaos in the presence of mutual coupling between theinductors of the constituent modules is demonstrated. Experimental results and MATLAB simulationsmatch remarkably and correlate the presence of coupling leads the system to chaos. Results are alsoverified using the circuit analysis package PSPICE and COMSOL simulations.
Synchronization transitions in coupled time-delay electroniccircuits
D V Senthilkumar1,4, K Srinivasan2, K Murali3, M Lakshmanan2, & J Kurths1,5
1 Potsdam Institute for Climate Impact Research, 14412 Potsdam, Germany2 Centre for Nonlinear Dynamics, Department of Physics, Bharathidasan University, Tiruchirapalli - 620 024,
India3 Department of Physics, Anna University, Chennai - 600 025, India4 Centre for Dynamics of Complex Systems, University of Potsdam, 14469 Potsdam, Germany5 Department of Physics, Humboldt University, 12489 Berlin, Germany
We have investigated the synchronization transitions from anticipatory to lag synchronization via com-plete synchronization [Physical Review E 71 016211 (2005)] and their inverse counterpart [Chaos 19 023107 (2009)]in unidirectionally coupled time-delay systems with excitatory and inhibitory time-delay couplings, re-spectively. The transition between different types of synchronization can be realized, for a fixed set ofparameters, as a function of the coupling delay τ2 along with a suitable stability condition following theKrasovskii-Lyapunov theory. We demonstrate the experimental realization of the above synchronizationtransitions in coupled time-delay electronic circuits with a threshold nonlinearity.
SNAs IN A QUASIPERIODICALLY FORCED SERIES LCRCIRCUIT
Appadurai Arulgnanam1, Kathamuthu Thamilmaran2,3, & Muthiah Daniel2,3
1 Department of Physics, St.John’s College, Palayamkottai, Tirunelveli-627002, Tamilnadu, India.2 Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Thiruchirappalli-620 024,
Tamilnadu, India.3 Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Thiruchirappalli-620 024,
Tamilnadu, India.
Strange nonchaotic attractors have been focussed as of considerable interest from both theoretical andexperimental points of view in the past few years, owing to their existence in real physical systems andtheir possible application in communication [1]. In this work, transitions from quasiperiodic attractorsto strange non chaotic attractors (SNAs) and then to chaos is observed experimentally [2] and verifiedanalytically in a simple quasiperiodically forced series LCR circuit, having Chua’s diode as its nonlinearelement. Rich varieties of tori dynamics is observed in this circuit, and in particular three prominentroutes namely, Heagy-Hammel, Fractalization and Type-I intermittent routes for the creation of SNAshave been identified in this single circuit [3,4]. These mechanisms through which SNAs are born, aredistinguished by characterizing the maxiaml Lyapunov exponent and its variance change as a function ofparameter, the extremely wrinkled nature of the Poincare maps and computing the spectral distributionfunction for SNAs and quasiperiodic attractor and are found to obey different scaling laws. Analyticaltoris and SNAs are found to match exactly with the experimentally observed toris and SNAs.
[1]. C.Grebogi, E.Ott, S.Pelikan and J.A.Yorke, Physica D 13, 261 (1984).[2]. T.Yang and K.Bilimgut Phys.Lett.A 236, 494 (1997).[3]. K.Thamilmaran, D.V.Senthilkumar, A.Venkatesan and M.Lakshmanan Phy.Rev.E74, 036205 (2006).[4]. A.Venkatesan, K.Murali and M.Lakshmanan Phys.Lett. A259, 246 (1999).
Experiments in noise-enhanced propagation and relatedphenomena: fault-tolerant behavior and other properties
Roberto R. Deza1 & Mauro F. Calabria2
1 IFIMAR (Mar del Plata Institute for Physics Research, UNMdP and CONICET), Dean Funes 3350,B7602AYL Mar del Plata, Argentina.
2 Electronics Department, Faculty of Engineering, Universidad Nacional de Mar del Plata (UNMdP), J. B.Justo 4302, B7608FDQ Mar del Plata, Argentina.
We study the propagation of a low-frequency periodic signal through a chain of one-way coupledbistable oscillators, subject to uncorrelated additive noises. The system can be regarded as a mock-upof synaptic transmission between neurons. This work focuses on optimizing input SNR and switchingthreshold of each oscillator, to achieve maximal coherence (measured as a Hamming distance) betweenthe last oscillator’s response and the input signal. At a further stage, we shall focus on the fault-tolerantbehavior of the system [Phys. Rev. E 61, R3287 (2000)].
Experimental realization of synchronization in enviromentallycoupled systems
Amit Sharma & Manish Dev Shrimali
The LNM Institute of Information Technology, Jaipur 302031 India
Synchronization phenomena in most cases deals with the mutual or uni-directional coupling, howevercommon periodic or stochastic driving also give rise to such interesting phenomena [1]. In some cases,synchronous behaviour can occur due to interaction through common dynamic environment [2, 3]. Animportant example of such systems is populations of cells in which oscillatory reactions are taking place,which communicate via chemicals that diffuse in the surrounding medium.
We report the experimental observation of chaotic in-phase and anti-phase synchronization in envi-ronmentally coupled Lorenz systems.
Two Lorenz oscillators and dynamic environment in circuit simulations are consists of passive resis-tors R, capacitors C and OPAMP UA741CP. The feedback of two Lorenz oscillator are connected byresistors to the dynamic environment circuit, which represent the coupling strength and the output ofthe environment connected to the Lorenz oscillators by resistors, which represent the coupling strength.
In case of the In-phase synchronization, the circuit equations are
x11 =1C1
(1R1
x12−x11
R2)+
R26
C1R28R24y x12 = − 1
C2(− 1R5
x11+R9
R3R8x11x13+
1R4
x12) x13 =1C3
(1R6
x11x12−1R7
x13)
(1)
x21 =1C4
(1R10
x22−x21
R11)− 1C1R27
y x22 = − 1C5
(− 1R14
x21+R18
R17R12x21x23+
1R13
x22) x23 =1C6
(1R15
x21x22−1R16
x33)
(2)
y =1C7
(−1R20
y − 1R19
x11 +R28
R21R29x22) (3)
Circuit Simulations shows both in-phase (for ε1 = R26R28R24
= 1R27
, ε2 = 1R19
= 1R27
, κ = 1R20
.) andanti-phase synchronization (for ε1 = R22
R24R23= R26
R28R27, ε2 = 1
R19= 1
R21= 1
R27, κ = 1
R20).
1. A. S. Pikovsky, M. G. Rosenblum, J. Kurths, Synchronization: A Universal Concept in NonlinearSciences, (Cambridge Nonlinear Science Series) 2003.
2. Synchronization of oscillators coupled through an environment, G. Katriel, Physica D. 237, 2933(2008).
3. Synchronization in systems coupled indirectly through dynamic environment, V. Resmi, G. Ambika,and R. E. Amritkar, Submitted to PRE 2010.
Torus doubling via Strange Nonchaotic Attractor inquasiperiodically forced Chua circuit
Thamilmaran kathamuthu1, Suresh Kumarasamy1, & Syamal Kumar Dana2
1 Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli-620 024,Tamilnadu, India,
2 Central Instrumentation, Indian Institute of Chemical Biology (Council of Scientific and Industrial Research),Kolkata 700032, India.
Under a quasiperiodic excitation the familiar Chua circuit is found to exhibit a sequence of n-torusinterspersed by strange non-chaotic attractor (SNA) regimes where n=1,2,3,...... Two different sequencesarise when the amplitude of one of the quasiperiodic excitations, considered as the control parameter,is increased and decreased. These torus doubling are observed experimentally in electronic circuit andconfirmed by numerical simulations.
Reference1.K. Thamilmaran, D.V. Senthilkumar, A. Venkatesan and M. Lakshmanan, Phys. Rev. E. Vol. 74,
036205, 2006.
Observation of chaos in small networks of Boolean-like logiccircuits
Daniel Gauthier1, Hugo Cavalcante1, Seth Cohen1, Rui Zhang1, Zheng Gao1, Joshua Socolar1, & DanielLathrop2
1 Duke University, Department of Physics, Center for Nonlinear and Complex Systems, Durham, NorthCarolina 27708, USA
2 University of Maryland, Department of Physics, College Park, Maryland 20742, USA
’Boolean chaos’ is observed in a simple network of electronic logic gates that are not regulated bya clocking signal [1]. We study a network three nodes realized with commercially available high-speedelectronic logic gates. The temporal evolution of the voltage at any given point in the circuit has anonrepeating pattern with clear binary state transitions and displays exponential sensitivity to initialconditions. The resulting power spectrum is ultrawide band, extending from dc to beyond 2 GHz. Becausethe circuit includes feedback loops with incommensurate time delays, it spontaneously produces dynamicalstates with the shortest possible pulse widths, a regime in which time-delay variations generate chaos. Theobserved behavior is reproduced qualitatively in an autonomous Boolean model with signal propagationtimes that depend on the histories of the gates and filtering of pulses of short duration [2]. Our device maybe used as a building block in secure spread-spectrum communication systems, an inexpensive ultrawide-band sensor or beacon, and possibly for high-speed random number generation. It can also be used as aconvenient platform for testing theories on complex networks. Efforts are underway to investigate chaossynchronization and private communication using these devices, including a parametric study on thesensitivity of the synchronization quality on network delays.
[1] R. Zhang, H.L.D. de S. Cavalcante, Z. Gao, D.J. Gauthier, J.E.S. Socolar, M.M. Adams, and D.P.Lathrop, ’Boolean chaos,’ Phys. Rev. E. 80, 045202(R) (2009).
[2] H. L. D. de S. Cavalcante, D. J. Gauthier, J. E. S. Socolar, and R. Zhang, ’On the Origin of Chaosin Autonomous Boolean Networks,’ Philos. Trans. Royal Soc. A 368, 495 (2010).
Part III
Quantum Chaos
Quantum-Resonance Ratchets: Experimental Realizations andPrediction of Stronger Effects
Itzhack Dana
Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
Classical low-dimensional Hamiltonian systems may exhibit the chaotic “ratchet effect” only for amixed phase space. However, the corresponding quantized systems generally feature significant quantum-ratchet effects also under full-chaos conditions. We shall consider here particularly strong such effects, i.e.,quantum momentum currents (ratchet accelerations), occurring in kicked systems for quantum-resonance(QR) values of a scaled Planck constant. These effects were studied in work [1] for kicked-rotor systemsand variants of them under most general conditions.
Experimental realizations of simple QR ratchets in Ref. [1] were performed in works [2,3] using atom-optics methods. Bose-Einstein condensates (BECs) were exposed to a pulsed standing light wave ap-proximating a completely symmetric (cosine) kicking potential. Also, the BEC was initially prepared ina superposition of two momentum states corresponding to a state with well-defined point symmetry. De-spite these symmetries and in accordance with predictions in Ref. [1], a QR ratchet effect was observeddue to the relative asymmetry associated with the generic non-coincidence of the symmetry centers ofthe symmetric potential and the initial state [3]. The experimental results were found to agree well withtheoretical ones [1] after taking properly into account the finite quasimomentum width of the BEC; inparticular, this width was shown to cause a suppression of the ratchet acceleration for exactly resonantquasimomentum, leading to a saturation of the directed current [3].
Quite recently [4], a new, statistical approach to the quantum-chaotic ratchet effect was proposed,featuring natural initial states that are phase-space uniform with the maximal possible resolution of onePlanck cell. It was shown that the average strength of the effect over these states, under QR conditions,is significantly larger than that over usual momentum states or superpositions of few momentum statessuch as those used in the experiments above. By increasing the number of momentum states in the su-perpositions, the average strength of the effect gradually increases, approaching that for the maximallyuniform states. These results were obtained for the kicked Harper models which are equivalent to kickedharmonic oscillators. The latter systems, as well as superpositions of many momentum states, are exper-imentally realizable. Thus, the very strong quantum ratchet effects predicted should be observable in thelaboratory.
References:[1] I. Dana and V. Roitberg, Phys. Rev. E 76, 015201(R) (2007).[2] M. Sadgrove, M. Horikoshi, T. Sekimura, and K. Nakagawa, Phys. Rev. Lett. 99, 043002 (2007).[3] I. Dana, V. Ramareddy, I. Talukdar, and G.S. Summy, Phys. Rev. Lett. 100, 024103 (2008).[4] I. Dana, Phys. Rev. E 81, 036210 (2010).
Chaos and the Quantum: Conditional Probabilities and BellInequalities
Wm. C. McHarris
Departments of Chemistry and Physics/Astronomy, Michigan State University
In recent years we have suggested that many of the so-called paradoxes resulting from the Copenhageninterpretation of quantum mechanics have more logical, less paradoxical parallels based in nonlinear dy-namics and chaos theory [WCM, Complexity 12(4), 12 (2007), and references therein]. This raises thepossibility that quantum mechanics may contain fundamental nonlinear elements. Indeed, experimentalsignatures of chaos in a quantum mechanical system have been reported only this past year [S. Chadhuryet al., Nature 461, 768 (8 Oct 2009)]. As an illustration of what can go wrong when nonlinear elements areignored, I examine Bell-type inequalities. In these inequalities, a classical system is found to impose up-per limits on the correlations between properties of two (entangled) particles at an effectively infinite (nocommunication) separation. Quantum mechanics removes these upper limits, allowing greater correlations— and experiments consistently have found quantum mechanics to be correct. The inference then be-comes that a measurement on one particle INSTANTANEOUSLY collapses the wave-function of the otherparticle, i.e., superluminal signals are transmitted between the particles, resulting in Einstein’s ”spookyaction at a distance.” I argue that there is nothing wrong with the quantum mechanical derivations ofsuch inequalities (the usual point of attack by those wishing to invalidate Bell-type inequalities), butimplicit in the so-called classical derivations is the concept of independent, uncorrelated particles. Thus,one is actually comparing uncorrelated with correlated, rather than classical versus quantum mechanicalsystems — making making any conclusions about wave-function collapse moot. Nonlinear systems areknown to exhibit correlations that can be as great as those in quantum systems — nonextensive thermo-dynamics, such as Tsallis entropy, have demonstrated this. When conditional (correlated) probabilitiesare included in the classical derivations, the statistical correlations can easily overlap with those predictedby the (entangled) quantum states. As an example of the nonintuitive nature of conditional probabilities,I examine the Monty Hall paradox, and I also show how non-ergodic behavior, common in nonlinearsystems, can ape action-at-a-distance. Nonlinear dynamics and chaos theory could well provide a bridgebetween the determinism so dear to Einstein and the statistics of the Copenhagen interpretation of quan-tum mechanics. Einstein and Bohr both could have been right in their debates about the fundamentalsof quantum mechanics.
Part IV
Elasticity and Fracture
Is the wave turbulence observed in elastic plates related to”weak turbulence” ?
Nicolas Mordant1, Pablo Cobelli2, Philippe Petitjeans2, Agnes Maurel3, & Vincent Pagneux4
1 LPS, Ecole Normale Superieure, 24 rue Lhomond, 75005 Paris, France2 PMMH, ESPCI, 10 rue Vauquelin, 75005 Paris, France3 Institut Langevin, ESPCI, 10 rue Vauquelin, 75005 Paris, France4 Lab. d’acoustique, Avenue Olivier Messiaen, 72085 Le Mans, France
It has been observed recently that wave turbulence can develop in vibrated elastic plates (MordantPRL 2008, Boudaoud et al. PRL 2008). A statistical theory of wave turbulence (so called weak turbulencetheory or WTT) exists for more than half a century and has been applied in a large variety of systemsranging from condensed matter physics to astrophysics. In particular, it has been applied to the caseof elastic plates (During et al. PRL 2006). The experimental single point spectra are not in agreementwith the WTT predictions. The measured frequency spectra are steeper than the prediction and theirscaling with the average injected power is also not that predicted by the WTT. The reasons for thisdisagreement with the WTT could be related to the level of non linearity, finite size effects or dissipation(if not restricted to small scales).
P. Cobelli, P. Petitjeans, A. Maurel (ESPCI, Paris) and V. Pagneux (Univ. du Mans) developed aFourier transform profilometry technique that we applied to the elastic plate turbulence (Cobelli et al.PRL 2009). It allows us to measure the deformation of the plate over a significant part of the surface ofthe plate. The time resolution is provided by the use of a high speed camera. In this way, movies of theplate deformation can be recorded. It allows us to get the full space and time Fourier spectrum and thusto probe in much more details the structure of the wave turbulence than with single point spectra. Weobserve in particular that energy is indeed localized on a surface in the 3D (kx, ky, ω) space as expectedfrom waves. The observed non linear dispersion relation is close to the linear dispersion relation whichconfirms a weak non linear coupling of the waves. The shift between the two dispersion relations is seento increase with the forcing. The thickness or the dispersion relation (energy surface in the (kx, ky, ω)space) is seen to also increase with the forcing. All these features are in qualitative agreement with thepredictions of the WTT and thus do not provide explanations for the observed disagreement with thetheory. Finite size effects are also observed but vanish as the forcing amplitude is increased. The FTPtechnique is a very promising tool for a extensive quantitative analysis of the wave turbulence observedin elastic plates. It can also be applied to turbulence of fluid surface waves. Preliminary studies show thatthe development strong linearities is observed in that case. The ability of the FTP technique to providethe space-time dynamics of surface deformations makes it a specially suited tool for the analysis of waveturbulence.
Experimental studies of defect dynamics in complex (dusty)plasmas
Celine Durniak & Dmitry Samsonov
Dept. of Electrical Engineering and Electronics, The University of Liverpool, Liverpool, L69 3GJ, UK.
Complex plasmas consist of micron sized microspheres immersed into ordinary ion-electron plasmas.Similar to colloids, they can exist in solid, liquid or gaseous states and exhibit phase transitions. Complexplasmas are found in space: planetary rings, comets or interstellar clouds. In plasma technology, dustcontamination has negative effects on the yield of semiconductor devices. The microparticles are chargednegatively by the plasma. They strongly interact with each other electrostatically via a Yukawa potential.As the grains are weakly damped by gas friction and traceable individually, dynamic and nonlinearphenomena such as shocks, Mach cones, solitons, waves, elastic and plastic deformations can be observedat the kinetic level.
The experiments were performed in a capacitively coupled radio-frequency (rf) discharge. A poweredlower electrode and a grounded ring upper electrode were placed in a vacuum chamber. A constantworking pressure was maintained by a flow of argon. Monodisperse plastic microspheres were levitatedin the sheath above the lower electrode. They were confined radially in a bowl shaped potential formedby a rim on the outer edge of the electrode and formed a monolayer hexagonal lattice. They were excitedby voltage pulses applied to wires stretched above the electrode at approximately the same height as theparticles. A horizontal thin sheet of laser light illuminated the particles, which were imaged by a digitalvideo camera.
We performed a molecular dynamics (MD) simulation in order to support the experimental results.The molecular dynamics simulation code that we have developed solves the equations of motion foreach microparticle moving in a global parabolic confinement potential and interacting with every othermicroparticle via a Yukawa potential [1]. The code is based on an object-oriented multi-threaded pro-gramming. It can be used to simulate various particle systems which can be characterised by interactionforces or potentials such as complex plasmas, colloids, granular media, plasma doping, ion beams, filmgrowth, ion implantation. The equations of motion are solved using the fifth-order Runge Kutta methodwith the Cash Karp adaptive step size control. The ion-electron plasma is not explicitly included in theequations. The grains are damped by the friction force (equal to the neutral gas damping). We considerthree- and two-dimensional (2D) systems of 3000 microparticles, which are first seeded randomly and thecode is run until a crystalline structure is formed. Then different excitation forces are applied during ashort time on the lattice.
We use an experimental model system (complex plasma) and MD simulation to study the dynamicsof defects in 2D hexagonal lattices: dislocations or penta-hepta defects. We focus on their interactionswith localized compressional waves in complex plasma crystals.
[1] C. Durniak, D. Samsonov, S. Zhdanov, and G. Morfill, EPL 88, 45001 (2009).
Modal interactions in thin structures: some experiments onnon-linear vibrations of spherical shells and percussion musicalinstruments
Olivier Thomas1 & Cyril Touze2
1 Structural Mechanics and Coupled Systems Laboratory, Conservatoire National des Arts et Metiers, Paris,France
2 Unite de Mecanique, Ecole Nationale Superieure des Techniques Avancees, Palaiseau, France
Structures with a thin geometry, like beams, plates and shells, can exhibit large amplitude flexuralvibrations, whose magnitude is comparable to the order of their thickness. In those cases, typical non-linear behaviors can be observed. Among others, the response of the structure can exhibit multiplestable solutions that lead to jump phenomena and significant non-linear energy transfers between modes,associated to quasi-periodic and chaotic motions. Those phenomena are encountered in various engineeringstructures, from macro-scale structures such as helicopter blades to micro and nano-electromechanicalstructures (M/NEMS). They are the main physical source of the particular sound of percussion musicalinstruments such as gongs and cymbals.
The purpose of the present study is to present some experiments on non-linear vibrations of percussionmusical instruments and similar circular plate and shell structure, in order to give insights in their non-linear vibratory behavior and to explain some features of their particular sound. In a first part, a chinesegong excited by a harmonic force in the vicinity of one natural frequency enables to exhibit a genericroute to chaos observed in those shell-like structures. For low excitation levels, periodic motions areobserved, with a motion dominated by one master natural mode. Then, a first bifurcation lead to a quasi-periodic regime where several vibration modes exchange energy with one another. This specific vibratoryregime appears when internal resonances (i.e. specific algebraic relations between the natural frequencies)between modes are present. Finally, a second bifurcation is observed, leading to a chaotic motion.
In a second part, a detailed study of some non-linear forced vibration regimes involving internalresonances is proposed. Two cases are studied: a 1:1 internal resonance in a circular plate and a 1:1:2internal resonance in a shallow spherical shell. In both cases, because of the rotationally symmetricgeometry of these structures, all modes with nodal diameters appear in pair, with both modes associatedto the same natural frequency (leading to the 1:1 resonance) and their modal shapes differing only bythe angular position of their nodal diameters. In the case of the spherical shell, the 1:1:2 resonance isobserved between an axisymmetric mode and two companion asymmetric modes of half its frequency.The amplitudes of the modes, as measured by accelerometers, are shown as a function of the excitationfrequency, its amplitude being kept constant. Various coupled regimes are exhibited, leading to jumpphenomena and traveling wave motions. Movies obtained with stroboscopic lighting are also available. Theobtained frequency response curves are successfully compared to reduced order models composed of twoor three non-linear oscillators with coupled quadratic and cubic non-linear terms, that help understandingthe observed particular coupled vibratory regimes.
Part V
Neuronal Dynamics
Synchronization of uncoupled excitable sytems induced bywhite and coloured noise
Riccardo Meucci1, Samuel Zambrano2, Ines P. Marino2, Jesus M Seoane2, Miguel A. F. Sanjuan2,Stefano Euzzor1, Andrea Geltrude1, & Tito F. Arecchi1
1 Istituto Nazionale di Ottica, Largo E. Fermi 6, 50125 Firenze, Italy2 Universidad Rey Juan Carlos, Tulipan s/n, 28933 Mostoles, Madrid, Spain
We study, both numerically and experimentally, the synchronisation of uncoupled excitable systemsdue to a common noise. We consider two identical FitzHugh-Nagumo (FHN) systems, which displayboth spiking and non-spiking behaviours in chaotic or periodic regimes. An electronic circuit provides alaboratory implementation of this dynamics. Synchronisation is tested with both white and coloured noiseshowing that coloured noise is more effective in inducing synchronisation of the systems. We also studythe effects on the synchronisation of parameter mismatch and of the presence of intrinsic (not common)noise, and we conclude that the best performance of coloured noise is robust under these distortions.Similar results are being obtained experimentally in a circuit with four uncoupled FHN with commonnoisy input.
Chaos may facilitate decision making in the brain
Yoshito Hirata1, Yoshiya Matsuzaka2, Hajime Mushiake2, & Kazuyuki Aihara1
1 Institute of Industrial Science, The University of Tokyo, Tokyo, Japan2 Department of Physiology, Tohoku University School of Medicine, Sendai, Japan
Although there are ample evidences for deterministic chaos in neuronal activity in vitro, few in vivostudies have reported the existence of chaos in the brain. Assuming that it exists, its functional role is stillunclear. In this presentation, we examine whether three regions of the brain are of deterministic chaosor not while a monkey performs an arm reaching task. For the analysis, we used the distance betweenspike trains two of us recently proposed (Hirata and Aihara, J. Neurosci. Methods (2009)) and examinedwhether two similar spike trains diverge or not, as the time elapses since the cue onset. We found that, insome regions of behaving monkeys, the initially similar spike trains diverged immediately after the onsetof cues. Therefore, deterministic chaos may play an important role in decision making in the brain.
NONTRIVIAL EFFECTS OF NOISE IN EXCITABLEELECTRONIC CIRCUITS
Guillermo V. Savino2, Roberto R. Deza1, & Carlos Formigli2
1 IFIMAR (UNMdP and CONICET) Mar del Plata, Argentina2 Fac. de Ciencias Exactas y Tecnologıa, Universidad Nacional de Tucuman, Argentina
We present experimental results on noise-induced synchronization, stochastic resonance, coherenceresonance and frequency matching using two non-identical weakly coupled electronic models of a neuron.Electronic neurons are always non-identical due to the value dispersion of the electronic components,and they are unavoidably coupled when using a common noise source. Our circuit can be tuned toself-oscillate so as to produce (i) single spikes at non-regular inter-spike intervals, or (ii) spikes thatare interspersed with two- and three-spike bursts. The phase portrait shows a stable limit cycle and asaddle point, originating thus a stable and an unstable manifold, both necessary to get noise-inducedphase synchronization according with previous theoretical models. By applying to two such “neurons”a common noise of increasing intensities, their initially very different instantaneous frequencies tend tomatch and the system‘s behavior to become periodic. We show that this effect is noise-mediated, ratherthan due to the weak coupling. The measured activation times become equal in both oscillators for adefinite noise intensity, and the same occurs for excursion times. Experimental evidences support thehypothesis that the mechanisms of coherence resonance are operating.
The plot of the phase differences between the spike sequences in both circuits as function of timefor different noise intensities shows plateaus with different durations, indicating phase synchronizationinduced by the common noise. Nevertheless, complete synchronization has not been observed.
Our experimental results are relevant for real neurons, since our circuit shares the same bifurcationscenarios, and the underlying mechanism—namely conductivity change—is the same. These experimentsmay thus help understand how neurons transmit, encode and process information.
Complex networks in the evaluation of brain injury therapy.
Inmaculada Leyva1, Nazaret Castellanos2, & Javier M. Buldu1
1 Dep. Signal Theory and Communications. Universidad Rey Juan Carlos, Madrid, Spain.2 Centro de Tecnologıa Biomedica, Escuela de Telecomunicaciones, Universidad Politecnica de Madrid, Madrid,
Spain.
Acquired Brain Injury (ABI) constitutes one of the leading causes of mortality and disability aroundthe world . The mechanisms that take place within the brain during the recovering process and the waycortical reorganization occurs have not been completely unveiled. Due to contradictory results reported inliterature about the increase or decrease of neuronal activation after rehabilitation, we consider necessaryto deal recovering from a point of view that takes into account the changes in interaction between brainareas, not just measuring the local changes in patterns of activation. Modern neuroscience research hasshown that the notion of localized brain functions is insufficient, especially when dealing with higher brainfunctions. Indeed, cognitive functions in the brain require the functional interactions between multipledistinct neural networks. The idea that the brain is a complex network of dynamical systems with abun-dant interactions between local and more remote brain areas with the potential capability to compensatefor lesions optimally fit with the study of the brain strategies for brain injury rehabilitation. Althoughanatomical reorganization also occurs in the cortex immediately after a lesion-induced injury, the ex-tension of this phenomenon to distant but interconnected areas has not been demonstrated. However,patients with ABI often undergo from diffuse alteration of cognitive functions that cannot be explained bya focal alteration of their brain functions, probably because lesion interferes with widespread functionalnetworks in the brain and not only in the adjacent region of the lesion. Most studies have focused onlocal dysfunction, reporting changes observed just in the spatial dimension of analysis. Our point of viewis to study the impact of a lesion on the brain on the functional interactions (functional connectivity)that takes place between brain regions. In the study of such interaction between brain areas the conceptof functional connectivity has emerged, referring to the statistical interdependencies between physiolog-ical time series recorded in various brain areas simultaneously. Functional connectivity is, probably, anessential tool for the study of brain functioning, and their deviation from healthy patterns could be usedas a reflect of lesion. To our knowledge, studies researching functional connectivity in ABI patients andcomparing with healthy controls in order to check the recovering have not been performed yet. In thiswork we aim to capture differences in connectivity pattern properties, from the point of view of graphtheory, in ABI patients before and after a rehabilitation treatment. In this work, we show as the nerworktheory tool help us to quantify and determine the network restoring, using different parameters thatevaluate the changes both in the global, lobe and local scales.
Part VI
Chemical Dynamics
Some Natural Geological Systems Possibly Related to theLiesegang Phenomenon
Rabih Sultan1 & Abdel-Fattah Abdel-Rahman2
1 Department of Chemistry, American University of Beirut, Beirut, Lebanon2 Department of Geology, American University of Beirut, Beirut, Lebanon
The Liesegang phenomenon is the display of parallel bands of precipitate formed periodically whenco-precipitate ions interdiffuse in a gel medium. Spectacular textural features occurring in geodes, agates,malachites, as well as in some mineral bands that characterize stratigraphic units of some rock formationshave been reported in the literature as examples of naturally appearing Liesegang patterns. In thiscontribution, we attempt to raise questions related to the possible presence of an explanation of whetherthe mechanism of the Liesegang phenomenon can be considered as a viable mechanism to produce similarfeatures observed at a small (mm) scale of strongly zoned feldspar crystals, as well as at large (km) scalemagma chambers. Questions such as: Could zonations characteristic of some large scale circular zonedplutons and anorogenic ring complexes that typically range in size from two to ten km be somehow relatedto the Liesegang phenomenon at a magma chamber level? Could cyclic layering in large mafic/ultramaficlayered intrusions represent a natural expression of the Liesegang mechanism? Could features observed inorbicular granites at hand sample (cm) scale be related to the Liesegang mechanism? We examine whetherLiesegang systems, which exhibit spatial oscillations due to periodic precipitation obtained through thecoupling of the precipitation reaction with diffusion are applicable to small-scale, as well as large-scaleself-organization geological features.
For geochemical self-organization to operate via a Liesegang-type mechanism, a necessary conditionis that the system be transiently out of equilibrium as established by the Brussels school led by I.Prigogine. The dynamical equations describing the evolution of the system are nonlinear, and involvethe coupling of chemical reaction kinetics to the laws of transport processes. Such a complex underlyingdynamics provides a clearly different scenario from mere seasonal variations, believed to be functionalin, say, sedimentary layering. Patterns in banded iron or goethite formation were shown to have beendifferentiated from an initially uniform sediment. Marl/limestone alternations arise from a diageneticself-organization mechanism, coupled to a very limited external trigger. A requirement for maintainingthe system out of equilibrium during the formation process is that free energy be constantly dissipated.Such conditions are fulfilled in a host of examples in geological processes. Local perturbations in T andP, as well as mass exchange near the contact zone between the magma and a neighboring solid inducechanges in the free energy. Stresses experienced by metamorphic and sedimentary rocks drive alterationsin the free energy of neighboring grains.
In this study, we analyze a wide spectrum of geological patterns and examine the viability of theprevailing conditions of their formation, in relation with the various requirements for the growth ofLiesegang structures.
Strong Field Double Ionization: Insights from NonlinearDynamics
Francois Mauger1, Cristel Chandre1, & Turgay Uzer2
1 Centre de Physique Theorique, UMR 6207, Campus de Luminy, case 907, 13288 Marseille cedex 9, France2 School of Physics, 837 State Street Atlanta, Georgia 30332-0430, U.S.A
One of the most striking surprises of recent years in laser-matter interactions has come from multipleionization by intense short laser pulses. Multiple ionization of atoms and molecules is usually treated as arapid sequence of isolated events. However, in the early 90’s, experiments using intense laser pulses founddouble ionization yields which departed from these predictions by several orders of magnitude. It hasmade the knee shape in the double ionization probability versus intensity curve one of the most dramaticmanifestation of electron-electron correlation in nature.
It turns out that entirely classical interactions are adequate to generate the strong two-electron cor-relation needed for double ionization: numerical simulations succeed to reproduce qualitatively the kneeshape observed experimentally. The central question is how two electrons leave the nucleus under theinfluence of a short and intense laser pulse? The precise mechanism that makes electron-electron corre-lation so effective follows the recollision scenario: An ionized electron, after picking up energy from thefield, is hurled back at the ion core upon reversal of the field and dislodges the second electron.
In this talk, I will revisit the recollision mechanism, a keystone of strong-field physics, using a nonlineardynamics perspective. I will show that this recollision scenario has to be complemented by the dynamicalpicture of the inner electron. Using this global picture of the dynamics, we were able to derive verifiablepredictions on the characteristic features of the ”knee”, a hallmark of the nonsequential process.
Many questions remain unanswered regarding strong-field double ionization, and one that is still com-pletely open concerns polarization. The stakes are high when it comes to understanding the influenceof polarization since it is well known that the emission of harmonics is strongly dependent on the ellip-ticity of the driving field. A common wisdom is that the recollision scenario is suppressed with circularpolarization (CP) since an ionized electron tends to spiral out from the core. The matter would restthere if it were not for conflicting experimental evidence: In some experiments using CP fields, the doubleionization yields follow the sequential mechanism whereas in others these yields are clearly several ordersof magnitude higher than expected. The question we resolve here is: Are recollisions possible in pure CPfields or does one have to rely on a small residual ellipticity? We explain these seemingly contradictoryfindings and show that, contrary to common belief, recollision can be the dominant mechanism leadingto enhanced double ionization yields in CP fields.
[1] F. Mauger, C. Chandre, and T. Uzer, Phys. Rev. Lett., v. 102, p. 173002, 2009.[2] F. Mauger, C. Chandre, and T. Uzer, Phys. Rev. Lett., v. 104, p. 043005, 2010.[3] F. Mauger, C. Chandre, and T. Uzer, http://arxiv.org/abs/1002.2903.
Pattern formation and chaotic dynamics in a three-waycatalytic reactor with cross-flow
Martin Kohout1, Otto Hadac1, Jaromir Havlica2, & Igor Schreiber1
1 Department of Chemical Engineering, Center for Nonlinear Dynamics of Chemical and Biological Systems,Institute of Chemical Technology, Prague, Technicka 5, 166 28 Prague 6, Czech Republic,
2 Institute of Chemical Process Fundamentals, Academy of Sciences of the Czech Republic, Rozvojova 135, 16502 Prague 6, Czech Republic
A three-way catalytic converter (TWC) is the most common reactor for detoxification of automobileexhaust gases. This catalytic reactor is typically operated with periodic variation of inlet oxygen concen-tration. In the TWC carbon monoxide, hydrocarbons and nitrogen oxides are transformed into carbondioxide, nitrogen and water vapor. Dynamics of models describing this complex catalytic reaction settaking place in a cross-flow tubular reactor are examined.
We begin with a detailed kinetic model proposed for three-way catalytic converters. In an effortto relate resulting patterns to specific pathways in the mechanism we select two reaction subsystemscombining CO oxidation with oxidation of C2H2 and with NOx reduction. The ability of these twosubsystems to generate nonlinear dynamical effects is examined first by neglecting transport phenomenaand studying a lumped (CSTR) system with the use of stoichiometric network and bifurcation analysis.
Spatiotemporal behavior due to reaction kinetics combined with transport processes have been furtherstudied in tubular reactor with cross-flow (TFR). Based on knowledge of the lumped dynamics, theobserved spatiotemporal patterns are classified as phase waves, travelling front and pulse waves andchaotic spatiotemporal patterns. Their dependence on input parameters is systematically studied andtheir relation to different unstable reaction pathways is discussed.
Time series analysis of an pH oscillatory chemical reaction
Igor Schreiber1, Daniel Bakes1, Lenka Schreiberova1, & Marcus Hauser2
1 Institute of Chemical Technology, Prague, Department of Chemical Engineering, Technicka 5, 166 28 Prague6, Czech Republic
2 Otto-von-Guericke Universitat Magdeburg, Institut fur Experimentelle Physik, Universitatsplatz 2,Magdeburg, Germany
We examine transition from periodic to chaotic oscillations experimentally observed in the continuousstirred tank reactor with the reaction of hydrogen peroxide, thiosulfate and sulfite in weakly acidicenvironment (HPTS) and presence of carbon dioxide. The HPTS reaction is an pH oscillator signifyingthat the hydrogen ions take part in the autocatalysis. Mixed-mode oscillations and chaos have beenobserved earlier but no detailed quantitative analysis of the degree of chaoticity were determined. Thereaction is sensitive to the presence of carbon dioxide and a controlled inflow of this reactant has beenchosen as the bifurcation parameter.
The measured time series of pH indicate simple periodic oscillations, mixed-mode oscillations of variousdegree of complexity and apparently chaotic oscillations with no distinct separation of amplitudes. We useSVD-based methods for reconstruction of phase portrait, noise reduction and determination of embeddingdimension. There seem to be a few dozens of modes involved in building up the attractor and its geometryappears quite complex. We also calculate maximum Lyapunov exponent, which turns to positive valuesas the periodic mixed-mode regime transforms into chaos.
Building on an early version of a mechanism of this complex chemical reaction, we present an ex-tended version and discuss its potential for reproducing the experiments using an approach based onstoichiometric network analysis.
Part VII
Dynamos
Kinematic dynamo threshold in time dependent velocity fields.
Miguel Lopez & Javier Burguete
C/Irunlarrea S.N., Dep. of Physics and Appl. Mathematics Edificio Los Castanos. , Pamplona, Navarra, Spain,31008
Conducting neutral fluid flows can be dramatically different from the non-conducting case because oftheir interaction with magnetic fields, either internal (self-sustained) or external (forcing). In this work wepresent an experimental analysis of a von Karman swirling flow and the influence of this hydrodynamicsin the generation of a magnetic filed.
The objective is to determine the effect of time dependent flows in the threshold of the dynamo action.To achieve this goal, we have characterized the flow before this instability in a model experiment (usingwater). This velocity field, determined only by the hydrodynamics, has been used to find out the MHDeffects. The fluid has been stirred in a cylindrical cavity up to a Reynolds number of 106. We show thatthe average velocity field of the turbulent flow bifurcates subcritically breaking some symmetries of theproblem and becomes time-dependent because of equatorial vortices moving with a precession movement.This subcriticality produces a bistable regime, with a hysteresis region for an extremely small range ofparameters. Three different time-scales are relevant to the dynamics, two of them very slow compared tothe impeller frequency.
We have studied the different time scales of the system, changing a enclosure volume (neutrallybuoyant spheres) assuming that the density of the sphere is homogeneous. We follow this volume in aperiod of time and we compare the results in different spatial scales.
The effect of these different time-scales and symmetry-breaking’s has been tested in a kinematicdynamo code. The threshold strongly depends on the existence of these features.
Large scale fluctuations and dynamics of the Bullard - vonKarman dynamo
Nicolas PLIHON, Gautier VERHILLE, Mickael BOURGOIN, Romain VOLK, & Jean-FrancoisPINTON
Laboratoire de Physique ENS Lyon - CNRS UMR 5672
The importance of turbulent induction processes in dynamo action has been recognized for mostnatural dynamos. More recently, the von-Karman Sodium dynamo showed the importance of turbulentfluctuations in the generation and dynamics of the magnetic field. We will present and analyze thefeatures of an experimental synthetic fluid dynamo built in the spirit of the Bullard dynamo. It is atwo-step dynamo in which one process stems from the fluid turbulence, while the other part is achievedby a linear amplification of currents in external coils, as in the Bullard device. The fluid turbulent processis based on a von-Karman gallium flow; hence the designation ”Bullard-von-Karman dynamo”.
The Bullard-von-Karman dynamo allows to investigate the influence of the statistical properties ofthe turbulent induction process on the dynamics of the dynamo. Modifications in the flow forcing areintroduced in order to change the dynamics of the flow, and hence of the turbulent induction.
On-off intermittency at onset of dynamo action has been characterized. The on-off intermittent featureappears to be very robust at onset but its range of existence strongly depends on the low frequencyspectrum of the turbulent induction process. For some conditions, magnetic field reversals have beenobserved. The waiting-time distribution between reversals has been found to evolve from power-law toPoisson-like depending on the distance from onset. The large scales fluctuations also have a significantimpact on these reversals.
Most of these experimental results can be understood as emerging form a supercritical system subjectto multiplicative noise. Some other features (such as reversals) requires the presence of additive noiseand their precise understanding remains a challenge. The links and differences with the dynamics of thevon-Karman Sodium dynamo will also be discussed.
Soft iron impellers: Induction mechanism and dynamo
Gautier Verhille1, Nicolas Plihon1, Mickael Bourgoin2, Philippe Odier1, & Jean-Francois Pinton1
1 Laboratoire de Physique, CNRS & Ecole Normale Superieure de Lyon, UMR5672, Universite de Lyon, 46Allee d’Italie, F69007, Lyon, France
2 Laboratoire des Ecoulements Geophysiques et Industriels, CNRS/UJF/INPG UMR5519, BP53, F38041Grenoble, France
The VKS experiments have shown a remarkable variety of dynamo regimes in a von Karman (VK) flowof liquid sodium, with following main characteristics which we want to address: i) dynamo action has onlybeen observed when soft iron impellers are used to drive the fluid motion, ii) for exact counter-rotation ofthe impellers, the magnetic field generated is an axial dipole whereas numerical simulation which do notinclude ferromagnetic boundaries predict a transverse dipole, iii) when the forcing is asymetric, dynamicalregime may occur and can be described by a low dimensional involving only 2 magnetic modes.
In order to understand the role of soft iron, we have studied induction processes in a gallium vonKarman flow, with impellers made of different materials (stainless steel, soft iron and copper). Ourresults show that the soft iron promotes induction processes localized near the impellers. Extending ourresults to VK flows in liquid sodium (at significantly higher magnetic Reynolds numbers), we proposea mechanism for dynamo generation in VKS. This mechanism successfully accounts for the 3 pointsmentioned above.
Part VIII
Cardiac Dynamics
Statistical monitoring of atrial fibrillation ?
Guillaume Attuel1, Patrick Attuel3, Nicolas Derval2, Leon Glass1, & Jean-Michel Haissaguerre2
1 CND McGIll, 3655 Promenade Sir William Osler, Montreal, Quebec H3G 1Y6, Canada2 Hopital Haut-Leveque Avenue de Magellan 33604 Pessac CEDEX, CHU Bordeaux, France3 CMC Parly II, 21 rue Mouxouris 78150 le Chesnay, Versailles, France
It is an open question, whether complex fragmented activity during fibrillation in the atrium, mightcharacterise the stage of the pathology. Eventually, this could be used as genuine monitoring during ab-lation. We adress it by analysing the statistical properties of human’s endocavitary electrograms duringablation. Particular attention is given to the fluctuations of the potential, which are in general not consid-ered as relevant, for lack of clear interpretation. We believe that these are prototypical of non-equilibriumfluctuations, and that interpretation can be confidently envisaged from their statistical properties. Arecent theoretical clarification on the probability distribution functions is a basic guideline for the study.
Part IX
Granular Materials
Transition Dynamics of Structural Motifs in a Granular ContactNetwork
David Walker1, Antoinette Tordesillas1, Gary Froyland2, & Robert Behringer3
1 Department of Mathematics and Statistics, University of Melbourne, Parkville, VIC 3010 Australia2 School of Mathematics and Statistics, University of New South Wales, Sydney NSW 2052 Australia3 Department of Physics, Duke University, Durham, NC 27708 USA
A deforming dense assembly of granular particles can be usefully represented by its evolving contactnetwork. A study of the 3-cycle motifs of the contact network and their interplay with the force chains ofstructural mechanics reveals that in an effort to ward off imminent failure a granular material rearrangesto form structures akin to the power towers seen in theme parks. A more detailed investigation of othernetwork motifs, in particular their transition dynamics, uncovers the most prevalent and almost-invarianttransition sets of motifs within the material. When further coupled, at the meso-scopic scale, to a measureof structural stability we begin to probe the role these granular motifs play in the self-organizationproperties and preferred configurations apparent in a granular material subject to loading. Results arepresented for an experimental biaxial apparatus of bi-disperse photo-elastic disks subject to pure shear.
Interaction of a bouncing ball with a sinusoidally vibrating table
Elbert Macau1, Marcus V. Carneiro2, & Joaquim J. Barroso3
1 Computing and Applied Mathematics Laboratory / National Institute for Space Research (INPE) / 12227-010- Sao Jose dos Campos - SP - Brazil
2 Swiss Federal Institute of Technology (ETH-Zurich)3 Associated Plasma Laboratory / National Institute for Space Research (INPE) / 12227-010 - Sao Jose dos
Campos - SP - Brazil
Exploring all its ramifications, this presentation gives an overview of the simple yet fundamentalbouncing ball problem, which consists of a ball bouncing vertically on a sinusoidally vibrating table underthe action of gravity. The dynamics is modeled on the basis of a discrete map of difference equations, whichnumerically solved fully reveals a rich variety of nonlinear behaviors, encompassing irregular non-periodicorbits, subharmonic and chaotic motions, chattering mechanisms, and also unbounded non-periodic orbits.For periodic motions, the corresponding conditions for stability and bifurcation are determined fromanalytical considerations of a reduced map. Through numerical examples, it is shown that a slight changein the initial conditions makes the ball motion switch from periodic to chaotic orbits bounded by a velocitystrip v = ±Γ/(1 − ε), where Γ is the non-dimensionalized shaking acceleration and e the coefficient ofrestitution which quantifies the amount of energy lost in the ball-table collision. Moreover, a detailednumerical discussion of the excitation of the unstable 1-periodic mode and the ensuing transition to itsstable counterpart mode is also given.
Bouncing trimer, bouncing droplet: bouncing modes
stephane dorbolo1, nicolas vandewalle1, denis terwagne1, francois ludewig1, & tristan gilet2
1 GRASP-Departement de Physique- Universite de Liege2 Mathematic department-MIT-Boston-USA
The bouncing ball on a vibrating surface is among the simplest systems that exhibit chaotic features.This problem involves non linear behaviours such as period doubling, orbits, and transition to chaos, thatare still far from being exhaustively investigated. The bouncing ball is often considered as a point particle,and we may wonder how a more complex item bounces on the vibrating surface. This communicationpresents some experiments in which degrees of freedom are progressively added to the bouncing item.First, we have studied objects constituted by two or three linked centimetrical beads (they are calleddimer and trimer), that may translate and rotate. Then, we introduced the deformation by studyingthe dynamics of a bouncing droplet on a high viscous silicone oil bath. In both cases, exotic bouncingmodes can be observed: self-propulsion for dimer, rotation and period-3 for trimer, rolling droplets, doubleemulsification,... Experimental and simulation movies will be shown for both studies.
Part X
Optical Systems
Temporally nonlocal electro-optic phase dynamics for 10 Gb/schaos communications
Laurent Larger, Roman Lavrov, & Maxime Jacquot
FEMTO-ST / Optics dept., University of Franche-Comte, 16 route de Gray, 25030 Besancon cedex, France
Since the demonstration of chaos synchronization 20 years ago, chaotic dynamics in photonic systemshas been intensively explored as a mean of providing enhanced physical layer data protection in opticalcommunications. Although many popular setups are based on chaotic behaviour of lasers subject toelectrical or optical feedback, this approach is currently limited to transmission rates of 2.5 Gbit/s,and requires additional error correction to obtain sufficient link quality (due to low synchronizationquality). On the other hand, chaos communications based on electro-optic feedback has been studiedand demonstrated as an alternative approach, and indeed has been also successfully used in earlier fieldexperiments at comparable bit rates. In this talk, we report on a new electro-optic approach based onthe architecture of nonlocal nonlinear delayed electro-optic phase modulation. The oscillator is ruled by a4-time scale dynamics spanning from the 10ps up to 10µs, and including two distinct time delays (a longone with 10s of ns, and a short one of about 500ps). Modeling, experimental and numerical results willexplore the route to chaos of the EO phase dynamics. A full emitter / receiver scheme will be reported,together with its synchronization capability over a bandwidth greater than 10GHz. Real world datatransmission over installed fiber network will be reported, with data rate as high as 10 Gbit/s over up to100 km of fiber, and bit error rates as low as 10−9. As far as we know, our recent results is representingthe best performance to date in optical chaos communication. Other applications of our EO setup willbe discussed, such as ultra-fats random number generator, and reservoir computing.
Experimental signature unveiling the new route to amplitudedeath in delay-coupled diode lasers system
Pramod Kumar1,2
1 Laboratoire Commun de Metrologie LNE-CNAM*, 61 rue du Landy, F-93210 La Plaine Saint Denis (France)2 Laser Physics and Quantum Optics Laboratory, School Of Physical Sciences , Jawaharlal Nehru University ,
New Delhi-110067, India.
The Radiation emitted from diode lasers, subjected to external optical perturbation, exhibits aplethora of dynamical instabilities such as, low frequency fluctuations appear in their radio-frequencyspectrum that are evident as dropout events in the intensity time traces. Traditionally these events wereobserved to occur at sporadic time intervals. However, recent experimental and theoretical measurements[1, 2] have shown that there are regions of the self-feedback strength and round trip time where theseevents appear at regular time intervals. Amplitude death is one of the fascinating collective behaviorwhere coupled lasers drive to each other to stabilize these low frequency dynamical instabilities. Couplinginduced stabilization is known to occur via either the change the stability of unstable fixed points whichis already exists in the absence of coupling or the stationary state can be entirely newly created by thecoupling. Either the large mismatch in the oscillation frequencies (Saddle-node Bifurcation) or the exis-tence of time delay in the coupling (Hopf Bifurcation) have been thought be the necessary conditions forthe route to occurrence of amplitude death state. But in this present work we report for the first timethe new route to ultimate amplitude death phenomena arising when External cavity diode laser (ECDL)is coupled with another solitary diode laser via pure optical injection. So in our coupled diode laserssystem, the ECDL works as optical amplifier (working below the free running lasing threshold becauseof optical self-feedback effect) and other optical injecting solitary diode laser work as oscillator (workingat free running lasing threshold). That is why the combined coupled diode lasers system is quit differentfrom well known coupled oscillators system. Therefore the route to stabilization (amplitude death)of oursystem will be different from traditional coupled oscillators. Physically, two delayed injecting fields (self-feedback by external cavity and delayed injection by solitary laser ) interact within the gain medium ofECDL and share the same population inversion and compete in kind of opposite directions. We find thatthe system undergoes series of transition during the road to amplitude death as the coupled cavity delaytime and relative coupling strength [1] are varied. The experimental observations are in good agreementwith the simulated results.
[1] Pramod Kumar, A. Prasad and R. Ghosh, J. Phys. B 41, 135402 (2008).[2] Pramod Kumar, A. Prasad and R. Ghosh, J. Phys. B 42, 145401 (2009).
Feedback Bandpass filter effects in the dynamics of anoptoelectronic wavelength nonlinear delay system
Maxime jacquot, Romain Martinenghi, Yanne Kouomou Chembo, & Laurent Larger
Optics Dept. / FEMTO-st / Besancon / France
In a previous work [1], we studied experimentally, numerically, and analytically the response of anonlinear optical oscillator subject to a delayed broadband bandpass filtering feedback. Its dynamicalresponse was described by an integro?DDE that differs from Ikeda family of first order DDEs, only bythe presence of an integral term. In this talk, we report on an optoelectronic wavelength nonlinear delaydynamics ruled by a feedback tunable bandpass filter. The particular influence of this filtering feedbackdetermining the differential process of the dynamics is presented both experimentally and numerically.Multiple time scales phenomena like slow and fast periodic regime, regular or chaotic breathers, envelopedynamics, complex self pulsing, and fully developed chaos are observed ranging over several orders ofmagnitude, under various parameter and filtering feedback conditions. Time-frequency approach withwavelet transform is proposed in order to analyze multi-scale behaviour of the recorded time series. Theinfluence of the characteristic delay frequency, and its location in the Fourier spectrum with respect tothe filtering feedback cut-off is also reported. The observed behaviour offer attractive potential for manyapplications, e.g. in chaos?based communications, high spectral purity microwave generation, randomnumber generation and chaos computing.
[1] M. Peil, M. Jacquot, Y.C. Kouomou, L. Larger, T. Erneux, ”Routes to Chaos and Multiple TimeScale Dynamics in Broadband Bandpass Nonlinear Delay Electro-Optic Oscillators”, Physical Review E,Vol.79, 026208, February 2009.
Experimental Evidence of Microwave Envelope Chaos using anIntegro-Differential Optoelectronic System
Yanne Chembo, Kirill Volyanskiy, Maxime Jacquot, & Laurent Larger
FEMTO-ST Institute (UMR CNRS 6174), Optics department, 16 route de Gray, 25030 Besancon cedex, France
A very wide variety of systems have been shown to display a chaotic behavior since the pioneeringwork of Lorentz in the early sixties. This ubiquity has been experimentally evidenced in a very wide rangeof frequencies, ranging from the low frequency of mechanical oscillators to the ultra-high frequencies ofamplitude/phase chaos in lasers.
In this communication, we experimentally evidence a spectrally interesting chaotic dynamics, wherea 3 GHz microwave is driven to a state where only its slowly varying complex envelope becomes chaotic.In the Fourier domain, the system has a quasi-white spectrum within a very narrow bandwidth (16 MHz)around the central frequency of the carrier.
This dynamics is generated using a narrow-band optoelectronic oscillator. The corresponding modelis an integro-differential delay differential equation, and it enables to analyze the essential dynamicalfeatures of the system. Beyond the interest to be devoted to this oscillator for its fondamental interest,it also appears to be the idoneous tool for many applications. In particular, we will explain how it couldbe used to implement chaos cryptography in free-space microwave telecommunication networks, or toimprove the performances of wideband radar systems.
Synchronization and mixed mode oscillations in a network ofcoupled light emitting diodes
Marzena Ciszak1, Sora F. Abdalah1,2, Kais Al-Naimee1,3, Francesco Marino4, Riccardo Meucci1, & TitoF. Arecchi1,4
1 CNR-Istituto Nazionale di Ottica, L.go E. Fermi 6, 50125 Florence, Italy2 High Institute of Telecommunications and Post, Al Salihiya, Baghdad, Iraq3 Physics Department, College of Science, University of Baghdad, Al Jadiriah, Baghdad, Iraq4 Physics Department, University of Florence, I-50019 Sesto Fiorentino (FI), Italy
We present results on the synchronization in a network of coupled light emitting diodes (LED) in thepresence of AC-filtered nonlinear opto-electronic feedback. Each LED can undergo a variety of dynamicalbehaviours like chaotic and periodic mixed mode oscillations. These scenarios are found in a simplifiedphysical model of the experimental system. The aim of the research is to create a miniaturized LEDnetwork containing many nodes imitating a neural network. Here we present experimental and numericalresults for the transition to synchronization of N ≤ 6 nodes coupled in the global configuration.
Bursting dynamics in a two-mode semiconductor laser withoptical injection: experimental results and theoretical analysis
Stephen O’Brien, Simon Osborne, David Bitauld, & Andreas Amann
Tyndall National Institute, Lee Maltings, University College, Cork, Ireland
In this work we describe our recent experimental and theoretical studies of bursting dynamics inan optically injected two-mode semiconductor laser. The device we consider is a specially engineeredFabry-Perot laser diode with a large (terahertz) primary mode spacing. This device can be biased suchthat both primary modes oscillate simultaneously with the same average power level. Where one of theprimary modes is optically injected, the presence of the second lasing mode leads to a very rich dynamicalscenario. In particular, we have found two distinct examples of dynamics that are associated with largeamplitude bursting of the intensity of the uninjected primary mode.
The first example is characterised by irregular bursting of the intensity of the uninjected mode inregions where the dynamics of the injected mode are chaotic. In contrast, the second example is charac-terised by regular bursts that are in antiphase and which have variable period. These regular dynamicsare found close to regions where dramatic switching between single and two-mode dynamical regimesoccurs.
We have found that both of these examples of dynamics are reproduced with remarkable accuracyby a deterministic four dimensional rate equation model. The structure of the model is such that thedynamics of the well-known model of the single mode injected system are contained in an invariant sub-manifold of the two-mode system. Irregular bursting dynamics are then described by on-off intermittencythat is associated with the transverse instability of chaotic dynamics in the injected mode submanifold.Experimentally, we have found significant departures from ideal scaling in the distribution of interbursttimes in this case. We are currently studying the effect of correlations on these distributions, which arein good agreement with modelling results.
On the other hand we show that the bifurcation scenario for regular bursting dynamics is organisedby codimension two points at which saddle node of limit cycle and transcritical bifurcation lines tan-gentially intersect. At the saddle node of limit cycle bifurcation line the time interval between burstsdiverges, and therefore gives rise to a dynamical behaviour which is similar to the Blue Sky Catastrophein generic systems. We discuss the associated phase space structure, and compare with other infiniteperiod bifurcations described in the literature.
Front dynamics in periodic modulated media
Florence Haudin1, Ricardo Gabriel Elias2, Rene Gabriel Rojas3, Umberto Bortolozzo1, Marcel GabrielClerc2, & Stefania Residori1
1 Institut Non Lineaire de Nice, Universite de Nice Sophia Antipolis, CNRS, 1361 route des Lucioles, 06560Valbonne, France
2 Departamento de Fisica, Facultad de Ciencias Fisicas y Matematicas, Universidad de Chile, Casilla 487-3,Santiago, Chile
3 Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso, Casilla 4059, Valparaiso, Chile
Front propagation in non equilibrium systems is a very rich and interesting phenomenon, present inmany different systems such as magnetic domains, chemical reactions or population dynamics [1]. Frontsare non linear solutions connecting two metastable states and propagating with a dynamics that dependson the nature of the states connected. For example, in a variational system, a front connecting two stablestates moves at a constant speed and always in such a way to develop the most stable state. In thatsituation, when one moves a single parameter, there is only one point where the energy of the two statesis equal and therefore, the front is motionless. A question that can be rised is how this motionless behaviorcan be extended to a large range of values of one control parameter. An answer to this question was givenby Pomeau [2], predicting that for fronts connecting a stable homogeneous state and a periodic state, apinning phenomenon of the front exists. Following this idea, the addition of spatial modulations on theoriginally homogeneous states, should be an efficient way to block the front over a large range of thecontrol parameter. In our work, we have investigated both experimentally and theoretically the pinning-depinning phenomenon in spatially modulated media. Experimentally, we have used a Liquid CrystalLight Valve (LCLV) with optical feedback. In a situation where fronts between two homogeneous statescan be observed, spatial intensity modulations were added on the input beam profile by using a SpatialLight Modulator. A 1d characterization of the dynamics with respect to the voltage applied to the liquidcrystal have been made first, and, then with respect to the spatial forcing parameters. The existence ofa pinning range was clearly highlighted and a front propagation by periodic leaps apart from this rangewas observed as well [3]. We have compared the experimental results with the theoretical predictionsobtained for the LCLV model accounting for the orientation of the liquid crystal molecules in presenceof an optical feedback and with spatial modulations of the input beam. It appears that close to thepoint of nascent bistability, it is possible to develop the model on a forced extended pitchfork bifurcationnormal form. Both results obtained with the complete LCLV model and with the normal form are ingood agreement with the experimental ones. A 2d extension of the 1d case was performed experimentallyusing stripe intensity masks as well as square and hexagonal modulations. The pinning phenomenon isobserved and characterized too. Finally, we show out that localized structures of different shape and sizecan be stabilized inside the pinning range.
Bibliography[1] M.C. Cross and P.C. Hohenberg, Rev. Mod. Phys. 65 851 (1993)[2] Y. Pomeau, Physica D, 23, 3 (1986)[3] F. Haudin, R. G. Elıas, R. G. Rojas, U. Bortolozzo, M. G. Clerc and S. Residori, Phys. Rev. Lett.
103, 128003 (2009)
Adaptive synchronization of a network of chaotic oscillators
Bhargava Ravoori, Adam Cohen, Francesco Sorrentino, Thomas Murphy, Edward Ott, & Rajarshi Roy
Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland20742, USA
Synchronization among networks of coupled chaotic systems is an interesting phenomenon with po-tential applications in sensor and communication networks. In order for a network of chaotic oscillatorsto admit a synchronous solution, each node must receive the same cumulative coupling from its peers.This constraint implies that the coupling matrix describing the network has a uniform row-sum. Thiscondition is difficult to achieve in practice. Moreover, even if synchrony is attained, environmental driftsand other network perturbations can cause the coupling strengths to change, making it impossible tomaintain synchrony over time.
We present here an adaptive control system [1] that overcomes these limitations. We experimentallyshow that the system can both acquire and maintain a state of global synchronization in a networkof chaotic oscillators even when the coupling matrix is unknown and time-varying [2]. Each node inthe network uses locally measured signals to construct a real-time estimate of its total input couplingstrength. A suitable multiplicative scaling is then applied to the coupling signal to ensure that all nodesin the network receive the same cumulative coupling, thus making synchronization feasible.
The network is comprised of three optoelectronic nonlinear time-delayed feedback loops which exhibithigh-dimensional chaotic dynamics [2, 3]. Each node is coupled to every other through a bidirectional fiber-optic link, and the coupling strengths are controlled using variable optical attenuators. Using the adaptivealgorithm we successfully synchronize the network under time-varying coupling conditions. Furthermore,we show that from the computed scale factors obtained at each node, we can deduce the coupling matrix,thereby enabling us to both track and localize disturbances and perturbations in the network.
References:[1] F. Sorrentino and E. Ott, Phys. Rev. Lett. 100, 114101 (2008); Phys. Rev. E 79, 016201 (2009).[2] B. Ravoori et al., Phys. Rev. E 80, 056205 (2009).[3] A. B. Cohen et al., Phys. Rev. Lett. 101, 154102 (2008).This work was supported by DOD MURI grant (ONR N000140710734).
Hybrid chaos based communication system - A chaoticallymasked electronic message transduced to an optical carrier fortransmission
Joshua Toomey1, Deborah Kane1, Aleksandar Davidovic2, & Elanor Huntington2
1 Physics Department, Macquarie University, Sydney, NSW 2109, Australia2 School of Information Technology and Electrical Engineering, University College, University of NSW,
Canberra 2600, Australia
Synchronised chaotic systems are the basis of secure communication using a chaotic carrier for mes-sage masking. Systems demonstrated to date have used nonlinear electronic circuits or nonlinear lasersystems to produce either an electronic or an optical chaotic carrier to which to add the data signal formasked transmission. The message can be recovered by virtue of a synchronised receiver only producinga match to the chaotic carrier, not the message. We have demonstrated a hybrid electronic/optical securecommunication system for chaotic signal masking. We use an electronic circuit to generate a chaoticcurrent signal in which a small message signal is added and masked. The combined chaos/message signalis added to the DC injection current of a semiconductor laser. The chaotic carrier plus message is repro-duced as the output power variations of the laser which is transmitted optically. Transmission is by line ofsight, free space propagation to an optical detector, although it is also possible to transmit via an opticalfibre. A matched receiver electronic circuit synchronises only to the chaotic part of the photodetectedsignal. We show the successful transmission and recovery of a chaos masked message. We will present theadvantages and disadvantages that this system has compared to all-optical or all-electronic chaos securecommunication systems and also the prospects for further research and development.
Joint polarization and spatial mode coding in isotropic two-lineCO2 laser
Riccardo Meucci1, Kais Al Naimee1, Sora Abdalah1, Tito Arecchi1, & Sergio De Nicola2
1 Istituto Nazionale di Ottica, CNR, Firenze, Italy2 Istituto Nazionale di Ottica, CNR, Pozzuoli, Italy
We study the dynamic interplay between the spatial distribution of low order modes ( say TEM01 andTEM10) and polarization in a CO2 laser with isotropic cavity, lasing on two different lines. We investigateon the role of optical feedback to achieve polarization stabilization or chaotic alternation between firstorder transverse modes. We discuss potential application of this dynamic interplay and we show that thepolarization of a given transverse mode can be controlled by means of a suitable optical feedback. In thisway, information can be encoded in the polarization process and it can be safely recovered by an identicalreceiver laser which is synchronized with the sender.
IDENTIFICATION OF MULTIPLE FOLDINGMECHANISMS OF CHAOS GENERATION BYTOPOLOGICAL ANALYSIS APPLIED TO A HIGHLYDISSIPATIVE SYSTEM
Juan Carlos Martın1 & Javier Used2
1 Department of Applied Physics, University of Zaragoza, C/ Pedro Cerbuna, 12, E-50009 Zaragoza, Spain2 Department of Physics, Univ. Rey Juan Carlos, C/ Tulipan s/n, E-28933 Mostoles, Madrid, Spain
The chaotic emission of an erbium-doped fiber laser with sine-wave pump modulation has been ana-lyzed for different modulation frequencies and modulation indexes. For each working condition considered,the template which summarizes the corresponding chaotic attractor has been determined by means oftopological analysis techniques. The interest of the work is double: on the one hand, because of the proce-dure employed for the analysis, which is not the conventional one; and on the other hand, because of thediversity of templates obtained, much wider than in any other experimental systems previously studied,and particularly because of the novelty of some of these templates.
As the system is highly dissipative, it is possible to complement the usual topological analysis proce-dure (1) with a different technique (2): the high dissipation causes that the Poincare sections obtainedare thin enough to be considered as a line. A continuous parameterization along this one-dimensionalobject can be defined so that the first-return map with regard to the parameter chosen is an application.Maxima and minima of the first-return map obtained determine a generating partition and, therefore, thenumber of branches of the template, the parity of each branch and the symbolic names of the unstableperiodic orbits identified are easily obtained. This way, the procedure of analysis is considerably simpli-fied. Concerning the templates found, apart from horseshoes, reverse horseshoes or jellyroll structureswith different global torsions, two more kinds of structures have been observed. One of them presentsthree branches folded the same way than a staple. The other one, also with three branches, presents thefolding mechanism of an S, which is especially notable as it does not fit the rolling scheme valid for alltemplates found in former experimental studies.
The variety of topological structures obtained strengthens the usefulness of templates as significantobjects for characterization of chaotic attractors of three-dimensional dynamical systems.
1 R. Gilmore, M. Lefranc, The Topology of Chaos (Wiley, New York, 2002).2 J. Used, J.C. Martin, Phys. Rev. E 79, 046213 (2009).
Cavity Solitons Laser and Localized Vortex Solitons
Patrice Genevet, Stephane Barland, Massimo Giudici, & Jorge Tredicce
Universite de Nice Sophia Antipolis, Institut Non Lineaire de Nice, Centre National de la RechercheScientifique, 1361 route des Lucioles, 06560 Valbonne
giudici [email protected]
We report on the experimental observation of localized laser structures in a compound laser systemconsisting of two mutually coupled broad-area Vertical Cavity Surface Emitting Lasers (VCSELs), oneof which is operated as a saturable absorber. As cavity solitons appearing in a VCSEL driven by acoherent driving beam, these localized structures coexist with a homogeneous background and they canbe individually addressed by a local perturbation. On the other hand, they are generated in a laser device(hence called Cavity Soliton Laser, CSL) that does not require a driving field. We explore the parameterspace of the CSL to map the region of existence of the localized laser structures or laser solitons and togive evidence of multi-peaks and ring-like laser states. We characterize the coherence properties of thesestructures, showing the difference between independent single-peak localized structures and multi-peakslocalized structures or complexes. We analyze the spectral properties of laser solitons, showing that theyhave multistable emission frequency associated to coexisting compound cavity longitudinal modes.
We describe the bifurcation diagram of single-peak laser soliton leading to the formation of complexes.In particular, we demonstrate the existence of localized vortex solitons characterized by the presence ofa topological defect in their phase profile. For a fixed set of parameters, we observe localized states withpositive or negative topological charge, both coexisting with a fundamental ”off” state. Several localizedvortex can be independently addressed in the transverse section of the compound system. This property,generically associated to localized structures, make localized vortex solitons attractive for the realizationof arrays of independent and controllable ”doughnut shaped” beams which would dramatically enhancethe efficiency of advanced optical nanoscopy techniques, especially in fast and compact sources such assemiconductor lasers.
Influence of Bragg-gratings-induced third-order dispersion onthe optical power spectrum of Raman fiber lasers
Pierre Suret, Nicolas Dalloz, & Stephane Randoux
Laboratoire Phlam / Universite de Lille 1 / bat. P5 / 59655 Villeneuve d’Ascq cedex
Raman fiber lasers (RFLs) are light sources made with long cavities in which a very large numberof modes (up to 106) interact through linear (dispersive) and nonlinear effects. They are good candidateto observe turbulent-like behaviors [1]. The generation of the multiple cavity modes in RFLs is nowcommonly described from a complex Ginzburg-Landau equation which has been analyzed from the weak-turbulence theory [1].
In particular, it is now admitted that the interplay between second-order dispersion and nonlinearoptical Kerr effect inside the laser cavity leads to the generation of an optical spectrum with a symetrichyperbolic secant shape [1]. Recent works have been devoted to the study of the influence of the sign ofthe second-order dispersion [2] and of the mirrors reflectivity spectra on the optical spectrum of RFLs[3].
Here, we show from experiments that the third order dispersion cannot be neglected even whenthe RFL is operated in a strongly normal dispersion regime. In particular, in our experiments, theoptical spectrum of a RFL oscillating near threshold is shown to be asymmetric. From a mean-fieldmodel (generalized Ginzburg-Landau equation), we use numerical simulations to show that the observedbehaviors arises from higher-order dispersive effects (third-order dispersion) breaking the symmetry ofthe laser spectra.
We show precisely that third-order dispersion effects arise from reflexions at the fiber Bragg gratings(FBGs) mirrors used to close the laser cavity. Our experimental setup is a very common configurationand the dispersion of the FBGs is always high on the side of the reflectivity spectra. This means that thephenomena presented here will arise in most of the experimental setups because the optical spectrum ofRFLs is generally broader than the FBGs spectral width.
From the theoretical point of view, we explore how third order dispersion influences the opticalspectrum of RFLs. Simple phase-matching arguments explain the origin of the asymetry in the opticalspectrum. We show that these results may have connection with anomalous thermalization recently de-scribed in nonlinear wave systems [4].
[1] S. A. Babin et al. J. Opt. Soc. Am. B (24), 8, (Aug 2007)[2] E.G. Turitsyna et al. Phys. Rev. A. (80), 031804(R) (2009)[3] E. G. Turitsyna et al. Opt. Express. (18), 5, p. 4469 (2010)[4] P. Suret et al. Phys. Rev. Lett. (104), 054101 (2010)
Anomalous Thermalization of Nonlinear Wave Systems
Stephane Randoux1, Antonio Picozzi1, Hans Jauslin2, & Pierre Suret2
1 Laboratoire de Physique des Lasers, Atomes et Molecules, UMR-CNRS 8523, Universite de Lille, France2 Institut Carnot de Bourgogne, UMR-CNRS 5209, Universite de Bourgogne, Dijon, France
In complete analogy with a system of classical particules colliding inside a gas medium, an incoherentoptical field can evolve, owing to nonlinearity, towards a thermodynamic equilibrium state [1]. In thisrespect, the spatiotemporal dynamics of the light field is governed by the nonlinear Schrodinger equationand its equilibrium spectrum has been determined in the framework of the weak turbulence theory [1,2].It is expected that experiments made in the field of nonlinear optics can possibly lead to the observationof turbulence or thermalization of nonlinear waves [1,2]. Here we present an experiment in which westudy the equilibrium spectra reached by a set of two partially-coherent light waves copropagating insidean ultra-low birefringence single-mode fiber. The two waves have opposite circular polarizations and arecoupled through optical cross-Kerr effect. Using kinetic wave theory, we show that the wave system mayexhibit a process of anomalous thermalization which is characterized by an irreversible evolution of thewaves towards a specific equilibrium state [3]. This equilibrium state is of a fundamental different naturethan the conventional RJ equilibrium state and in particular, the tails of the equilibrium spectra do notmeet the property of energy equipartition. The theoretical analysis reveals that the interaction is submit-ted to degenerate resonances which prevent the system to reach the usual thermodynamic Rayleigh-Jeans(RJ) equilibrium distribution. The anomalous thermalization is characterized by a process of entropy pro-duction: The novel family of equilibrium states is associated to a maximum of the nonequilibrium entropysubject to an additional constraint due to the existence of a local invariant in frequency space. In theexperiments, the Raman effect induces a non negligible dissipation over only a few nonlinear interactionlengths so that only the transient nonlinear regime leading to anomalous thermalization is experimen-tally accessible. However the observation of this transient regime reveals that some of the phenomenomsignatures which are predicted in the kinetic regime (where linear effects dominates nonlinear effects),are robust enough to be preserved in the nonlinear interaction regime. The robustness of the behaviorsfound in experiments performed far from the kinetic regime opens theoretical questions about nonlinearpropoagtion of incoherent waves in dispersive nonlinear media.
[1] A. Picozzi, Opt. Express, 15 9063 (2007)[2] S. Dyachenko, A. C. Newell, A. Pushkarev, and V. E. Zakharov, Physica D, 57 96 (1992)[3] P. Suret, S. Randoux, H. R. Jauslin, and A. Picozzi, Phys. Rev. Lett. 104 054101 (2010)
Part XI
Other
A non-ordinary route to chaos and complexity .
Ued Maluf
Master Degree Program of Art Science, Universidade Federal Fluminense, Niteroi, R. J., Brasil
I will present unusual routes into the domains of chaos and complexity in the set of natural num-bers,under the following conventions: 1) non-ordinary chaos : given a row of numbers, take the absolutevalues of the last two and move back as many numbers as indicated by these numbers;add them up;2)non- ordinary complexity: I devised a 7-levels Fibonacci Molecule (FM) - given Fibonacci Numbers (FN:1, 1, 2, 3, 5, 8, 13, 21 ...) a corresponding algebraic structure (AB) can be presented in such a way thateach FN is recorded simultaneously at 7 levels: 1) A level ; 2) the exponents (p) of A; 3)the exponents (q)of B; 4)the sum of these exponents; 5)B exponentiated to (4); 6) B exponentiated to (3); 7)the whole ABstablished by steps (1) through (6)following. 3) Difference of particular powers without their respectivecalculus: it suffices to, first, multiply the sum of the basis by the square power of the greater basis, andmultiply the results by the difference between the basis;proceed similarly for the lesser one: multiplythe sum by the square power of the lesser basis; multiply the result by the difference; finally, add bothresults: instead of writing 7x7x7x7-3x3x3x3 = 2401-81 = 2320;simply do this = 4(7x7x10)+4(3x3x10)=4x490+4x90= = 1960+360 = 2320. I have devellopped another unusual formulae for dealing with chaosand complexities which I hope to present at the Conference.
A Matched Filter for Chaos: The Missing Piece for ChaosCommunications
Ned Corron, Mark Stahl, & Jonathan Blakely
U. S. Army RDECOM, Redstone Arsenal, Alabama 35898, USA
In conventional communication systems, a matched filter provides optimal receiver performance in thepresence of noise. As such, matched filters are highly desirable, yet they are practical only when a rela-tively small number of basis functions are used to encode information. For communications using chaoticwaveforms, it is generally assumed that the unpredictable and nonrepeating nature of chaos precludes theuse of a matched filter; consequently, it is widely accepted that using chaos for communications resultsin lower performance capabilities compared to conventional, nonchaotic systems. Here, we show this as-sumption is not necessarily true. We report the construction and operation of a novel chaotic electronicoscillator that admits a simple matched filter. The audio-frequency circuit, which contains both analogand digital components, is modeled by a hybrid dynamical system including both a continuous differentialequation and a discrete switching condition. Surprisingly, an exact analytic solution for the system can bewritten as the linear convolution of a symbol sequence and a fixed basis function, similar to conventionalcommunications waveforms. Waveform returns sampled at switching times are conjugate to a shift map,effectively proving the circuit is chaotic, and the analytic solution accurately reconstructs a measuredwaveform, thereby validating the circuit model. A matched filter for the basis function is derived in theform of a delay differential equation. An experimental realization of the matched filter is implementedin a simple analog circuit. The filter is used to detect the symbolic dynamics of the oscillator waveform,and an analytic bit-error rate is found to be comparable to binary phase-shift keying (BPSK). Scaled tohigher frequencies, this oscillator has potential application in Hayes-type chaos communications where amessage signal is encoded in the symbolic dynamics via small perturbation control. The discovery of apractical matched filter finally provides a coherent receiver to complement the elegant encoding in suchsystems.
Complexity of the Particle Dynamics in Time-DependentFocusing Billiards
Alexander Loskutov1 & Alexei Ryabov2
1 Physics Faculty, Moscow State University, Moscow 119992, Russia2 ICBM, University of Oldenburg, 26111 Oldenburg, Germany
In recent years there has been growing interest to billiard systems because they are a tempting topic ofthe experimental and theoretical physics, mathematics and mechanics. Billiards provide a fertile sourceof new ideas in optics, statistics, geometry, molecular physic, hyperbolic systems, spectral theory andother fields of natural sciences. Lately, billiard models with perturbed boundaries formed a good basisfor understanding of underlying mechanisms of many dynamical systems.
Billiards with perturbed boundaries belong to a relatively fresh area of physics, which opens widerhorizons in investigating certain fundamental problems of classical statistical mechanics. In particular, itgives a new approach to the problem of cosmic-particle acceleration to high energies, i.e. Fermi acceler-ation. Ever since the classical study by Fermi, this problem has attracted the attention of researchers invarious branches of the science: plasma physics, astrophysics, mechanics, high-energy physics, etc. Similarideas were recently invoked to account for new experiments in atomic physics.
Time-dependent billiards of different forms may also be applied to study the phenomenon of Fermi ac-celeration. Such systems have the distinctive feature that they could be used, after a suitable modification,in experimental investigations.
As is known, dynamical properties of billiards play a principal role for the presence of Fermi accel-eration: if a billiard system possesses chaotic behavior, then the boundary perturbation may lead to theparticle acceleration. Furthermore, if the static billiard is a nearly integrable system, then the particledynamics can be very complex. In this case, all invariant curves in the phase space are surrounded bystochastic layers. This leads at a certain particle velocity to a resonance between external periodicalperturbations and the motion within stability islands of the unperturbed billiard [1, 2].
We found that the resonance may suppress the Fermi acceleration phenomenon. This implyies thatseparation of billiard particles by their velocities is observed. If the initial velocity is less than the res-onance value, the average particle velocity decreases. Otherwise, the billiard particles will on averagebe accelerated. This phenomenon may be treated as a peculiar billiard Maxwell’s Demon, when weakperturbations of a system lead the particle ensemble to separation [3].
It is also shown [3] that similar phenomena can be observed in quite general billiard systems whereone time scale occurs in the unperturbed system because of the particle motion along a quasiperiodicstable trajectory, and another time scale is given by an external perturbation.
[1] A.Loskutov, A.B.Ryabov and L.G.Akinshin. J . Phys. A, 2000, v.33, p.7973.[2] A.Loskutov and A.Ryabov. J. Stat. Phys., 2002, v.108, p.995.[3] A.B.Ryabov and A.Loskutov. J . Phys. A, 2010, v.43, 125104.
Gottwald-Melbourne test for chaos of nonlinear fluctuations incomplex laboratory plasmas
Dola Roychowdhury1, Sudeshna Lahiri2, & A.N.Sekar Iyengar3
1 Techno India, EM4/1, Sector V, Salt Lake, Kolkata 700091, Kolkata, India.2 Dinabandhu Mahavidyalaya, Bongaon, North 24 Parganas, 743235, Kolkata, India3 Saha Institute of Nuclear Physics, 1/AF Bidhan nagar, Kolkata 700064
Plasma is a highly complex system exhibiting a rich variety of nonlinear dynamics over a rangeof parameters. Glow discharge plasmas possess a unique characteristic of not only being complex butalso have a negative resistance under some conditions. Hence depending on the conditions, it can exhibiteither a transition from order to chaos or vice versa. Chaos in laboratory plasmas are explored by standardtechniques of analysis like correlation dimension, and Largest Lyapunov exponent. As far as we are awareno work has been reported of correlating Largest Lyapunov exponent with Hurst exponent which is astandard diagnostics for long range correlations. In our work we have found that at the transistion fromorder to chaos, the Largest Lyapunov exponent exhibits a sharp jump by a factor of ten, while the Hurstexponent shows a drop from 1 to 0.72 which is a typical value of real world fractal signals(chaotic). Inaddition we have for the first time carried out a 0-1 test suggested by Gottwald and Melbourne[1] onlaboratory plasma data and observe clear transition from order to chaos which will be reported in thispaper.
1. A new test for chaos in deterministic system Georg A. Gottwald and I.Melbourne, Proc. ofSoc.Lond.A, 2004, 460, 603-611
Modified Extended Active Control for Tracking Control andSynchronization of Chaotic and Hyperchaotic Systems
A. N. Njah
(Nonlinear Dynamics Research Group ), Department of Physics, University of Agriculture Abeokuta (UNAAB),Ogun State, Nigeria.
The active control which is outstanding for its robustness and ease of design has limitation on practicalimplementation partly due to the fact that the number of control functions, which is usually equalto the dimension of the system, are too many and the fact that its control signals are fixed and toolarge. In this paper a modified extended active control technique suitable for practical implementation isproposed. By applying the Lyapunov stability theory (LST) and the Rourth-Hurwitz criteria (RHC) tothe extended active control technique, single active control functions are designed for the effective controland synchronization of chaotic and hyperchaotic systems. The single controller design, which could beachieved in different ways (via a manipulation of the LST and RHC, or a suitable choice of the controlmatrix, or a suitable choice of the control strength matrix) leads to a significant reduction in controllercomplexity. By varying the control strength matrix the control signal can be made as low as desired. Thereduction in both controller complexity and the strength of the control signal in the proposed modifiedactive control technique makes it suitable for practical implementation. Numerical result are provided forcertain classes of chaotic and hyperchaotic systems to demonstrate the effectiveness of the technique.
Experimental study of dislocation avalanches during unstableplastic deformation
Mikhail Lebyodkin1, Nikolay Kobelev2, Youcef Bougherira1, Denis Entemeyer1, Claude Fressengeas1,Tatiana Lebedkina2,3, & Ivan Shashkov1,2
1 Laboratoire de Physique et Mecanique des Materiaux, UPVM / CNRS, Ile du Saulcy, 57045 Metz Cedex,France
2 Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Russia3 Institut Jean Lamour, Ecole des Mines, Parc de Saurupt, CS14234, 54042 Nancy Cedex, France
The plasticity of crystalline materials is a collective phenomenon which results from the motion andinteraction of defects of the crystal structure, particulary dislocations and solute atoms. Jerky flow ofdilute alloys, also referred to as the Portevin-Le Chatelier (PLC) effect, is a spectacular example of theself-organization of nonlinear dynamical systems. Statistical and dynamical analyses of serrated stress-time series revealed such complex phenomena as self-organized criticality and deterministic chaos [1].These dynamical regimes are characterized by power laws reflecting the property of scale invariance.Independently, power-law statistics were found for bursts of acoustic emission (AE) and local strainrate recorded during deformation of pure crystalline solids [2], which bears evidence to an intermittent,avalanche-like character of plastic activity, although at a macroscopic scale, the deformation process isviewed as being regular and homogeneous. These observations suggest that self-organization phenomenaare of a general nature in dislocation ensembles, and may become apparent at various plastic event scales.
So far, the mesoscopic scale remains unexplored in the studies of jerky flow. Such experimental inves-tigation is realized in the present work on an AlMg alloy - a classical material exhibiting the PLC effect.The multiscale character of the experimental approach is warranted by the application of a variety oftechniques, including the measurement of stress-strain curves, the accompanying AE, and the local strainfield through high-resolution extensometry. Correlation, statistical, and multifractal analyses are appliedto these signals, each reflecting a specific aspect of the deformation processes, in order to characterize theorganization of the dislocation dynamics during the PLC effect. The results show that the intermittencyof plasticity in these conditions is not solely related to the macroscopic stress serrations, but manifestsitself at a mesoscopic scale throughout the deformation. A particular accent is put on the statistical distri-butions of AE. It is found that AE is characterized by power-law statistics in all experimental conditions.In contrast, depending on the applied strain rate, the stress serrations display various types of statisticaldistributions, including power-law, peaked, and bimodal histograms. The observed behavior is discussedin terms of self-organized criticality and synchronization in extended dynamical systems.
1. L.P. Kubin, C. Fressengeas, G. Ananthakrishna, Collective behaviour of dislocations in plasticity,in Dislocations in Solids, edited by F.R.N. Nabarro and M.S. Duesbery, Elsevier, Amsterdam, 2002.
2. Weiss, J., T. Richeton, F. Louchet, et. al., Phys. Rev. B, 76, 224110, 2007.
Experimental Transition to Chaos in Low-Temperature Plasma
Dan-Gheorghe Dimitriu
Faculty of Physics, Alexandru Ioan Cuza University, 11 Carol I Blvd., RO-700506 Iasi, Romania
Experimental results are reported on the transition to chaos in plasma by way of two scenarios: typeI intermittency and cascade of spatio-temporal sub-harmonics generations, respectively. Both of thesescenarios develop in connection with the generation and dynamics of patterns in plasma, in form ofsimple or multiple concentric fireballs.
It is well known that a very luminous, almost spherical structure (fireball) appears in front of apositively biased electrode immersed into low-temperature plasma up to a threshold value of the potentialapplied on the electrode. Up to a second threshold value of the potential applied on the electrode, thisstructure passes into a dynamic state, in which the double layer at its border periodically disrupts andre-aggregates. In certain experimental conditions, regular oscillations interrupted by random bursts wereobserved in the time series of the current collected by the electrode. By increasing the voltage applied onthe electrode, the random bursts appear more frequently, the final state of plasma being a chaotic one. Byapplying the modern methods of the nonlinear dynamics, we identified a scenario of transition to chaosby type-I intermittencies. The recorded time series were also analyzed by recurrence plot quantification.
In certain experimental conditions, a more complex pattern appears in front of electrode, in form ofmultiple concentric fireballs (like an onion shape). By gradually increasing the voltage applied on theelectrode, we have observed that each new luminous sheet appears simultaneously with the appearanceof a new sub-harmonic in the power spectrum of the complex structure dynamics. After a cascade ofsuch sub-harmonics generation (both spatial and temporal ones), the final state of the plasma system is achaotic one. This seems to be a new scenario of transition to chaos, being different from quasi-periodic orFeigenbaum scenarios. A further experimental and theoretical analysis of this new scenario of transitionto chaos will be necessary.
All experimental data were analyzed by the methods of the nonlinear dynamics, including the recon-struction of the states space by time delay method and recurrence plot quantification.
Nonlinear Dusty Plasma Instabilities
Maxime Mikikian, Marjorie Cavarroc, Lenaıc Couedel, Yves Tessier, Laıfa Boufendi, & Olivier Vallee
GREMI, Groupe de Recherches sur l’Energetique des Milieux Ionises, UMR6606, CNRS/Universite d’Orleans,14 rue d’Issoudun, BP6744, 45067 Orleans Cedex 2, France
In this work, some strongly nonlinear instabilities occurring in dusty plasmas are experimentallyobserved and characterized. Their similarity with mixed-mode oscillations (MMOs) is investigated.
Dusty (or complex) plasmas (complex, in analogy with complex fluids) are partly ionized gases con-taining solid dust particles with sizes ranging from a few nm to cm[1]. In the plasma, dust particles acquirea negative electric charge that determines their interaction with the plasma and induces collective effectsin the dust cloud. These multi-component systems have many similarities with colloidal suspensions orgranular media. They are encountered in many environments such as astrophysics, industrial processesand thermonuclear fusion.
In experiments, dust clouds are often characterized by a central dust-free region (void)[2] maintainedby two forces of opposite directions. Self-excited oscillations of the void size can appear due to a breakin this equilibrium[3]. This ”heartbeat” instability (due to its apparent similarity with a beating heart)can stop by its own through an ending phase characterized by the occurrence of more and more failedcontractions. During this phase, electrical or optical measurements show well-defined behaviors recentlyidentified as mixed-mode oscillations (MMOs)[4]. MMOs consist of an alternation of small and large(spikes) amplitude oscillations often considered as subthreshold oscillations and relaxation mechanisms.They exist in a wide variety of fields such as chemistry (e.g. in the Belousov-Zhabotinskii reaction) andnatural sciences (e.g. in the Hodgkin-Huxley model of neuronal activity). MMOs are intensively studiedwith dynamical system theories (canards, subcritical Hopf-homoclinic bifurcation, ...).
Here, we report on the first experimental evidence of MMOs in dusty plasmas. A particular attentionis paid to the evolution of the number of small amplitude oscillations in between spikes. This workhighlights new situations of MMOs that could be of interest for improving dynamical system theories.We also underline close similarities with MMOs observed in neuronal activity and oscillating chemicalsystems. These fields use well-known sets of equations giving rise to MMOs and this scientific backgroundcould be used to explore the dusty plasma dynamics. This aspect is currently underway through severaltheoretical approaches[5].
[1]M. Mikikian, et al., Eur. Phys. J. Appl. Phys. 49, 13106 (2010)[2]M. Cavarroc et al., Phys. Rev. Lett. 100, 045001 (2008)[3]M. Mikikian et al., New J. Phys. 9, 268 (2007)[4]M. Mikikian et al., Phys. Rev. Lett. 100, 225005 (2008)[5]O. Vallee et al., High Temp. Mat. Proc. 3, 227 (1999)
Influence of pulse power to dynamics of laser droplet generation
Blaz Krese & Edvard Govekar
University of Ljubljana, Faculty of Mechanical Enginineering, Laboratory of Synergetics, SI 1000, LjublanaSlovenija
A metal droplet can be used in various industrial applications [1]. Due to this different droplet gen-eration processes are subject of intensive investigations. The laser droplet generation is a process wherea laser pulse is used to melt the tip of the vertically fed metal wire [2]. The process phenomenologicallyconsists of two phases. In the first phase from the molten tip of the wire a pendant droplet is formeddue to the surface tension and gravity force. The second phase represents the detachment of the pendantdroplet from the solid tip of the wire. To achieve this, the surface tension force needs to be overcome. Inorder to stimulate the detachment of the droplet we append an additional short pulse, i.e., detachmentpulse at the end of the pendant droplet formation phase. In the paper we characterize experimentallythe influence of the power of the detachment pulse on dynamics of the laser droplet generation. For thatpurpose a set of experiments were performed with a selected fixed laser pulse frequency rate while step-wise changing the detachment pulse power from 0 kW to 8kW. For the characterization of the processdynamics, scalar time series were generated from the snapshots of high speed infrared camera. Based ontime series analysis we are able to observe qualitatively different dynamics regimes of droplet generation,from spontaneous chaotic [3] to forced periodic dripping when changing the power of detachment pulsefrom 0 kW to 8kW. Different linear and nonlinear characteristics [4, 5] are used to detect and quanti-tatively characterize observed dynamical regimes. The transition between observed regimes presumablyresembles an intermittency scenario.
References: [1] GOVEKAR, Edvard, JERIC, Anze. Laser droplet generation: Application to dropletjoining. CIRP ann., 2009, vol. 58, iss. 1, 205-208. [2] KOKALJ, Tadej, KLEMENCIC, Jure, MUZIC, Peter,GRABEC, Igor, GOVEKAR, Edvard. Analysis of a laser droplet formation process. J. manuf. sci. eng.,2006, vol. 128, iss. 1, 307-314. [3] KRESE Blaz,PERC Matjaz, GOVEKAR Edvard; Dynamics of laserdroplet generation. Accepted in Chaos, March 2010 issue. [4] KANTZ Holger, SCHREIBER Thomas.Nonlinear time series analysis. Cambridge University Press, second edition, 2004. [5] MARWAN Norbert,ROMANO M. Carmen, THIEL Marco, KURTHS Jurgen. Recurrence plots for the analysis of complexsystems. Physics Reports, 2007, vol. 438, iss. 5-6, 237-329.
Dynamics of multi-arm pendulums excited parametrically
Jose Carlos Sartorelli1 & Walter Lacarbonara2
1 Caixa Postal 66318, 05314-970 Sao Paulo, Brazil2 Via Eudossiana 18, 00184 Roma, Italy
Parametric instabilities have been studied, since the early experiments of Faraday (1831), in a varietyof physical systems such as in the propagation of electromagnetic waves in media with a periodic structure;in the motions of electrons in a crystal lattice; in dynamic buckling of columns, plates and shells; in waterwaves propagating in vertically forced containers. Parametrically excited pendulum-type systems, in whichan additional torque is provided by the vertical periodic acceleration, have been studied extensively. Theypresent the peculiar feature of stabilization of the inverted unstable equilibrium positions when they aresubject to high-frequency excitations. We have studied experimentally and numerically the stabilizationregions of all fixed points in the parameter space (a,f),where a and f denote, respectively, the amplitudeand the frequency of the external excitation. The equations of motion were integrated numerically byassuming a sinuousdaly external acceleration as well as a non-sinuousdaly excitation. We present theresults of a double pendulum (two arms) with two degrees of freedom possessing four fixed points. Wealso present and discuss the results of a three degree-of-freedom pendulum system (two arms in thesame axis) exhibiting seven fixed points, but two of them are degenerate leaving only five different fixedpoints.We observed regions of stability of each fixed point in the parameter space and when they areoverlapped all the fixed points are stable. At the boundary lines we observed Hopf bifurcations (supercritical and subcritical) and blue-sky catastrophe or boundary crisis.
The first ”lost” international conference on non linear
Jean-Marc GINOUX1 & Loıc PETITGIRARD2
1 [email protected] [email protected]
In a famous article entitled The nonlinear theory of electric oscillations published in 1934 in theProceedings of the Institute of Radio Engineers Balthazar Van der Pol ended his introduction by thissentence: “. . . a special international conference dedicated solely to the problems arising in the nonlinearoscillation theory was recently held in Paris, on January 28-30, 1933”. Celebrating the centenary of thebirth of Papaleksi in 1981, the Russian Vladimir Vasil’evich Migulin told that during the first internationalConference on Nonlinear Oscillations which took place in January 1933 in Paris, Nikolaı DimitrievichPapaleksi presented two papers on the studies being conducted in the USSR along this line. Twenty fiveyears later, the Russian Academician Evgenu L’vovich Feinberg, still celebrating Papaleksi wrote: “Itis not surprising that, when the first international conference on nonlinear oscillations was convened inParis in 1932 (among its participants were such pioneers in this field as B. Van der Pol, L. Brillouin, andothers), it was Papaleksi who represented the Moscow school of Mandel’shtam and Papaleksi, their closestdisciples and colleagues Andronov, A. A. Vitt, Khaikin, and others, reporting on its achievements”. Theproblem is that, apart from these references, there was no trace of this conference: no announcement, nolocation (in Paris), no proceedings, no list of participants and no program. So, has it really happened?The aim of this article is to clarify this question. Thus, it will be shown that the first (lost) internationalconference on nonlinear do happened in Paris at the Institut Henri Poincare under the presidence ofBalthazar Van der Pol and Nikolaı Dimitrievich Papaleksi and in presence of Alfred Lienard, Elie andHenri Cartan, Ernest Esclangon, Henri Abraham, Leon Brillouin, Philippe Le Corbeiller, Yves Rocard,Camille Gutton, . . . Then, the importance of such a meeting on the emergence of Non-Linear Mechanicsin France during this period as well as the full list of participants and the thematic of the discussions willbe analyzed.
Instabilities in Coupled Huygens Pendula
Jose R Rios Leite & Josue S Fonseca
Departamento de Fisica - Universidade federal de Pernambuco - 50670-901, Recife, Brazil
The behavior of two coupled pendula, as described originally by C. Huygens (see for instance(1,2),will be presented in their nonlinear regime of oscillations. Empirical observations in a real system shallbe described and compared with numerical solutions of the classical equations of motion. Including fric-tional dissipation terms the evolution of the system presents instabilities due to mode frequency-locking.Bifurcations from periodic initial conditions into quasi-periodic and chaotic motion was characterizedfor a range of parameters of the oscillators. The role of symmetry on the dynamics of the system willbe discussed. The connection between energy dissipation and symmetry was also exploited. Includingpump term similar to Van der Pol nonlinearity in the pendula1, relations to the dynamics of Huygens’sclocks(3,4) were investigated .
ReferencesM. Sargent III, M. Scully and W. E. Lamb,Jr., ”Laser Physics”, Addison Wesley Pub. Co. 1974.A. Pikovsky, M. Rosenblum and J. Kurths, ”Synchronization, A Universal Concept in Nonlinear
Science”, Cambridge University Press, 2001.E. Klarreich, ”Huygens’s Clocks Revisited”, American Scientist, 90, 1 (2002).M. Bennett , M. F. Schatz , H. Rockwood and K. Wiesenfeld , ”Huygens’s clocks”, Proc. Royal Society,
Series A, 458, 563-579 (2002).
Comparative Analysis of Chaos-based and ConventionalPseudo-noise Sequences for Spread Spectrum Applications
Angel A. M. Gonzalez1, Marcio Eisencraft2, & Clodoaldo A. M. Lima1
1 Escola de Engenharia, Universidade Presbiteriana Mackenzie2 Centro de Engenharia, Modelagem e Ciencias Sociais Aplicadas, Universidade Federal do ABC
The Spread Spectrum (SS) technique is used in many broadband modulation systems. A system issaid to be spread spectrum if the modulated signal bandwidth is much greater than the message signalbandwidth and if this spectral spreading is performed by a code that is independent of the message signal[1].
SS signals have some very interesting properties [1]: i) they are difficult to intercept for an unauthorizedperson; ii) they are easily hidden, i.e., for an unauthorized person it is difficult to even detect their presencein many cases; iii) they are resistant to jamming; iv) they provide a measure of immunity to distortiondue to multipath propagation; v) they have multiple-access capability.
By definition, to implement a SS system it is necessary a code sequence independent of the message.This code is the so-called pseudonoise (PN) sequence. These binary sequences are periodic and must havesome statistical characteristics: they must appear to be unpredictable to an outsider, though they can begenerated by deterministic means [1].
There are many conventional techniques of generating PN sequences, e.g., m-sequences [1], Gold [2],Kazami [3]. Recently some chaos-based techniques have been proposed, e.g. [4,5]
The objective of this work is to compare the conventional PN sequences and chaos-based ones interms of parameters really important when it comes to practical implementations of SS systems, theautocorrelation and cross-correlation. We intend to verify some recent published papers that affirms thatchaos-based sequences can have a superior performance than conventional ones, e.g., [6].
References
[1] B. P. Lathi, Modern Digital and Analog Communication Systems, 3rd ed. New York, NY, USA:Oxford University Press, Inc., 1998.
[2] R. Gold, Optimal binary sequences for spread spectrum multiplexing.IEEE Transactions on Infor-mation Theory., vol. IT-13, no. 5, pp. 619-621, 1967.
[3] T. Kasami, Some lower bounds on the minimum weight of cyclic codes of composite length, IEEETransactions on Information Theory., vol. IT-14, no. 6, pp. 814-818, 1968.
[4] M. P. Kennedy, G. Setti, and R. Rovatti, Eds., Chaotic Electronics in Telecommunications. BocaRaton, FL, USA: CRC Press, Inc., 2000.
[5] Netto, F. S. ; Eisencraft, M. Spread Spectrum Digital Communication System Using ChaoticPattern Generator. In: 10th Experimental Chaos Conference, Catania, 2008.
[6] R. Rovatti, G. Mazzini, and G. Setti, On the ultimate limits of chaos-based asynchronous ds-cdma-i: basic definitions and results, IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 51,no. 7, pp. 1336-1347, 2004.
A new experimental probe for investigating the spatiotemporaldynamics of relativistic electrons in storage rings
Serge Bielawski1,2, Christophe Szwaj1,2, Clement Evain7, Marc Le Parquier2, Masahito Hosaka3, MihoShimada4, Masahiro Adachi5, Heishun Zen5, Masahiro Katoh5, Yoshifumi Takashima3, Shin-ichiKimura5, Toshiharu Takahasahi6, Naoto Yamamoto3, & Takanori Tanikawa5
1 PhLAM Bat. P5, Universite des Sciences et Technologies de lille, 59655 Villeneuve d’Ascq (France)2 CERLA, Universite des Sciences et Technologies de lille, 59655 Villeneuve d’Ascq (France)3 Graduate School of Engineering, Nagoya University 464-8603 Nagoya, Japan.4 High Energy Accelerator Research Organization, KEK 305-0801, Tsukuba, Japan5 UVSOR Facility, Institute for Molecular Science, National Institutes of Natural Sciences, Okazaki 444-8585,
Japan6 Research Reactor Institute, Kyoto University, 590-049 Osaka, Japan7 Synchrotron SOLEIL, Saint Aubin, BP 34, 91 192 Gif-sur-Yvette, France
In an electron storage ring, relativistic electrons are ”trapped” during a long time (typically severalhours). This type machine is of particular interest for producing producing synchrotron radiation, asvarious wavelengths for users. However the operation of such machines involves complicated nonlineardynamics issues.
From the theoretical point of view, the electron bunch experiences spatiotemporal dynamics, in a phasespace (in the thermodynamical sense) with 6 dimensions. As an ubiquitous feature, a perturbation withwavenumber k will experience both rotation in space space at a slow frequency, typically in the 10 KHzrange for our accelerator (UVSOR-II, Japan) called the synchrotron frequency, and a diffusion process.An important point is that these processes provide only a slow damping of perturbations. Thereforeinstabilities of the system are likely to occur easily. A important destabilizing ingredient is the interactionbetween electrons of the bunch, via the so-called wakefield effect. This leads to the so-called microwaveand CSR (coherent synchrotron radiation) instabilities.
Although theoretical desriptions exists since a long time, few direct comparisons between theory andexperiments have been performed up to now, essentially because of the high difficulty to observe in realtime the space space evolution of the electrons. Moreover, though of major importance for the dynamics,theoretical and experimental investigations of the electron wakefield is a difficult task.
In this work, we adopt an alternate strategy. We have constructed an experimental setup allowing toperturb selectively the electron bunch using various wavenumbers, and to study the transient followingthe perturbations. This uses an external laser, as already presented in the last ECC conference [1],and an additional setup for analyzing the damping/growth of perturbations from the terahertz emissionanalysis. This allows to compare new features of theoretical models against experiments. In particular wewill make comparison with the Fokker-Planck-Vlasov equations, and show that characteristic features ofthe dynamics are due to the presence of wakefields, and thus interactions between electrons.
[1] Tunable narrowband terahertz emission from mastered laser-electron beam interaction S. Bielawski,C. Evain, T. Hara, M. Hosaka, M. Katoh, S. Kimura, A. Mochihashi, M. Shimada, C. Szwaj, T. Takahashi,and Y. Takashima Nature Physics 4, 390 (2008)
Pulse splitting effects in short wavelength seeded Free-ElectronLasers
Nicolas Joly1, Marie Labat2, Serge Bielawski3, Christophe Szwaj3, Christelle Bruni4, &Marie-Emmanuelle Couprie2
1 University of Erlangen Nuremberg, Gunther-Scharowsky 1 / Bau 24. D-91058 Erlangen, Germany2 Synchrotron SOLEIL, Saint Aubin, BP 34, 91192 Gif-sur-Yvette, France3 PhLAM/CERLA, Bat. P5, Universite des Sciences et Technologies de lille, 59655 Villeneuve d’Ascq, France4 Laboratoire de l’Accelerateur Lineaire, Orsay, France
The present state of the art in electron accelerators allows to realize optical amplifiers in the VUVand X range, with very high gain. As a consequence, powerful emission can be obtained at very shortwavelengths, using a single pass in the amplifier. To achieve temporal coherence of the output light,a strategy consists of injecting a low power coherent seed pulse from a classical (table-top) source.Experimental feasibility using harmonics generated in gases has been shown recently by part of theauthors [1].
The way opened by these feasibility studies motivates systematic studies of the dynamics of thepulse propagation. In addition, the complexity of the experiments requires preliminary numerical andtheoretical studies, before testing new setups, or operation in new conditions.
With this purpose, we present a theoretical and numerical study of the process, and show that acomplex dynamics affects pulse propagation. In particular a pulse-splitting effect [2] is shown to affectpropagation inside the FEL. We describe here the modeling of the effect and the numerical results. Inparticular, we use the FEL equations (the so-called Colson-Bonifaccio FEL pendulum equations) in anadimentional form in which relevant reduced parameters appear. Inspection of the reduced parametersshould allow to anticipate the dynamical behavior of FELs prior to the design of new injection experi-ments.
[1] Injection of harmonics generated in gas in a free-electron laser providing intense and coherentextreme-ultraviolet light, G. Lambert, T. Hara, D. Garzella, T. Tanikawa, M. Labat, B. Carre, H. Kita-mura, T. Shintake, M. Bougeard, S. Inoue, Y. Tanaka, P. Salieres, H. Merdji, O. Chubar, O. Gobert, K.Tahara, and M.-E. Couprie, Nature Physics 4, 296 - 300 (2008)
[2] Pulse splitting in short wavelength seeded Free Electron Lasers, M. Labat, N. Joly, S. Bielawski, C.Szwaj, C. Bruni, and M. E. Couprie, Phys. Rev. Lett. 103, 264801 (2009)
Detachment regimes in laser droplet generation
Andrej Jeromen & Edvard Govekar
University of Ljubljana, Faculty of Mechanical Engineering, Laboratory of Synergetics, Askerceva 6, SI-1000Ljubljana, Slovenia
The laser droplet generation is a process where the tip of the vertically fed metal wire is melted bya laser pulse. The outcome and the dynamics of the process of sequential droplet generation is governedby detachment of pendant droplet that can be influenced by numerous process variables. The complexityof this engineering process is additionaly increased by the interaction between the laser pulse frequencyand the dynamics of a pendant droplet.
A series of experiments is presented where the frequency of the square laser pulses was varied keep-ing both the average laser power and the feeding speed of the metal wire constant. Depending on thedecreasing laser pulse frequency from 300 Hz to 50 Hz three different detachment regimes accompaniedby different dynamics have been identified: a) dripping, caused by the force of gravity alone, b) resonantdetachment, caused by a combination of the gravity force and the laser induced normal oscillation modesof the pendant droplet, and c) break-up caused by the Rayleigh-Plateau instability. The observed regimesare characterized based on the geometrical properties of the generated droplets and the time series gener-ated from the high speed IR camera records. Dripping can experimentally be characterized as a periodicdroplet detachment with larger droplet volume of low scatter. Decreasing the laser pulse frequency leadsto a decrease of the periodically detached droplets volume and a transition to resonant detachment whichis observed at 150 Hz. At this frequency a periodic detachment with the lowest scattering of the detacheddroplets volume is identified. Further decreasing the frequency leads to the transition to break-up dropletdetachment regime where the smallest droplets are observed while the droplet detachment and corre-sponding droplet volume become very irregular. The frequency of 150 Hz that corresponds to the lowestobserved droplet volume scattering presumably coincides with the half of the normal droplet oscillationmode frequency fl=2.
Part XII
Geophysics
Spectral analysis of interannual bed level variations at a beachin Duck, North Carolina, USA.
Magar Vanesa1, Reeve Dominic1, Lefranc Marc2, & Hoyle Rebecca3
1 School of Marine Science and Engineering, University of Plymouth, UK2 Phlam and CERLA, Universite des Sciences et Technologies de Lille, France3 Department of Mathematics, University of Surrey, UK
The nearshore dynamics of a sandbarred beach at Duck, N.C., U.S.A., surveyed monthly for 26 years,is analysed using spectral methods and recurrence plots. The first part of the study focused on two shore-normal bathymetric profiles at locations where the beach is quasi longshore uniform. A singular spectrumanalysis (SSA) permitted the identification of the fundamental, dominant frequencies of oscillation. Theidentification of interannual quasi-periodic cycles of varying periodicities at different locations along theprofile led to the characterisation of bathymetric regions based on the properties of the local quasi-periodic oscillations. Yearly and quasi-yearly cycles were linked to the monthly averaged wave conditions,and some regime changes observed in the temporal behaviour agreed well with observations of sandbarconfiguration changes and sandbar dynamics. In these cases such changes could generally be associated toextreme storm events, as found by previous authors. Some of the interannual patterns may be associatedwith the North Atlantic Oscillation.
The second part of the study concentrated on an in-depth investigation of coherent temporal patternsand their likely origin. It is shown that these patterns are linked to large-scale phenomena using amultivariate EOF (MEOF) analysis and a Multichannel SSA (MSSA). These methods were applied tothe whole bathymetry and to three potentially important monthly forcings: the North Atlantic Oscillation(NAO), the monthly wave height (MWH) and the monthly mean water level (MWL). Even though nointerannual coherent patterns were found, a few at monthly timescales were identified. Of these, theyearly and semi-yearly patterns forced by the MWH were clearly dominant, followed by a few patternsat shorter timescales linked to the NAO.
Tidal instability in exoplanetary systems
David Cebron1, Rim Fares2, Michael Le Bars1, Pierre Maubert1, Claire Moutou2, & Patrice Le Gal1
1 Institut de Recherche sur les Phenomenes Hors Equilibre2 Laboratoire d’Astrophysique de Marseille
Due to their observationnal method, many of the discovered exoplanets are massive gas giants called’hot Jupiters’ orbiting rapidly very close to their stars. Because of this proximity, these binary bodies (starsand planets) are strongly deformed by gravitationnal tides. Therefore, a certain number of them must bethe site of an hydrodynamic instability, called the tidal instability. Starting from measured astrophysicalcharacteristics of these systems (masses, orbit radius, eccentricity and period, spin velocity...), we showthat this instability is, as expected, present in some of the stars when the ratio of the planet orbitingperiod to the star spinning period is not in a ”forbidden range”. In this case, the instability should drivestrong flows in the different fluid layers of both bodies. These flows must be taken into account to modelthe binaries interiors and subsequent properties (synchronization, dynamos, zonal winds...). Of particularinterest is the possibility of modifying the alignment of the rotation axes of stars and planets by this tidalinstability.
Modeling of volcanomagnetic dynamics by recurrent orthogonalleast-squares learning system
Stanislaw Jankowski1, Gilda Currenti2, Rosalba Napoli2, Zbigniew Szymanski1, Luigi Fortuna3, CiroDel Negro2, & Marek Dwulit1
1 Warsaw University of Technology,Poland2 Istituto Nazionale di Geofisica e Vulcanologia, Sezione di Catania,Italy3 Dipartimento Di Ingegneria Elettrica Elettronica e dei Sistemi Universita di Catania,Italy
We present a new model of volcanomagnetic dynamics created by means of recurrent orthogonalleast squares. The advantages of our approach are: low complexity algorithm as compared to recurrentkernel machines and parsimonious representation of observed dynamical system that enables physicalinterpretation. The observations of the geomagnetic time series from the magnetic network on Etnavolcano are analyzed to investigate the dynamical behavior of magnetic anomalies. The predictability ofthe geomagnetic time series was evaluated to establish a possible low-dimensional deterministic dynamics.The analysis of the 10-minutes differences at PDN station with respect to the reference station located faraway from the volcano edifice shows prominent peaks centered around diurnal components at the periodof 8, 12 and 24 h. After having removed the dominant periodic components, the filtered differences appearto be aperiodic and broadband. We attempt to explain the mechanism generating the time dependentvariations by constructing the recurrent learning system. The data from PDN station was normalized tothe range [-1,1]. We used a learning data set from 7th to 13th January 2008. The testing data set spansfrom 15th to 21st January 2008. The idea of recurrent model of nonlinear dynamical system is based onthe general NARMAX form. The idea is to find the mapping rule between the past values of the observedprocess and its prediction. Hence, the learning algorithm consists of 2 phases. In the phase 1 the modelstate inputs are delayed measured output values of the process for the input-output representation. In thelearning phase 2 the measured output values are replaced by the estimated output values of the predictorbefore performing the new learning phase. The performed model has the form of linear combination ofRBF functions selected by Gram-Schmidt orthogonalisation from the hierarchical basis function system.The result of embedding analysis shows that the geomagnetic time series is 3rd order dynamical system.The recurrent orthogonal least squares system was first used as model of the Chua circuit dynamics andapplied to predict the Etna geomagnetic time series. The obtained models are accurate enough to explainthe chaotic mechanism of observed processes and to distinguish various modes of behavior. As comparedto the recurrent least-squares support vector machines tested on the same data sets, the orthogonal leastsquares systems require 10 times less number of regressors at higher accuracy due to the ability to exploreRBF basis functions with flexible width parameters.
Part XIII
Dynamics and Systems Biology
Physics of Age-Related Macular Degeneration
Fereydoon Family
Physics Department, Emory University, Atlanta, GA 30322, USA
Age related macular degeneration (AMD) is the leading cause of blindness in the adult population.Choroidal neovascularization, which is the abnormal growth of blood vessels in the choroidal region, isthe most common cause of AMD. CNV is produced with age by accumulation of residual material in theretinal pigment epithelium cells (RPE). With time, incompletely degraded membrane material build upin the RPE in the form of lipofuscin, cause abnormal growth of blood vessels that break through theBruchs membrane, and raise the macula and eventually lead to blindness. The fact that a number of farfrom equilibrium dynamical processes are involved in the formation and growth of AMD makes this a richfield for application of many techniques of statistical and nonlinear physics. I will give some examplesof the open problems and discuss the results of a kinetic Monte Carlo simulation of a deposition andaggregation model of lipofuscin formation in the RPE cells, as well as both two and three-dimensionalsimulations of the formation of CNV, that we have recently carried out.
Dynamical overlap of protein interaction networks: A methodto predict protein functions
Irene Sendina-Nadal1, Yanay Ofran2, Juan Antonio Almendral1, Daqing Li3, Inmaculada Leyva1, JavierM. Buldu1, Shlomo Havlin3, & Stefano Boccaletti4,5
1 Complex Systems Group, Dept of Signal Theory and Communications, Rey Juan Carlos University, Caminodel Molino s/n, 28943 Fuenlabrada, Madrid, Spain
2 The Mina and Everard Goodman Faculty of Life Sciences, Bar Ilan University, 52900 Ramat Gan, Israel3 Department of Physics, Minerva Center, Bar Ilan univeristy, 52900 Ramat Gan, Israel4 Embassy of Italy in Tel Aviv, 25 Hamered St., 68125 Tel Aviv, Israel5 CNR-Istituto dei Sistemi Complessi, Via Madonna del Piano 10, 50019 Sesto Fiorentino, Firenze, Italy
The latest advances in the field of genome sequencing technologies have tremendously increase thenumber of known proteins. The challenge is now how to characterize those proteins and elucidate theirfunction within the different biological processes. One recent approach to assign a function to one proteinis by means of the network of its interactions with other proteins [Sharan07]. Novel high-throughputtechniques for protein-protein interaction measurements have let to obtain those networks of proteininteraction from different organisms [Aebersold03, Field05]. Using this network representation, proteinsas nodes and detected physical interactions among them as links, it is possible to apply the tools fromcomplex networks theory to predict and annotate a function to a given protein.
While most of the works on functional annotation of proteins via their network of interactions areexclusively based in topological measurements from the properties of the PIN, we propose the applicationof an algorithm based on the synchronization behavior emerging from a modular network organization.The method relies on how phase oscillators organize in a network structure of dynamical interactions,and on a recently proposed technique for the identification of synchronization interfaces and overlappingcommunities [Li08] in ensembles of networking dynamical systems. The combination of the synchroniza-tion behavior of the PIN structure and an initial modular classification of proteins drawn from a manualassignment available from a ten years old database from the Munich information Center for Protein Se-quences (MIPS) allows for protein function predictions that is in genuine agreement with more recentand better refined manual assignments obtained from Gene Ontology database.
[Aebersold03] R. Aebersold, and M. Mann, Mass spectrometry-based proteomics, Nature 422, 198(2003).
[Fields07] S. Fields, High-throughput two-hybrid analysis. The promise and the peril, FEBS J 272,5391 (2005).
[Li08] D. Li et al., Synchronization Interfaces and Overlapping Communities in Complex Networks,Phys Rev Lett 101, 168701 (2008).
[Sharan07] R. Sharan, I. Ulitsky, and R. Shamir, Network-based prediction of protein function, Molec-ular Systems Biology 3, 88 (2007).
Dynamics of the interactions between the cell cycle and stressresponses in yeasts
Marco Thiel
Institute for Complex Systems and Mathematical Biology, University of Aberdeen (UK)
Candida albicans is a common fungal pathogen responsible for wide-spread infections in patients witha weakened immune system. For the development of an effective treatment it is highly important tounderstand how the pathogen reacts to different stresses, that it encounters in its host. Crucially, theresponse to the different stresses depends on the phase of the cell cycle of the fungi, e.g., the response toosmotic stress during the G1 or G2 phases is substantially different. Conversely, the stresses also causethe cell cycle to arrest at different phases.
I will discuss interactions between the cell cycle and stress responses in yeasts (S. cerevisiae andC. albicans). Based on techniques from network and dynamical systems theory, I will study how thesignalling pathways control the stress response and the cell cycle.
The model will be compared to experimental data, and predictions of the model will be discussed.
Direct observation of spontaneous veins formation and thicknessoscillations in Physarum polycephalum
Paul Dely1, Christophe Szwaj1, Serge Bielawski1, Olivier Hugon2, Olivier Jacquin2, Eric Lacot2, &Toshiyuki Nakagaki3
1 Lab. PhLAM, Universite de Lille 1 (France)2 Lab. Spectro, Universite J. Fourier, Grenoble (France)3 RIES, Hokkaido University (Japan)
Physarum polycephalum (or slime mold) is a giant biological cell of the myxomycete family, whichsize is typically in the several cm range. Though primitive, this system displays complex spatiotemporalbehaviors. In particular, this organism exhibits thickness oscillations (with temporal period around 1min.) that generate cytoplasmic movement and a structuration of the cell with channels and veins [1].
Here we focus on experimental analysis (by infrared microscopy) of velocity fields in regions wherea transition occurs from liquid cytoplasm to gel state, i.e., at places of vein formation. In addition, wepresent study of the thickness oscillations by the laser imaging technique LOFI [2].
The main objective is to obtain time-resolved, quantitative data, against which microfluidic theoriesof vein formation will be developed and tested.
[1] T. Nakagaki, Nature 417, 470 (2000); Yamada et al. PRE 59, 1009 (1999); Nakagaki et al., J. TheorBiol. 197, 497 (1999).
[2] E. Lacot, O. Hugon, Applied Optics, 2004, 43, 4915
Robustness of circadian clocks to daylight fluctuations: hintsfrom an unicellular alga
Benjamin Pfeuty1,2,3, Quentin Thommen1,2,3, Pierre-Emmanuel Morant1,2,3, Florence Corellou4,Francois-Yves Bouget4, & Marc Lefranc1,2,3
1 Universite Lille 1, Laboratoire de Physique des Lasers, Atomes et Molecules, UFR de Physique, 59655Villeneuve d’Ascq, France
2 CNRS, UMR8523, CERLA, FR2416, 59655 Villeneuve d’Ascq, France3 Universite Lille 1, Institut de Recherche Interdisplinaire, 59655 Villeneuve d’Ascq, France4 CNRS UMR7628, Universite Pierre and Marie Curie, Laboratoire d’Oceanographie Microbienne, Observatoire
oceanologique, F66651, Banyuls sur mer, France
pfeuty [email protected]
The development of systemic approaches in biology has put emphasis on identifying genetic moduleswhose behavior can be modeled accurately so as to gain insight into their structure and function. How-ever most gene circuits in a cell are under control of external signals and thus quantitative agreementbetween experimental data and a mathematical model is difficult. Circadian biology has been one notableexception: quantitative models of the internal clock that orchestrates biological processes over the 24-hourdiurnal cycle have been constructed for a few organisms, from cyanobacteria to plants and mammals.
Here we present first modeling results for the circadian clock of the green unicellular alga Ostreococcustauri. Two plant-like clock genes have been shown to play a central role in Ostreococcus clock. Wefind that their expression time profiles can be accurately reproduced by a minimal model of a two-genetranscriptional feedback loop. Remarkably, best adjustment of data recorded under light/dark alternationcan be obtained for vanishing coupling between the oscillator and the forcing cycle, suggesting thatcoupling to light is restricted to specific time intervals and has a limited effect when the circadian oscillatoris synchronized to the diurnal cycle. We indeed find that there exist gated coupling schemes whichgenerate oscillations close to those of the uncoupled model and thereby preserve adjustment of model toexperimental data.
These coupling schemes are shown to minimize the impact of daylight fluctuations on the core circadianoscillator, a type of perturbation that has been seldom considered when assessing the robustness ofcircadian entrainment. These robustness properties are interpreted in terms of the structure of the Arnoldtongue (i.e. the region of synchronization in the forcing amplitude-frequency plane). Finally, we show howthe shape of the phase response curve (PRC) characterizing a light coupling mechanism indicates whetherit gives rise to robust entrainment of the circadian clock.
Part XIV
Ecological Systems
Hyperbolic extremes and species dynamics in polychaetepopulations
Benjamin Quiroz-Martinez1,2,3, Francois G. Schmitt1,2,3, Jean-Claude Dauvin1,2,3, & Jean-MarieDewarumez1,2,3
1 Univ Lille Nord de France, F-59000 Lille, France2 USTL, LOG, F-62930 Wimereux, France3 CNRS, UMR 8187, F-62930 Wimereux, France
One of the key features of environmental and geophysical field studies is their high variability atmany different time and space scales. The dynamics of many natural populations involve the alternationover variable periods of time of phases of extremely low abundance and short outbreaks. The objectiveof this work is to characterise the dynamics of three diverse polychaete populations based on long-termbenthic surveys of shallow fine sand communities in the Bay of Morlaix (Western English Channel) and inGravelines (South of the North Sea), France. Abundance and species richness of polychaete populationsdisplay high variability, which was analysed using scaling approaches; we found that population densityhad heavy tailed probability density functions. We analysed the dynamics of relative species abundancein a community of trophically similar species, by estimating a diffusion coefficient which characterisesits temporal fluctuations. We conclude on the necessity of using new tools to approach and model suchhighly variable population dynamics in coastal marine ecosystems.
ANALYZING A COMPLEX SYSTEM
Jean - Marc GINOUX & Bruno ROSSETTO
PROTEE Lab., Toulon University, BP 20132, 83957, LA GARDE Cedex (France)
AbstractThe aim of this work is to explore some ways to draw out information from the solutions of a dynamical
system having two kinds of complexity, a high number of interacting freedom degrees and time varyingcoefficients. Some geometrical properties conferred by the system to the phase space are used to split upthe system in simple elements and to analyze the symmetries. The model taken as an example concernsthe dimethylsulfide (DMS) cycle. It consists of an eight-dimensional dynamical system with periodiccoefficients. This problem asks more mathematical questions than it is possible to answer given what weknow at the moment. But some features of the behavior of the solutions can be analyzed.
IntroductionThe dimethylsulfide (DMS) molecule dissolved in sea water evaporates under some conditions and
helps to supply most of the cloud condensation nuclei in the atmosphere. So the DMS cycle of ecosystemscontributes to scatter and absorb incoming solar radiation and to moderate anthropogenic forcing ofclimate. This field gives rise to a broad interest and to a large number of papers, but the magnitude ofthe climate feedback of the DMS is difficult to appreciate.
The modelThe first part of this work is devoted to the construction of a model of the biogeochemical cycle of
DMS based on works of A. J. Gabric & al.[1]. The variables of an eight-dimensional mathematical modelare concentration of phytoplankton, bacteria, zooflagellates, large protozoa, micro and mesozooplankton,dissolved inorganic nitrogen, dissolved dimethylsulfonio-propionate (DMSP) and dissolved DMS. The air-sea exchange of DMS depends in a complex way on the wind velocity and on the sea surface temperaturewhich is a function of time.
Mathematical studyAt first, the asymptotic behavior of solutions is analyzed with the data of biologists and the interactions
between the populations are compared to reduce the number of dimensions of the dynamical systemThen, the equation of an invariant manifold of an associated constant coefficient equivalent system is
computed in a very simple way using differential geometry results. This manifold is periodically crossedby the solutions and is involved in the structure of the attractor. On the other hand, the manifold maybring to light some symmetries of the solutions.
ConclusionThe respective influence of other set of variables could be studied by this method.Reference1. Gabric A. J., Gregg W., Najjar R., Erickson D., Matrai P., 2001. Modeling the biogeochemical
cycle of dimethylsulfide in the upper ocean: a review. Chemosph. Global Change Sc. 3: 377-392.
Part XV
Fluid Dynamics
Plasma Confinement in Tokamaks with Robust Torus
Ricardo Egydio de Carvalho1, Caroline G. L. Martins1, Ibere L. Caldas2, & Marisa Roberto3
1 Univ Estadual Paulista-UNESP - Rio Claro/SP - Brazil2 Universidade de Sao Paulo-USP - Sao Paulo/SP - Brazil3 Instituto Tecnologico da Aeronautica-ITA - Sao Jose dos Campos/SP - Brazil
The non-twist standard map occurs frequently in many fields of science specially in modeling thedynamics of the magnetic field lines in tokamaks. Robust tori, dynamical barriers that impede the ra-dial transport among different regions of the phase space, are introduced in the non-twist standard mapin a conservative fashion. The resulting Non-Twist Standard Map with Robust Tori (NTRT) is an im-proved model to study transport barriers in plasmas confined in tokamaks. The robust torus preventsthe magnetic field lines to reach the tokamak wall and reduces, in its vicinity, the destruction of is-lands and invariant curves due to the action of resonant perturbations. Our results indicate that the RTimplementation would decrease the field line transport at the tokamak plasma edge.
Turbulent flows in rotating spherical layers - dynamicalbehavior vs. meridional spatial structure: experiment.
Dmitry Zhilenko
Michurinski pr.1, Moscow, Russia
Properties of turbulent flow states are investigated near the threshold of theirs generation in the flow ofviscous incompressible fluid in the gap between two rotating spherical boundaries. The steady-state flowin a spherical layer is determined by the following dimensionless parameters: two Reynolds numbers Reiand Reo, and the relative layer thickness. Experiments were performed in the gap with the size equal tothe radius of the inner sphere. Here the properties of turbulent flows, developed under different boundaryconditions, are compared. Two types of boundary conditions were used. In the first case the ratio ofboundary velocities varies during the laminar-turbulent transition. In the second this ratio was constant,namely Rei = -Reo. In both cases spheres rotate in opposite directions. The structures of both turbulentflows, as we conclude from visualization, were different, as well as spectra and correlation dimensionscalculated from the time series of velocity component, measured by LDA.
In the first case correlation dimension changes abruptly and significantly, when the flow becomesturbulent, in contrast to the second case where correlation dimension demonstrates monotone growthduring the transition to chaos. Velocity pulsation spectrum of the turbulent flow in the first case iscontinuous without separated frequencies, the spectrum in the second case has separated frequenciesand it background exceeds the same in the first case more than 100 times. It should be noted that thestochasticity level is related with the regularity of the flow pattern in the meridional plane. The regularityof the flow pattern may be characterized by the number of degrees of freedom for the line separating thecirculations in the upper and lower hemispheres and the line separating the outer and inner circulationsin the meridional plane. In the first case, both separation lines may be displaced over their entire lengthin both the meridional and the radial direction. In the second case, Rei = -Reo, part of the separationlines coincides with the outer boundary and so cannot be displaced in the radial direction, i.e. the numberof degrees of freedom is smaller than in the asynchronous case. Hence, we may conclude that the greaterthe number of degrees of freedom of the separation lines, the greater the correlation dimension, whichquantitatively characterizes the stochasticity level.
Turbulent flows in rotating spherical layers: dynamical behaviorvs. meridional spatial structure. DNS.
Olga Krivonosova
Michurinski pr.1, Moscow, Russia
Three-dimensional time-dependent Navier-Stokes equations and continuity equation were solved forthe flow of a viscous incompressible fluid in a spherical layer. The no-slip and impermeability conditionswere imposed on the spherical boundaries. Computation algorithm, developed by N.V. Nikitin, is basedon a second-order central difference approximation in space and a third-order semi-implicit Runge-Kuttascheme for time advancement. Presented computational results have been obtained for statistically sta-tionary flow states: time averaged values of torques exerted on the inner and outer sphere are equal inmagnitude, opposite in sign and independent from run steps number. Time averaged quantities wereobtained over 5000 time steps, or 80 revolutions of inner sphere and 40 of the outer.
Here DNS is used for investigations of flow structure in meridional plane, particularly turbulent states.Gap size equal to inner sphere radius have been examined in the case of counter rotating boundaries.Under these conditions meridional circulation in axisymmetric steady base flow consists of two largevortices in each hemisphere with direction of circulation from pole to equator along rotating sphericalboundary. Present calculations have shown that azimuthal vorticity and radial velocity may representthe structure of base flow as well as stream function, usually used for two dimension flows. Next, time-averaged values were calculated for turbulent states, particularly azimuthal vorticity and radial velocity.Their spatial distribution allow us to conclude that averaged circulation in meridional plane of turbulentflow looks as typical meridional circulation in base flow with the same ratio of Reynolds numbers Rei / Reo.Dependency of velocity fluctuations on normalized distance from inner sphere has a maximum near theline, separating inner-circulation vortexes and outer-circulation vortexes. Velocity fluctuations intensityrapidly decreases in the directions from maximum to both spheres. Therefore, varying the Reynoldsnumbers ratio Rei/Reo, one can change velocity fluctuation maximum placement, and, probably, changeturbulent flow properties.
This possibility was examined by two sets of experiments: during the first ratio Rei/Reo was variedunder the condition Reo = - 900. During the second both Reynolds numbers were varied under thecondition Rei = - Reo. It was shown that difference in the spatial structures of obtained turbulentflows lead to the difference in their velocity fluctuation power spectra and in the behavior and values ofcorrelation dimension. It was found that turbulent level of the flow in the spherical layer, determined bycorrelation dimension value, may decrease with increase in the regularity of the meridional-flow pattern.
Pattern formation on sandy bottom: front propagation intosand ripples under the action of regular surface waves.
Julie Lebunetel-Levaslot1, Armelle Jarno-Druaux1, Alexander Ezersky2, & Francois Marin1
1 FRE CNRS 3102 Universite du Havre, 25 rue Philippe Lebon, 76058 Le Havre, France2 CNRS 6143 M2C Universite de Caen, 2-4 rue des Tilleuls, 14000 Caen, France
Pattern formation on a bottom under the action of surface waves is a manifestation of instabilitycaused by relative motion of sand and water. The morphological characteristics of sand ripples patternsare important for the prediction of the dissipation of waves energy, and for the sediment transport.They also influence the biological processes occurring on the bottom and the dispersion of pollutants.We report our results of an experimental study of pattern formation on sandy bottom under the actionof regular harmonic surface waves. It was found that two modes of pattern formation occurred: eitherfrom localized nucleation sites or from everywhere on the bottom as a uniform pattern. In the firstregime sandy ripples appeared in the isolated regions of bottom (patches) increasing in size and frontpropagation speed was measured. Simple dynamical model based on Ginzburg-Landau equation wasproposed to explain characteristics of patches. We have found that the propagating front characteristicsdepend on the direction of surface waves which generate ripples. If the velocity of front is co-directedwith the surface waves propagation, the front has a larger celerity, is steeper and more irregular than thefront which propagates in the opposite direction of surface wave.
Complex flows inside drops under acoustical and mechanicalvibrations
Philippe Brunet1, Michael Baudoin1, Farzam Zoueshtiagh1, Virginia Palero2, & Julia Lobera2
1 IEMN - UMR CNRS 8520. Avenue Poincare - BP 60069, Villeneuve d’Ascq Cedex 59652, France2 Departamento de Fısica Aplicada Grupo de Tecnologıas Opticas Laser (TOL) Instituto de Investigacion en
Ingenierıa de Aragon (I3A). Universidad de Zaragoza, Spain
We investigate experimentally the flow inside a sessile droplet subjected to acoustic or mechanicalforcing. The drop is in partial wetting on its substrate. The surface acoustic wave (SAW) of a few tens ofMHz induces a streaming flow inside the drop, and the acoustic radiation pressure acting at the liquid/airinterface generates oscillations that can unpin the drop contact-line. The mechanical vibrations prescribean oscillatory gravity field that also causes the unpinning of the contact-line. We give details of the innerflow and discuss the most efficient way to move the drop by combining acoustic and mechanical actions.
Stability analysis of turbulent boundary layer flows withadverse pressure gradient
Jean-Philippe LAVAL1,2, Matthieu MARQUILLIE1,2, & Uwe EHRENSTEIN3
1 CNRS, UMR 8107, F-59650 Villeneuve d’Ascq, France2 Univ Lille Nord de France, F-59000 Lille, France3 Aix Marseille Univ, IRPHE UMR 6594, CNRS, F-13384 Marseille 13, France
The turbulent boundary layer flow subjugated to adverse pressure gradient coming from curvatureare of crucial importance for many applications including aerodynamics of airfoils, ground vehicles orturbine blades. Significant progress are needed in understanding the near wall turbulence in order toimprove the theoretical and numerical models. The available numerical models usually fail as they arebased on scaling of wall turbulence which are no more valid with pressure gradient. Therefore, a carefulanalysis of turbulent structures generation are the only opportunity to make progress in designing accuratestatistical models for turbulence. The Direct Numerical Simulation (DNS) of the Navier Stokes equationsis an efficient tool to study the complete time and 3D space behaviors of the full range of turbulentstructures. DNS was already used to identify and to study the cycle of generation of turbulent structuresin turbulent boundary layer without pressure gradient. A large experimental and numerical database ofturbulent boundary layer were generated through the European project WALLTURB in order to extractphysical understanding of these flows.
In flows with sufficiently high pressure gradients, a strong peak of turbulent kinetic energy have beenobserved and not yet fully explained. Through the analysis of a DNS database of a converging-divergingchannel, the origine of intense coherent structures was identified and linked to the linear instability ofthe flow. The instability of the normal profile of the mean streamwise velocity is not satisfactory to fullyexplain the generation of the coherent vortices observed in the DNS. However, the linear stability analysisof the spanwise varying average streak (which is the most energetic long structure in the vicinity of thewall) superimposed to the normal profile is able to predict both the streamwise location and the shapeof the coherent structures. These structures quickly evolve according to the non-linearity of the NavierStokes equations to elongated vortical structures which are able to redistribute the turbulent kineticenergy in the three directions.
The drawback of the DNS is the limitation in term of Reynolds number. On the other hand, theprogress on experimental tools for flow characterization are significant as quantitative analysies in threedimensions are now possible. However, the accuracy and the spatial resolution of methods such as to-mographic Particles Image Velocimetry are not yet satisfactory for careful investigations of near wallturbulent structures.
Instabilities of conducting fluid flows in cylindrical shells underexternal forcing
Javier Burguete & Montserrat Miranda-Galceran
Depto. Fisica y Mat Aplicada, Universidad de Navarra, Irunlarrea 1, E-31008 Pamplona, Spain
Flows created in neutral conducting flows remain one of the topics less studied of fluid dynamics.But there is a great variety of unexplained behaviours in these systems, with strong consequences bothin fundamental research (dynamo action, MHD instabilities, turbulence suppression) and applications(casting, aluminium production, biophysics).
Having in mind a biological application, in this experiment we present the effect of a time-dependentmagnetic field parallel to the axis of an annular cavity. Due to the Lenz’s law, a current is induced in thebulk when the magnetic field increases or decreases, producing a radial force that alternatively changesits orientation. This force produces the destabilization of the static fluid layer, and a flow is created.
The geommetry of the experimental cell is a cylindrical layer with external and internal diameters94 and 84 mm respectively. The layer is 20mm depth, and we use as conducting fluid an In-Ga-Snalloy. There is no external current applied on the problem, only an external magnetic field. This fieldevolves harmonically with a frequency up to 10Hz, small enough to not to observe skin depth effects. Themagnitude ranges from 0 to 0.1 T. With a threshold of 0.01T a dynamical behaviour is observed, and themain characteristics of this flow have been determined.
Previous works have shown that very thin layers (extended drops) destabilize from a circular shape tostar-like or labyrinth shapes. With these geometries, induced currents can be interrupted, and there is nodynamical behaviour. Here, we deal with a shallow layer and bulk forces caused by the induced currentscannot disappear.
Pattern formation of buble periodically emerging at a liquidfree surface
HARUNORI YOSHIKAWA, Christian Mathis, Philippe Maıssa, & Germain Rousseaux
Laboratoire J.-A. Dieudonne, Universite de Nice Sophia-Antipolis-Parc Valrose, 06108 Nice Cedex 2, France
Patterns formed by bubbles of centimeter scale on the free surface of a viscous liquid are investigated.The liquid is contained in a vertical cylindrical tank. Bubbles are released into the liquid periodicallyby continuous gas injection through an orifice at the center of the tank bottom. These bubbles ascendvertically in a regular chain and emerge at the surface. Their radial emission due to the interaction witheach other at the emergence and to radial surface flow generated by their ascending motion leads to theformation of a variety of patterns. At low flow rate of the gas injection, successive emerging bubblesare emitted with a constant angular shift equal to π. Two opposed arms of bubbles are then exhibitedon the surface. Beyond a critical flow rate, the angular shift departs from π through a supercriticalbifurcation and decreases with the flow rate increasing. Bubbles on the surface form a variety of patternswith different numbers of spiral or straight arms. For revealing the mechanism of this pattern formation,measurements of bubble motion and liquid flow are performed, respectively, by image processing andby the PIV technique. We analyze these results with using the tools and concepts of the study of leafarrangement in botany (phyllotaxis). Close similarities between these two pattern formations will bepresented.
Droplet traffic at a junction: dynamics of path selection
Axelle Amon, David Sessoms, Laurent Courbin, & Pascal Panizza
Institut de Physique de Rennes, UMR UR1-CNRS 6251, Universite de Rennes 1, Campus de Beaulieu, 35042Rennes cedex
Understanding the flow of discrete elements through networks is of importance for diverse phenomena,for example, multiphase flows in porous media and microfluidic devices, and repartition of cells in bloodflows. Addressing this issue requires a description of the mechanisms that govern flow partitioning at anode. In the case of diluted flows of droplets in microfluidic devices, it is known that a droplet reachinga node flows into the arm having the smallest hydrodynamic resistance. Despite this robust and simplerule, complex dynamics of the path selection can be observed, even for a simple and widely-studiedsystem consisting of a train of droplets reaching the inlet node of an asymmetric loop. In particular,periodic and aperiodic behaviors with complex patterns of the droplets partitioning have been reported.Such complexity emerges from time-delayed feedback: the presence of droplets in a channel modifies itshydrodynamic resistance, so that the path selection of a droplet at a node is affected by the trajectories ofthe previous ones. To our knowledge, a complete understanding of the physical parameters and relationsthat govern the dynamical response of these systems is still lacking.
We present a numerical, theoretical, and experimental investigation of droplets partitioning at the inletnode of an asymmetric loop. Our model which describes the discrete dynamics of a binary variable canbe viewed as a type of cellular automata. We obtain discrete bifurcations between periodic regimes andwe show that these dynamics can be characterized by two invariants for a set of parameters. We predicttheoretically the bifurcations between consecutive periodical regimes and account for the variations ofthe invariants with the relevant physical parameters of the system. To demonstrate the pertinence of ourmodel, we perform experiments using a microfluidic device. We observe experimentally complex dynamicsof droplet partitioning; these results are well described by our theoretical predictions. Specifically, ourexperiments show the existence of multistability between different periodical regimes. Multistability canbe reproduced numerically by introducing noise in our simulations, an intrinsic feature of experimentalsystems. Our results, which provide a complete description of droplet partitioning at a single node, suggestthat microfluidic experiments are model systems for the study of more complicated networks.
Part XVI
Dynamical Networks
Synchronization of time-delayed diffusively coupled systems: Anexperimental case study with Hindmarsh-Rose oscillators
Erik Steur, Patrick Neefs, & Henk Nijmeijer
Eindhoven University of Technology, Dept. Mechanical Engineering, Dynamics and Control Group, P.O.Box513, 5600 MB Eindhoven, The Netherlands
We discuss synchronization in networks of systems that are interconnected via diffusive coupling. Wepresent theoretical results for a general class of nonlinear systems that are interacting with or withouttime-delay. These theoretical results are supported by experiments with a setup consisting of sixteenelectronic Hindmarsh-Rose neurons. The experiments are performed for the non-delayed case as well asthe situation where interaction delay is explicitly taken into account. We will focus in particular on theinfluence of the network topology on the synchronization in case of delayed interactions.
References[1] Erik Steur and Henk Nijmeijer, Synchronization in networks of linearly time-delay coupled systems:
a passivity based approach, (submitted for publication) 2009[2] P.J. Neefs, E. Steur and H. Nijmeijer, Network complexity and synchronous behavior: an experi-
mental approach, accepted for publication in Int. J. Neuro. Syst., 2010
The stability of adaptive synchronization of chaotic systems
Adam Cohen, Bhargava Ravoori, Francesco Sorrentino, Thomas Murphy, Edward Ott, & Rajarshi Roy
Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland20742 USA
In order to achieve identical synchronization of a network of N coupled chaotic oscillators, eachnode must be set to have nominally identical parameters and the N2 elements of the adjacency matrixmust be fine-tuned to ensure that the synchronous solution is admitted and stable. The analytic toolfor determining whether a particular network configuration can maintain a synchronous state is givenby the master stability function formulation. Recently, an adaptive strategy was presented [1] that canmaintain a globally synchronous state even when the coupling strengths are unknown and time-varying.This is a distributed technique that runs at each node and employs only local information, i.e. an internalsignal and an aggregate signal representing the superposition of transmitted signals from the other nodes.This adaptive synchronization strategy has been demonstrated with experiments on a network of chaoticoptoelectronic oscillators [2] and with numerical simulations of large networks. In this talk, the stabilityof this scheme is addressed through an extension of the master stability function technique to includeadaptation [3]. The results of the stability study are compared with experimental measurements.
References:[1] F. Sorrentino and E. Ott, Phys. Rev. Lett. 100, 114101 (2008).[2] B. Ravoori et al., Phys. Rev. E 80, 056205 (2009).[3] F. Sorrentino et al., Chaos 20, 013103 (2010).This work was supported by DOD MURI grant (ONR N000140710734).
Dynamics and augmentation patterns in adaptive networks
Casey Schneider-Mizell1, Jack Parent2, Eshel Ben-Jacob3, Leonard Sander1, & Michal Zochowski1
1 Department of Physics, University of Michigan, Ann Arbor, USA2 Department of Neurology, University of Michigan Medical School, Ann Arbor, USA3 Tel Aviv University, Tel Aviv, Israel
In many cases interacting networks are adaptive system themselves, that undergo constant reorgani-zation. The brain is a prime example of such a system. In this case the network reorganization not onlyconsists of reorganization of network connectivity but may also include addition of new network nodesand deletion of existing ones. In hippocampal formation, new neurons are generated throughout life andintegrate into the network via the process of adult neurogenesis. This process is thought to have an impor-tant functional role in healthy networks, but also may lead to pathological structural changes in epilepticbrain. What controls this neural augmentation remains unknown. We use computational simulations toinvestigate the effect of network environment on structural and functional outcomes of neurogenesis. Wefind that small-world networks with external stimulus are able to be augmented by activity-seeking neu-rons in a manner that enhances activity at the stimulated sites without altering the network properties asa whole. However, when inhibition is decreased or connectivity patterns are changed, new cells are bothless responsive to stimulus and the new cells are more likely to drive the network into bursting dynamics.These patterns are being compared with the experimental ones observed in a culture system.
Non-Linear Kalman Filtering Techniques for Estimation andPrediction of Rat Sleep Dynamics
Madineh Sedigh-Sarvestani1, Steven L. Weinstein3, Steven J. Schiff1,2, & Bruce J. Gluckman1,2
1 Engineering Science and Mechanics, Pennsylvania State University, University Park, PA,2 Department of Neurosurgery, Pennsylvania State University, University Park, PA.3 Pediatric Epilepsy, Weill Cornell Medical College, New York City, NY
Our laboratory has ongoing efforts to utilize model based controller-predictor systems to better un-derstand the non-linear dynamics of the brain, with particular attention to sleep and seizure. Towardsthis end, we have implemented several published and novel computational models of the brain to inves-tigate its behavior in a variety of different states (i.e. sleep vs. wake). These models have been modifiedso that they simulate the sleep dynamics of our experimental rodents within small sampling times. Wehave implemented these models in an Unscented Kalman Filter (UKF) framework to serve as duplicatesource and tracker models and show that the UKF-based data assimilation algorithm we have developedis extremely robust and can reconstruct hidden dynamics even when the tracker model is intentionallymade inadequate. In parallel with these computational efforts, we have obtained a feature set of experi-mental data from our continuously cabled rodents and have used these features to classify state of sleepand to develop a seizure prediction algorithm. Several of these discrete and continuous features are thenused as the noisy observables in the implemented UKF framework to recursively reconstruct all of theinaccessible variables of the dynamic sleep model. Results from this reconstruction are promising andallow us access to hidden variables, such as sleep driven changes in neurotransmitter concentrations thatwould be hard or impossible to measure directly from our rodents. Furthermore, we have augmentedour algorithm to make short-time predictions of sleep state. We then use these predictions of sleep-statetransitions to improve the performance of our seizure prediction algorithm by reducing the confoundingeffect of sleep state on seizure prediction.
Recent published literature has begun to illuminate the intimate link between seizure and sleep, arelationship with a long clinical history in human patients. It is becoming increasingly clear that inorder to predict and control seizure dynamics, we must first be able to grasp the non-linear dynamicsof sleep and sleep-state transitions. Thus, our work bridges experimental and control theory techniquesto investigate a crucial missing link which will give us insight into the dynamics of seizures and maydrastically improve seizure prediction.
Part XVII
Extreme Events
Rare and extreme events in temporal and spatial opticalsystems
Eric LOUVERGNEAUX, Arnaud MUSSOT, Alexandre KUDLINKSI, Mikhail KOLOBOV, MarcDOUAY, & Majid TAKI
Laboratoire de Physique des Lasers, Atomes, Molecules, UFR de Physique, Universite Lille 1, F-59655Villeneuve d’Ascq, France
Abstract: We theoretically and numerically study optical rare and strong events generated in fibersupercontinua and optical feedback system patterns.
In the ocean, giant waves (also called killer waves, freak or rogue waves) are extremely rare andstrong events. They are not well understood yet and the conditions which favour their emergence areunclear. Very recently, it was shown that the governing equations [1] as well as the statistical propertiesof an optical pulse propagating inside an optical fibre [2] mimic very well these gigantic surface wavesin the ocean. Here we generate both experimentally and numerically optical rogue waves in a photoniccrystal fiber (microstructured fiber) with continuous wave (CW) pumps. This is relevant for establishingan analogy with rogue waves in an open ocean. After recalling fundamental rogue waves [3] known asAkhmediev breathers that are solutions of pure nonlinear Schrodinger (NLS) equation, we analyticallydemonstrate that a generalized NLS equation, which governs the propagation of light in the fiber, exhibitsconvective modulationnal instability [4]. The latter provides one of the main explanations of the opticalrogue wave extreme sensitivity to noisy initial conditions at the linear stage of their formation [5]. In thehighly nonlinear regime, we provide the evidence that optical rogue waves result from soliton collisionsleading to the rapid appearance/disappearance of a powerful optical pulse [6].
In this talk we also report on the experimental observation of giant waves in a spatially extendedfeedback system. These giant spatial optical waves have probability density function with long tails thatare characteristics of extreme events.
References[1] C. Kharif, E. Pelinovsky, and A. Slunyaev, ”Rogue Waves in the ocean”, Springer Berlin Heidelberg,
2009[2] D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, ”Optical rogue waves” Nature 450, 1054-1058,
(2008).[3] N. Akhmediev, A. Ankiewicz, and M. Taki, ”Waves that appear from nowhere and disappear
without a trace”, Phys. Lett. A 373, 675 (2009).[4] A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, Delage, and M. Taki, ”Optical fiber
systems are convectively unstable”, Phys. Rev. Lett. 101, 113904 (2008).[5] M. Taki, A. Mussot, A. Kudlinski, E. Louvergneaux, M. Kolobov, M. Douay, ”Third-order disper-
sion for generating optical rogue solitons”, Phys. Lett. A 374, 691-695 (2010).[6] A. Mussot, A. Kudlinski, M. Kolobov, E. Louvergneaux, M. Douay and M. Taki, ”Observation of
extreme temporal events in CW-pumped supercontinuum”, Opt. Express 17 (19), 17010 (2009).
Part XVIII
Nanosystems
Stability of low-friction surface sliding of nanocrystal withrectangular symmetry and application to graphite flakes ongraphite and W on NaF(001)
Astrid S. de Wijn
Radboud University Nijmegen, Institute for Molecules and Materials, Heyendaalseweg 135, 6525AJ Nijmegen,the Netherlands
Theoretical consideratons show that the sliding of an atomic layer weakly interacting with an incom-mensurate periodic substrate can occur with vanishingly low friction. Indeed, extremely low friction hasbeen observed experimentally in several systems and this effect has been named superlubricity. However,there is recent evidence that the incommensurate superlubric state is destroyed by rotation of the slidingflake [2], leading to a commensurate state with high friction.
In this work, we study the dynamics of finite rigid nanocrystals consisting of graphite flakes andW crystals on a graphite and NaF(001) surfaces. In numerical simulations, we find that after an initialshort period, the graphite flake either rotates and locks into a commensurate orientation or it remainsincommensurate and slides with extremely low friction. We construct a simple model system whichcaptures the essential dynamics, and for which the stability can be investigated analytically. We showthat for a realistic system periodic orbits exist that correspond to the commensurate and incommensuratestates and that they may be stable. We investigate the robustness of the incommensurate low-friction stateagainst parameters such as sliding velocity and temperature. We find that the geometry and high typicalcorrugation of substrates with square lattices such as NaF(001) increase the robustness of low-frictionstates compared to typical hexagonal lattices, such as graphite.
[1] M. Dienwiebel et al., Phys. Rev. Lett. 92, 126101 (2006).[2] A.E. Filippov et al., Phys. Rev. Lett. 100, 046102 (2008).[3] A.S. de Wijn, C. Fusco, and A. Fasolino, Phys. Rev. 81, in press (2010).