M lefranc, S. Boccaletti, B. Gluckman, C. Grebogi, J. K¨ Urths, L. Pecora

Our recent work toward very large-scale integration of nanoelectromechanical systems (see nanovlsi.com), now makes feasible studies of the complex dynamics of arrays of coupled nonlinear devices. I will show that even a system of two interacting nonlinear nanomechanical vibrating structures, despite its apparent simplicity, manifests very rich dynamics – including the strongly tunable nonlinearity, bistability, hysteresis, spontaneous amplitude modulation oscillations, and the onset of deterministic chaos in the nanomechanical domain. Together with our successful recent demonstration of NEMS-based self-sustained oscillators, advances with NEMS arrays offer the prospect of assembling and attaining synchronization in large coupled arrays of nonlinear oscillators. The unprecedented level of control of the underlying physical parameter space provides an exceptional opportunity to investigate the properties of such phenomena as correlated noise reduction, pattern formation, and soliton propagation.

We anticipate that nonlinear NEMS and NEMS arrays will play a very central future role in substantially deepening our theoretical and experimental understanding of nonlinear systems.

This work is done in collaboration with Professors Michael Roukes and Michael Cross (Caltech, Professor Ron Lifshitz (Tel Aviv), and Philippe Andreucci and coworkers at CEA/LETI-MINATEC in Grenoble in the Caltech/LETI partnership - the Alliance for Nanosystems VLSI (nanovlsi.com).

3

0

Strong field double ionization: insights from nonlinear dynamics

Franc¸ois Mauger1, Cristel Chandre1, & Turgay Uzer

21

2Centre de Physique Th ´ eorique, UMR 6207, Campus de Luminy, case 907, 13288 Marseille cedex 9, France

[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 .

3

1School of Physics, 837 State Street Atlanta, Georgia 30332-0430, U.S.A [e-mail]

One of the most striking surprises of recent years in laser-matter interactions has come from multiple ionization by intense short laser pulses. Multiple ionization of atoms and molecules is usually treated as a rapid sequence of isolated events. However, in the early 90’s, experiments using intense laser pulses found double ionization yields which departed from these predictions by several orders of magnitude. It has made the knee shape in the double ionization probability versus intensity curve one of the most dramatic manifestation of electron-electron correlation in nature.

It turns out that entirely classical interactions are adequate to generate the strong two-electron correlation needed for double ionization: numerical simulations succeed to reproduce qualitatively the knee shape observed experimentally. The central question is how two electrons leave the nucleus under the influence of a short and intense laser pulse? The precise mechanism that makes electron-electron correlation so effective follows the recollision scenario: An ionized electron, after picking up energy from the field, 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 nonlinear dynamics perspective. I will show that this recollision scenario has to be complemented by the dynamical picture of the inner electron. Using this global picture of the dynamics, we were able to derive verifiable predictions 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 completely open concerns polarization. The stakes are high when it comes to understanding the influence of polarization since it is well known that the emission of harmonics is strongly dependent on the ellipticity of the driving field. A common wisdom is that the recollision scenario is suppressed with circular polarization (CP) since an ionized electron tends to spiral out from the core. The matter would rest there if it were not for conflicting experimental evidence: In some experiments using CP fields, the double ionization yields follow the sequential mechanism whereas in others these yields are clearly several orders of magnitude higher than expected. The question we resolve here is: Are recollisions possible in pure CP fields or does one have to rely on a small residual ellipticity? We explain these seemingly contradictory findings and show that, contrary to common belief, recollision can be the dominant mechanism leading to enhanced double ionization yields in CP fields

.

Quantum simulators: studying the Anderson model with a quantum-chaotic system

Jean-Claude GARREAU

Laboratoire de Physique des Lasers, Atomes, Mol ´ ecules, Universit ´ e Lille 1 - Sciences et Technologies, France

Using a simple model taking into account the effect of disorder in the dynamics of electrons in a crystal, Anderson predicted in 1958 the existence of a quantum phase transition between a metal (diffusive) phase and an insulator (quantum-localized) phase, when the disorder level increases. Despite the wide interest generated by this model, few experimental studies have been possible so far, mainly because decoherence sources are difficult to control in a real crystal. Moreover, probability distributions for the electrons inside the crystal are not accessible experimentally, which limits the measurements to ”bulk quantities” like conductivity or dielectric constant. This situation completely changed with the advent of atom cooling and trapping in optical potentials. In such systems, decoherence can be controlled to a large extent, and probability distributions can be directly measured in real or in momentum space. We thus realized a quantum-chaotic system simply by placing laser-cooled atoms in a pulsed standing wave. In adequate conditions, such a system can be proved to be equivalent to the Anderson model, with the underlying classically-chaotic dynamics playing the role of the disorder. This allowed us to observe the Anderson phase-transition in very good conditions, to deduce its critical exponent, and to study the shape of the critical wavefunctions, which are found to perfectly obey the scaling properties characteristic of the phase transition.

3

2

Quantum-resonance ratchets: experimental realizations and prediction of stronger effects

Itzhack Dana

Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel [e-mail]

Classical low-dimensional Hamiltonian systems may exhibit the chaotic “ratchet effect” only for a mixed 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 systems and 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 approximating a completely symmetric (cosine) kicking potential. Also, the BEC was initially prepared in a superposition of two momentum states corresponding to a state with well-defined point symmetry. Despite these symmetries and in accordance with predictions in Ref. [1], a QR ratchet effect was observed due to the relative asymmetry associated with the generic non-coincidence of the symmetry centers of the symmetric potential and the initial state [3]. The experimental results were found to agree well with theoretical ones [1] after taking properly into account the finite quasimomentum width of the BEC; in particular, this width was shown to cause a suppression of the ratchet acceleration for exactly resonant quasimomentum, 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 one Planck 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 states such as those used in the experiments above. By increasing the number of momentum states in the superpositions, the average strength of the effect gradually increases, approaching that for the maximally uniform states. These results were obtained for the kicked Harper models which are equivalent to kicked harmonic oscillators. The latter systems, as well as superpositions of many momentum states, are experimentally realizable. Thus, the very strong quantum ratchet effects predicted should be observable in the laboratory.

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).

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3

Wave/Quantum Chaos: universal properties and practical applications

Steven M. ANLAGE

Center for nanophysics and advanced materials, University of Maryland

Chaos is a ubiquitous phenomenon in the classical world. It appears in dripping faucets, human heartbeats, electrical circuits, lasers, etc. However, there is now interest in the wave and quantum properties of systems that show chaos in the classical (short wavelength) limit. These ’wave chaotic’ systems appear in many contexts: nuclear physics, acoustics, two-dimensional quantum dots, and electromagnetic enclosures, for example. It has been hypothesized that Random Matrix Theory (RMT) makes predictions for many universal fluctuating properties of quantum/wave systems that show chaos in the classical/ray limit. Microwave cavities, with classically chaotic ray dynamics, have proven to be a fruitful test-bed for the experimental tests of universal fluctuations in wave-chaotic systems. We have developed a microwave cavity experiment that mimics solutions to the Schr ¨ odinger equation for a two-dimensional infinite square well potential, and developed protocols to eliminate system-specific details (coupling, short-orbits) that would otherwise obscure the underlying universal properties. I will present experimental tests of RMT predictions of both closed and open quantum systems, as simulated by our microwave cavity analog experiment [1]. As a specific example we have examined quantum interference effects in the transport properties of mesoscopic systems, as simulated in the microwave cavity. The Landauer-B ¨ uttiker formalism is applied to obtain the conductance of a corresponding mesoscopic quantum-dot device, and we find good agreement for the probability density functions of the experimentally derived surrogate conductance (universal conductance fluctuations), as well as its mean and variance, with the theoretical predictions based on RMT. We are also investigating the physics of fidelity decay (a concept borrowed from quantum mechanics) through measurement of the Loschmidt echo with classical waves. These studies exploit ray chaos and a single-channel time-reversal mirror, and have led to development of a new class of wave-based sensors [2].

[1] Jen-Hao Yeh, James Hart, Elliott Bradshaw, Thomas Antonsen, Edward Ott, Steven M. Anlage, ”Universal and non-universal properties of wave chaotic scattering systems,” Phys. Rev. E 81, 025201(R) (2010).

[2] Biniyam Tesfaye Taddese, James Hart , Thomas M. Antonsen, Edward Ott, and Steven M. Anlage, ”Sensor Based on Extending the Concept of Fidelity to Classical Waves,” Appl. Phys. Lett. 95 , 114103 (2009)

.* In collaboration with Thomas Antonsen, Edward Ott, Biniyam Taddese, Jen-Hao Yeh, Elliott Bradshaw, and James Hart. This work is supported by AFOSR and by ONR MURI N000140710734 and ONR DURIP N000140710708. For more information and reprints, see: ¡a href=”http://www.cnam.umd.edu/anlage/AnlageHome.htm”¿http://www.cnam.umd.edu/anlage/AnlageHome.htm.¡/a¿

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4

Topological entanglement and transport barriers in the chaotic mixing of fluids

Emmanuelle GOUILLART

Joint Unit CNRS/Saint-Gobain, Saint-Gobain Recherche, France

In the absence of turbulence, mixing viscous fluids by stirring at low Reynolds number is difficult. Efficient mixing is realized by protocols promoting chaotic advection, where neighboring Lagrangian particles separate exponentially fast. For 2-dimensional flows, the phase space of Lagrangian trajectories corresponds to the physical fluid domain, and can therefore be visualized directly. Our research seeks to understand the mechanisms that control the speed of mixing, and to identify relevant criteria of mixing quality. We study mostly rod-stirring protocols, that model many industrial mixing protocols.

Historically, the characterization of chaotic mixing has relied on Poincar ´ e sections and Lyapunov exponents. New methods inspired by braid theory have emerged since the 2000’s, paving the way for a topological study of chaotic mixing. We have proposed a topological description of mixing by the entanglement of periodic orbits that we called ”ghost rods”. In particular, a lower boundary on the topological entropy of the flow (hence, the stretching factor of material lines and dye filaments) is given by the braiding factor of periodic orbits. We discuss the extension of such methods to non-periodic orbits.

We also examine the link between the phase portrait of mixing protocols, and the rate of homogenization of a diffusive dye. When the chaotic region extends to the no-slip walls of the fluid vessel, we observe a slow algebraic decay of the inhomogeneity. The peripheral fluid region ”sticking” to the no-slip vessel wall is shown to slow down mixing in the whole domain, as unmixed fluid initially close to the wall ends up escaping in the bulk. On the other hand, when the wall of the vessel is rotated, the fluid domain is divided into a central isolated chaotic region and a peripheral regular region. As a result, the bulk is insulated from the slow stretching region at the wall, and we observe an exponential decay of scalar inhomogeneity, and the convergence of the dye pattern to a self-similar pattern that repeats over time. For all these mixing experiments, we make quantitative predictions of the rate of mixing from the rate at which particles in the regions of slowest stretching escape in the bulk.

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5

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, Universit ´ e de Rennes 1, Campus de Beaulieu, 35042 Rennes cedex [e-mail]

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 blood flows. Addressing this issue requires a description of the mechanisms that govern flow partitioning at a node. In the case of diluted flows of droplets in microfluidic devices, it is known that a droplet reaching a node flows into the arm having the smallest hydrodynamic resistance. Despite this robust and simple rule, complex dynamics of the path selection can be observed, even for a simple and widely-studied system 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 its hydrodynamic resistance, so that the path selection of a droplet at a node is affected by the trajectories of the previous ones. To our knowledge, a complete understanding of the physical parameters and relations that govern the dynamical response of these systems is still lacking.

We present a numerical, theoretical, and experimental investigation of droplets partitioning at the inlet node of an asymmetric loop. Our model which describes the discrete dynamics of a binary variable can be viewed as a type of cellular automata. We obtain discrete bifurcations between periodic regimes and we show that these dynamics can be characterized by two invariants for a set of parameters. We predict theoretically the bifurcations between consecutive periodical regimes and account for the variations of the invariants with the relevant physical parameters of the system. To demonstrate the pertinence of our model, we perform experiments using a microfluidic device. We observe experimentally complex dynamics of droplet partitioning; these results are well described by our theoretical predictions. Specifically, our experiments show the existence of multistability between different periodical regimes. Multistability can be reproduced numerically by introducing noise in our simulations, an intrinsic feature of experimental systems. Our results, which provide a complete description of droplet partitioning at a single node, suggest that microfluidic experiments are model systems for the study of more complicated networks.

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6

Pattern formation of buble periodically emerging at a liquid free surface

Harunori Yoshikawa, Christian Mathis, Philippe Ma ¨ issa, & Germain Rousseaux

Laboratoire J.-A. Dieudonn ´ e, Universit ´ e de Nice Sophia-Antipolis-Parc Valrose, 06108 Nice Cedex 2, France [e-mail]

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 periodically by continuous gas injection through an orifice at the center of the tank bottom. These bubbles ascend vertically in a regular chain and emerge at the surface. Their radial emission due to the interaction with each other at the emergence and to radial surface flow generated by their ascending motion leads to the formation of a variety of patterns. At low flow rate of the gas injection, successive emerging bubbles are emitted with a constant angular shift equal to  . Two opposed arms of bubbles are then exhibited on the surface. Beyond a critical flow rate, the angular shift departs from  through a supercritical bifurcation and decreases with the flow rate increasing. Bubbles on the surface form a variety of patterns with 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 and by the PIV technique. We analyze these results with using the tools and concepts of the study of leaf arrangement in botany (phyllotaxis). Close similarities between these two pattern formations will be presented.

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7

Complex flows inside drops under acoustical and mechanical vibrations

Philippe Brunet1, Michael Baudoin1, Farzam Zoueshtiagh1, Virginia Palero2, & Julia Lobera

21

2IEMN - UMR CNRS 8520. Avenue Poincar ´ e - BP 60069, Villeneuve d’Ascq Cedex 59652, France

Departamento de F ´ isica Aplicada Grupo de Tecnolog ´ ias ´ Opticas L ´ aser (TOL) Instituto de Investigaci ´ on en Ingenier ´ ia d

eArag ´ on (I3A). Universidad de Zaragoza, Spain [e-mail]

We investigate experimentally the flow inside a sessile droplet subjected to acoustic or mechanical forcing. The drop is in partial wetting on its substrate. The surface acoustic wave (SAW) of a few tens of MHz induces a streaming flow inside the drop, and the acoustic radiation pressure acting at the liquid/air interface generates oscillations that can unpin the drop contact-line. The mechanical vibrations prescribe an oscillatory gravity field that also causes the unpinning of the contact-line. We give details of the inner flow and discuss the most efficient way to move the drop by combining acoustic and mechanical actions.

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8

Chaos and turbulence in vibrating plates

Arezki BOUDAOUD

Laboratoire de Physique Statistique, ENS Paris, France & Reproduction et D ´ eveloppement des Plantes, ENS Lyon, France

The presence of a fluid is generally implied when using the concept of turbulence. In contrast, our experiments concern the large amplitude vibrations of an elastic plate. In a first setup, we found period doubling, aperiodic motion, and a transition whereby the plate rotates at constant velocity. In a second set-up, we reconsidered the apparatus that was used in theatres to mimic the sound of thunder and showed that it shares many features with hydrodynamic turbulence.

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9

Experimental study of dislocation avalanches during unstable plastic deformation

Mikhail Lebyodkin1, Nikolay Kobelev2, Youcef Bougherira1, Denis Entemeyer1, Claude Fressengeas2;3, Tatiana Lebedkina, & Ivan Shashkov1;2

11

2

3Laboratoire de Physique et M ´ ecanique des Mat ´ eriaux, UPVM / CNRS, Ile du Saulcy, 57045 Metz Cedex, France

Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Russia

2. Weiss, J., T. Richeton, F. Louchet, et. al., Phys. Rev. B, 76, 224110, 2007.

4

0Institut Jean Lamour, Ecole des Mines, Parc de Saurupt, CS14234, 54042 Nancy Cedex, France [e-mail]

The plasticity of crystalline materials is a collective phenomenon which results from the motion and interaction of defects of the crystal structure, particulary dislocations and solute atoms. Jerky flow of dilute alloys, also referred to as the Portevin-Le Chatelier (PLC) effect, is a spectacular example of the self-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 strain rate 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 is viewed as being regular and homogeneous. These observations suggest that self-organization phenomena are 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 investigation 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 of techniques, including the measurement of stress-strain curves, the accompanying AE, and the local strain field through high-resolution extensometry. Correlation, statistical, and multifractal analyses are applied to these signals, each reflecting a specific aspect of the deformation processes, in order to characterize the organization of the dislocation dynamics during the PLC effect. The results show that the intermittency of plasticity in these conditions is not solely related to the macroscopic stress serrations, but manifests itself at a mesoscopic scale throughout the deformation. A particular accent is put on the statistical distributions 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 statistical distributions, including power-law, peaked, and bimodal histograms. The observed behavior is discussed in 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

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Modal interactions in thin structures: some experiments on non-linear vibrations of spherical shells and percussion musical instruments

Olivier Thomas1& Cyril Touz ´ e2

1

2Structural Mechanics and Coupled Systems Laboratory, Conservatoire National des Arts et M ´ etiers, Paris, France

Unit ´ e de M ´ ecanique, ´ Ecole Nationale Sup ´ erieure des Techniques Avanc ´ ees, Palaiseau, France

[e-mail]

Structures with a thin geometry, like beams, plates and shells, can exhibit large amplitude flexural vibrations, 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 multiple stable 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 engineering structures, from macro-scale structures such as helicopter blades to micro and nano-electromechanical structures (M/NEMS). They are the main physical source of the particular sound of percussion musical instruments such as gongs and cymbals.

The purpose of the present study is to present some experiments on non-linear vibrations of percussion musical 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 chinese gong excited by a harmonic force in the vicinity of one natural frequency enables to exhibit a generic route to chaos observed in those shelllike structures. For low excitation levels, periodic motions are observed, 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 vibratory regime 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 internal resonances is proposed. Two cases are studied: a 1:1 internal resonance in a circular plate and a 1:1:2 internal resonance in a shallow spherical shell. In both cases, because of the rotationally symmetric geometry of these structures, all modes with nodal diameters appear in pair, with both modes associated to the same natural frequency (leading to the 1:1 resonance) and their modal shapes differing only by the angular position of their nodal diameters. In the case of the spherical shell, the 1:1:2 resonance is observed 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 excitation frequency, its amplitude being kept constant. Various coupled regimes are exhibited, leading to jump phenomena and traveling wave motions. Movies obtained with stroboscopic lighting are also available. The obtained frequency response curves are successfully compared to reduced order models composed of two or three non-linear oscillators with coupled quadratic and cubic non-linear terms, that help understanding the observed particular coupled vibratory regimes.

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1

Is the wave turbulence observed in elastic plates related to ”weak turbulence”?

Nicolas Mordant1, Pablo Cobelli2, Philippe Petitjeans2, Agn ` es Maurel3, & Vincent Pagneux

41

2

3LPS, Ecole Normale Sup ´ erieure, 24 rue Lhomond, 75005 Paris, France

PMMH, ESPCI, 10 rue Vauquelin, 75005 Paris, France

Institut Langevin, ESPCI, 10 rue Vauquelin, 75005 Paris, Franc

e4Lab. d’acoustique, Avenue Olivier Messiaen, 72085 Le Mans, France [e-mail]

It has been observed recently that wave turbulence can develop in vibrated elastic plates (Mordant PRL 2008, Boudaoud et al. PRL 2008). A statistical theory of wave turbulence (so called weak turbulence theory or WTT) exists for more than half a century and has been applied in a large variety of systems ranging from condensed matter physics to astrophysics. In particular, it has been applied to the case of elastic plates (D ¨ uring et al. PRL 2006). The experimental single point spectra are not in agreement with the WTT predictions. The measured frequency spectra are steeper than the prediction and their scaling with the average injected power is also not that predicted by the WTT. The reasons for this disagreement 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 a Fourier 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 of the plate. The time resolution is provided by the use of a high speed camera. In this way, movies of the plate deformation can be recorded. It allows us to get the full space and time Fourier spectrum and thus to probe in much more details the structure of the wave turbulence than with single point spectra. We observe in particular that energy is indeed localized on a surface in the 3D (k;!) space as expected from waves. The observed non linear dispersion relation is close to the linear dispersion relation which confirms a weak non linear coupling of the waves. The shift between the two dispersion relations is seen to increase with the forcing. The thickness or the dispersion relation (energy surface in the (kx;kyx;ky;!) space) is seen to also increase with the forcing. All these features are in qualitative agreement with the predictions of the WTT and thus do not provide explanations for the observed disagreement with the theory. Finite size effects are also observed but vanish as the forcing amplitude is increased. The FTP technique is a very promising tool for a extensive quantitative analysis of the wave turbulence observed in elastic plates. It can also be applied to turbulence of fluid surface waves. Preliminary studies show that the development strong linearities is observed in that case. The ability of the FTP technique to provide the space-time dynamics of surface deformations makes it a specially suited tool for the analysis of wave turbulence.

4

2

Engineered genetic oscillations

Jeff HASTY

Departments of Molecular Biology and Bioengineering University of California, San Diego

One defining goal of synthetic biology is the development of engineering-based approaches that enable the construction of gene-regulatory networks according to design specs generated from computational modeling. This has resulted in the construction of several fundamental gene circuits, such as toggle switches and oscillators, which have been applied in novel contexts such as triggered biolm development and cellular population control. In this talk, I will first describe an engineered genetic oscillator in ¡em¿ Escherichia coli¡/em¿ that is fast, robust, and persistent, with tunable oscillatory periods as fast as 13 minutes. This oscillator was designed using a previously modeled network architecture comprising linked positive and negative feedback loops. Experiments show remarkable robustness and persistence of oscillations in the designed circuit; almost every cell exhibited largeamplitude fluorescence oscillations throughout observation runs. The period of oscillation can be tuned by altering inducer levels. Computational modeling reveals that the key design principle for constructing a robust oscillator is a ¡em¿small¡/em¿ time delay in the negative feedback loop, which can mechanistically arise from the cascade of cellular processes involved in forming a functional transcription factor. I will then describe an engineered network with global intercellular coupling that is capable of generating synchronized oscillations in a growing population of cells. The network is based on the interaction of two quorum sensing genes; luxI, which produces an intercellular transcriptional activator (AHL, acyl-homoserine lactone), and aiiA, which degrades AHL intracellularly. Microfluidic devices tailored for cellular populations at differing length scales are used to demonstrate collective synchronization properties along with spatiotemporal waves occurring on millimeter scales. The period of the bulk oscillations ranges from 55-90 minutes, depending on the effective degradation rate of the AHL coupling molecule. In large monolayer colonies of cells, the time scale for the diffusive coupling of AHL is characterized by wavefront velocities that range from 8-30 microns/min.

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3

Robustness of circadian clocks to daylight fluctuations: hints from an unicellular alga

Benjamin Pfeuty1;2;3, Quentin Thommen1;2;3, Pierre-Emmanuel Morant1;2;3, Florence Corellou4, Francois-Yves Bouget, & Marc Lefranc1;2;3

41

2

3

4Universite Lille 1, Laboratoire de Physique des Lasers, Atomes et Molecules, UFR de Physique, 59655 Villeneuve d’Ascq, France

CNRS, UMR8523, CERLA, FR2416, 59655 Villeneuve d’Ascq, France

Universite Lille 1, Institut de Recherche Interdisplinaire, 59655 Villeneuve d’Ascq, France

CNRS UMR7628, Universite Pierre and Marie Curie, Laboratoire d’Oceanographie Microbienne, Observatoire oceanologique, F66651, Banyuls sur mer, Franc

epfeuty [e-mail]

The development of systemic approaches in biology has put emphasis on identifying genetic modules whose behavior can be modeled accurately so as to gain insight into their structure and function. However most gene circuits in a cell are under control of external signals and thus quantitative agreement between experimental data and a mathematical model is difficult. Circadian biology has been one notable exception: quantitative models of the internal clock that orchestrates biological processes over the 24-hour diurnal 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 Ostreococcus tauri. Two plant-like clock genes have been shown to play a central role in Ostreococcus clock. We find that their expression time profiles can be accurately reproduced by a minimal model of a two-gene transcriptional feedback loop. Remarkably, best adjustment of data recorded under light/dark alternation can be obtained for vanishing coupling between the oscillator and the forcing cycle, suggesting that coupling to light is restricted to specific time intervals and has a limited effect when the circadian oscillator is synchronized to the diurnal cycle. We indeed find that there exist gated coupling schemes which generate oscillations close to those of the uncoupled model and thereby preserve adjustment of model to experimental data.

These coupling schemes are shown to minimize the impact of daylight fluctuations on the core circadian oscillator, a type of perturbation that has been seldom considered when assessing the robustness of circadian entrainment. These robustness properties are interpreted in terms of the structure of the Arnold tongue (i.e. the region of synchronization in the forcing amplitude-frequency plane). Finally, we show how the shape of the phase response curve (PRC) characterizing a light coupling mechanism indicates whether it gives rise to robust entrainment of the circadian clock.

4

4

Dynamics of translation: modelling the synthesis of proteins

M. Carmen ROMANO

Institute for Complex Systems and Mathematical Biology & Institute of Medical Sciences, University of Aberdeen, United Kingdom

We focus on the process of translation, i.e., how ”molecular machines” called ribosomes translate the messenger RNA molecules into proteins that can be utilised by the cell for a huge variety of different processes. In order to model the process of translation, we propose a simple stochastic model based on the totally asymmetric exclusion process. We study the role that different distributions of nucleotides, i.e., different mRNA sequences, play in the maximal flow or production rate of proteins that can be achieved. We then relate the rich dynamical behaviour generated by the model to the different biological functions of the analysed proteins.

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5

Dynamical overlap of protein interaction networks: a method to predict protein functions

Irene Sendi ˜ na-Nadal1, Yanay Ofran2, Juan Antonio Almendral1, Daqing Li3, Inmaculada Leyva1, Javier M. Buld ´ u, Shlomo Havlin3, & Stefano Boccaletti4;5

11

2

3

4

5Complex Systems Group, Dept of Signal Theory and Communications, Rey Juan Carlos University, Camino del Molino s/n, 28943 Fuenlabrada, Madrid, Spain

The Mina and Everard Goodman Faculty of Life Sciences, Bar Ilan University, 52900 Ramat Gan, Israel

Department of Physics, Minerva Center, Bar Ilan univeristy, 52900 Ramat Gan, Israel

Embassy of Italy in Tel Aviv, 25 Hamered St., 68125 Tel Aviv, Israel

[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

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6CNR-Istituto dei Sistemi Complessi, Via Madonna del Piano 10, 50019 Sesto Fiorentino, Firenze, Italy [e-mail]

The latest advances in the field of genome sequencing technologies have tremendously increase the number of known proteins. The challenge is now how to characterize those proteins and elucidate their function within the different biological processes. One recent approach to assign a function to one protein is by means of the network of its interactions with other proteins [Sharan07]. Novel high-throughput techniques for protein-protein interaction measurements have let to obtain those networks of protein interaction from different organisms [Aebersold03, Field05]. Using this network representation, proteins as nodes and detected physical interactions among them as links, it is possible to apply the tools from complex 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 are exclusively based in topological measurements from the properties of the PIN, we propose the application of 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 overlapping communities [Li08] in ensembles of networking dynamical systems. The combination of the synchronization behavior of the PIN structure and an initial modular classification of proteins drawn from a manual assignment available from a ten years old database from the Munich information Center for Protein Sequences (MIPS) allows for protein function predictions that is in genuine agreement with more recent and better refined manual assignments obtained from Gene Ontology database.

(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, Molecular

Systems Biology 3, 88 (2007)

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Dynamics of the interactions between the cell cycle and stress responses in yeasts

Marco Thiel

Institute for Complex Systems and Mathematical Biology, University of Aberdeen (UK) [e-mail]

Candida albicans is a common fungal pathogen responsible for wide-spread infections in patients with a weakened immune system. For the development of an effective treatment it is highly important to understand how the pathogen reacts to different stresses, that it encounters in its host. Crucially, the response to the different stresses depends on the phase of the cell cycle of the fungi, e.g., the response to osmotic stress during the G1 or G2 phases is substantially different. Conversely, the stresses also cause the cell cycle to arrest at different phases.

I will discuss interactions between the cell cycle and stress responses in yeasts (S. cerevisiae and C. albicans). Based on techniques from network and dynamical systems theory, I will study how the signalling 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.

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Steady and pulsed laser cavity solitons in semiconductor microcavities

Robert KUSZELEWICZ

Laboratoire de Photonique et de Nanostructures, CNRS UPR20, Marcoussis, France

Cavity solitons (CS) are localized optical states forming in the transverse plane of a large Fresnel number (micro)resonator, under the competition of the nonlinear susceptibility of the cavity material (III-V semiconductors) and transverse effects such as diffraction and eventually carrier diffusion. They form as particular states of a larger family of structures, emerging from the translational invariance symmetry breaking, such as hexagonal or roll patterns. CSs have bistable properties in specific regions of the phase space and can therefore be written or erased independently in any location of the transverse plane provided they are distant one from each other of more than their diameter. At shorter distances they can form compound states or clusters. Moreover, an original property of CS resides in their possibility to be manipulated by controlled gradients of the external parameters. All these properties not only reveal fascinating mechanisms of the light-matter interaction in a resonator but also open the way to quite powerful fuctionalities that can translate in quite efficient all optical processing schemes.

This talk will concentrate and develop on the experimental observation of such CSs obtained in laser microresonators systems defined by a gain/saturable absorber competition. Both cw and pulsed regimes will be reported in different configurations. The conditions in which stable periodic pulses can be observed and controlled will be analyzed. Applications of such temporal regimes will be finally considered.

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Front dynamics in periodic modulated media

Florence Haudin1, Ricardo Gabriel Elias2, Ren ´ e Gabriel Rojas3, Umberto Bortolozzo1, Marcel Gabriel Clerc12, & Stefania Residor

i1

2Institut Non Lin ´ eaire de Nice, Universit ´ e de Nice Sophia Antipolis, CNRS, 1361 route des Lucioles, 06560 Valbonne, France

Departamento de Fisica, Facultad de Ciencias Fisicas y Matematicas, Universidad de Chile, Casilla 487-3, Santiago, Chil

e3Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso, Casilla 4059, Valparaiso, Chile [e-mail]

Front propagation in non equilibrium systems is a very rich and interesting phenomenon, present in many different systems such as magnetic domains, chemical reactions or population dynamics [1]. Fronts are non linear solutions connecting two metastable states and propagating with a dynamics that depends on the nature of the states connected. For example, in a variational system, a front connecting two stable states moves at a constant speed and always in such a way to develop the most stable state. In that situation, when one moves a single parameter, there is only one point where the energy of the two states is equal and therefore, the front is motionless. A question that can be rised is how this motionless behavior can be extended to a large range of values of one control parameter. An answer to this question was given by Pomeau [2], predicting that for fronts connecting a stable homogeneous state and a periodic state, a pinning phenomenon of the front exists. Following this idea, the addition of spatial modulations on the originally homogeneous states, should be an efficient way to block the front over a large range of the control 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 Crystal Light Valve (LCLV) with optical feedback. In a situation where fronts between two homogeneous states can be observed, spatial intensity modulations were added on the input beam profile by using a Spatial Light Modulator. A 1d characterization of the dynamics with respect to the voltage applied to the liquid crystal have been made first, and, then with respect to the spatial forcing parameters. The existence of a pinning range was clearly highlighted and a front propagation by periodic leaps apart from this range was observed as well [3]. We have compared the experimental results with the theoretical predictions obtained for the LCLV model accounting for the orientation of the liquid crystal molecules in presence of an optical feedback and with spatial modulations of the input beam. It appears that close to the point of nascent bistability, it is possible to develop the model on a forced extended pitchfork bifurcation normal form. Both results obtained with the complete LCLV model and with the normal form are in good agreement with the experimental ones. A 2d extension of the 1d case was performed experimentally using stripe intensity masks as well as square and hexagonal modulations. The pinning phenomenon is observed and characterized too. Finally, we show out that localized structures of different shape and size can 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. El ´ ias, R. G. Rojas, U. Bortolozzo, M. G. Clerc and S. Residori, Phys. Rev. Lett. 103,

128003 (2009)

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Generating truly random bits at high rates with chaotic lasers

Michael ROSENBLUH

Department of Physics and The Jack and Pearl Resnick Institute for Advanced Technology, Bar-Ilan University, Ramat-Gan, Israel 52900

We report on the design and performance of a true random bit generator operating at rates as high as 300 Gbits/s. The generator is based on a chaotic diode laser and a simple algorithm for processing the data stream generated by the chaotic intensity fluctuations of the laser intensity. The physical setup can, in principle, be miniaturized and lead to ”chip scale” random bit generators at near THz rates.

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Temporally nonlocal electro-optic phase dynamics for 10 Gb/s chaos communications

Laurent Larger, Roman Lavrov, & Maxime Jacquot

FEMTO-ST / Optics dept., University of Franche-Comte, 16 route de Gray, 25030 Besancon cedex, France [e-mail]

Since the demonstration of chaos synchronization 20 years ago, chaotic dynamics in photonic systems has been intensively explored as a mean of providing enhanced physical layer data protection in optical communications. Although many popular setups are based on chaotic behaviour of lasers subject to electrical 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 synchronization quality). On the other hand, chaos communications based on electro-optic feedback has been studied and demonstrated as an alternative approach, and indeed has been also successfully used in earlier field experiments at comparable bit rates. In this talk, we report on a new electro-optic approach based on the architecture of nonlocal nonlinear delayed electro-optic phase modulation. The oscillator is ruled by a 4-time scale dynamics spanning from the 10ps up to 10 s, and including two distinct time delays (a long one with 10s of ns, and a short one of about 500ps). Modeling, experimental and numerical results will explore 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 data transmission over installed fiber network will be reported, with data rate as high as 10 Gbit/s over up to 100 km of fiber, and bit error rates as low as 109. As far as we know, our recent results is representing the best performance to date in optical chaos communication. Other applications of our EO setup will be discussed, such as ultra-fats random number generator, and reservoir computing.

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Nonlinear dusty plasma instabilities

Maxime Mikikian, Marjorie Cavarroc, L ´ ena ¨ ic Cou ¨ edel, Yves Tessier, La ¨ ifa Boufendi, & Olivier Vall ´ ee

GREMI, Groupe de Recherches sur l’Energ ´ etique des Milieux Ionis ´ es, UMR6606, CNRS/Universit ´ e d’Orl ´ eans, 14 rue d’Issoudun, BP6744, 45067 Orl ´ eans Cedex 2, France

[e-mail]

In this work, some strongly nonlinear instabilities occurring in dusty plasmas are experimentally observed 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 containing solid dust particles with sizes ranging from a few nm to cm[1]. In the plasma, dust particles acquire a negative electric charge that determines their interaction with the plasma and induces collective effects in the dust cloud. These multi-component systems have many similarities with colloidal suspensions or granular media. They are encountered in many environments such as astrophysics, industrial processes and thermonuclear fusion.

In experiments, dust clouds are often characterized by a central dust-free region (void)[2] maintained by two forces of opposite directions. Self-excited oscillations of the void size can appear due to a break in 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 failed contractions. During this phase, electrical or optical measurements show well-defined behaviors recently identified 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) and natural sciences (e.g. in the Hodgkin-Huxley model of neuronal activity). MMOs are intensively studied with dynamical system theories (canards, subcritical Hopf-homoclinic bifurcation, ...).

Here, we report on the first experimental evidence of MMOs in dusty plasmas. A particular attention is paid to the evolution of the number of small amplitude oscillations in between spikes. This work highlights 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 chemical systems. These fields use well-known sets of equations giving rise to MMOs and this scientific background could be used to explore the dusty plasma dynamics. This aspect is currently underway through several theoretical 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. Vall ´ ee et al., High Temp. Mat. Proc. 3, 227 (1999)

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2

From bifurcations and spiral waves to chaos: The many dynamics of cardiac tissue

Flavio FENTON

Department of Biomedical Sciences, Cornell University

N/A

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3

Chaos may facilitate decision making in the brain

Yoshito Hirata1, Yoshiya Matsuzaka2, Hajime Mushiake2, & Kazuyuki Aihara

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2Institute of Industrial Science, The University of Tokyo, Tokyo, Japan

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4Department of Physiology, Tohoku University School of Medicine, Sendai, Japan [e-mail]

Although there are ample evidences for deterministic chaos in neuronal activity in vitro, few in vivo studies have reported the existence of chaos in the brain. Assuming that it exists, its functional role is still unclear. In this presentation, we examine whether three regions of the brain are of deterministic chaos or not while a monkey performs an arm reaching task. For the analysis, we used the distance between spike trains two of us recently proposed (Hirata and Aihara, J. Neurosci. Methods (2009)) and examined whether two similar spike trains diverge or not, as the time elapses since the cue onset. We found that, in some regions of behaving monkeys, the initially similar spike trains diverged immediately after the onset of cues. Therefore, deterministic chaos may play an important role in decision making in the brain

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How do antiepileptic drugs and epileptogenic mutations change cell and network dynamics?

Theoden NETOFF

Biomedical Engineering, University of Minnesota, Minneapolis

Epilepsy is characterized by periods of excessive neuronal activity called seizures. While much is known about population behaviors of neurons during seizures, as measured by EEG electrodes, very little is known about the activity at the cellular level. The etiology of the disease can often be traced to specific mutations in particular ion channels. These same ion channels are often the targets of antiepileptic drugs. Bridging the molecular scale causes and treatment of epilepsy to the network scale phenotype is a multi-scale problem that needs to be solved in order to develop more rational approaches to treating epilepsy.

Our research seeks to understand the basic mechanisms of epilepsy by understanding how network synchrony is affected by molecular level changes caused by epileptogenic mutations and antiepileptic drugs. Our approach is guided by experimental evidence, in a rat model of epilepsy, indicating that synchrony in the network changes over the different phases of the seizure. Synchrony among neurons is relatively high between seizures, drops during the peak of a seizure and then is strongly synchronous towards the end of a seizure. These changes in synchrony may hold a key to understanding what makes some people prone to seizures and how to treat epilepsy. However, why synchrony changes during a seizure is still a mystery.

To better understand how neurons synchronize, we use pulse coupled oscillator theory. We reduce the dynamics of the neuron to a simple input-output relationship by measuring how synaptic inputs applied at different phases of a periodically firing neuron advances or delays the spike, resulting in a Phase-Response Curve (PRC). From the measured PRC, it is possible to predict how a network of neurons will synchronize. We then measure how epileptogenic mutations and antiepileptic drugs affect the neuron’s PRC to infer how it changes the synchronizability of the network. By measuring the effects of these changes at the molecular level we know causes epilepsy, we can bridge the effect to a population.

This talk will present our computational simulations and in vitro experiments measuring PRCs from neurons. We find that epileptogenic mutations in voltage gated sodium channels and potassium channels affect the neurons’ PRCs to increase network synchrony while antiepileptic drugs decrease synchrony. We hypothesize that while many antiepileptic drugs have very different mechanisms of action, their common feature may be that they decrease network synchrony. PRCs can also explain why synchrony changes during the seizure. At very high firing rate, the neurons’ PRCs are shifted so that a network of excitatory neurons will actively desynchronize, as we might find at the peak of the seizure. If the firing rate of the neuron slows over the duration of the seizure, the PRC shape changes so that the network will synchronize, resulting in the late synchronous phase of the seizure.

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Complex networks in the evaluation of brain injury therapy

Inmaculada Leyva1, Nazaret Castellanos2, & Javier M. Buldu

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2Dep. Signal Theory and Communications. Universidad Rey Juan Carlos, Madrid, Spain.

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6Centro de Tecnolog ´ ia Biom ´ edica, Escuela de Telecomunicaciones, Universidad Polit ´ ecnica de Madrid, Madrid, Spain. [e-mail]

Acquired Brain Injury (ABI) constitutes one of the leading causes of mortality and disability around the world . The mechanisms that take place within the brain during the recovering process and the way cortical reorganization occurs have not been completely unveiled. Due to contradictory results reported in literature about the increase or decrease of neuronal activation after rehabilitation, we consider necessary to deal recovering from a point of view that takes into account the changes in interaction between brain areas, not just measuring the local changes in patterns of activation. Modern neuroscience research has shown that the notion of localized brain functions is insufficient, especially when dealing with higher brain functions. Indeed, cognitive functions in the brain require the functional interactions between multiple distinct neural networks. The idea that the brain is a complex network of dynamical systems with abundant interactions between local and more remote brain areas with the potential capability to compensate for lesions optimally fit with the study of the brain strategies for brain injury rehabilitation. Although anatomical reorganization also occurs in the cortex immediately after a lesion-induced injury, the extension 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 by a focal alteration of their brain functions, probably because lesion interferes with widespread functional networks in the brain and not only in the adjacent region of the lesion. Most studies have focused on local dysfunction, reporting changes observed just in the spatial dimension of analysis. Our point of view is 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 concept of functional connectivity has emerged, referring to the statistical interdependencies between physiological time series recorded in various brain areas simultaneously. Functional connectivity is, probably, an essential tool for the study of brain functioning, and their deviation from healthy patterns could be used as a reflect of lesion. To our knowledge, studies researching functional connectivity in ABI patients and comparing with healthy controls in order to check the recovering have not been performed yet. In this work we aim to capture differences in connectivity pattern properties, from the point of view of graph theory, in ABI patients before and after a rehabilitation treatment. In this work, we show as the nerwork theory tool help us to quantify and determine the network restoring, using different parameters that evaluate the changes both in the global, lobe and local scales

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Predictability and prediction of extreme events

Holger KANTZ

Research group Nonlinear Dynamics and Time Series Analysis, Max Planck Institut for the Physics of Complex Systems, Dresden, Germany

Many systems with complex dynamical behaviour are capable of generating large or even huge fluctuations: Either autonomously or in response to invisible perturbations the may deviate considerably from their average behaviour. Such behaviour is known from weather (called ”extreme weather” by some weather services), from ocean waves (called ”rogue waves” or ”freak waves”), from seismic activity (called ”earthquakes”), and very many other natural phenomena [1]. A first approach to their characterization is to study recurrence time distributions, which, in the presence of temporal correlations, can display interesting structure [2,3]. Beyond that, extreme events call for their prediction, since they possess usually a large impact on our lives. Due to the complexity of the systems generating extreme events, predictions are very often wrong. It is therefore a challenge to extract meaningful information from unreliable predictions and to design scoring rules for their usefulness. This is done through probabilistic predictions and cost functions. In the talk, the main concepts related to the probabilistic prediction of extreme events are introduced [4,5]. They are illustrated using several data sets of natural phenomena such as weather extremes, traffic data, seismic activity. We also discuss the limit of effectively unpredictable events.

[1] S.A. Albeverio, V. Jentsch, H. Kantz (Eds.), EXTREME EVENTS IN NATURE AND SOCIETY (Springer, Berlin, 2006)

[2] A. Bunde, J.F. Eichner, J.W. Kantelhardt, S. Havlin, Long-Term Memory: A Natural Mechanism for the Clustering of Extreme Events and Anomalous Residual Times in Climate Records, Phys. Rev. Lett. 94, 048701 (2005).

[3] E.G. Altmann, H. Kantz, Recurrence time analysis, long-term correlations, and extreme events, Phys. Rev. E 71, 056106 (2005).

[4] S. Hallerberg, E.G. Altmann, D. Holstein, H. Kantz, Precursors of extreme increments, Phys. Rev. E 75 016706 (2007).

[5] S. Hallerberg, H. Kantz, Predicting extreme avalanches in self-organized critical sandpiles, Phys. Rev. E 80, 026124 (2009).

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Rare and extreme events in temporal and spatial optical systems

Eric Louvergneaux, Arnaud Mussot, Alexandre Kudlinski, Mikhail Kolobov, Marc Douay, & Majid Taki

Laboratoire de Physique des Lasers, Atomes, Mol ´ ecules, UFR de Physique, Universit ´ e Lille 1, F-59655 Villeneuve d’Ascq, France

[e-mail]

Abstract: We theoretically and numerically study optical rare and strong events generated in fiber supercontinua and optical feedback system patterns.

In the ocean, giant waves (also called killer waves, freak or rogue waves) are extremely rare and strong events. They are not well understood yet and the conditions which favour their emergence are unclear. Very recently, it was shown that the governing equations [1] as well as the statistical properties of an optical pulse propagating inside an optical fibre [2] mimic very well these gigantic surface waves in the ocean. Here we generate both experimentally and numerically optical rogue waves in a photonic crystal fiber (microstructured fiber) with continuous wave (CW) pumps. This is relevant for establishing an analogy with rogue waves in an open ocean. After recalling fundamental rogue waves [3] known as Akhmediev breathers that are solutions of pure nonlinear Schr ¨ odinger (NLS) equation, we analytically demonstrate that a generalized NLS equation, which governs the propagation of light in the fiber, exhibits convective modulationnal instability [4]. The latter provides one of the main explanations of the optical rogue wave extreme sensitivity to noisy initial conditions at the linear stage of their formation [5]. In the highly nonlinear regime, we provide the evidence that optical rogue waves result from soliton collisions leading 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 extended feedback system. These giant spatial optical waves have probability density function with long tails that are 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 dispersion 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).

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Extreme weather and probabilistic forecast approaches

Petra FRIEDERICHS

Meteorogical Institute, Universit ¨ at Bonn, Germany

Present day weather forecast models usually cannot provide realistic descriptions of local and particularly extreme weather conditions. However, for certain lead times which depend on the scale of the phenomenon, they provide reliable forecasts of the atmospheric circulation that encompasses the sub-scale processes leading to extremes. Hence, forecasts of extreme events can only be achieved through a combination of dynamical and statistical analysis methods, where a stable and significant statistical model based on a-priori physical reasoning establishes a-posterior a statistical-dynamical model between the local extremes and the large scale circulation. We will present approaches to derive probabilistic forecasts for (extreme) local weather.

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Otto R ¨ ossler 1975-76

Christophe Letellier

Universit ´ e de Rouen, UMR CNRS 6614, Complexe de Recherche Interprofessionnal en A ´ erothermochimie (CORIA), [e-mail]

For celebrating Otto R ¨ ossler’s 70th birthday, we will revisit the 1975-1976 period that preceded the discovery of the second system producing a chaotic attractor. In particular, we will show how Art Winfree stimulated Otto a lot. The content of the first paper on chaos published by R ¨ ossler (before the well known paper introducing the so called ”R ¨ ossler system”) will be discussed with respect of its small influence. Very first results obtained by Otto R ¨ ossler about the possibility to identify chaos in the Belousov-Zhabotinski reaction will be also presented as well as contributions published at the same period.

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Time’s arrow and Hubble’s law from the reduced three-body problem with/without sign flip

Otto E. R ¨ OSSLER

Universit ¨ at T ¨ ubingen, Germany

Dissipative thermodynamics and an anti-dissipative phenomenon (the ”cooling” of fast particles traversing a cosmos of randomly moving heavy particles) are brought together. A very simple model of thermodynamics consists of but 2 particles placed into a frictionless T-tube, one heavy, one light. The heavy one in the vertical tube contains much more kinetic energy at first. If the light one’s kinetic energy is close to zero initially, it indeed gets heated up: a ”tendency for equipartition” is found. The potential can even be ”very smooth” hereby (Newtonianrepulsive). If the potential is inverted, however (ordinary Newtonian), the opposite behavior occurs: An initially fast (but low-kinetic energy), very low-mass horizontal particle in the T-tube gets ”cooled down” even further by its interaction with the heavy vertical one. Much like a fast cosmic-ray particle traversing the universe is. The new deterministic-chaos theory was first discovered in a statistical Brownian-motion context by Chandrasekhar in 1943. For J.O.R.

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