Plenary Talks

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[divider_title title=”Nail Akhmediev (Australia)” heading=h3]
Australian National University, Australia

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[toggle title=”Rogue waves, FPU recurrence and radiation phenomena in nonlinear dynamics” color=gray]

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Abstract:  Mathematical theory of rogue waves is based on the nonlinear Schrödinger equation and its extensions. These include Hirota, Sasa-Satsuma and similar equations. The extensions that describe rogue waves in dissipative systems are based on complex Ginzburg-Landau equation and its variations. In this talk, I will discuss exact solutions and the results of numerical simulations that produce rogue waves. The rogue wave evolution can be described as the “wave that appears from nowhere and disappears without a trace”. Return of the system back to the initial state is closely related to the so called Fermi-Pasta-Ulam recurrence. In real physical systems this process is often accompanied by radiation. These complicated phenomena are also discussed in the talk.

N. Akhmediev, A. Ankiewicz and M. Taki, “Waves that appear from nowhere and disappear without a trace”, Physics Letters A 373, 675-678 (2009).

 C. Lecaplain, Ph. Grelu, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative RogueWaves Generated by Chaotic Pulse Bunching in a Mode-Locked Laser”, Phys. Rev. Lett., 108, 233901 (2012).

U. Bandelow, and N. Akhmediev, ” Persistence of rogue waves in extended nonlinear Schrödinger equations: Integrable Sasa — Satsuma case”, Phys. Lett. A,376, 1558 (2012).

J. M. Soto-Crespo, A. Ankiewicz, N. Devine, and N. Akhmediev, “Modulation instability, Cherenkov radiation, and Fermi – Pasta – Ulam recurrence”, J. Opt. Soc. Am. B,  29, 1930 (2012).

A. Chabchoub, N. P. Hoffmann, M. Onorato and N. Akhmediev, ” Super Rogue Waves: Observation of a Higher-Order Breather in Water Waves”, Phys. Rev. X, {\bf 2}, 011015 (2012).

D. J. Kedziora, A. Ankiewicz, and N. Akhmediev, Second-order nonlinear Schrödinger equation breather solutions in the degenerate and rogue wave limits,
Phys. Rev. E, 85, 066601 (2012).

N. Akhmediev and E. Pelinovsky (Editors), “Rogue waves – towards a unifying concept?: Discussions and debates”, European Physical J., Special Topics, 185, (2010), 266 pages.

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[divider_title title=”Marc Brachet (France)” heading=h3]
Laboratoire de Physique Statistique, École Normale Superieure de Paris, France.                                                                                                                 

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[toggle title=”Numerical simulations of the incompressible Euler equations are performed using the Taylor-Green vortex initial conditions and resolutions up to 4096^3” color=gray]

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Abstract:  The results are analyzed in terms of the classical analyticity strip method and Beale, Kato and Majda (BKM) theorem. A well-resolved acceleration of the time-decay of the width of the analyticity strip δ(t) is observed at the highest resolution for 3.7<t<3.85 while preliminary 3D visualizations show the collision of vortex sheets. The BKM criterium on the power-law growth of supremum of the vorticity, applied on the same time-interval, is not inconsistent with the occurrence of a singularity around t≈4. These new findings lead us to investigate how fast the analyticity strip width needs to decrease to zero in order to sustain a finite-time singularity consistent with the BKM theorem. A new simple bound of the supremum norm of vorticity in terms of the energy spectrum is introduced and used to combine the BKM theorem with the analyticity-strip method. It is shown that a finite-time blowup can exist only if δ(t) vanishes sufficiently fast at the singularity time. In particular, if a power law is assumed for δ(t) then its exponent must be greater than some critical value, thus providing a new test that is applied to our 4096^3 Taylor-Green numerical simulation. Our main conclusion is that the numerical results are not inconsistent with a singularity but that higher-resolution studies are needed to extend the time-interval on which a well-resolved power-law behavior of δ(t) takes place, and check whether the new regime is genuine and not simply a crossover to a faster exponential decay.

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[divider_title title=”Helmut Brand (Germany)” heading=h3]

Theoretische Physik III – Universität Bayreuth, Germany

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[toggle title=”Stable localized structures in one and two spatial dimensions: a review and a perspective ” color=gray]

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Abstract

We give an overview over stable localized solutions in nonlinear driven non-equilibrium systems, often denoted as dissipative solitons [1]. We cover different mechanisms to generate stable localized structures in various types of prototype equations namely  envelope equations, order parameter equations and phase equations. For envelope equations nonvariational effects are a key ingredient as emphasized first by Thual and Fauve [2]. This mechanism turns out to be very robust and allows for many different stable particle- and hole-like solutions in one and  two spatial dimensions. The interaction of localized solutions can give rise to many different types of outcomes including propagating holes as a result of a collision of propagating particles of fixed shape [3]. For order parameter equations a trapping mechanism can generate localized solutions of arbitrary lengths [4]. A third type of localized solutions involves nonlinear phase dynamics giving rise to stable localized patterns in the wavelength for a nonlinear phase equation [5] or in coupled envelope and phase equations [6]. We also cover briefly recent work on the effects of noise on localized solutions in  envelope equations [7,8] and close with an overview of possible  applications to systems as diverse as surface reactions under UHV conditions [9], binary fluid convection [10] or holes observed in corn and potato starch suspensions [11]. 

[1] N. Akhmediev and A. Ankiewicz, Eds. Dissipative Solitons, Springer, Heidelberg (2005).

[2] O. Thual and S. Fauve, J.Phys. France 49, 1829 (1988).

[3] O. Descalzi, J. Cisternas, and H.R. Brand, Phys. Rev. E 74, 065201 (2006).

[4] H. Sakaguchi and H.R. Brand, Physica D 97, 274 (1996).

[5] H.R. Brand and R.J. Deissler, Phys. Rev. Lett. 63, 508 (1989).

[6] H. Sakaguchi, Prog. Theor. Phys. 87, 1049 (1992).

[7] O. Descalzi, J. Cisternas, D. Escaff, and H.R. Brand, Phys. Rev. Lett. 102, 188302 (2009).

[8] C. Cartes, J. Cisternas, O. Descalzi, and H.R. Brand, Phys. Rev. Lett. 109, 178303 (2012).

[9] H.H. Rotermund, S. Jakubith, A. von Oertzen, and G. Ertl, Phys. Rev. Lett. 66, 3083 (1991).

[10] P. Kolodner, Phys. Rev. A 44, 6448 (1991);
Phys. Rev. A  44, 6466 (1991).

[11] H. Ebata and M. Sano, Phys. Rev. Lett. 107, 088301 (2011).

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[divider_title title=”Javier Burguete (Spain)” heading=h3]
Departamento de Física y Matemática Aplicada. Universidad de Navarra, Spain.

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[toggle title=”Slow dynamics in experiments with fluids” color=gray]

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Abstract: Far from equilibrium systems exhibit a large variety of behaviors, ranging from pattern formation to complex dynamics. In many cases these effects are associated to fast (small) time scales. ¬†But in some situations, even when the experiment is very far from any instability threshold, a slow dynamics appears that can restore some order in the (spatial or temporal) complexity. Here we will analyze two of these experiments, the first one is a convective system that can develop chaos, but where a very simple dynamics can be explained using a phenomenological model, and the second one is a turbulent flow, where the slow dynamics is dominant and affect the large scale evolution of the vortices present in the flow.

(*) In collaboration with M. Lopez-Caballero, M.Miranda and H.L. Mancini

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[divider_title title=”Fereydoon Family (USA)” heading=h3]

Emory University, Department of Physics, Atlanta, Georgia 30322, USA

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[toggle title=”Synchronization and Chaos in Driven Deterministic Ratchets” color=gray]

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Abstract: The ratchet effect was initially proposed as a model for molecular motors, but more recently considerable theoretical and experimental work on ratchets have appeared in a wide range of other areas, including the route to quasiperiodicity in cold atoms, the driven motion of domain walls in extended amorphous magnetic films, voltage rectification by a SQUID ratchet, relativistic flux quantum trapped in a Josephson junction, and magnetic vortices in superconducting devices. Two phenomena that have received less attention in the study of ratchets are synchronization and chaos. Bifurcations, chaos and multiple synchronization are typical behaviors of many nonlinear systems.  Here we present the result of a study of synchronization and chaotic phenomena appearing in overdamped ratchets driven by a periodic rectangular force. This driving force is especially interesting because it can lead to bifurcations, chaos and multiple synchronization in the ratchet system without adding inertia or quenched noise. The system has neither temporal nor quenched noise but the strong nonlinearity of the driving force produces a very rich bifurcation pattern with synchronized as well as chaotic regions. This pattern disappears if a sinusoidal force replaces the square force. This unexpected behavior is explained by decomposing the system into two exactly solvable subsystems, each with its own characteristic transit time, so that the ratio between the period of the driving force and the transit times can be analyzed. The transition from synchronized to chaotic motion can be explained by means of a one-dimensional Poincaré map.  Our results can be experimentally confirmed in a number of systems, including the three-junction SQUIDs ratchet, the rocking ratchet effect for cold atoms, and the Josephson vortex ratchet.

(*) In collaboration with D. G. Zarlenga, H. A. Larrondo, C. M. Arizmendi (Departamento de Física, Facultad de Ingeniería, Universidad Nacional de Mar del Plata, Mar del Plata, Argentina)

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[divider_title title=”Mario Ferreira (Portugal)” heading=h3]
University of Aveiro, Portugal

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[toggle title=”Impact of higher-order effects on pulsating and chaotic solitons in dissipative systems” color=gray]

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Abstract:  We investigate numerically, both in time and frequency domains, the influence of some higher-order effects, namely the third-order dispersion, intrapulse Raman scattering, and self-steepening, on the dynamics of different pulsating and chaotic solitons in dissipative systems, which are described by a generalized complex Ginzburg-Landau equation. We show that the higher-order effects can have a dramatic impact on the dynamics of such pulses and that, for some ranges of the parameter values, they can be transformed into fixed-shape solitons. Some interesting cases regarding the combined action of all higher-order effects will deserve a particular attention.

(*) In collaboration with Sofia C. V. Latas

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[divider_title title=”Theo Geisel (Germany)” heading=h3]

Max-Planck Institute for Dynamics and Self-Organization, Dept. of Nonlinear Dynamics, Göttingen, Germany

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[toggle title=”The Beat Generation – and its Perception” color=gray]

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Abstract: Even the best musicians do not play rhythms with perfect precision. Slight deviations from an ideal beat pattern are a fundamental characteristic of music played by humans. The talk discusses the statistical laws underlying rhythmic fluctuations and their role in musical perception. Based on these findings one can make computer generated music sound more human. Audio examples from stochastic music to The Art of Fugue highlight the general role of long range correlations for music and for its perception by the information processing in our brains.

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[divider_title title=”Edgar Knobloch (USA)” heading=h3]
Department of Physics, University of California at Berkeley, Berkeley, USA

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[toggle title=”Colliding Convectons” color=gray]

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Abstract: Convectons are strongly nonlinear spatially localized states found in thermally driven fluid systems. In binary fluid convection with midplane reflection symmetry convectons of odd and even parity lie on a pair of intertwined branches (J. Fluid Mech. 667 (2011) 586) that form the backbone of the snakes-and-ladders structure of the so-called pinning region. These branches are connected by branches of asymmetric localized states that drift. When the midplane reflection symmetry is broken, the odd parity convectons also drift, greatly modifying the snakes-and-ladders structure of the pinning region. The resulting speed depends on the magnitude of the symmetry-breaking and the convecton length. Head-on and follow-on collisions between odd parity drifting convectons of different lengths are described and the results compared with corresponding dynamics in a Swift-Hohenberg model studied by Houghton and Knobloch (PRE 84 (2011) 016204).

This talk is based on work with S Houghton (University of Leeds) and I Mercader, O Batiste and A Alonso (Universitat Politecnica de Catalunya, Barcelona).


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[divider_title title=”Jürgen Kurths (Germany)” heading=h3]
Potsdam-Institut für Klimafolgenforschung, Germany

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[toggle title=”Network of Networks and the Climate System” color=gray]

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Abstract: Network of networks is a new direction in complex systems science. One can find such networks in various fields, such as infrastructure (power grids etc.), human brain or Earth system. Basic properties and new characteristics, such as cross-degree, or cross-betweenness will be discussed. This allows us to quantify the structural role of single vertices or whole sub-networks with respect to the interaction of a pair of subnetworks on local, mesoscopic, and global topological scales. Next, we consider an inverse problem: Is there a backbone-like structure underlying the climate system? For this we propose a method to reconstruct and analyze a complex network from data generated by a spatio-temporal dynamical system. This technique is then applied to 3-dimensional data of the climate system. We interpret different heights in the atmosphere as different networks and the whole as a network of networks. This approach enables us to uncover relations to global circulation patterns in oceans and atmosphere. The global scale view on climate networks offers promising new perspectives for detecting dynamical structures based on nonlinear physical processes in the climate system. This concept is applied to Indian Monsoon data in order to characterize the regional occurrence of strong rain events and its impact on predictability.
(*) In collaboration with J. Donges, R. Donner, N. Malik, N. Marwan, H. Schultz and Y. Zou References
Arenas, A., A. Diaz-Guilera, J. Kurths, Y. Moreno, and C. Zhou, Phys. Reports 2008, 469, 93.
Donges, J., Y. Zou, N. Marwan, and J. Kurths, Europhys. Lett. 2009, 87, 48007.
Donner, R., Y. Zou, J. Donges, N. Marwan, and J. Kurths, Phys. Rev. E 2010, 81, 015101(R ).
Mokhov, I. I., D. A. Smirnov, P. I. Nakonechny, S. S. Kozlenko, E. P. Seleznev, and J. Kurths, Geophys. Res. Lett. 2011, 38, L00F04.
Malik, N., B. Bookhagen, N. Marwan, and J. Kurths, Climate Dynamics, DOI 10.1007/s00382 (2011)
Donges, J., H. Schultz, N. Marwan, Y. Zou, J. Kurths, Eur. J. Phys. B 2011, 84, 635-651.
Donges, J., R. Donner, M. Trauth, N. Marwan, H.J. Schellnhuber, and J. Kurths, PNAS 2011, 108, 20422-20427.
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[divider_title title=”Katja Lindenberg (USA)” heading=h3]
Department of Chemistry and Biochemistry – University of California, USA

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[toggle title=”Anomalous transport and diffusion in weakly disordered periodic potentials” color=gray]

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Abstract: Diffusion of particles over periodic surfaces exhibits a variety of behaviors that one does not usually associate with simple diffusion. For instance, in periodic potentials with low friction, one sees dispersion less transport over extremely long times when external forces exceed a critical force. Also, in these systems, in both overdamped and underdamped regimes, there is a pronounced peak in the diffusion coefficient when the external force crosses the critical force that allowed the coexistence of locked and running states. This latter behavior has been seen experimentally. Our results are important and intriguing in pointing to the occurrence of what one would ordinarily assume to be “anomalous” behavior  arising in perfectly “normal” contexts. In particular, small amounts of randomness may lead to a large variety of seemingly anomalous behaviors usually associated with CTRWs with long-tailed waiting time distributions. These behaviors are observed to occur over sufficiently long times to cover all experimentally relevant regimes. The results arise in periodic systems with a very  small contribution of random spatial disturbances of the potential, and point to the desirability of experiments with more corrugated surfaces than have been used so far. It is this corrugation, even in the presence of very small amounts of randomness, that leads to the broad range of identified behaviors.

(*) In collaboration with M. Khoury, A. M. Lacasta and J. M. Sancho
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[divider_title title=”Boris Malomed (Israel)” heading=h3]
Tel Aviv University, Israel

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[toggle title=”Bright solitons from defocusing nonlinearities”  color=gray]

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Abstract: The talk aims to give a review of recently obtained results which demonstrate that defocusing cubic media with spatially inhomogeneous nonlinearity, whose strength increases rapidly enough toward the periphery (faster than r^D in the D-dimensional space, D = 1,2,3, where r is the radial coordinate), can support a variety of stable solitons in all three dimensions, including one-dimensional fundamental and multihump states, two-dimensional vortex solitons with arbitrary topological charges, and fundamental solitons in three dimensions. Solitons maintain their coherence in the state of motion, oscillating in the nonlinear potential as robust quasiparticles. In addition to numerically found soliton families, particular solutions are found in an exact analytical form, and accurate approximations are developed for the entire families by means of the variational and Thomas-Fermi approximations. Related numerical and numerical results demonstrate the existence of stable dissipative solitons in media with the uniform linear gain and nonlinear loss whose local strength grows toward the periphery faster than r^D.

(*) In collaboration with Olga V. Borovkova, Yaroslav V. Kartashov, Lluis Torner

Publications on the topic:

O. V. Borovkova, Y. V. Kartashov,B A. Malomed, and L. Torner, Opt. Lett. 36, 3088 (2011);

O. V. Borovkova, Y. V. Kartashov, L. Torner, and B A. Malomed, Phys. Rev. E 84, 035602(R) (2011);

Y. V. Kartashov, V. A. Vysloukh, L. Torner, and B. A. Malomed, Opt. Lett. 36, 4587 (2011);

O. V. Borovkova, Y. V. Kartashov, V. A. Vysloukh, V. E. Lobanov, B. A. Malomed, and L. Torner, Opt. Exp. 20, 2657
(2012).


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[divider_title title=”Gabriel Mindlin  (Argentine)”  heading=h3]
Departamento de Fisica, Facultad de Ciencias Exactas,  UBA

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[toggle title=”Gesture dynamics are encoded by premotor cortical neurons in birdsong production” color=gray]

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Abstract:  Biomechanical models can help to identify control parameters used during movements, and movement parameters encoded by motor cortical neurons. We fit a dynamical systems model including subsyringeal pressure, syringeal biomechanics, and upper respiratory tract filtering to the songs of zebra finches. This reduced the dimensionality of singing dynamics, described as trajectories in pressure-tension space (motor ‚Äúgestures‚Äù) near regions of bifurcation of the model. We fitted model parameters by characterizing the auditory response “replay” of song premotor cortical HVC neurons to presentation of artificial song model variants in sleeping birds, and also examined HVC activity in singing birds. We report that HVC encodes vocal motor output via the timing of extreme points of movement trajectories.

(*) In collaboration with A. Amador, Y. Sanz Perl and D. Margoliash

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[divider_title title=”Michel Moreau (France)” heading=h3]
Université Paris VI, France

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[toggle title=”The shadow of the warrior: an optimal strategy for escaping random predators” color=gray]

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Abstract:  We study the optimal trajectory of a prey trying to escape a random predator, both of them moving on a regular lattice. It is assumed that the predator cannot detect the prey unless it approaches it at a short distance: otherwise, it performs random displacements. Similarly, the prey cannot see the predator before meeting it, too late for running away efficiently. If the predator is “quasistatic ” , i.e. if at any time its most probable position coincides with its initial position, the prey optimal strategy is given, in certain, broad conditions, by the Pascal principle: the survival probability of the prey is maximum if it stays Immobile, a result which was derived in 2003. If, on the contrary, the most probable position of the predator evolves with time, the best survival trajectory of the prey can be deduced simply from the stochastic motion of the predator, provided that relevant conditions are satisfied. We called this optimal trajectory of the prey the “shadow ” of the predator, a name reminiscent of the celebrated film by A. Kurosawa: ” Kagemusha, the shadow of the warrior “.

(*) In collaboration with O. Bénichou, G. Oshanin and R. Voituriez

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[divider_title title=”Stefan Mueller (Germany)” heading=h3]
Otto von Guericke Universitat Magdeburg.

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[toggle title=”Chemically Driven Convection” color=gray]

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Abstract: Chemical waves of excitation in the Belousov-Zhabotinsky reaction are a thoroughly studied example of pattern formation. Propagation of wave fronts through space is predominantly based on the molecular diffusion of an autocatalytic chemical species which results in local coupling to the neighborhood of the front. Frequently, there occurs an additional spatial transport process, which is hydrodynamic convection caused by concentration dependent surface tension changes around the location of the traveling front. The flow has a significant influence on wave speed and wave geometry including turbulent wave decomposition and global synchronization effects. We present an overview of these complex patterns and explain characteristic features in the framework of a reaction-diffusion-convection model. [/toggle]
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[divider_title title=”Angel Plastino (Argentine)” heading=h3]
Instituto de Fisica, UNLP, Argentine

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[toggle title=”Thermodynamics’ aspects of  Schrödinger’s equation” color=gray]

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Abstract: By recourse to information theory methods we uncover a hidden, thermodynamic-like invariance in Schrödinger’s equation, that derives from its Legendre-transform properties.

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[divider_title title=”Harald Pleiner (Germany)” heading=h3]

Max Planck Institute for Polymer Research

PO Box 3148 55021 Mainz Germany

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[toggle title=”Localized Chaotic States in Parametrically Driven Dissipative Systems”  color=gray]

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Abstract: The generalized parametrically driven damped nonlinear Schrödinger equation describes the dynamics close to the parametric resonance of many dynamic systems. Among them are the easy-plane magnetic wire, the pendulum chain, and vertically moving liquid and granular layers, when the effects of parametric forcing and dissipation are taken into account. A new family of localized states is numerically found that connects asymptotically the uniform state with a localized spatio-temporal chaotic pattern. Such states emerge from the stationary pattern state after a Hopf bifurcation and a subsequent secondary one,  when the driving force is increased. We discuss the statistical properties of these states and provide their existence range in parameter space.

(*) In collaboration with D. Urzagasti and D. Laroze.

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[divider_title title=”Günter Radons (Germany)” heading=h3]

Institute of Physics  TU-Chemnitz, Germany

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[toggle title=”Nonlinear Dynamics of Systems with Complex Hysteresis” color=gray]

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Abstract: Complex hysteresis is a well-known phenomenon in many branches of science. The most prominent examples come from materials with a complex microscopic structure such as magnetic materials, shape-memory alloys, or, porous materials. Their hysteretic behaviour is characterized by the existence of multiple internal system states for a given external parameter and by a non-local memory. The input-output behaviour of such systems is described in a standard phenomenological approach by the so-called Preisach operator. What is not well understood, are scenarios, where a hysteretic system is dynamically coupled to its environment. After introducing the general concepts, I present results for such combined dynamical systems with hysteretic nonlinearity, which were obtained by solving numerically the associated operator-differential or operator-difference equations. We find, for instance, a fractal dependence of the asymptotic behaviour as function of the starting values. The sensitivity of the system to perturbations is investigated by several methods, such as the 0-1 test for chaos and sub-Lyapunov exponents. The power spectral density is also calculated and compared with analytical results for simple input-output scenarios (G. Radons, Phys. Rev. Lett. 100, 240602).

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[divider_title title=”Harm Rotermund (Canada)” heading=h3]

Department of Physics & Atmospheric Science,

Dalhousie University, Halifax, Nova Scotia, Canada

PO Box 3148 55021 Mainz Germany

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[toggle title=”Imaging of Non-Linear Surface Reactions and Control of Pattern Formation in Heterogeneous Catalysis” color=gray]

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Abstract: Simple surface reactions like the CO-oxidation on single crystal Pt surfaces show a rich variety of pattern formation under specific reaction parameters. To visualize those patterns we have conceived several unique imaging methods starting around 1990. In the introduction I will discuss those methods, and illustrate them with a variety of encountered patterns, including spirals, standing waves, turbulence, and target patterns.

The interaction of a multitude of micrometer scale concentration waves and fronts on the surface complicate our understanding the underlying mechanisms for such patterns. Experiments with modified catalytic activity using stationary, inactive boundaries, produced by microlithography, have therefore been designed. These fixed structures allow us to isolate individual features (for example single pulses) and study interaction mechanisms quantitatively. In addition we have been able to dynamically change the surface catalytic activity in real time and space by focusing an addressable laser beam to differentially heat a Pt(110) single crystal surface.

Imaging the local coverage of the reactants with an ellipso-microscope enabled us to close the loop between sensing and actuation, both being spatial-temporally resolved. Pulses and fronts, the basic building blocks of patterns, can now be formed, accelerated, modified, guided and destroyed at will. A temperature heterogeneity moving along a line may ignite waves along its path, or can drag preexisting pulses.

The combination between the fixed microstructures of metals with different catalytic activities and local laser heating of the surface has been preliminarily explored and opens exiting new avenues. Currently we study the influence of temperature gradients generated by the reaction itself and the role of a third species, i.e. subsurface oxygen.

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[divider_title title=”Aneta Stefanovska (UK)” heading=h3]

Nonlinear Biomedical Physics Group Department of Physics, Lancaster University, UK

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[toggle title=”Cronotaxic systems” color=gray]

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Abstract: Living systems are characterised by time-dependent structures and functions. In this lecture we will concentrate on function. We will motivate the talk by experiments related to cellular, cardiovascular and brain dynamics and introduce a new class of dynamical systems which we name chronotaxic (from  chronos (time) + taksi (order, class)). The main characteristics of chronotaxic systems are that they are oscillatory and non-autonomous [1-4]. They undergo continuous perturbation and are characterised by time-dependent charactersitic frequencies and coupling functions [1]. We will demonstrate that chronotaxic systems retain their stability. When perturbed, their limit cycles are not destroyed but can instead become time-dependent.

Generally, perturbation theory with separation of phase and amplitude dynamics cannot be applied directly to chronotaxic systems. We can separate the fast from the slow dynamics, but we should bear in mind that the trajectories in phase space change continuously with time. When we do not know the properties of the external and the inherent dynamics, we can apply methods to study what is then an inverse problem. Numerically, we can analyse chronotaxic system by applying methods that allow for the study of time-evolution [5], such us time-phase, time-frequency (e.g. wavelets) and time-phase space methods, or recently introduced dynamical inference method [1]. These will be discussed briefly, and results relevant to living systems will be illustrated. Recently, they have been observed also in physical systems: similar, reproducible dynamics have been measured in the currents of surface state electrons on liquid helium [6]. We will argue that the chronotaxic systems are often misclassified and treated as stochastic systems although, for most of the time, they can be fully deterministic.

[1] Stankovski T, Duggento A, McClintock PVE, Stefanovska A, ”Inference of time-evolving coupled dynamical systems in the presence of noise”, {\em Phys Rev Lett} {\bf 109}: 024101, 2012. 

[2]Petkoski S and Stefanovska A, ”Kuramoto model with time-varying parameters”, {\em Phys Rev E} {\bf 86}: 046212, 2012. 

[3]Shiogai Y, Stefanovska A, McClintock PVE, ”Nonlinear dynamics of cardiovascular ageing”, {\em Phys Rep} {\bf 488}: 51-110, 2010.

[4] Suprunenko Y and Stefanovska A, ”Cell membrane potential: oscillations and self-regulation”, in preparation. 

[5]Clemson P and Stefanovska A, ”Dynamics of non-autonomous systems as an inverse problem”, in preparation. 

[6]Clemson P, Konstantinov D, Watanabe M, Kono K, McClintock PVE, Stefanovska A, ”Chronotaxic dynamics of electrons on the surface of liquid 4He and 3He”, in preparation.

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[divider_title title=”Enrique Tirapegui (Chile)” heading=h3]
Facultad de Ciencias Fisicas y Matematicas -Universidad de Chile, Chile

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[toggle title=”Universal behavior in neurons dynamics” color=gray]

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Abstract: The knowledge we have of the biophysical mechanisms responsible for generating neuronal activity has provided the basis for constructing neuron models. The electrical dynamics of a single neuron is well described by sets of nonlinear differential equations based on conductances which are in very good agreement with experiments. The basic variables are the fluxes of ions through the plasmatic membrane and the potential difference between the interior and the exterior of the neuron. In the last 50 years a series of simplified phenomenological models, some of them differing even in the number of variables, which reproduce the principal characteristics of the models based on conductances, have been proposed. Each of these models reach the “truth” in some sense and the fundamental question is what is common to all these models and if we can costruct a minimal model which caughts all the essential features of the dynamics. We address these two questions in this talk and we prove using the tools of dynamical systems and normal form theory that such a minimal model exists and turns out to be quite simple. This minimal model is of course universal \ and describes the robust behaviors of neuron dynamics.

(*) In collaboration with Ulises Pereira

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[divider_title title=”Constantino Tsallis (Brazil)” heading=h3]
Centro Brasileiro de Pesquisas Fisicas, Brazil

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Abstract: Complexity in natural, artificial and social systems appears to be conveniently characterized by the nature and strength of the (strong) correlations between the elements of the system. This in turn determines the number of allowed microscopic possibilities, typically much smaller than the total number of such possibilities if there were no correlations. This fact mandates the class of entropic functionals to be used in order to satisfy the thermodynamic requirement of the entropy to be extensive. We shall briefly discuss the main concepts emerging in this approach, and shall illustrate its predictive and descriptive usefulness with recent theoretical, experimental, computational and observational applications in physics and elsewhere.

BIBLIOGRAPHY:

(i) C. Tsallis, “Nonextensive Statistical Mechanics – Approaching a Complex World” (Springer, 2009);

(ii) J.S. Andrade Jr., G.F.T. da Silva, A.A Moreira, F.D. Nobre and E.M.F. Curado, Phys. Rev. Lett. 105, 260601 (2010);

(iii) F.D. Nobre, M.A. Rego-Monteiro and C. Tsallis, Phys. Rev. Lett. 106, 140601 (2011);

(iv) http://tsallis.cat.cbpf.br/biblio.htm

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[divider_title title=”Stefan Wehner (Germany)” heading=h3]
Universität Koblenz-Landau, Institut für Integrierte Naturwissenschaften – Physik

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Abstract: CO oxidation under ultra high vacuum (UHV) conditions is surely the most often studied surface reaction. It is known for more than three decades, that catalytic CO oxidation to CO2 on noble metal surfaces follows the Langmuir-Hinshelwood reaction mechanism. Nearly ten years ago it was shown for the Iridium(111) surface that even on a non reconstructing surface spatio-temporal pattern formation takes place since there is a bistable regime with respect to the feed gas composition for a wide range of temperatures. Such adsorbate patterns were recorded in situ on Iridium, Platinum and Palladium using photo electron emission microscopy (PEEM). In a few cases the changes in coverage during the ongoing reaction could be analyzed by photo electron spectroscopy (PES) utilizing synchrotron radiation. In recent years the focus shifted to the influence of different types of noise superposed externally on the feed gas composition to the product rate. In the case of Iridium(111) small to medium noise narrows the bistable region and long time transients (up to 100000 s) were found for the transition from the locally stable to the globally stable state of adsorbates, determining the catalytic activity of the surface. Large noise on the other hand produces rare (bursts) or frequent (switching) changes between both states. On Palladium(111) superposed external noise results in a transition to a stable state, the faster the stronger the noise. In case of intrinsic noise rare reversible excursions from the reactive state to a less reactive state are observed. They last between 10^2 and 10^3 seconds, showing an asymmetric behavior between leaving and returning to the initial CO2 rate, which is mainly constant for more than 10^5 seconds. Their frequency depends on the feed gas composition and have up to now not been observed on other platinum group metal surfaces.

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[divider_title title=”José Wesfreid (France)” heading=h3]
École Supérieure de Physique et de Chimie Industrielles, Paris, France

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Abstract: Since the pioneering work of Sir O. Reynolds in 1883, there is still no satisfying explanation of the transition to turbulence in confined shear flows. It remains one of the most fundamental and practical problem still unsolved in fluid mechanics. Different nonlinear models for subcritical transition to turbulence have been proposed during the last years. Most are Galerkin truncations and reduced variable dimension models of the full Navier-Stokes equations or phenomenological amplitude equations, for the amplitude of the fluctuations. Recent models [1] are based on coupled amplitude equations for a local variable as the transversal turbulent roll fluctuation (q) and a global variable as the centerline velocity (u_cl), which is the measure of the mean flow distortion. We have highlighted the importance of the deformation of the mean velocity in a recent paper [2]. Experiments on the subcritical transition to the turbulence are carried out on a plane Poiseuille flow in a hydraulic channel, perturbed by controlled jet normal to the wall. For different values of Reynolds number Re and different amplitude of the perturbation u_jet/u_cl, u_jet being the jet velocity and u_cl the centreline streamwise velocity, different states are observed, from laminar to turbulent state. Using Particle Image Velocimetry, we study the dynamics of the fluctuations of the transverse velocity component q and, simultaneously, the deformation of the mean velocity profile u=u_cl/u_{cl,unperturbed}, (u_{cl,unperturbed} is the centreline streamwise velocity without perturbations). We discuss the evolution in the phase space of those variables as a function of the amplitude of the perturbation and compare it to predictions made using low dimensional models. In addition, we perform a full observation of the velocity field in a plane normal to the streamwise direction and in an plane parallel to the wall. This observations allow us to identify the inner structure of a localized “puff” and to identify the phase velocity of different structures.

[1] D. Barkley, Phys. Rev. E 84, 016309 (2011)

[2] G. Lemoult, J.L. Aider & J.E. Wesfreid , Phys. Rev. E 85, 025303 (2012)}

(*) In collaboration with Grégoire LEMOULT and Jean-Luc AIDER

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