Monday, May 29, 2006
Monday Morning
08:00 Registration open
08:30 Opening Remarks - Organizers
08:40 Construction of a Chaotic Computer Chip
William Ditto, University of Florida, william.ditto@bme.ufl.edu
Sudeshna Sinha, Institute of Mathematical Sciences, Chennai, INDIA
K. Murali, Anna University, Chennai, INDIA
Abraham Miliotis, University of Florida, Gainesville, FL USA
Chaotic systems are great pattern generators and their defining feature, sensitivity to initial conditions, allows them to switch between patterns exponentially fast.
We exploit such pattern generation by “tuning” representative continuous and discrete chaotic systems to generate all logic gate functions. We then exploit
exponential sensitivity to initial conditions to achieve rapid switching between all the logic gates generated by each representative chaotic element. With this as a
starting point we will present our progress on the construction of a chaotic computer chip consisting of large numbers of individual chaotic elements that can be
individually and rapidly morphed to become all logic gates. Such a chip of arrays of morphing chaotic logic gates can then be programmed to perform higher order
functions (such as memory, arithmetic logic, input/output operations, …) and to rapidly switch between such functions. Thus we hope that our reconfigurable chaotic
computer chips will enable us to achieve the flexibility of field programmable gate arrays (FPGA), the optimization and speed of application specific integrated circuits
(ASIC) and the general utility of a central processing unit (CPU) within the same computer chip architecture. Results on the construction and commercialization of the
ChaoLogixTM chaotic computer chip will also be presented to demonstrate progress being made towards the commercialization of this technology. (www.chaologix.com).
09:30 The Dynamics of Medium-Scale Arrays
Mark Spano, NSWC Carderock Laboratory, mark.spano@mailaps.org
Frank Moss, Univ. of Missouri at St. Louis
Jorge Brea, Univ. of Missouri at St. Louis
Alexander Neiman, Ohio Univ.
The dynamics of systems with few elements (N < 3) and with many elements (N ~ 1023) are well understood, but systems with
intermediate numbers of elements (on the order of tens to thousands) are difficult to treat either analytically or experimentally.
To explore this regime, we have constructed arrays of Duffing and Rossler oscillator expressed in analog electronics. The Duffing
array is sinusoidally driven, while the Rossler array is free running. (The latter suggests comparison to arrays of neurons.) The
coefficients of each equation can be chosen to be the same for all oscillators or can be allowed to vary from oscillator to oscillator,
allowing some to operate (when uncoupled) in a periodic regime while others operate in a chaotic regime. Noise may be added as desired.
Each array consists of up to 32 elements coupled together with variable resistors that allow computer-controlled modification
of the coupling strength. We acquire data from up to 32 channels simultaneously for either array.
Of interest is the case of sparse coupling between the array elements, in particular tree-like coupling and small world coupling.
We present here the results for network synchronization and Shannon entropy with various noise amplitudes for several different
network configurations
09:50 Experimental Observation of a Torus Doubling of a Metal/Ferroelectric Film/Semiconductor-Capacitor
Martin Diestelhorst, Martin-Luther-University Halle-Wittenberg, Dept. of Physics, martin.diestelhorst@physik.uni-halle.de
Kay Barz, Martin-Luther-University Halle-Wittenberg, Dept. of Physics
Horst Beige, Martin-Luther-University Halle-Wittenberg, Dept. of Physics
Marin Alexe, Max Planck Institute of Microstructure Physics Halle, Experimental Dept. II
Dietrich Hesse, Max Planck Institute of Microstructure Physics Halle, Experimental Dept. II
A metal-ferroelectric-semiconductor (MFS)-structure was used as nonlinear capacitor in a series resonance circuit. The following
materials were used as components of the MFS-structure: Aluminium as metal electrode, Bi4Ti3O12-film as ferroelectric and p-type
silicon as semiconductor. The system was driven by a single frequency at suitably chosen amplitudes. Besides the sequences of period
doubling bifurcations which were already observed in the series resonance circuit with pure ferroelectric capacitor [e.g. 1, 2] we
found regions with torus doubling bifurcations by varying the frequency of the driving voltage at suitably high amplitudes. Comparing
the behaviour of the series resonance circuit with pure ferroelectric capacitor and with MFS-structure we attribute the reason for the
new effect of torus doubling to the properties of the ferroelectric/semiconductor boundary layer.
References:
[1] M. Diestelhorst, R. P. Kapsch, H. Beige: Nonlinear amplification effects in a periodically perturbed period-doubling series resonance
circuit, Int. J. of Bif. and Chaos 9, 243-250 (1999)
[2] M. Diestelhorst, Application of small-signal amplification in a series resonance circuit with TGS-capacitor as pyroelectric detector,
in St. Boccaletti, B. J. Gluckman, J. Kurths, L. M. Pecora, R. Meucci, O. Yordanov (eds.): Experimental Chaos, Melville, New York,
2004, 39-44
10:10-10:40 Break
10:40 Mixed chaos, dynamical tunneling, micro-lasers and resonant multi- cavities
Germán A. Luna-Acosta, Instituto de Física, Universidad Autónoma de Puebla, gluna@sirio.ifuap.buap.mx
J.A. Méndez-Bermúdez, Max-Planck-Institute für Dynamik und Selborganisation, Göttingen, Germany
U. Kuhl, Fachbereich Physik der Philipps Universität Marburg, Germany
H.-J. Stöckmann, Fachbereich Physik der Philipps Universität Marburg, Germany
Dynamical tunneling is a purely quantum phenomena occurring in mixed 2D chaotic systems. The wave tunnels through
classical impenetrable barriers ( KAM curves) that separate chaotic regions from islands of stability
( regular motion). This tunneling takes place only at certain set of discrete frequencies ( or energies for quantum
systems).[1] Here we show how this difference between wave ( quantum) and ray (particle) behavior can be used to
design various types of opto-electronic devices, such as semiconductor micro-lasers, multi-cavities and beam splitters[2].
We also show results on a microwave experimental realization of the model.
References:
[1] J. A. Méndez-Bermúdez, G.A. Luna-Acosta, P. Seba, and K.N. Pichugin, Phys. Rev. B. 67, 161104(R).
[2]. O. Bendix, J.A. Méndez-Bermúdez, G.A. Luna-Acosta, U. Kuhl, and H.-J. Stöckmann, Microlelectronics Journal,
38, ( 2005) 285-288.
11:20 Period doubling in Single Bubble Sonoluminescence
Mogens Levinsen, Niels Bohr Institute, levinsen@nbi.dk
Single Bubble Sonoluminescence (SBSL) is an extremely nonlinear effect. It is therefore natural to look for period
doubling in this system. Surprisingly we find the period doubling which can be observed directly in and only in the
emission amplitude to be connected with a shape instability. We discuss the different spatial symmetries involved
and touch on the controversy related to previous claims that period doubling could only be observed in the timing
of the emission relative to the sound field.
11:40 Experimental exploration of chaos for wave-particle interaction with a specially designed traveling wave tube
Alessandro Macor, Universite' de Provence - CNRS EquipeTurbulence Plasma, macor@up.univ-mrs.fr
Fabrice Doveil, CNRS EquipeTurbulence Plasma
We make experiments on chaos with a specially designed Traveling Wave Tube where a test electron beam interacts
with electrostatic waves; such a system has paradigmatic Hamiltonian behavior which we describe in our different
tests.
By recording the beam energy distribution at the output of the tube with a trochoidal analyzer , we observe the
resonant domain of a single wave and the overlap of the resonance domains of two waves associated to the destruction
of Kolmogorov-Arnold-Moser tori constituting barriers in phase space [1].
Paying attention to small non linear effects we evidence a nonlinear synchronization due to a single wave at the
root of Landau Damping an important phenomenon especially in Plasma Physics; The results are explained by second
order perturbation theory in the wave amplitude [2].
It is also possible to remark how chaos may appear in simple Hamiltonian system composed by the beam and only one
excited frequency: for such a model we recorded the direct signature of fractal structure which rules the diffusion
of the beam velocities into the trapping domain of the wave [3].
Reaching higher performance from system based on many-body interactions where diffusion represents a severe obstacle
often means working against chaos, e.g., in free electron laser or particle accelerators; recently we tested a general
theory to channel chaos by building barriers in phase space and proved how it is possible to achieve control of
test beam velocity diffusion by adding small apt modifications with a low additional cost of energy [4].
References:
[1] F.Doveil, Kh. Auhmani, A.Macor, and D.Guyomarc'h, Experimental observation of resonance overlap responsible for
Hamiltonian chaos, Phys. Plasmas 12, 010702 (2005).
[2] F.Doveil, D. F. Escande and A.Macor Experimental observation of nonlinear synchronization due to a single wave,
Phys. Rev. lett 94, 085003 (2005).
[3] A.Macor, F.Doveil, and Y. Elskens Electron Climbing a ‘‘Devil’s Staircase’’ inWave-Particle Interaction, Phys.
Rev. lett 95, 264102 (2005).
[4] C. Chandre, G. Ciraolo, F.Doveil, R. Lima, A.Macor, and M.Vittot, Channeling chaos by building barriers, Phys.
Rev. lett 94, 074101 (2005).
12:00 Nonlinear three-wave interactions and drift-wave turbulence in fusion plasmas
Ricardo Viana, Department of Physics, Universidade Federal do Parana, viana@fisica.ufpr.br
S. R. Lopes, Universidade Federal do Parana, Curitiba, Parana, Brazil
A. M. Batista, Universidade Estadual de Ponta Grossa, Ponta Grossa, Parana, Brazil
I. L. Caldas, Universidade de Sao Paulo, Sao Paulo, Sao Paulo, Brazil
W. Horton, Institute for Fusion Studies, University of Texas at Austin, Austin, Texas, United States
P. Morrison, Institute for Fusion Studies, University of Texas at Austin, Austin, Texas, United States
We considered a three-wave interaction model with quadratic nonlinearities and growth/decay rates to investigate
the occurence of drift-wave turbulence arising from pressure gradients in the plasma edge of a tokamak. The three-wave model
arises from a truncation performed on the Fourier decomposition of the electrostatic potential satisfying a partial differential
equation proposed by Hasegawa and Mima to describe drift-wave turbulence. The model parameters are taken from a typical set
of measurements of temperature and density profiles, as well as the floating electrostatic potential in the plasma edge of
the tokamak TBR-1 (Instituto de Fisica, Universidade de Sao Paulo, Brazil). We investigated some aspects of the temporal
dynamics exhibited by the three-wave interaction model, with special emphasis on a chaotic regime found for a wide range of
the wave decay rate. We analyzed the intermittent transition to chaos for certain parameter values and found evidence of a
Pomeau-Manneville type-I intermittency scenario. We also studied the existence of spikes in the behavior of the two daughter
waves and some of their statistical properties. We included, in a self-consistent way, a fourth mode of small amplitude
which can be used to control chaotic dynamics.
12:20-14:00 Lunch
Monday Afternoon
14:00 Chaos in 3F Problems: Modeling and Experiments
Marian Wiercigroch, Centre for Applied Dynamics Research, University of Aberdeen, M.Wiercigroch@abdn.ac.uk
Despite of a significant progress in deriving practical solutions for nonlinear problems with friction, fracture
and fatigue (3F problems), the fundamental understanding of their complex dynamics is far from the stage where we can
harness or control their dynamic behaviour. This lecture will focus on modeling and experimental studies of three dynamical
systems where main nonlinearities come from 3Fs. The unifying theme of the considered problems is non-smooth dynamics for
which a general methodology will be presented.
The first system with dry friction mimicking a vibro-impact moling has some unconventional dynamics as its solution
drifts [1]. The drift is critical for this system as it relates to the system efficiency measured by penetration rates. Low
dimensional maps have been developed to effectively study of the system dynamics [2]. The results from these investigations
are significant for generating a dynamic fracture in ultrasonic drilling of hard materials [3] and rocks [4]. We explain how
to control a surprising phenomenon of penetration rates fall under large static loads by identifying an important transition
from periodicity to chaos. In the last considered system creation of chaotic strange attractor is used in identifying the
dangerous fatigues crack growth regimes [5].
References:
1. Pavlovskaia, E.E., Wiercigroch, M. and Grebogi, C. 2001 Physical Review E 64, 056224. Modeling of an impact
system with a drift.
2. Pavlovskaia, E.E., Wiercigroch, M. and Grebogi, C. 2004 Physical Review E 70, 036201. Two dimensional map for
impact oscillator with drift.
3. Wiercigroch, M., Neilson, R.D. and Player, M.A. 1999 Physics Letters A 259(2), 91-96. Material removal rate
prediction for ultrasonic drilling of hard materials using impact oscillators approach.
4. Wiercigroch, M., Wojewoda, J. and Krivtsov, A.M. 2005 Journal of Sound and Vibration 280(3-5), 739-757. Dynamics
of ultrasonic percussive drilling of hard rocks.
5. Foong, C-H., Wiercigroch, M., Deans, W.F. and Pavlovskaia, E.E. 2003 Chaos, Solitons and Fractals 16, 651-659.
Chaos caused by fatigue crack growth
14:40 In-situ monitoring of friction surface and their sequence pattern image analyses
Seisuke Kano, National Institute of Advanced Industrial Science and Technology, s.kano@aist.go.jp
In-situ monitoring of a friction surface is quite difficult because of the friction occurred between solid surfaces and
sometime with lubricant. Understanding of the tribological subjects, it is important to know the changing of friction
surfaces. In many cases, the surfaces were observed after tribological tests and remove the test piece from the tribo-tester.
Some cases transparent materials were used for surface study but these cases the tribological conditions far from the real
friction conditions. In this study a laser-strobe technique applied to friction surface observation and storaged surface
pictures were analyzed by means of pattern matching methods and discussed their correlations. A test carried by pin-on-plate
methods with carbon-steels at the reciprocating motion speed of 10 Hz for 4.9 N. A machine base-oil was coated on the
surface as a lubricant just before tribo-test. The pulsed laser light (Nd:YAG SHG = 532 nm, 5 nsec/pulse) was induced by
optical microscope, which located just side of the pin, and irradiated on the friction surface. The laser pulse was
synchronism with the plate motion which was a trigger of the laser pulse. The surface picture was storaged for every cycle
and these sequences were calculated and analyzed their correlations as a function of the surface pattern and the friction
track size and shape. As the result of the analysis there are some groups were distinguish as a parameter of the scars size
and shape.
15:00 Scaling laws for the fragmentation of rubble-pile asteroids
Fernando Roig, National Observatory, froig@on.br
Gabriel Denicol, Institute of Physics, UFRJ
Takeshi Kodama, Institute of Physics, UFRJ
We analyze different scaling laws for the fragmentation of ruble-pile asteroids that have been obtained with our recently
introduced model of Interacting Ellipsoids (Roig et al., Icarus 165, 355, 2003). In this model, the rubble-pile asteroids
are represented by an overlap of ellipsoidal rigid bodies that interact among them according to an atractive force given by
the multipolar gravitational mutual potential plus a repulsive force that models the surface contact between the bodies and
a dissipative force that represents the mutual friction. We studied two different regimes: (i) a large target impacted by a
small projetile (less than 10% of the target mass) at high velocities (~5 km/s) typically found in main belt asteroid binary
colisions; and (ii) two large rubble-pile bodies of comparable mass colliding at very low velocities (~100 m/s) typicaly found
in accretion processes. We have determined different scaling laws in the gravitational regime, either by fixing the impact velocity
or by fixing the mass ratio projectile/target. Our results can be fit by power laws with exponent values similar to those found in
the literature. However, our scaling laws provide values of the catastrophic energy threshold about an order of magnitude
smaller than those predicted by scaling laws for monolithic asteroids obtained with hydrocodes (e.g. Benz & Asphaug, Icarus
142, 5, 1999). We discuss these results and their possiible consequences for colisional evolution models.
15:20 Experimental Method for the Measurement of Large Amplitude Non-Linear String Vibrations
Mark L. Gordon, Department of Mechatronics, Nelson Mandela Metropolitan University, mark.gordon@nmmu.ac.za
Modify A.E. Kaunda, School of Mechanical Engineering, University of Kwazulu-Natal
We propose a novel technique for the measurement of non-linear transverse, string vibrations.A theoretical analysis of the
linear model has been discussed, previously. In this paper emphasis is placed on the experimental method and data analysis.
The existance of basic non-linear behaviour is discussed and investigated, under the infuence of mean velocity and mean
acceleration measurements. Small-amplitude string vibrations are well-documented. Using this measurement technique,
large-amplitude vibrations can be studied, with particular reference to overhead-conductor, wind induced oscillations
15:40-16:30 Poster Session
16:30 Experimental evidence of intermittency of magnetic field fluctutations in the solar wind using GEOTAIL satellite
Daiki Koga, DGE-INPE and World Institute for Space Environment Research (WISER), daiki@dge.inpe.br
A. C. -L. Chian, DGE-INPE and WISER
E. L. Rempel, ITA and WISER
T. Hada, ESST, Kyushu University
A wealth of nonlinear phenomena can be found in space and astrophysical plasmas. For instance, large amplitude
magnetohydrodynamic (MHD) waves, which have characteristic waveforms, are commonly found near the Earth's bow shock region,
and the Universe displays a rich pattern of galaxy clusters. At the early stages (linear stage) of the evolution, the waves
or galaxy clusters evolve independently from Gaussian random fluctuations. Then, they interact with each other nonlinearly
as the amplitude becomes finite (nonlinear stage). They could thus be characterized by quantifying the phase correlation
associated with nonlinear interactions among waves or galaxy clusters.
We have developed the phase coherence index as a tool to quantify the phase correlation among waves. The index is
not only related to nonlinear interactions (phase correlation) but also non-Gaussianity (intermittency).
In this presentation, we would like to show the relation between intermittency and phase correlation using GEOTAIL
magnetic field data in the solar wind.
References:
[1]Hada et al., 2003, Space Sci. Rev., 107, 1-2, 463
[2]Koga and Hada, 2003, Space Sci. Rev., 107, 1-2, 495
[3]Koga and Hada, submitted 2005, Nonlinera Processes in Geophysics
[4]Koga and Chian, to be submitted, Solar Physics
16:50 Synchronization of bistable chaotic electronic circuits
Alexander Pisarchik, Centro de Investigaciones en Optica, apisarch@cio.mx
Rider Jaimes-Reátegui, Universidad de Guadalajara
J. H. García-López, Universidad de Guadalajara
We report on the first, to our knowledge, experimental study on synchronization of coupled systems with coexisting
attractors. The experiments are carried out with two coupled identical chaotic electronic circuits in a master-slave
configuration. When the coupling strength increases, synchronization manifests itself, first, by intermittent jumps between
two coexisting attractors demonstrating type-I and on-off intermittences. For small coupling strengths, intermittent
anticipated phase synchronization is observed. The relatively strong coupling shifts the natural frequency of the slave
system inducing phase synchronized period-doubling oscillations terminated by complete synchronization. The results of
numerical simulations are in good agreement with experiments.
17:10 Interaction of noise with excitable dynamics
Punit Parmananda, FC-UAEMor., punit@caos.fc.uaem.mx
The interaction of noise with excitable system is studied experimentally in an electrochemical cell. Both external
and internal noise scenarios are considered. Numerous noise invoked resonance phenomena are observed and quantified. Results
from the different resonances invoked indicate that noise, if used judiciously, can play a constructive role in chemical
systems. Moreover, experimental evidence involving the successful manipulation in the regularity of the noise provoked
dynamics is presented. Using a delayed feedback control strategy, an enhancement in the regularity of the coherence
resonance dynamics is achieved.
17:50 Chaos in an enzyme reaction
Marcus J. B. Hauser, Universität Magdeburg, Biophysics Group, Dept. of Experimental Physics, marcus.hauser@physik.uni-magdeburg.de
Lars Folke Olsen, University of Southern Denmark at Odense, Dept. of Biochemistry and Molecular Biology
Biological rhythms are ubiquitous phenomena which play important roles in physiological context. Generally, the
mechanisms that give rise to such phenomena rely on quite complex metabolic networks, thus allowing for a high specificity
and a fine tuning of the physiological processes. However, the complexity hampers the fundamental understanding of the
underlying mechanisms which may give rise to oscillatory or other types of nonlinear dynamical behaviour.
In order to examine if enzyme reaction networks may give rise to nonlinear dynamical behaviours, we studied a
simple enzyme reaction system, since enzymes are the specific catalysts of almost any physiological reaction. The
investigated enzyme system is the the oxidation of NADH by O2 catalysed by peroxidase. This so-called peroxidase-oxidase
(PO) reaction consists of a single enzyme and its substrates. This reaction displays rich dynamics, as observed experimentally
under in vitro conditions: the dynamics encompasses periodic oscillations as well as chaotic oscillations. Depending on the
pH value of the reaction medium, different routes to chaos (period-doubling and period-adding) are observed. Analysis of
the chaotic time-series indicates the existence of a homoclinic orbit in the chaotic domain. Experiments in cell extracts
suggest that such oscillations may also occur in vivo. Investigations at a bistable regime – where oscillations and a
stationary state were simultaneously stable under a given s et of conditions – suggest that one possible function of
the oscillations may be the protection of the enzyme against degradation by reactive oxygen species.
18:10 Experimental Results on Fire Safety
Eugenio Degroote, Universidad Politecnica de Madrid-Laboratorio de Sistemas Complejos, eugenio.degroote@upm.es
Fire Safety on fuel containers depends, during the ignition period, on the evolution of the flame front propagation
over the liquid fuel. This propagation has been found to be controlled by the initial fuel surface temperature: by varying
this control parameter, we can reduce the flame velocity. This experimental fact is extremely important, since it provides
an extra time for the extinction process on fuel containers.
Experiments carried out in long channels for a large number of fuels show that the spreading process occurs close to
the surface (d<1.5cm). The propagation of a flame over a liquid fuels produces (in a region close to the flame front)
strong gradients, both in the liquid fuel and in the gas phase. Therefore, a strong surface tension gradient is observed
near the flame, that moves hot fuel beneath flame front. The appearance of this region modifies flame spreading stability
producing, in some cases, a pulsating behavior and many different spreading regimes. They are clearly different from those
observed for solid fuels, where convection cannot occur.
Flame spreading over liquid fuels present at least five different spreading regimes, separated by four critical
temperatures T1, T2, T3, T4. T1 corresponds to a stationary bifurcation, T2 is a transcritical bifurcation, while T3
corresponds to a Hopf Bifurcation (subcritical) and T4 is a homoclinic connection.
Based on our experimental results, a heat and momentum transfer analysis has been carried out, that will help us to
understand the basic mechanisms involved in this process and, therefore that will enhance security conditions. It has been
found that two factors are enough to control flame spreading:
• The Initial Fuel Surface Temperature.
• The preheating zone observed in the liquid phase ner the flame front.
Based on these results, a small fuel reservoir has been constructed. The first experimental results in this applied
field will be shown here.
Tuesday, May 30, 2006
Tuesday Morning
08:00 Registration desk opens
08:30 Experimental Analysis of Discontinuous System Dynamics
Hans Weber, PUC/Rio, hans@mec.puc-rio.br
Sandor Divenyi, COPPE/UFRJ
Marcelo A. Savi, COPPE/UFRJ
Luiz Fernando P. Franca, CSIRO Petroleum
Nature is full of non-smooth nonlinearities that are usually related to either the friction phenomenon or the
discontinuous characteristics as intermittent contacts. In general, non-smooth characteristics are the source of
difficulties for the modeling and simulation of natural systems. This contribution uses a smoothened switch model in order
to analyze non-smooth systems. The procedure reveals to be effective to deal with this kind of system, presenting advantages
for the numerical implementation. As an application of the general formulation, a single-degree of freedom oscillator with
discontinuous support is analyzed. An experimental apparatus is developed in order to verify the capability of the mathematical
formulation and the numerical procedure to describe the system general behavior. The apparatus is composed by an oscillator
constructed by a car, free to move over a rail, connected to an excitation system. The discontinuous support is constructed
considering a spring and a gap related to the car position. This apparatus is instrumented to obtain all the system
state variables, making possible the comparison of experimental results with those obtained by numerical simulations.
System dynamical behavior shows a rich response, presenting dynamical jumps, bifurcations and chaos. Numerical simulation
presents a close agreement with those obtained from experimental apparatus. Besides this analysis, different configurations
of the experimental set up are treated in order to evaluate the influence of the internal impact within the car and also
support characteristics in the system dynamics
08:50 Attractor Reconstruction from Sonar Data
Alan Fenwick, Air Systems, QinetiQ & CADR University of Aberdeen, a.j.fenwick@abdn.ac.uk
As part of a three year programme to investigate the use of chaotic signals in sonar sponsored by the UK MoD, a
trial was conducted in 2004 at the Waterlip outdoor acoustic test facility. The measurements were organised into four
experiments, designed to provide data on different aspects of the use of chaotic signals in a practical sonar system. After
an outline of the sonar problem and how chaotic signals can help, the experimental set up will be presented. So far, the
analysis has been restricted to linear and non-linear analysis of the echoes from a hard target, which produces a replica
of the signal. Attempts to reconstruct the attractor of the echo by standard methods show a lower dimensionality than might
be expected when the effect of the transducers is accounted for. A selection of the results will be presented
09:10 Versatile Recurrences
Marco Thiel, University of Potsdam, thiel@agnld.uni-potsdam.de
M. Carmen Romano, University of Potsdam, Germany
Jürgen Kurths, University of Potsdam, Germany
In this talk we discuss new developments in the field of recurrences and especially effective ways to exploit
recurrences for the study of dynamical systems.
We therefore present the concept of the recurrence matrix and show that it contains relevant information about a
dynamical system. The recurrence plot, a graphical representation of the recurrence matrix is a powerful tool to visualise
dynamical behaviour.
Various quantifications of the recurrence matrix can give insights into the dynamics of a system and allow studying
the interaction between several systems. We demonstrate how recurrences can be used to e.g. estimate dynamical invariants
and to construct measures for synchronisation. The recurrence matrix contains all necessary information for generating
alternative evolutions of dynamical systems (surrogates of trajectories of dynamical systems) which allow testing for
synchronisation. We apply the recurrence based analysis to test for synchronisation in fixational movements of the left and
right eye and mention several further applications (e.g. mother-foetus heartbeat synchronisation)
09:50 Towards a knotless topological analysis of chaos
Marc LEFRANC, Laboratoire PhLAM (CNRS/Université Lille 1), marc.lefranc@univ-lille1.fr
Pierre-Emmanuel MORANT, Laboratoire PhLAM (CNRS/Université Lille 1)
Michel Nizette, Optique nonlinéaire théorique, Université Libre de Bruxelles
Many quantitative measures of chaos (e.g., fractal dimensions or Lyapunov exponents) rely on constructing an
approximation of the natural measure on a strange attractor, which requires observing the system for at least a few
hundreds of cycles at fixed control parameters. Thus, it is difficult to assess deterministic chaos in a real system
that experiences parameter drifts on a time scale comparable to the mean dynamical period. An important question then
is: can we infer the existence of an underlying chaotic dynamics from a very short and/or nonstationary time series?
Positive-entropy periodic orbits are extremely powerful tools in this context. These are periodic orbits whose knot type
can only be found in a chaotic system because if a deterministic and continuous dynamics is assumed, it forces a certain
amount of stretching and mixing in the complement of the orbit, which can be quantified by a strictly positive lower bound
on topological entropy [1]. Positive-entropy orbits have recently been har nessed to obtain signatures of deterministic
chaos in a nonstationary optical system [2]. However, knots formed by periodic orbits are only defined in three-dimensional
embeddings, whereas techniques for obtaining entropy estimates would be most useful in higher dimensions, where time series
are inherently short. Thus, we reformulate the principles of determinism and continuity so that they adapt to phase space
dimension: rather than requiring that curves do not intersect, which leads to knot theory, we enforce preservation of
volume orientation in phase space [3]. As a first step towards a formalism applicable in higher dimensions, we show that
in dimension three, the new formalism predicts the correct topological entropies for periodic orbits of the horseshoe map.
We also discuss preliminary results that suggest that information about the structure of the unstable manifold of the
periodic orbit and about its symbolic dynamics can be extracted from the generalized braid.
References:
[1] P. Boyland, Topology Appl. 58, 223 (1994).
[2] A. Amon and M. Lefranc, Phys. Rev. Lett. 92, 094101 (2004).
[3] M. Lefranc, ArXiv preprint nlin.CD/0503006
10:10-10:40 Break
10:40 Dynamics of Sandripples under Water
Clive Ellegaard, Niels Bohr Institute, ellegaard@nbi.dk
Karsten Scheibye Knudsen, Niels Bohr Institute
Frederik Bundgaard, Niels Bohr Institute
Experimental studies of sandripples under water are important for sand transport along coasts, around bridges etc,
but also as a rich pattern-forming system. We study the dynamics of sandripples under changing conditions.
We find surprisingly sharp and well-defined transitions as a function of the amplitude, frequency and angle of the
driving force, and also a great sensitivity to the shape of the driving force function. The system exhibits a set of both
subcritical and supercritical bifurcations
11:00 Predicting the wind direction using observations taken from two separate points
Yoshito Hirata, Department of Mathematical Informatics, The University of Tokyo, yoshito@sat.t.u-tokyo.ac.jp
Danilo P Mandic, Department of Electrical and Electronic Engineering, Imperial College London
Hideyuki Suzuki, Institute of Industrial Science, The University of Tokyo
Kazuyuki Aihara, Institute of Industrial Science, The University of Tokyo/Aihara Complexity Modelling Project, ERATO, JST
We need to predict the wind direction when we want to adjust wind turbines for generating more electricity.
However, it is not straightforward since the wind direction takes a value on a ring. To overcome this difficulty, we
consider several setups for predicting the wind direction. To evaluate these setups, we prepared two identical anemometers
and observed the wind. As a smaller scale problem, we measured the wind outside in our institute with 50 Hz at two
observation points, which were 5m apart from each other. Since the data set looks noisy, we applied the moving average of 2
seconds and resampled it every 2 seconds. We found that the wind direction was better predicted when we built a nonlinear
model that predicts the vector field of the wind and calculated wind direction based on the vector field than when we let
the wind direction 2 seconds before as a prediction (persistent prediction). We also showed that the nonlinear prediction
was better than the corresponding persistent prediction even if we try to predict the further future
11:20 Macro-instability: a chaotic flow component in stirred tanks
Pavel Hasal, Institute of Chemical Technology, Prague, Pavel.Hasal@vscht.cz
Milan Jahoda, Institute of Chemical Technology, Prague
Ivan Fort, Czech Technical University in Prague
A decade ago, a pseudo-periodic macro-scale flow has been identified in stirred vessels manifesting itself on a
spatial scale comparable to the size of the vessel and occurring with characteristic frequencies significantly lower than
the impeller frequency. This flow has been named the macro-instability (MI) of the flow pattern. The MI existence has been
confirmed by various experimental methods and has also been predicted by computational fluid dynamics. Until now the most
of experimental and also modelling efforts has been focused on the frequency of the macro-instability occurrence and to the
MI kinetic energy. Our earlier analyses, however, have also pointed to the chaotic nature of the macro-instability fluid
flow components. Chaotic features of macro-instability components of fluid motions in stirred tanks are addressed in this
paper.
We analyse several experimental data sets obtained by measuring distinct fluid flow related quantities in a
flat-bottomed cylindrical mixing vessels (inner diameter of 0.3 m) stirred either with pitched blade turbine (PBT)
impellers or with Rushton turbine (RTI) impellers using water or aqueous glycerol solutions as working liquids. First, a
presence of the MI component in the data is examined by spectral analysis. Then, the MI components are identified in the
data and time evolution of MI is reconstructed using the proper orthogonal decomposition (POD) technique. The attractors of
the macro-instability are further reconstructed using either the POD eigenmodes or a method of delays and finally attractor
invariants are evaluated (fractal dimensions, Lyapunov exponents, entropy production rates etc.) and their dependences on
the vessel operational conditions and spatial distributions in the vessel are further determined.
No significant spatial variability of the correlation dimension value was observed. Its value has been, however,
strongly influenced by operating conditions of the vessel, by liquid viscosity and by the vessel – impeller geometry. The
correlation dimension of the MI attractor is therefore suitable for analysis of transitions between different flow patterns
in the vessel and of different MI types resulting from these transitions.
More profound spatial distribution was displayed by the maximum Lyapunov exponent (taking distinctly positive values)
and the entropy production rate. These two invariants can be used for locating regions with different MI dynamics within
the mixing vessel. Results of such analyses can be used, for example, for finding proper location of inlet and outlet ports
of continuous flow mixers, location of gas spargers or analytical probes etc.
11:40 Controlling Symbolic Dynamics - Recent Advances
Scott Hayes, U.S. Army RDECOM, sthayes@rcn.com
Significant progress has been made in the control of symbolic dynamics since the original experiments in 1994,
though much of the work has not been openly published and thus has remained largely unknown. In this talk, I will reveal
some new ideas in this area, and discuss several experimental hardware implementations. (Much of the discussion will involve
the interpretation of chaos signals as information-bearing waveforms, although symbolic dynamics control is more general.)
I start with an overview of the original concept and experimental control of a Rossler-type oscillation in an electronic
circuit using micropulse injection. Next, other methods and experimental results for controlling symbolic dynamics in
practical situations are described. For example, it is possible to guide the symbolic dynamics of an oscillator from the
continuous-time signal generated by a method called segment hopping. In this method, an orbit following a prescribed symbol
sequence is generated without computation, such that it shadows an actual orbit, and a high-powered oscillator is
synchronized to the signal. Since the signal produced by the guided oscillator is higher-power copy of the input signal,
the chaotic oscillator is operating as an amplifier. Experimental results for this method using a radio-frequency Colpitts
oscillator are shown. New methods for signal processing that emerge from the unique properties of chaos signals; such as
matched predictive filtering, are briefly covered. Finally, the intrinsic determinism of chaos signals is interpreted as a
form of intersymbol interference, a concept from classical communication theory. This connection is made through the
construction of a Lorenz-like bipolar signal via linear pulse synthesis. The linear synthesis method is related to linear
filter theory, and thus leads to an interpretation of symbolic dynamics communication using concepts from classical
communication theory. An experiment showing how reverse-time chaos can be produced with a passive linear filter is then
described, and its implications for matched filtering are outlined. This interpretation leads to an interesting question
about the nature of chaos signals and chaotic processes in general: Are they truly different from traditional communication
signals? How can the linear superposition of basis functions, or the excitation of a linear filter yield chaos?
12:00 Experimental separation of chaotic signals through synchronization
Luigi Fortuna, University of Catania, lfortuna@diees.unict.it
Arturo Buscarino, University of Catania
Mattia Frasca, University of Catania
In this paper, by using a negative feedback scheme we study the problem of synchronizing two systems, each of them
made of n independent piece-wise linear (PWL) chaotic circuits, through the transmission of a unique signal (i.e. a scalar
variable). The signal is the linear combination of the chaotic signals generated by the n circuits and, thus, to synchronize
the two groups of chaotic circuits the slave circuit has first to separate the contributions of the subunits constituting
the master system. To find the appropriate values of the feedback gains, we use a theoretical approach based on the design
of an asymptotic observer, which lead to a set of linear matrix inequalities. We report numerical results showing the
suitability of the approach and we describe the experiment showing separation and synchronization of two pairs of chaotic
circuits.
In the experiment, two pairs of chaotic oscillators are synchronized through the transmission of a scalar variable
obtained as a linear combination of the state variables of the two circuits. In particular, the double-scroll-like chaotic
oscillators modelled by the ODE system introduced by Elwakil [Elwalkil et al., ISCAS 2000] have been used for the
experiment. Despite the presence of parameter mismatches, separation and synchronization of the two systems can be
achieved. This is an experimental demonstration of the successful possibility of multiplexing two (or more) chaotic signals
in the same channel.
12:20-14:00 Lunch
Tuesday Afternoon
14:00 The criticality hypothesis: How local cortical networks might optimize information processing
John Beggs, Indiana University, Physics, jmbeggs@indiana.edu
Wei Chen, Indiana University, Physics
Clayton Haldeman, Indiana University, Physics
Jon Hobbs, Indiana University, Physics
Aonan Tang, Indiana University, Physics
Shaojie Wang, Indiana University, Physics
Theory has predicted that networks composed of locally interacting non-linear units can exhibit complex emergent
properties that extend over a wide range of spatial and temporal scales. Here we provide experimental support for this
prediction as we describe the propagation of spontaneous activity in networks of cortical neurons in vitro. Rat cortical
tissue from culture as well as from acute slices was placed on 60 channel microelectrode arrays where spontaneous activity
in the form of local field potentials (LFPs) was monitored for up to 10 hrs. Negative peaks of LFPs were binned at 1-16 ms,
revealing spatio-temporal patterns of activity. When the probability of a pattern was plotted against its size, the
distribution followed a power law with an exponent of -3/2, as would be predicted for a critical branching process. Since
these patterns statistically resembled avalanches found in critical sand pile models, we called them “neuronal avalanches.”
Direct measurements revealed that activity on one electrode was, on average, followed by activity on one other electrode,
as would be expected for a critical branching process. Moreover, activity did not occur randomly, but in precisely timed
patterns that were stable and repeatable over the 10 hr recording sessions. This precision and stability suggests that the
avalanches could be used for storing information. To examine implications of critical branching on information processing,
we measured information transfer and storage in simulated recurrent networks with binary excitatory neurons and random
weights. This parsimonious model captured both the power law distribution of avalanche sizes and the repeating activity
patterns. When this model was tuned to the critical point, it was found that information transmission and storage were
simultaneously optimized. In addition, trajectories produced at the critical point had neutral dynamics, with Lyapunov
exponents near zero. Such trajectories are stable and also easily controllable. At this state characterized by a critical
branching process, the network may satisfy the competing demands of information transmission and storage, while also
preserving network stability.
14:40 ASTROCYTES MODULATE THE NEURAL ACTIVITY
Angelo Di Garbo, CNR - Istituto di Biofisica, angelo.digarbo@pi.ibf.cnr.it
Michele Barbi, CNR - Istituto di Biofisica, barbi@pi.ibf.cnr.it
Santi Chillemi, CNR - Istituto di Biofisica, chillemi@ib.pi.cnr.it
Susanna Alloisio, CNR - Istituto di Biofisica, alloisio@ge.ibf.cnr.it
Mario Nobile, CNR - Istituto di Biofisica, nobile@ge.ibf.cnr.it
For a long time astrocytes have been considered as passive elements of the brain, providing structural and
metabolic support to the neurons. But, during the last decade, this traditional point of view has rapidly changed.
Astrocytes are non excitable cells and their transient changes of intracellular calcium level provide them some form of
calcium excitability, analogous to the generation of action potentials in neurons. Recent findings have revealed that
astrocytes located near synapses respond to neurotransmitters (including glutamate, GABA, ATP etc.) with an elevation of
their intracellular calcium levels (Finkbeiner, 1993; Porter and McCarthy 1996; Porter and McCarthy 1997; Kang et al.,1998;
Wang et al., 2000; Nobile et al., 2003; Fellin and Carmignoto 2004; Perea and Araque, 2005; Zhang and Haydon, 2005; Koizumi
et al., 2005). Then, the elevation of the intracellular calcium in astrocytes mediates the release of glutamate and other
neuroactive substances that are capable of modulating the synaptic communication between neurons (Fellin and Carmignoto
2004; Perea and Araque, 2005; Zhang and Haydon, 2005; Koizumi et al., 2005).
This report investigates some of the above phenomena either experimentally or using a biophysical modeling approach.
The experiments were performed on cultured cortical astrocytes, in order to characterize their calcium response in the
presence of extracellular ATP. Then, a model of the calcium dynamics in astrocyte was built and used to reproduce the
corresponding experimental results. In particular it is shown that, in agreement with the experimental findings, the
ionotropic and metabotropic ATP receptors play a key role in shaping the calcium response of the astrocyte to ATP
stimulation. Moreover, still using a biophysical modelling, we analyse a minimal neural network model consisting of a
neuron (a pyramidal cell model) receiving modulator inputs from the astrocyte. The main motivation of this study is to
compare our results with those recently obtained by Nadkarni and Jung (2003, 2004). These authors in particular showed that
the model parameter, describing the IP3 production rate triggered by the neuron firing, is critical for the generation of
firing activity even in absence of external stimulation. The results obtained with our model are contrasting with these
findings, and an explanation of this discrepancy will be presented.
References:
[1]Fellin, T., Carmignoto, G., 2004. Neuron-to-astrocyte signalling in the brain represents a distinct
multifunctional unit. J. Physiol. 559.1, 3-15.
[2]Finkbeiner, S.M., 1993. Glia Calcium. Glia, 9, 83-104.
[3]Kang, J., Jiang, L., Goldman, S.A., Nedergaard, M., 1998. Astrocyte-mediated potentiation of inhibitory synaptic
transmission. Nature Neurosci., 1, 683–692.
[4]Koizumi, S., Fujishita, K., Inoue, K., 2005. Regulation of cell-t-cell communication mediated by astrocytic ATP
in the CNS. Purinergic Signalling, 1, 211-217.
[5]Nadkarni, S., Jung, P, 2003. Spontaneous oscillations of dressed neurons: a new mechanism for epilepsy? Phys.
Rev. Letters, 91, 268101(4).
[6]Nadkarni, S., Jung, P, 2004. Dressed neurons: modelling neural-glia interactions. Phys. Biol., 1, 35-41.
[7]Nobile, M., Monaldi, I., Alloiso, S., Cugnoli, C., Ferroni, S., 2003. ATP-induced, sustained signalling in
cultured rat cortical astrocytes: evidence for a non-capacitive, P2X7-like-mediated calcium entry. FEBS. Letters, 538,
71-76.
[8]Perea, G., Araque, A., 2005. Synaptic regulation of the astrocyte calcium signal. J. Neural Transm., 112, 127–135.
[9]Porter, J.T., McCarthy, K.D., 1996. Hippocampal astrocytes in situ respond to glutamate released from synaptic
terminals. J. Neurosci., 16, 5073-5081.
[10]Porter, J.T., McCarthy, K.D., 1997. Astrocytic neurotransmitter receptors in situ and in vivo. Prog. Neurobiol.,
51, 439-455.
[11]Wang, Z., Haydon, P.G., Yeung, E.S., 2000. Direct observation of calcium-independent intercellular ATP
signalling in astrocytes. Anal. Chem., 72, 2001–2007.
[12]Zhang, Q, Haydon, P. G., 2005. Roles for gliotransmission in the nervous system. J. Neural Transm. ,112, 121–125.
15:00 The multifractal fly: a system on the edge of chaos.
Roland Köberle, Inst. de Fisica - Sao Carlos, Univ. of Sao Paulo, rk@if.sc.usp.br
The optical system of flies lends itself to a thorough quantitative study of it's information transmitting
capabilities. An enormous amount of data can be acquired in a systematic and repeatable manner "in vivo".
We stimulate the visual system of the fly presenting a horizontally moving image to it's compound eyes. We record
from a particular neuron, situated four synapses behind the photoreceptors and which generates identical spikes in response
to a stimulus. All the information about the stimulus is contained in the sequence of spike-times. As everything in biology,
the system adapts to the different statistical properties of the stimulus. The sequence of spike-times can now be
used/analyzed by several methods: information theory, stimulus reconstruction from the spike-times etc. One of the aims,
probably the top one, is: given the stimulus s(t) for say, t<0, what is the probability P(spike|stimulus) of a spike
emission for t>0 ?. The is a probabilistic formulation, since a real biological system is always subject to noise.
15:40-16:30 Poster Session
16:30 Stationary Solutions of a Torque-Free Dual-Spin Spacecraft with an Axial Nutation Damper
Mário Ricci, INPE, mcr@dem.inpe.br
Gilberto Arantes Júnior, INPE
This work deals with nonlinear dynamics in the movement of the dual-spin spacecrafts. Spacecrafts with large rotors
and despun (oriented) platforms are called dual spinners. The interest in the spinning stability in dual-spin have been
grown after abnormalities observed due to structural imperfections and inherent model´s nonlinearities. Several
investigators have bem studied the attitude stability and behavior due to structural parametric changes but few works has
been focused instabilities due to model´s nonlinearities. The system under investigation consists of an external torque-free,
dual-spin, spacecraft with an axisymmetric rotor attached to an asymmetric platform that contains an axial nutation damper
(spring-mass-dashpot). The equations of motion for the system are obtained using Lagrange’s equations with dissipation. The
stationary solutions of the equations of motion were investigated besides showing some simulations of the system dynamics
for an internal sinusoidal rotor torque. Four equilibrium states were found. The spacecraft parameter configuration and
inertia ratios adopted here is similar to those expected in present communication satellites. The results show that The
stability configuration of the system may be determined completely with knowledge of the angular momentum and initial energy
of the system, allowing the equilibrium states to be reduced to a finite number of possible critical points.
16:50 Coarse grained variables for a deterministic excitable system
Jose Roberto Rios Leite, Universidade Federal de Pernambuco, rios@df.ufpe.br
José Roberto Rios Leite, Departamento de Física - Universidade Federal de Pernambuco - Brazil
Jhon Fredy Martinez Avila, Departamento de Física - Universidade Federal de Pernambuco - Brazil
Hugo L. D. de S. Cavalcante, Departamento de Física - Universidade Federal de Pernambuco – Brazil
We show how temporally coarse grained variables can be used to study Chaotic Low Frequency Fluctuations in diode
lasers with optical feedback. Experimental data series, obtained from the laser output power, are consistently confronted
with numerical data series, extracted from the integration of a single-mode model.
The coarse grained laser carrier population nearly follows the laser power, and so it is not a relevant variable for
the coarse grained system. Phase portraits were constructed with the laser power coarse grained variable and used to get
quantitative and qualitative system properties. A phenomenological, effective phase space [1], is established for the time
coarse grained variable, with two main fixed points: One point is a stable node. A second one is a nearby hyperbolic fixed
point. Its unstable manifold has a connexion with the stable manifold of the node. Instead of external noise we show how
the ultra fast pulsation of the system plays the role of fluctuation noise in making the coarse grained variable jumps from
the stable node to make a cycle trajectory along the hyperbolic connexion.The erratic power drop events are interpreted as
spikes in a deterministic excitable system [2]. We verify, numerical and experimentally, that the early stage of the drop
and the recovery, have exponential behavior in their time evolution. Then two time constants are measured and related to
igenvalues of the fixed points. The time constant for the fast drop is related to the inverse of the eigenvalue of the
unstable manifold of the hyperbolic point. The time constant of recovery is the inverse of the eigenvalue of the stable
manifold of the node [3].
[1] A. M. Yacomotti and M. C. Enguia and J. Aliaga and O. E. Martinez and G. B. Mindlin, Interspike Time
Distribution in Noise Driven Excitable Systems, Physical Review Letters, 83, 292, (1999).
[2] J. F. Martinez Avila and H. L. D. de S. Cavalcante and J. R. Rios Leite, Experimental Deterministic
Coherence Resonance, Physical Review Letters, 93, 144101, (2004).
[3] J. F. Martinez Avila and H. L. D. de S. Cavalcante and J. R. Rios Leite, Exponential Recovery of Low Frequency
Fluctuations in a Diode Laser with Optical Feedback, nlin.CD/0511046}, November, (2005).
17:10 Control and stabilization of the longitudinal dynamics of a storage-ring free-electron laser
De Ninno Giovanni, Sincrotrone Trieste, giovanni.deninno@elettra.trieste.it
G. De Ninno, Sincrotrone Trieste
The ultimate performance of a storage-ring free-electron laser depends on the possibility of simultaneously
controlling the coupled electron-beam and laser dynamics. In the ideal case, i.e. for a perfectly stable electron beam,
the laser evolution displays a "natural" Hopf bifurcation which is induced by a slight temporal laser-electron detuning.
When electron-beam instabilities come into play, the picture becomes more complicated and the laser intensity may show
stochastic and/or chaotic regimes. In this paper we review the experimental and theoretical work carried out in the last
few years in the aim of understanding, controlling and stabilizing the system dynamics.
17:50 Control of spatiotemporal systems with advection: theoretical and experimental results in pulsed lasers
Serge Bielawski, Lab. PhLAM, serge.bielawski@univ-lille1.fr
Control of systems exhibiting irregular behaviors in space and time remain challenging at the present time. As for
low-dimensional systems, two types of approaches can be used: (i) "invasive" control techniques, for which finite-size
parameter modifications are permanently needed, and (ii) "non-invasive" control techniques, for which parameter
modifications vanish, once the target state is reached. The latter strategies initiated by Ott, Grebogi, and Yorke (OGY)
are based on the stabilization of a preexisting state of the system.
In the case of low-dimensional systems, the non-invasive "OGY-like" approaches have been very often preferred, not
only because the needed parameter modifications are arbitrary small, but also because systematic rules (as opposed to
case-by-case trials) can be established.
Here, we show that in the case of spatio-temporal systems with advection, that the situation can be very different.
We propose a feedback method that is "invasive" from the mathematical point of view, thought needing parameter modifications
that are extremely small in practice (1e-8 in the experimental example presented here). We validate this feedback method
experimentally on a pulsed laser, that is erratic both in space and time (the space variable being the longitudinal
coordinate of the pulse). We analyze and interpret the results in the framework of the laser model. General rules for
stabilization are discussed
Wednesday, May 31, 2006
Wednesday Morning
08:00 Registration Desk Opens
08:30 Phase-transitions in granular non-equilibrium steady states
Mark D. Shattuck, City College of New York, The Benjamin Levich Institute, shattuc1@optonline.net
Equilibrium statistical mechanics is generally not applicable to systems with energy input and dissipation present,
and identifying relevant tools for understanding these far-from-equilibrium systems poses a serious challenge. Excited
granular materials or granular fluids have become a canonical system to explore such ideas since they are inherently
dissipative due to inter-particle frictional contacts and inelastic collisions. Granular materials also have far reaching
practical importance in a number of industries, but accumulated ad-hoc knowledge is often the only design method. An
important feature of granular fluids is that the driving and dissipation mechanisms can be made to balance such that a
Non-Equilibrium Steady-State (NESS) is achieved. We present strong experimental evidence for a NESS first-order phase
transition in a vibrated two-dimensional granular fluid. The phase transition between a gas and a crystal is characterized
by a discontinuous change in both density and temperature and exhibits rate dependent hysteresis. We compare and contrast
this type of transition with an equilibrium first-order phase transition and a hysteretic backward bifurcation in a
nonlinear pattern forming system.
09:10 Forces and Fluctuations in Granular Materials
Robert Behringer, Duke University, bob@phy.duke.edu
Trushant Majmudar, Duke University
Matthias Sperl, Duke University
Karen Daniels, NC State University
Junfei Geng, Duke University
Brian Utter, James Madison University
This work describes a series of experiments on dense granular materials. The goal is to understand the nature of
forces within granular materials, how they are transmitted and the nature of fluctuations. We are concerned with both
static systems of grains and also with systems that can deform and that ultimately can unjam and flow. We use several
different experimental approaches. In the first approach, we use photoelastic particles, which are birefringent under
stress. Using this type of particle, we have probed the nature of forces in sheared and compressed static systems, and
the way in which such systems respond to small local force perturbations (i.e. the force Green's function). By and large,
these experiments support an elastic picture for force transmission. By preparing states of photoelastic particles that
have been subject to pure shear or to isotropic compression, we have also shown that anisotropy has a significant influence
on the contact force distributions. We have explored the nature of jamming in photoelastic disk systems, where we find that
the contact number is discontinuous at the onset of jamming, and then varies as the square root of the distance in packing
fraction from the jamming value. When systems of photoelastic particles are subject to significant shear, they deform
plastically; ongoing work is probing the nature of plastic failure, and possible connections to Shear Transformation Zone
(STZ) theory, which is used to described plasticity in molecular systems. In experiments on sheared systems, we have
characterized diffusion, and also explored the applicability of STZ events. We find an equivalence between a measure of
STZ's proposed by Falk and Langer, and the diffusivity. In a different experimental approach, we have developed a 3D shear
experiment that permits shearing of an annular layer of spheres from above, and simultaneous vibration from below. This
allows us to probe the nature of jamming/unjamming. Surprisingly, the presence of vibration, which might heuristically be
associated with a thermalizing effect, leads to the crystallization of the sample.
09:50-10:20 Break
10:20 Searching chaos and coherent structures in the atmospheric turbulence above the Amazon forest
Fernando M. Ramos, LAC/INPE, fernando@lac.inpe.br
Andriana S. L. O. Campanharo, LAC/INPE
Elbert E. N. Macau, LAC/INPE
Reinaldo R. Rosa, LAC/INPE
Amazonia is one of the last great tropical forest domains, the largest hydrological system in the planet, and plays
an important role in the function of regional and global climates. Many aspects of this fragile and highly complex system
remain unclear for the scientific community. A subject of great relevance for understanding how the Amazon terrestrial
biosphere interacts with the atmosphere is the correct modeling of the turbulent exchange of heat, humidity, greenhouse
gases, and other scalars at the vegetation–air interface. Here we investigate the possible chaotic nature of the turbulence
of the atmospheric boundary layer above the forest. For this, we use fast-response (60 Hz) experimental temperature and wind
velocity data obtained during the wet-season campaign of the large-scale biosphere–atmosphere experiment in Amazonia
(known as the LBA project), carried out during the months of January–March 1999, in the southwestern part of the Brazilian
Amazonia. Our results show that, under certain circumstances, large coherent structures control turbulence dynamics at the
forest canopy. In this particular context, temperature data exhibit ramp-like patterns whose dynamical properties are
consistent with deterministic chaos, and support the existence of a low-dimensional chaotic attractor in the atmosphere,
with correlation dimension between 3 and 4, and the largest Lyapunov exponent slightly positive.
11:00-20:00 Experimental Session.
Thursday, June 1, 2006
Thursday Morning
08:00 Registration desk open
08:30 Dynamics, bifurcations and chaos in coupled lasers
Asa M Lindberg, Department of Physical Sciences, University of Helsinki, asa.lindberg@helsinki.fi
Thomas Fordell, Department of Physical Sciences, University of Helsinki
Simo Valling, Department of Physical Sciences, University of Helsinki
Due to the interplay between the available gain of the medium and the light during its lifetime in the laser cavity,
the output of most lasers varies regularly in time. In order to enrich this scenario, one possibility is to disturb the
laser oscillation by light from another laser. The exact nature of the dynamical states that this coupled laser can support
depends on the laser parameters. In this study, the focus is upon two different optically coupled lasers: an edge-emitting
semiconductor laser and a solid-state laser.
In the experiments, the output of the lasers were recorded both in the frequency domain through optical spectra and
in the time domain by recording intensity time-series. The recordings were analyzed with the aim to plot maps of dynamics in
the plane spanned by the control parameters frequency detuning between lasers and the amount of injected light. The
scenarios for the semiconductor laser include a small area of frequency locking, large islands of chaotic behavior embedded
in and mixed with different periodic doubling scenarios. The strength in the case with the solid-sate laser was the ability
to use the intensity time-series from which it was possible to directly construct maps of dynamics. Boundaries of different
dynamical regions could clearly be observed in the maps together with the recognization of different routes to locking for
positive and negative frequency detuning.
The coupled systems can be studied numerically using the same laser equations if only the appropriate parameters
are used. In case of the semiconductor laser, it was convenient to compute the largest Lyapunov exponents as a measure of
the stability of equilibria and for the amount of chaos in chaotic regimes and to map the periodic windows inside the
chaotic islands. The found boundaries of dynamical regions for the solid-state laser coincide with principal bifurcation
curves that were identified as Hopf, saddle-node, torus and period-doubling bifurcations. The amount of free parameters
were brought to a minimum in the modeling because most of the parameter values used had been determined from the
experiments.
References:
T. Fordell, and Å.M. Lindberg: Numerical stability maps of an optically injected semiconductor laser, Opt Commun,
242, 613-622 (2004)
S. Valling, T. Fordell, and Å.M. Lindberg: Maps of the dynamics of an optically injected solid state laser, Phys
Rev A, 72, 033810 (2005)
S.Valling, T. Fordell, and Å.M. Lindberg: Experimental and numerical time series of an optically injected solid
state laser, Opt Commun, 254, 282-289 (2005)
T.Fordell, S. Valling, and Å.M. Lindberg: Modulation and the linewidth enhancement factor of an optically pumped
Nd:YVO4 laser, Optics Letters, 30, 3036-3038, (2005)
09:10 Advection-induced spectro-temporal defects in a pulsed laser
Christophe Szwaj, Lab. PhLAM, christophe.szwaj@univ-lille1.fr
Spatio-temporal systems subjected to drift are known to exhibit hypersensitivity to noise, that can lead to turbulent behavior (in particular through convective instabilities). Here, we present a combined experimental/theoretical study of the first steps of the destabilisation process occuring when the drift velocity is increased.
The system is a pulsed laser (a free-electron laser), for which an optical pulse experiences round trips between two mirrors, and is amplified periodically by its interaction with the electron bunch of an accelerator. The internal structure of the pulses typically exhibits complex "turbulent" regimes [1] . A main advantage of this system is the possibility to record directly the erratic space-time evolutions, thanks to convenient time scales (picosecond order).
The evolution of the pulse shape versus time can be described by a one-dimensional convection-diffusion model with global saturation coupling. We show that the first step of the destabilization is associated with the appearance of spectrotemporal defects [2], recalling the Eckhaus-type phase slips. Finally we show that the main features of the instability are preserved in simple Ginzburg-Landau equations with advection.
References:
[1] F.X.Kartner, D.M. Zumbuhl, and N. Matuschek, Phys. Rev. Lett. 82, 4428 (1999)
[2] S. Bielawski et al., Phys. Rev. Lett. 95, 034801 (2005)
09:30 Attractor selection in lasers and electronic circuits
Riccardo Meucci, Istituto Nazionale di Ottica Applicata, ric@ino.it
Stefano Brugioni, Istituto Nazionale di Ottica Applicata
F. Salvadori, Dept. of Physics, University of Florence,
K. Al-Naimee, Dept. of Physics, College of Sciences, University of Baghdad,
B. K. Goswami, Laser and Plasma Technology Division, Bhabha, Atomic Research Centre, Mumbai 400085, India;
S. Boccaletti, CNR- Istituto Nazionale di Ottica Applicata
F. T. Arecchi, Dept. of Physics, University of Florence, Italy
By tuning a control parameter, a chaotic system can either display two attractors (generalized multistability) or
exhibit an interior crisis, whereby a chaotic attractor suddenly expands including the region of an unstable orbit (bursting
regime). Recently controlling multistability (bursting) has been experimentally proved in a modulated class B laser by
means of a feedback method [1]. This method relies on the knowledge of the frequency components of the two attractors in a
bistable regime or orbits competing in the same chaotic attractor near an interior crisis. The presented method can be
applied in different systems as in the epidemiological models like the SEIR considering its topological equivalence with
the modulated laser. Recent experimental and theoretical reports suggest that suitable modulation of some system parameters
(non feedback methods) are also appropriate in controlling multistability [2-3]. We show that in autonomous systems the
parameter-modulation concept is suitable to destroy the periodic/chaotic states, created in subcritical Hopf bifurcation,
bringing the system back to steady states. We investigated these effects on an analog circuit of the Lorenz model for
thermal fluid convection [4]. We choose the parameter values appropriately so that the circuit remains at the chaotic
attractor in the multistable regime. By applying a suitable modulation we observe that for every given modulation
frequency, the chaotic attractor is destroyed under boundary crisis. The threshold control amplitude depends on the control
frequency and on the location of the operating point in the bistable regime. After the boundary crisis, the system remains
at steady state even if the control is switched off, demonstrating controlled destruction of Lorenz's attractor. To demonstrate controlling multi-state intermittency, we introduce white noise (in the circuit parameters) of adequate strength so that the circuit exhibits hopping between chaotic and steady states.
Analogies with neurodynamics will be presented reporting some experimental results on the Fitz-Hugh Nagumo electronic
circuit and on synchronization between two lasers in a bursting regime [5].
[1] R. Meucci, E. Allaria, F. Salvadori, and F. T. Arecchi, Phys. Rev. Lett. 95, 184101 (2005).
[2] A. N. Pisarchik and B. K. Goswami, Phys. Rev. Lett. 84, 1423 (2000);
[3] B. K. Goswami and S. Basu, Phys. Rev. E 66, 026214 (2002);
[4] B. K. Goswami, R. Meucci, S. Brugioni, F. Salvadori and F. T. Arecchi. Control of generalized multistability and noise-induced multi-state intermittency, submitted.
[5] R. Meucci, F. Salvadori, F. T. Arecchi, K. Al-Naimee, and S. Boccaletti, submitted.
10:10-10:40 Break
10:40 Living cell motility
Oscar N. Mesquita, Universidade Federal de Minas Gerais, mesquita@fisica.ufmg.br
Motility of living cells is a complex process driven mainly by polymerization and depolymerization of actin
filaments (actin cytoskeleton) underneath the plasmatic membrane. The name motility refers to motion of the cell as a whole,
like in chemotaxis (cell motion along a concentration gradient), as well as to surface motion of the cell cytoskeleton
(ruffles and lamellipodia), responsible for many important cell functions. We will concentrate in this presentation, on
experiments performed on living macrophages (an important cell of the innate immune system), and how their motility
correlates with the cell function of phagocytosis, which is the process of ingestion and destruction of invader organisms.
By using our recently developed “defocusing microscopy” [1,2,3], we are able to study macrophage surface fluctuations, and
determine shape and velocity of ruffles as well as viscoelastic properties of the actin/membrane cortex. Image contrast
obtained with defocusing microscopy is proportional to the local curvature of the cell surface, allowing clear and
quantitative observation of cell surface dynamics. Ruffles and lamellipodia seem to originate as instabilities on
macrophage surfaces and their presence accelerates phagocytosis [3]. There are theoretical models (ratchet models) that
show how a polymerizing actin filament can exert force on the plasmatic membrane and cause motion [4,5]. Actin
polymerization can be triggered by a group of proteins, which diffuse in the plasmatic membrane. Recently, a theoretical
model was proposed, where coupling between motion of these membrane proteins and membrane curvature can lead to local actin
polymerization with surface instabilities and generation of ruffles and lamellipodia [6]. Our data seem to confirm some
aspects of these models. There are still unexplained experimental results, which will be discussed.
References:
[1] U. Agero, C.H. Monken, B.R.A. Neves, R.T. Gazzinelli, and O.N. Mesquita, Phys. Rev. E 67, 051904 (2003).
[2] U. Agero, L.G. Mesquita, C. Ropert, R.T. Gazzinelli, and O.N. Mesquita, Microsc. Res. Tech. 65, 159 (2004).
[3] J. Coelho Neto, U. Agero, D.C.P. Oliveira, R.T. Gazzinelli, and O.N. Mesquita, Exp. Cell Res. 303, 207 (2005).
[4] C.S. Peskin, G.M. Odell, and G. Oster, Biophys. J. 65, 316 (1993).
[5] A. Molginer and G. Oster, Biophys. J. 71, 3030 (1996).
[6] N. Gov and A. Gopinathan, Biophys. J. 90, 454 (2006).
11:20 Recurrence plots and Shannon entropy for identifying asynchronisms in non invasive mechanical ventilation
Letellier Christophe, CORIA - Université de Rouen, Christophe.Letellier@coria.fr
Rabarimanantsoa, CORIA - Université de Rouen
Achour, ADIR Association
Cuvelier, Hopital de Bois-Guillaume
Muir, Hopital de Bois-Guillaume
Recurrence plots were introduced by Eckmann, Kamphorst and Ruelle [1]. Few years later, a set of quantifiers was
introduced to convert a graphical representation (recurrence plots) into a statistical analysis of the dynamics underlying
the data [2]. Among the quantifiers, a so-called ``Shannon entropy'' was introduced but unfortunately, it decreases as the
chaotic regime is developed. Consequently, it was not a measure of the complexity as the usual Shannon entropy quantifies.
We thus propose a new definition of the Shannon entropy, still based on recurrence plots, which is found to be in agreement
with the usual meaning. In particular, the Shannon entropy is found to be correlated to the largest Lyapunov exponent and
can thus be used to estimate it. The Shannon entropy estimation is also compared with an estimation using a symbolic
dynamics [3].
Recurrence plots analysis is often used in biomedicine (see [4] for instance). Recurrence plots analysis as well as
a Shannon entropy estimation is then used to identify asynchronisms in non invasive mechanical ventilation. One of the most
important criterion for a successful assistance by non invasive ventilation is the comfort. Unfortunately, the comfort is
quite subjective to estimate (most of the time, estimated by using answers to some basic questions asked after each trial).
It is believed that the comfort is strongly related to the presence of asynchronisms but this is still not very clearly
evidenced. By using phase portraits, first-return maps, the rate of non triggered cycles (a breathing cycle with
inspiratory effort unable to trigger the ventilator), recurrence plots and Shannon entropy, we showed that one dynamical
property are relevant in the quality of the mechanical ventilation~: the phase coherence. Indeed, we showed that,
surprisingly, some patients with chronic respiratory diseases or healthy subjects can have a high rate of asynchronisms and
have a regular breathing rhythm. We showed that the phase coherence can be easily identified using a Shannon entropy.
Moreover, it is shown that the type of mask used (facial, nasal, with proximal leaks or not) affects the phase
synchronization which is well quantified by the Shannon entropy. Some quantifiers which can be estimated in real time are
therefore proposed to estimate the quality of the non invasive ventilation. They could be used by the chest physician to
quickly tune the ventilator.
References
[1] J.-P. Eckmann, S. Oliffson Kamphorst & D. Ruelle, Recurrence Plots of Dynamical Systems, Europhysics Letters,
4, 973-977, 1987. [2] L. L. Trulla, A. Giuliani, J. P. Zbilut & C. L. Webber Jr., Recurrence quantification analysis of the
logistic equation with transients, Physics Letters A, 223 (4), 255-260, 1996. [3 ] C. Letellier, Estimating the Shannon
entropy: recurrence plots versus symbolic dynamics, Physical Review Letters, submitted.
[4] N. Marwan, N.Wessel, U. Meyerfeldt, A. Schirdewan & J. Kurths, Recurrence-plot-based measures of complexity and
their application to heart-rate-variability data, Physical Review E,66, 026702, 2002.
11:40 WYDSIWYG (What You Don’t See Is What You Get)
Jaroslav Stark, Department of Mathematics, j.stark@imperial.ac.uk
Daniel Brewer, Institute of Child Health, UCL, London
Martino Barenco, Institute of Child Health, UCL, London
Daniela Tomescu, Institute of Child Health, UCL, London
Robin Callard, Institute of Child Health, UCL, London
Mike Hubank, Institute of Child Health, UCL, London
Modern high throughput and imaging experimental techniques are generating increasingly large and complex data sets.
Paradoxically, however, often key variables required to deduce biological functions cannot be measured, or at least not
easily. Thus for instance, DNA microarrays can measure transcript concentrations of a large number of genes simultaneously,
but give no direct information on the activity of the transcription factors which control their production. Often such
transcription factors are activated by phosphorylation and/or dimerization events which may be much more difficult to
quantify experimentally.
It turns out that quantitative mathematical models, apart from facilitating the analysis of complex networks of
interactions, may often also allow us to estimate such “hidden” variables and parameters. This is done by incorporating the
hidden variables into the model and then systematically varying them in order to obtain the best match between the model
output and the observed data. Informally, this is simply a more sophisticated version of linear regression which is used to
fit a straight line to a scatter plot of two variables. We shall present an ex-ample of such an approach to the analysis of
DNA microarray time series from a set of DNA damage response experiments. We shall show how given a small set of genes known
to be targets of p53, the key transcription factor controlling this response we can predict the unknown activity profile of
p53. This in turn can then be used to identify new p53 sensitive genes. We also show an extension of this approach which
yields a screening method which can reveal new transcription factor profiles, and identify the genes sensitive to these
12:20-14:00 Lunch
Thursday Afternoon
14:00 Experimental evidence of coherence resonance under colored noise in a chemical reaction
Irene Sendiña-Nadal, Universidad Rey Juan Carlos, irene.sendina@urjc.es
Valentina Beato, Technische Universität Berlin
Ingebogr Gerdes, Technische Universität Berlin
Harald Engel, Technische Universität Berlin
We study both experimentally and numerically the temporal coherence of noise-induced wave nucleations in excitable
media subjected to external fluctuations with finite correlation time. The experiments are performed with the
light-sensitive variant of the Belousov-Zhabotinsky BZ reaction forced by an exponentially correlated dichotomous
fluctuating illumination. We find that there exists an optimal correlation time for which nucleations coherence reaches a
maximum. The same behavior is obtained in numerical simulations with a stochastic Oregonator model, modified to describe
the light-sensitive BZ reaction.
14:40 Control of turbulence in catalytic CO oxidation reaction through heterogeneous pacemakers
Michael Stich, Centro de Astrobiología (CSIC/INTA), Instituto Nacional de Técnica Aeroespacial, stichm@inta.es
Carsten Beta, Max Planck Institute for Dynamics and Self-Organization, Göttingen
Christian Punckt, Fritz Haber Institute of the Max Planck Society, Berlin
Harm Hinrich Rotermund, Fritz Haber Institute of the Max Planck Society, Berlin
Control of spatiotemporal chaos is achieved in the catalytic CO oxidation on Pt(110) by localized modification of
the kinetic properties of this surface chemical reaction. In the experiment, a small temperature heterogeneity is created on
the surface by a focused laser beam. This heterogeneity constitutes a pacemaker and starts to emit target waves. These
waves slowly entrain the medium and suppress the spatiotemporal chaos that is present in the absence of control. This
experimental result is motivation for a systematic numerical study using the Krischer-Eiswirth-Ertl model for the CO
oxidation on Pt(110). We find control regimes with different properties and compare to other control schemes. New results
of systematic experiments for oscillatory, excitable, and turbulent regimes may be presented at the conference.
15:00 Forcing and Coupling of Spatiotemporal Patterns in Reaction-Diffusion Systems
Irving Epstein, Brandeis University, epstein@brandeis.edu
Igal Berenstein, Brandeis University
Milos Dolnik, Brandeis University
Lingfa Yang, Brandeis University
A number of reaction-diffusion systems that exhibit temporal periodicity when well-mixed also display spatio-temporal
pattern formation in a spatially distributed, unstirred configuration. These patterns can be traveling (e.g., spirals,
concentric circles, plane waves) or stationary (Turing structures). The behavior of forced and coupled temporal oscillators
has been well studied, but much less is known about the phenomenology of forced and coupled patterns. I shall present
experimental results and computer simulation on such processes in two chemical systems - the chlorine dioxide-iodine-malonic
acid (CDIMA) reaction and the Belousov-Zhabotinsky (BZ) reaction.
15:40-16:30 Poster Session
16:30 Announcements – poster winners, next meeting site
16:40 Central nervous tissue - an excitable medium
Wolfgang Hanke, University of Hohenheim 230, hanke@uni-hohenheim.de
Vera Maura Fernades de Lima, Univeristy of Sao Paulo, IPEN
Neuronal tissue and especially the central nervous system (CNS) is widely accepted to be an excitable medium.
Consequently, self-organisation, pattern formation and propagating excitation waves as typical events of excitable media
have been observed in such tissue. The properties of these phenomena do critically depend on the parameters of the system,
to which among others, chemicals, electromagnetic fields and gravity, as a permanently present stimulus under terrestrical
conditions belongs. The spreading depression (SD), a propagating excitation depression wave of neuronal activity, is the
best described of the above mentioned phenomena in the CNS. Especially in the retina as a true part of the CNS it can be
easily observed with optical techniques due to the high intrinsic optical Signal (IOS) of this tissue. This allows a two
dimensional observation of the complete process in time and makes the SD comparable to other two dimensional waves in
excitable media that can be investigated with the same methods.
In this presentation we will discuss basic properties of the retinal SD, especially velocity and onset of waves,
and demonstrate in some detail their dependency on changes in gravity.
17:00 The physics and neural control of birdsong
Gabriel Mindlin, University of Buenos Aires, gabo@df.uba.ar
Out of the 10,000 bird species known to exist, some 4,000 share with humans the need of a tutor in order to learn
their vocalizations. For this reason, birds have turned into a favourite animal system to study learning.
In this presentation I will review the main physical mechanisms involved int he process of generating song, as well
as experiments performed to validate the theories proposed.
We also will show that a diversity of experimentally recorded pressure patterns used to produce a variety of
different sounds can be understood as the solutions of a low dimensional nonlinear system. We propose a model that explains
these solutions, that involves the peripheral respiratory system and its governing neural nuclei. This shows that a
diversity of complex motor gestures can be the result of a simple neural nonlinear substrate.
Posters