Plenarvorträge - DPG-Tagungen

Dynamik und Statistische Physik Donnerstag
quantities, dissipation and of boundary conditions is elaborated. The
questions are investigated for standard maps and circle maps with different
types of couplings. We find, for instance, that diffusive couplings do
not support hydrodynamic Lyapunov modes. In contrast, for force-like
interactions between maps such modes can be found.
DY 46.27 Do 16:00 Poster D
The OFC earthquake model in d = 1 dimension — •Felix Wissel
and Barbara Drossel — Institut für Festkörperphysik TU-Darmstadt
Hochschulstrasse 6 64285 Darmstadt
We present analytical and numerical results for the one-dimensional
version of the earthquake model by Olami, Feder and Christensen. In the
analytical part, we prove that trajectories in state space approach each
other when they have the same toppling sequence. This implies that the
dynamics of the model cannot show chaos. In the numerical part, we
study the transition time into the stationary state as function of the system
size N and the coupling parameter α, and the statistical properties
of the stationary state.
DY 46.28 Do 16:00 Poster D
Magnetic Billiards as Hamiltonian Ratchets — •Manamohan
Prusty and Holger Schanz — Max-Planck Institut für Strömungsforschung
und Institut für Nichtlineare Dynamik der Universität
Göttingen, Bunsenstr. 10, 37073 Göttingen
Hamiltonian ratchets are periodic systems which show directed and
ballistic transport due to the presence of a mixed regular and chaotic
phase space and a mechanism breaking time-reversal symmetry. We show
that certain billiard chains can be a paradigm for this type of behaviour.
A magnetic field perpendicular to the billiard plane separates in a suitable
geometry regularly skipping trajectories from chaotic ones. Both
sets of trajectories transport ballistically in opposite directions. We show
how one can apply a classical sum rule for ratchet transport to predict
the chaotic transport velocity analytically and confirm the result by numerical
simulations. We study also the quantized versions of the billiard
ratchets and discuss their spectral properties.
[1] H. Schanz et al., Phys. Rev. Lett. 87(01)070601.
DY 46.29 Do 16:00 Poster D
Traveling waves in a reaction-diffusion system under periodic
forcing — •E. P. Zemskov 1 , K. Kassner 1 , and S. C. Mueller 2
— 1 Institut fuer Theoretische Physik, Otto-von-Guericke-Universitaet,
Universitaetsplatz 2, 39106 Magdeburg — 2 Institut fuer Experimentelle
Physik, Otto-von-Guericke-Universitaet, Universitaetsplatz 2, 39106
Magdeburg
A one-component reaction-diffusion system under external force is considered.
The simplest case of a periodic forcing of cosine type is chosen.
Exact analytical solutions for the two basic types of traveling waves,
fronts and pulses, are obtained in the case of a piecewise linear approximation
of the non-linear reaction term. Velocity equations are derived
from the matching conditions. Restrictions that arise during the derivation
of the pulse velocity equations are stated and their origin is explained.
It is found that in the presence of nonconstant forcing there
exists a set of wave solutions with different phases (matching point coordinates).
The general characteristic feature is that nonmoving waves
become movable under forcing. However, for specific choices of forcing
parameters, the traveling waves are pinned (stopped). The pinning conditions
are obtained and discussed. It is found that in the case of periodic
forcing there are infinite sets of the pinning positions. The phase portraits
of specific types of solutions are shown and briefly discussed.
References
E. P. Zemskov, K. Kassner, S. C. Mueller, Eur. Phys. J. B 34, 285
(2003).
DY 46.30 Do 16:00 Poster D
Dynamics of colloidal particles in a toroidal optical trap —
•Michael Reichert and Holger Stark — Universität Konstanz,
Fachbereich Physik, D-78457 Konstanz, Germany
A theoretical study of the collective non-Brownian motions of colloidal
particles circulating in a toroidal trap is presented. We consider equalsized
spheres in the regime of low Reynolds numbers whose interactions
are solely of hydrodynamic origin. The concrete physical situation we
have in mind are optical vortices, i.e., focussed helical light modes carrying
an orbital angular momentum [1]. We mimick this in our simulations
by applying a tangential driving force and a harmonic radial trap force
on each particle.
The orbital velocities of the circulating particles depend on the particle
number and the ring radius. We analyze them for different arrangements,
e.g., regular symmetric or random configurations. It turns out that the
random configurations lead effectively to a higher velocity compared to
the regular arrangements due to “drafting” effects.
Furthermore, we study the time-dependent dynamics of the random
configurations. The simulations show that, after an irregular transient
regime, the system tends towards a periodic dynamic state of oscillating
particle distances. During this synchronisation process, the viscous drag
is lowered.
[1] J. E. Curtis, D. G. Grier, Phys. Rev. Lett. 90, 133901 (2003).
DY 46.31 Do 16:00 Poster D
Dissipative Solitonen-Moleküle in Reaktions-Diffusions-
Systemen — •A. W. Liehr, M. C. Röttger und H.-G. Purwins
— Westfälische Wilhelms-Universität Münster, Institut für Angewandte
Physik, Corrensstr. 2/4, 48149 Münster
Dissipative Solitonen sind großamplitudige lokalisierte Strukturen mit
ausgeprägten Teilcheneigenschaften, die in diesem Beitrag anhand eines
dreikomponentigen Reaktions-Diffusions-Systems untersucht werden.
In der Nähe der Drift-Bifurkation kann die Dynamik und Wechselwirkung
der dissipativen Solitonen mittels einen Teilchenansatzes durch
Ordnungsparametergleichungen beschrieben werden, wobei als relevante
Größen die Positionen und die Propagatormodenamplituden der dissipativen
Solitonen erfasst werden [1]. Ausgehend von dieser reduzierten
Dynamik diskutieren wir die Eigenschaften gebundener Zustände dissipativer
Solitonen, sogenannte dissipative Solitonen-Moleküle, wobei sowohl
dynamische Eigenschaften starrer Moleküle [2,3], als auch innere
Freiheitsgrade größerer Moleküle behandelt werden.
[1] Bode, M. et al.: Interaction of dissipative solitons: particle-like behaviour
of localized structures in a three-component reaction-diffusion system. Physica
D 161, 2002, S. 45ff.
[2] Moskalenko, A. S. et al.: Rotational bifurcation of localized dissipative
structures. Europhysics Letters 63, 2003, S. 361ff.
[3] Liehr, A. W. et al.: Transition from stationary to rotating bound states of
dissipative solitons. In: E. Krause (Hrsg.), W. Jäger (Hrsg.), M. Resch (Hrsg.):
High Performance Computing in Science and Engineering ’03, Springer 2003,
S. 225ff.
DY 46.32 Do 16:00 Poster D
Universal behavior in complex front systems — •Andreas
Amann, Andreas Wacker, and Eckehard Schöll — Institut für
Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse
36, D–10623 Berlin
We show that the bifurcation scenario in a high-dimensional system
with interacting fronts can be related to the universal U-sequence which
is known from the symbolic analysis of iterated one-dimensional maps.
This connection is corroborated for a model of a semiconductor superlattice
[1], which describes the complex dynamics of electron accumulation
and depletion fronts. By a suitable Poincaré section we reduce the dynamics
to a low dimensional iterated map, for which in the most elementary
case the bifurcation points can be determined analytically.
[1] A. Amann, K. Peters, U. Parlitz, A. Wacker, E. Schöll
Phys. Rev. Lett. 91, 066601 (2003).
DY 46.33 Do 16:00 Poster D
The effect of long-term correlations on clustering of extreme
events — •Jan F. Eichner 1 , Armin Bunde 1 , Jan W. Kantelhardt
1 , and Shlomo Havlin 2 — 1 Institut für Theoretische Physik
III, Justus-Liebig-Universität, Giessen, Germany — 2 Dept. of Physics
and Minerva Center, Bar-Ilan University, Ramat-Gan, Israel
Long-term correlations, indicated by a power-law decay of the autocorrelation
function C(s) ∼ s −γ , appear in many natural records (e.g.
temperatures, river flows, and heartbeat intervals). In uncorrelated data
the return intervals r between events above a certain threshold q are
uncorrelated and follow the Poissonian statistics. We show that in the
presence of long-term correlations, the return intervals are also correlated
with the same correlation exponent γ, and follow a stretched exponential
distribution. As a consequence the extreme events show a tendency of
clustering. We give many examples of observational and reconstructed
data where this behavior is observed. The long-term correlations may
present a natural mechanism for the observed clustering of hazardous
floods between 1300 and 2000.