Plenarvorträge - DPG-Tagungen

Dynamik und Statistische Physik Mittwoch
Phasensynchronisation von Herzschlag und Atmung [1] bei gesunden Probanden
in den verschiedenen Schlafstadien (Leicht-, Tief-, und REM-
Schlaf) unterscheiden. In der Schlafphase sind Störungen durch willentliche
Aktivitäten ausgeschaltet, welche die interessierenden intrinsischen
Schwankungen überdecken und somit eine Erkennung der Regulationsmechanismen
erschweren können. Bei der Phasensynchronisation wird
zu jedem Datensatz durch Hilbert-Transformation die zugehörige kom-
plexe Reihe gebildet und daraus die Phasenreihe berechnet. Man spricht
von Phasensynchronisation, wenn die Phasendifferenz zweier Reihen modulo
2 Pi statistisch zu einem Wert tendieren. Um den Einfluss einer
Zeitverzögerung zu ermitteln, analysieren wir die Phasensynchronisation
auch unter Verschiebung um verschiedene Zeitintervalle.
[1] C. Schäfer, M.G. Rosenblum, J. Kurths, H.H. Abel, Nature 392
(1998) 239.
DY 40 Lyapunov Instability of Many-Body Systems
Zeit: Donnerstag 09:30–11:30 Raum: H2
Hauptvortrag DY 40.1 Do 09:30 H2
Lyapunov instability of many-body systems — •Harald A.
Posch — Institute for Experimental Physics, University of Vienna,
Boltzmanngasse 5, A-1090 Wien, Austria
The evolution of classical many-body systems is highly unstable with
respect to (infinitesimal) perturbations of phase-space states. Such perturbations
grow, or shrink, exponentially with time. This is described by
a set of rate constants, the Lyapunov spectrum. We demonstrate that in
thermodynamic equilibrium the perturbations associated with the slowest
growth rates are coherently spread out in space, reminiscent of the
modes of fluctuating continuum mechanics. The “Lyapunov modes” display
a linear dispersion relation for small wave numbers, which allows to
construct the relevant part of the Lyapunov spectrum for systems close to
the thermodynamic limit. For dynamically- thermostated systems in stationary
nonequilibrium states the phase-space probability distribution
is a fractal set with a dimension smaller than the dimension of phase
space. This reduction in dimensionality is computed from the Lyapunov
spectrum. It is shown to be an extensive quantity and may, by far, exceed
the dimensions contributed by the thermostated degrees of freedom.
The fractal nature of phase space is a fingerprint of the second law of
thermodynamics and is the consequence of a constant rate of entropy
production.
DY 40.2 Do 10:00 H2
Static and Dynamic Correlations in Many-Particle Lyapunov
Vectors — •Günter Radons and Hongliu Yang — Institut für
Physik, Theoretische Physik I, Technische Universität Chemnitz, D-
09107 Chemnitz
We introduce static and dynamic correlation functions for the spatial
densities of Lyapunov vector fluctuations. They enable us to show,
for the first time, the existence of hydrodynamic Lyapunov modes in
chaotic many-particle sytems with soft core interactions. Our investigations
for Lennard-Jones fluids yield in addition to the Lyapunov exponent
- wave vector dispersion, the collective dynamic excitations, which dominate
a given Lyapunov vector. In contrast to the Lyapunov vectors, which
are time-dependent quantities, the Lyapunov vector correlation functions
represent global properties of the dynamical system. For purely translational
Lyapunov modes they reduce to the ordinary static and dynamic
structure factor of many-particle systems.
DY 40.3 Do 10:15 H2
Examination of Taylor hypothesis — •Stephan Barth, Stephan
Lueck, and Joachim Peinke — University of Oldenburg
In open flows Taylor-hypothesis is commonly used to investigate small
scale turbulence. The Taylor-hypothesis enables transfering temporal
measurements with a localized probe to spatial structures of turbulence.
Here we examine the validity of the Taylor-hypothesis in a turbulent
wake flow. By means of two X-hotwire-probes positioned transversal to
the mean flow and a LDA positioned in flow direction in front of one
hotwire-probe measurements are performed. The Taylor-hypothesis was
verified on the basis of the statistics of small scale turbulence including intermittency
effects. The statistics of the longitudinal and the transversal
velocity increments obtained by Taylor-hypothesis and by direct measurements
at two points in the flow are compared.
DY 40.4 Do 10:30 H2
Force driven Stokes-flow between parallel plates — •Marcin
Kostur 1 , P Talkner 1 , Z Guttenberg 2 , S Keller 3 , J.O Rädler 3 ,
and A Wixforth 1 — 1 Institut für Physik, Universität Augsburg 86135
Augsburg — 2 Advalytix AG, EugenSanger Strasse 53.0 85649 Brunnthal
— 3 Ludwig-Maximilians-Universität München, 80539 München
Mixing and moving of small amounts of fluid poses a severe prob-
lem caused by the inherently small Reynolds numbers in micro- and
nanoflows. Surface acoustic waves that can be excited by the application
of a radio frequency wave to an interdigital transducer on a piezoelectric
substrate generate a localized force field acting on a fluid placed above
the transducer. We present the analytical as well as numerical solution of
the 3-dimensional flow generated by a line force. The calculated velocity
field is compared with experimental results for a 0.2mm thick fluid layer
driven by surface acoustic waves.
DY 40.5 Do 10:45 H2
Diffusion on a solid surface: Anomalous is normal — •Sokolov
Igor 1 , Sancho Jose Maria 2 , Lindenberg Katja 3 , Lakasta Ana
Maria 4 , and Romero Aldo 5 — 1 Institut für Physik, Humboldt Universitæt
zu Berlin — 2 Facultat de Física, Universitat de Barcelona, Spain
— 3 Department of Chemistry and Biochemistry, University of California,
San Diego, USA — 4 Departament de Física Aplicada, Universitat
Politècnica de Catalunya, Barcelona, Spain — 5 Advanced Materials Department,
IPICyT, San Luis Potosí, Mexico
We discuss results of a numerical study of classical particles diffusing
on a solid surface. The particles’ motion is modeled by an underdamped
Langevin equation with additive thermal noise under delailed-balance
conditions. The particle-surface interaction is described by a periodic or
a random two dimensional potential. The model leads to a rich variety
of different transport regimes, some of which correspond to anomalous
diffusion such as has recently been observed in experiments and Monte
Carlo simulations. We show that this anomalous behavior is controlled
by the friction coefficient, and stress that it emerges naturally in a system
described by ordinary canonical Maxwell-Boltzmann statistics.
DY 40.6 Do 11:00 H2
Short-range type critical behavior in spite of long-range interactions:
phase transition of a Coulomb system on a lattice —
•Arnulf Möbius and Ulrich K. Rößler — Leibniz-Institut für
Festkörper- und Werkstoffforschung, D-01171 Dresden
The problem under which conditions Coulomb glasses exhibit genuine
phase transitions has been under controversial debate for a long time,see
e.g. [1,2]. In this context, the relation to the Ising model with short-range
interaction is of great interest. It would be very useful to know how replacing
its nearest-neighbor coupling by an “antiferromagnetic” long-range
Coulomb interaction modifies the critical behavior of a system without
static disorder.
One- to three-dimensional hypercubic lattices half-filled with localized
particles interacting via a Coulomb potential are investigated numerically.
Temperature dependences of specific heat, mean staggered occupation,
and of a generalized susceptibility indicate order-disorder phase
transitions in two- and three-dimensional systems. The critical properties,
clarified by finite-size scaling analysis, are consistent with those of
the Ising model with short-range interaction [3]. Thus, in spite of the
long-range interaction, the Coulomb system considered seems to belong
to the same universality class as the Ising model with short-range interaction.
This suggests that the lattice Coulomb-glass model might have
the same critical properties as the random-field short-range Ising model.
[1] E.R. Grannan, C.C. Yu, Phys. Rev. Lett. 71, 3335 (1993).
[2] T. Vojta, M. Schreiber, Phys. Rev. Lett. 73, 2933 (1994).
[3] A. Möbius and U.K. Rößler, cond-mat/0309001.
DY 40.7 Do 11:15 H2
Anomalous behavior of the localization length in onedimensional
Anderson localization. — •Rüdiger Zillmer —
Institut für Physik, Universität Potsdam
A common example of exponential localization of the wavefunction
in disordered systems is given by the Anderson model. The localization