Plenarvorträge - DPG-Tagungen

Dynamik und Statistische Physik Donnerstag
length can be assigned to the Lyapunov exponent of the corresponding
product of random transfer matrices. We consider the largest Lyapunov
exponent and the second generalized one, which are associated to different
average procedures. In case that single parameter scaling holds, these
two exponents coincide. We show analytically and numerically that at the
band center the largest exponent is not differentiable with respect to the
energy whereas the generalized exponent behaves regularly. This difference
corresponds to a different behavior of the typical and the average
conductivity, respectively.
DY 41 Symposium SYFT: Fat-Tail Distributions - Applications from Physics to Finance
Zeit: Donnerstag 09:30–13:00 Raum: H1
DY 41.1 Do 09:30 H1
Symposium SYFT: Fat-Tail Distributions - Applications from
Physics to Finance — • —
Details zum Programm sind unter SYFT zu finden.
DY 42 Long-Range Correlations and Multifractals
Zeit: Donnerstag 11:30–13:00 Raum: H2
DY 42.1 Do 11:30 H2
Effects of Membrane Potential Slope and Refractoriness
on Spike Synchronization — •Sven Goedeke 1 , Tom Tetzlaff
1,2 , Theo Geisel 1 , and Markus Diesmann 1,2 — 1 MPI für
Strömungsforschung und Institut für Nichtlineare Dynamik der
Universität Göttingen — 2 Neurobiologie und Biophysik, Biologie III,
Universität Freiburg
Neuron models based on the instantaneous spiking probability f(t) are
a convenient mathematical tool in the study of neural networks. Often f
is expressed in terms of a state variable, e.g. the membrane potential u(t).
Recent studies [1,2] have applied f(u)-models to spike synchronization
in feed-forward networks, emphasizing the dominant role of refractoriness.
We show that f(u) is inconsistent with integrate-and-fire dynamics.
An expression exhibiting the dependence of f on u and its temporal
derivative ˙u is derived. We use a bilinear f(u, ˙u) for an analytical investigation
of feed-forward synchronization. The system displays bistability
and quantitatively reproduces integrate-and-fire simulation results. The
˙u-dependence is a powerful mechanism of synchronization, taking effect
prior to refractoriness. The main function of refractoriness is normalizing
the number of spikes.
[1] Gewaltig M-O (2000) Aachen, Germany: Shaker
[2] Kistler WM & Gerstner W (2002) Neural Comput 14:987
DY 42.2 Do 11:45 H2
Controlling noise-induced motion by time-delayed feedback
— •Natalia Janson 1,2 , Alexander Balanov 1 , and Eckehard
Schöll 1 — 1 Institut für Theoretische Physik, Technische Universität
Berlin, 10623 Berlin, Germany — 2 Department of Mathematical Science,
Loughborough University, Leicestershire, LE11 3TU, UK
Time delayed feedback control that was earlier introduced by Pyragas
for the purpose of control of deterministic chaotic oscillations in nonlinear
dynamic systems, is exploited for controlling noise-induced motion.
Such noise-induced oscillations are widespread in systems near bifurcations,
and in excitable systems. Under appropriate choice of time delay,
one can either increase or decrease the regularity of motion. In an excitable
system, delayed feedback stabilizes the frequency of oscillations
against variation of noise strength. Also, for fixed noise intensity, the phenomenon
of entrainment of basic periods of oscillations by the delayed
feedback is found. This allows one to steer the timescales of noise-induced
motion by changing the time delay.
DY 42.3 Do 12:00 H2
Multifractal Detrended Fluctuation Analysis: Application to
Rainfall Records — •Diego Rybski 1,2 , Jan W. Kantelhardt 1 ,
Armin Bunde 1 , and Shlomo Havlin 2 — 1 Institut für Theoretische
Physik III, Justus-Liebig-Universität Giessen — 2 Department of Physics
and Minerva Center, Bar-Ilan University, Ramat-Gan, Israel
We use the Multifractal Detrended Fluctuation Analysis (MF-DFA)
[1] in order to characterize the fluctuations of long daily precipitation
records. We find that the records cannot be characterized by a single
multifractal model. For some records, the multifractal spectrum is described
by a modified binomial multifractal process, while for others a
bifractal model is most appropriate. For positive moments, the Lovejoy-
Schertzer ansatz provides a good fit to most records.
[1] J.W. Kantelhardt et al., Physica A 316, 87 (2002).
DY 42.4 Do 12:15 H2
Rückkopplung in chemischen Reaktionen — •Knud Zabrocki
und Steffen Trimper — Fachbereich Physik, Friedmann-Bach-Platz,
06108 Halle
Die klassischen Ratengleichungen in den diffusions- bzw. reaktionsgesteuerten
Regimes werden durch den Einschluss nicht-Markovscher
Terme erweitert. Solche Terme ergeben sich durch Ankopplungen an
zusätzliche Freiheitsgrade und stellen gewöhnlich konkurrierende Mechanismen
für die konventionellen instantanen nichtlinearen Kopplungen
dar. Wir untersuchen systematisch zwei verschiedene Fälle, die als
äußere bzw. innere Rückkopplungen charakterisiert werden. Während
im Fall externer Kopplung die Gedächtniseffekte durch deterministische
Funktionen hervorgerufen werden, sind es im Falle interner Kopplungen
selbst-organisierte Mechanismen. Relevante Realisierungen äußere
Rückkopplungen führen auf endliche Laufzeiteffekte, allmähliches oder
gedämpft periodisches Abschalten der Gedächtnisterme. Während in
diesem Fall die stationären Fixpunkte ungeändert bleiben, führt ein
interner Feedback zu neuen stabilen Fixpunkten, die das Phasendiagramm
entscheidend beeinflussen. Die Modelle werden durch den Einschluss
räumlich variierender Terme und inhomogene Anfangsbedingungen
zusätzlich verallgemeinert. Die analytischen Ergebnisse werden durch
numerische Untersuchungen gestützt. Mögliche Anwendungen auf Transportprozesse
in ungeordneten Medien und in der Biologie werden diskutiert.
Hauptvortrag DY 42.5 Do 12:30 H2
Long-range correlations in nature: On test-beds for climate
models, global warming and natural clustering of hazardous
floods — •Armin Bunde — Institut für Theoretische Physik III, Universität
Giessen, D-35392 Giessen
A large number of natural records (e.g. temperatures, river flows, heartbeat
intervals, internet traffic) exhibit long-term correlations characterized
by a power-law decay of the auto-correlation functions C(s) ∼ s −γ .
Typical values of γ are γ = 0.7 for continental temperature records,
γ = 0.4 for sea surface temperatures, γ = 0.3 for river flows, and γ = 0.4
for heartbeat intervals during REM-Sleep. Here we discuss applications
and consequences of the long-term correlations. We show that (i) the temperature
correlations can be used as an effective test-bed for climate models
and discuss (ii) the effect of long-term correlations on the estimation
of global warming. Finally we show explicitely that (iii) long-term correlations
represent a natural mechanism for clustering of extreme events,
by which both the observed clustering of hazardous floods in Europe as
well as (at least partially) the increase of floods in the past decades can
be explained.