Plenarvorträge - DPG-Tagungen

Dynamik und Statistische Physik Montag
DY 14.3 Mo 15:00 H2
On a Fokker-Planck perspective of stochastic systems with delay
— •Till Frank — Institute for Theoretical Physics, University of
Münster,Wilhelm-Klemm-Str. 9, 48149 Münster, Germany
We will describe non-Markov processes defined by stochastic delay
differential equations from the perspective of Fokker-Planck equations.
First, we will derive a multivariate Fokker-Planck equation for stochastic
processes with delay. Second, it will be shown how to derive the delay
Fokker-Planck equation proposed by Guillouzic et. al. from this multivariate
Fokker-Planck equation. Third, we will derive the exact stationary
solution of a linear stochastic delay equation. Finally, we will briefly
address the issue of data analysis for stochastic delay systems. (S. Guillouzic
et al., Phys. Rev. E 59 (1999) 3970; T.D. Frank and P.J. Beek,
PRE 64 (2001) 021917; T.D. Frank, PRE 66 (2002) 011914; T.D. Frank
et al. PRE 68 (2003) 021912)
DY 14.4 Mo 15:15 H2
Path Integral Solutions for Continuous Time Random Walks
— •Adrian Baule — Institut für theoretische Physik, Westfälische
Wilhelms-Universität, 48149 Münster
Continuous time random walks are successful in modelling the stochastic
process underlying the velocity statistics of turbulence in a lagrangian
framework. Recent experimental results motivate the investigation of two
point probability density functions of the velocity increments. The knowledge
of the joint probability distributions is required for definitely assessing
the stochastic process of lagrangian motions. A path integral formulation
of continuous time random walks is introduced and solutions are
presented.
DY 14.5 Mo 15:30 H2
Probabilistic Description of Traffic Flow — •Reinhard
Mahnke 1 , Jevgenijs Kaupuˇzs 2 , and Ihor Lubashevsky 3 — 1 FB
Physik, Univ. Rostock, D–18051 Rostock — 2 Univ. Latvia, LV–1459
Riga, Latvia — 3 Physics Inst., Russian Acad. Sc., Moscow, Russia
A stochastic description of traffic flow, called probabilistic traffic flow
theory, is developed. The general master equation is applied to relatively
simple models to describe the formation and dissolution of traffic congestions.
Our approach is mainly based on spatially homogeneous systems
like periodically closed circular rings without on– and off–ramps. We consider
a stochastic one–step process of growth or shrinkage of a car cluster
(jam). As generalization we discuss the coexistence of several car clusters
of different sizes. The basic problem is to find a physically motivated
ansatz for the transition rates of the attachment and detachment of individual
cars to a car cluster consistent with the empirical observations
in real traffic. The emphasis is put on the analogy with first–order phase
transitions and nucleation phenomena in physical systems like supersaturated
vapour. The results are summarized in the flux–density relation,
the so–called fundamental diagram of traffic flow, and compared with
empirical data. Different regimes of traffic flow are discussed: free flow,
congested mode as stop–and–go regime, and heavy viscous traffic. The
traffic breakdown is studied based on the master equation as well as
the Fokker–Planck approximation to calculate mean first passage times
or escape rates. In conclusion, the calculated flux–density relation and
characteristic breakdown times coincide with empirical data measured
on highways.
DY 14.6 Mo 15:45 H2
The Totally Asymmetric Exclusion Process with Langmuir Kinetics
— •Thomas Franosch, Andrea Parmeggiani, and Erwin
Frey — Hahn-Meitner Institut
We discuss a new class of driven lattice gases obtained by coupling
the one-dimensional totally asymmetric exclusion process to Langmuir
kinetics. In the limit where these dynamics compete, the resulting nonconserved
flow of particles on the lattice leads to stationary regimes for
large but finite systems. We observe unexpected properties such as localized
boundaries (domain walls) that separate coexisting regions of
low and high density of particles (phase coexistence). We rationalize the
findings for the average density and current profiles obtained from simulations
within a mean-field approach in the continuum limit. The ensuing
analytic solution is expressed in terms of Lambert W-functions. It allows
to fully describe the phase diagram and to extract unusual mean-field
exponents that characterize the critical properties of the domain wall.
DY 14.7 Mo 16:00 H2
Lattice models for movements of molecular motors — •Stefan
Klumpp and Reinhard Lipowsky — Max-Planck-Institut für Kolloidund
Grenzflächenforschung, 14424 Potsdam
Movements of molecular motors which bind to and unbind from cytoskeletal
filaments can be studied using lattice models. Motors bound
to filaments perform biased random walks, while unbound motors perform
symmetric random walks. Motor–motor interactions such as mutual
exclusion from binding sites of the filaments are easily incorporated into
these models, which then represent new variants of driven lattice gas
models or exclusion processes, where the driving is localized to the filaments.
These models exhibit stationary states characterized by traffic jams
and by the coexistence of a crowded region with a low density region
[1] and boundary-induced phase transitions related to those of the onedimensional
asymmetric simple exclusion process [2].
[1] R. Lipowsky, S. Klumpp, and T. M. Nieuwenhuizen, Phys. Rev. Lett.
87, 108101 (2001).
[2] S. Klumpp and R. Lipowsky, J. Stat. Phys. 113, 233 (2003).
DY 14.8 Mo 16:15 H2
Noise induced oscillations in resonant tunneling structures —
•Grischa Stegemann and Eckehard Schöll — Institut für Theoretische
Physik, Technische Universität Berlin, 10623 Berlin, Germany
The presence of noise can strongly affect the behaviour of (deterministic)
dynamical systems. In particular we study noise induced current oscillations
in the double barrier resonant tunneling diode using a reactiondiffusion
model. Oscillating spatio-temporal patterns corresponding to
breathing current filaments may be induced in a regime where the deterministic
system does not exhibit self-sustained oscillations.
DY 14.9 Mo 16:30 H2
Consequences of coarse grained Vlasov equations — •K.
Morawetz 1,2 and R. Walke 3 — 1 Institute of Physics, Chemnitz
University of Technology, 09107 Chemnitz, Germany — 2 Max Planck
Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187
Dresden, Germany — 3 Max-Planck-Institute for demographic research,
Rostock, Germany
The Vlasov equation is analyzed for coarse grained distributions resembling
a finite width of test-particles as used in numerical implementations.
It is shown that this coarse grained distribution obeys a kinetic equation
similar to the Vlasov equation, but with additional terms. These terms
give rise to entropy production indicating dissipative features due to a
nonlinear mode coupling The interchange of coarse graining and dynamical
evolution is discussed with the help of an exactly solvable model for
the selfconsistent Vlasov equation and practical consequences are worked
out. The condition for approaching a stationary solution is derived. Observable
consequences of this coarse graining are: (i) spatial correlations
in observables, (ii) too large radii of clusters or nuclei in self-consistent
Thomas-Fermi treatments, (iii) a structure term in the response function
resembling vertex correction correlations or internal structure effects and
(iv) a modified centroid energy and higher damping width of collective
modes.
[1] K. Morawetz, R. Walke, Physica A 330/3-4 (2003) 475–501