933 research outputs found
Critical properties of phase transitions in lattices of coupled logistic maps
We numerically demonstrate that collective bifurcations in two-dimensional
lattices of locally coupled logistic maps share most of the defining features
of equilibrium second-order phase transitions. Our simulations suggest that
these transitions between distinct collective dynamical regimes belong to the
universality class of Miller and Huse model with synchronous update
Large scale flow around turbulent spots
Numerical simulations of a model of plane Couette flow focusing on its
in-plane spatio-temporal properties are used to study the dynamics of turbulent
spots.Comment: 16 pages, 6 figure
Grain boundary dynamics in stripe phases of non potential systems
We describe numerical solutions of two non potential models of pattern
formation in nonequilibrium systems to address the motion and decay of grain
boundaries separating domains of stripe configurations of different
orientations. We first address wavenumber selection because of the boundary,
and possible decay modes when the periodicity of the stripe phases is different
from the selected wavenumber for a stationary boundary. We discuss several
decay modes including long wavelength undulations of the moving boundary as
well as the formation of localized defects and their subsequent motion. We find
three different regimes as a function of the distance to the stripe phase
threshold and initial wavenumber, and then correlate these findings with domain
morphology during domain coarsening in a large aspect ratio configuration.Comment: 8 pages, 8 figure
Lyapunov analysis captures the collective dynamics of large chaotic systems
We show, using generic globally-coupled systems, that the collective dynamics
of large chaotic systems is encoded in their Lyapunov spectra: most modes are
typically localized on a few degrees of freedom, but some are delocalized,
acting collectively on the trajectory. For globally-coupled maps, we show
moreover a quantitative correspondence between the collective modes and some of
the so-called Perron-Frobenius dynamics. Our results imply that the
conventional definition of extensivity must be changed as soon as collective
dynamics sets in.Comment: 4 pages, 4 figures; small changes, mostly stylistic, made in v
On the decay of turbulence in plane Couette flow
The decay of turbulent and laminar oblique bands in the lower transitional
range of plane Couette flow is studied by means of direct numerical simulations
of the Navier--Stokes equations. We consider systems that are extended enough
for several bands to exist, thanks to mild wall-normal under-resolution
considered as a consistent and well-validated modelling strategy. We point out
a two-stage process involving the rupture of a band followed by a slow
regression of the fragments left. Previous approaches to turbulence decay in
wall-bounded flows making use of the chaotic transient paradigm are
reinterpreted within a spatiotemporal perspective in terms of large deviations
of an underlying stochastic process.Comment: ETC13 Conference Proceedings, 6 pages, 5 figure
Orientational instabilities in nematics with weak anchoring under combined action of steady flow and external fields
We study the homogeneous and the spatially periodic instabilities in a
nematic liquid crystal layer subjected to steady plane {\em Couette} or {\em
Poiseuille} flow. The initial director orientation is perpendicular to the flow
plane. Weak anchoring at the confining plates and the influence of the external
{\em electric} and/or {\em magnetic} field are taken into account. Approximate
expressions for the critical shear rate are presented and compared with
semi-analytical solutions in case of Couette flow and numerical solutions of
the full set of nematodynamic equations for Poiseuille flow. In particular the
dependence of the type of instability and the threshold on the azimuthal and
the polar anchoring strength and external fields is analysed.Comment: 12 pages, 6 figure
On the degenerated soft-mode instability
We consider instabilities of a single mode with finite wavenumber in
inversion symmetric spatially one dimensional systems, where the character of
the bifurcation changes from sub- to supercritical behaviour. Starting from a
general equation of motion the full amplitude equation is derived
systematically and formulas for the dependence of the coefficients on the
system parameters are obtained. We emphasise the importance of nonlinear
derivative terms in the amplitude equation for the behaviour in the vicinity of
the bifurcation point. Especially the numerical values of the corresponding
coefficients determine the region of coexistence between the stable trivial
solution and stable spatially periodic patterns. Our approach clearly shows
that similar considerations fail for the case of oscillatory instabilities.Comment: 16 pages, uses iop style files, manuscript also available at
ftp://athene.fkp.physik.th-darmstadt.de/pub/publications/wolfram/jpa_97/ or
at http://athene.fkp.physik.th-darmstadt.de/public/wolfram_publ.html. J.
Phys. A in pres
Ergodicity Breaking in a Deterministic Dynamical System
The concept of weak ergodicity breaking is defined and studied in the context
of deterministic dynamics. We show that weak ergodicity breaking describes a
weakly chaotic dynamical system: a nonlinear map which generates subdiffusion
deterministically. In the non-ergodic phase non-trivial distribution of the
fraction of occupation times is obtained. The visitation fraction remains
uniform even in the non-ergodic phase. In this sense the non-ergodicity is
quantified, leading to a statistical mechanical description of the system even
though it is not ergodic.Comment: 11 pages, 4 figure
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