176 research outputs found
Disordered Regimes of the one-dimensional complex Ginzburg-Landau equation
I review recent work on the ``phase diagram'' of the one-dimensional complex
Ginzburg-Landau equation for system sizes at which chaos is extensive.
Particular attention is paid to a detailed description of the spatiotemporally
disordered regimes encountered. The nature of the transition lines separating
these phases is discussed, and preliminary results are presented which aim at
evaluating the phase diagram in the infinite-size, infinite-time, thermodynamic
limit.Comment: 14 pages, LaTeX, 9 figures available by anonymous ftp to
amoco.saclay.cea.fr in directory pub/chate, or by requesting them to
[email protected]
General framework of the non-perturbative renormalization group for non-equilibrium steady states
This paper is devoted to presenting in detail the non-perturbative
renormalization group (NPRG) formalism to investigate out-of-equilibrium
systems and critical dynamics in statistical physics. The general NPRG
framework for studying non-equilibrium steady states in stochastic models is
expounded and fundamental technicalities are stressed, mainly regarding the
role of causality and of Ito's discretization. We analyze the consequences of
Ito's prescription in the NPRG framework and eventually provide an adequate
regularization to encode them automatically. Besides, we show how to build a
supersymmetric NPRG formalism with emphasis on time-reversal symmetric
problems, whose supersymmetric structure allows for a particularly simple
implementation of NPRG in which causality issues are transparent. We illustrate
the two approaches on the example of Model A within the derivative expansion
approximation at order two, and check that they yield identical results.Comment: 28 pages, 1 figure, minor corrections prior to publicatio
Langevin equations for reaction-diffusion processes
For reaction-diffusion processes with at most bimolecular reactants, we
derive well-behaved, numerically tractable, exact Langevin equations that
govern a stochastic variable related to the response field in field theory.
Using duality relations, we show how the particle number and other quantities
of interest can be computed. Our work clarifies long-standing conceptual issues
encountered in field-theoretical approaches and paves the way for systematic
numerical and theoretical analyses of reaction-diffusion problems.Comment: 5 pages + 6 pages supplemental materia
Absorbing states and elastic interfaces in random media: two equivalent descriptions of self-organized criticality
We elucidate a long-standing puzzle about the non-equilibrium universality
classes describing self-organized criticality in sandpile models. We show that
depinning transitions of linear interfaces in random media and absorbing phase
transitions (with a conserved non-diffusive field) are two equivalent languages
to describe sandpile criticality. This is so despite the fact that local
roughening properties can be radically different in the two pictures, as
explained here. Experimental implications of our work as well as promising
paths for future theoretical investigations are also discussed.Comment: 4 pages. 2 Figure
Characterizing dynamics with covariant Lyapunov vectors
A general method to determine covariant Lyapunov vectors in both discrete-
and continuous-time dynamical systems is introduced. This allows to address
fundamental questions such as the degree of hyperbolicity, which can be
quantified in terms of the transversality of these intrinsic vectors. For
spatially extended systems, the covariant Lyapunov vectors have localization
properties and spatial Fourier spectra qualitatively different from those
composing the orthonormalized basis obtained in the standard procedure used to
calculate the Lyapunov exponents.Comment: 4 pages, 3 figures, submitted to Physical Review letter
To synchronize or not to synchronize, that is the question: finite-size scaling and fluctuation effects in the Kuramoto model
The entrainment transition of coupled random frequency oscillators presents a
long-standing problem in nonlinear physics. The onset of entrainment in
populations of large but finite size exhibits strong sensitivity to
fluctuations in the oscillator density at the synchronizing frequency. This is
the source for the unusual values assumed by the correlation size exponent
. Locally coupled oscillators on a -dimensional lattice exhibit two
types of frequency entrainment: symmetry-breaking at , and aggregation
of compact synchronized domains in three and four dimensions. Various critical
properties of the transition are well captured by finite-size scaling relations
with simple yet unconventional exponent values.Comment: 9 pages, 1 figure, to appear in a special issue of JSTAT dedicated to
Statphys2
Vortex Glass and Vortex Liquid in Oscillatory Media
We study the disordered, multi-spiral solutions of two-dimensional
homogeneous oscillatory media for parameter values at which the single
spiral/vortex solution is fully stable. In the framework of the complex
Ginzburg-Landau (CGLE) equation, we show that these states, heretofore believed
to be static, actually evolve on ultra-slow timescales. This is achieved via a
reduction of the CGLE to the evolution of the sole vortex position and phase
coordinates. This true defect-mediated turbulence occurs in two distinct
phases, a vortex liquid characterized by normal diffusion of individual
spirals, and a slowly relaxing, intermittent, ``vortex glass''.Comment: 4 pages, 2 figures, submitted to Physical Review Letter
Long-Range Ordering of Vibrated Polar Disks
Vibrated polar disks have been used experimentally to investigate collective
motion of driven particles, where fully-ordered asymptotic regimes could not be
reached. Here we present a model reproducing quantitatively the single, binary
and collective properties of this granular system. Using system sizes not
accessible in the laboratory, we show in silico that true long-range order is
possible in the experimental system. Exploring the model's parameter space, we
find a phase diagram qualitatively different from that of dilute or point-like
particle systems.Comment: 5 pages, 4 figure
Synchronization of Coupled Systems with Spatiotemporal Chaos
We argue that the synchronization transition of stochastically coupled
cellular automata, discovered recently by L.G. Morelli {\it et al.} (Phys. Rev.
{\bf 58 E}, R8 (1998)), is generically in the directed percolation universality
class. In particular, this holds numerically for the specific example studied
by these authors, in contrast to their claim. For real-valued systems with
spatiotemporal chaos such as coupled map lattices, we claim that the
synchronization transition is generically in the universality class of the
Kardar-Parisi-Zhang equation with a nonlinear growth limiting term.Comment: 4 pages, including 3 figures; submitted to Phys. Rev.
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