224 research outputs found
Quantitative Phase Diagrams of Branching and Annihilating Random Walks
We demonstrate the full power of nonperturbative renormalisation group
methods for nonequilibrium situations by calculating the quantitative phase
diagrams of simple branching and annihilating random walks and checking these
results against careful numerical simulations. Specifically, we show, for the
2A->0, A -> 2A case, that an absorbing phase transition exists in dimensions
d=1 to 6, and argue that mean field theory is restored not in d=3, as suggested
by previous analyses, but only in the limit d -> .Comment: 4 pages, 3 figures, published version (some typos corrected
Spatiotemporal perspective on the decay of turbulence in wall-bounded flows
Using a reduced model focusing on the in-plane dependence of plane Couette
flow, it is shown that the turbulent-to-laminar relaxation process can be
understood as a nucleation problem similar to that occurring at a thermodynamic
first-order phase transition. The approach, apt to deal with the large
extension of the system considered, challenges the current interpretation in
terms of chaotic transients typical of temporal chaos. The study of the
distribution of the sizes of laminar domains embedded in turbulent flow proves
that an abrupt transition from sustained spatiotemporal chaos to laminar flow
can take place at some given value of the Reynolds number R_{low}, whether or
not the local chaos lifetime, as envisioned within low-dimensional dynamical
systems theory, diverges at finite R beyond R_{low}.Comment: 9 pages, 3 figures, published in 2009 as a Rapid Communication in
Phys. Rev. E, vol. 79, article 025301, corrected to include erratum Phys.
Rev. E 79, 039904. References to now published material have been updated. A
note has been added pointing to recent related work by D. Barkley
(arXiv:1101.4125v1
Long-range nematic order and anomalous fluctuations in suspensions of swimming filamentous bacteria
We study the collective dynamics of elongated swimmers in a very thin fluid
layer by devising long, filamentous, non-tumbling bacteria. The strong
confinement induces weak nematic alignment upon collision, which, for large
enough density of cells, gives rise to global nematic order. This homogeneous
but fluctuating phase, observed on the largest experimentally-accessible scale
of millimeters, exhibits the properties predicted by standard models for
flocking such as the Vicsek-style model of polar particles with nematic
alignment: true long-range nematic order and non-trivial giant number
fluctuations.Comment: 6 pages, 4 figures. Supplemental Material: 6 pages, 3 figure
Long transients and cluster size in globally coupled maps
We analyze the asymptotic states in the partially ordered phase of a system
of globally coupled logistic maps. We confirm that, regardless of initial
conditions, these states consist of a few clusters, and they properly belong in
the ordered phase of these systems. The transient times necessary to reach the
asymptotic states can be very long, especially very near the transition line
separating the ordered and the coherent phases. We find that, where two
clusters form, the distribution of their sizes corresponds to windows of
regular or narrow-band chaotic behavior in the bifurcation diagram of a system
of two degrees of freedom that describes the motion of two clusters, where the
size of one cluster acts as a bifurcation parameter.Comment: To appear in Europhysics Letter
Harmonic forcing of an extended oscillatory system: Homogeneous and periodic solutions
In this paper we study the effect of external harmonic forcing on a
one-dimensional oscillatory system described by the complex Ginzburg-Landau
equation (CGLE). For a sufficiently large forcing amplitude, a homogeneous
state with no spatial structure is observed. The state becomes unstable to a
spatially periodic ``stripe'' state via a supercritical bifurcation as the
forcing amplitude decreases. An approximate phase equation is derived, and an
analytic solution for the stripe state is obtained, through which the
asymmetric behavior of the stability border of the state is explained. The
phase equation, in particular the analytic solution, is found to be very useful
in understanding the stability borders of the homogeneous and stripe states of
the forced CGLE.Comment: 6 pages, 4 figures, 2 column revtex format, to be published in Phys.
Rev.
Randomly connected cellular automata: A search for critical connectivities
I study the Chate-Manneville cellular automata rules on randomly connected
lattices. The periodic and quasi-periodic macroscopic behaviours associated
with these rules on finite-dimensional lattices persist on an
infinite-dimensional lattice with finite connectivity and symmetric bonds. The
lower critical connectivity for these models is at C=4 and the mean-field
connectivity, if finite, is not smaller than C=100. Autocorrelations are found
to decay as a power-law with a connectivity independent exponent approx. equal
to -2.5. A new intermitten chaotic phase is also discussed.Comment: 9 pages, 5 figures, compressed with uufiles. One figure (too large)
missing, available via e-mail ([email protected]) To appear in
Europhys. Let
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
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