37 research outputs found
Spiral Motion in a Noisy Complex Ginzburg-Landau Equation
The response of spiral waves to external perturbations in a stable regime of
the two-dimensional complex Ginzburg-Landau equation (CGLE) is investigated. It
is shown that the spiral core has a finite mobility and performs Brownian
motion when driven by white noise. Combined with simulation results, this
suggests that defect-free and quasi-frozen states in the noiseless CGLE are
unstable against free vortex excitation at any non-zero noise strength.Comment: RevTex, 4 pages, 3 figures, submitted to Phys. Rev. Let
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
Collective Motion of Self-Propelled Particles with Memory
International audienceWe show that memory, in the form of underdamped angular dynamics, is a crucial ingredient for the collective properties of self-propelled particles. Using Vicsek-style models with an Ornstein-Uhlenbeck process acting on angular velocity, we uncover a rich variety of collective phases not observed in usual overdamped systems, including vortex lattices and active foams. In a model with strictly nematic interactions the smectic arrangement of Vicsek waves giving rise to global polar order is observed. We also provide a calculation of the effective interaction between vortices in the case where a telegraphic noise process is at play, explaining thus the emergence and structure of the vortex lattices observed here and in motility assay experiments
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]
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
Phase chaos in the anisotropic complex Ginzburg-Landau Equation
Of the various interesting solutions found in the two-dimensional complex
Ginzburg-Landau equation for anisotropic systems, the phase-chaotic states show
particularly novel features. They exist in a broader parameter range than in
the isotropic case, and often even broader than in one dimension. They
typically represent the global attractor of the system. There exist two
variants of phase chaos: a quasi-one dimensional and a two-dimensional
solution. The transition to defect chaos is of intermittent type.Comment: 4 pages RevTeX, 5 figures, little changes in figures and references,
typos removed, accepted as Rapid Commun. in Phys. Rev.
Flat Spacetime Vacuum in Loop Quantum Gravity
We construct a state in the loop quantum gravity theory with zero
cosmological constant, which should correspond to the flat spacetime vacuum
solution. This is done by defining the loop transform coefficients of a flat
connection wavefunction in the holomorphic representation which satisfies all
the constraints of quantum General Relativity and it is peaked around the flat
space triads. The loop transform coefficients are defined as spin foam state
sum invariants of the spin networks embedded in the spatial manifold for the
SU(2) quantum group. We also obtain an expression for the vacuum wavefunction
in the triad represntation, by defining the corresponding spin networks
functional integrals as SU(2) quantum group state sums.Comment: 20 pages, 6 figure
Detection and construction of an elliptic solution to the complex cubic-quintic Ginzburg-Landau equation
In evolution equations for a complex amplitude, the phase obeys a much more
intricate equation than the amplitude. Nevertheless, general methods should be
applicable to both variables. On the example of the traveling wave reduction of
the complex cubic-quintic Ginzburg-Landau equation (CGL5), we explain how to
overcome the difficulties arising in two such methods: (i) the criterium that
the sum of residues of an elliptic solution should be zero, (ii) the
construction of a first order differential equation admitting the given
equation as a differential consequence (subequation method).Comment: 12 pages, no figure, to appear, Theoretical and Mathematical Physic
Coupled Maps on Trees
We study coupled maps on a Cayley tree, with local (nearest-neighbor)
interactions, and with a variety of boundary conditions. The homogeneous state
(where every lattice site has the same value) and the node-synchronized state
(where sites of a given generation have the same value) are both shown to occur
for particular values of the parameters and coupling constants. We study the
stability of these states and their domains of attraction. As the number of
sites that become synchronized is much higher compared to that on a regular
lattice, control is easier to effect. A general procedure is given to deduce
the eigenvalue spectrum for these states. Perturbations of the synchronized
state lead to different spatio-temporal structures. We find that a mean-field
like treatment is valid on this (effectively infinite dimensional) lattice.Comment: latex file (25 pages), 4 figures included. To be published in Phys.
Rev.