446 research outputs found
Phase-ordering and persistence: relative effects of space-discretization, chaos, and anisotropy
The peculiar phase-ordering properties of a lattice of coupled chaotic maps
studied recently (A. Lema\^\i tre & H. Chat\'e, {\em Phys. Rev. Lett.} {\bf
82}, 1140 (1999)) are revisited with the help of detailed investigations of
interface motion. It is shown that ``normal'', curvature-driven-like domain
growth is recovered at larger scales than considered before, and that the
persistence exponent seems to be universal. Using generalized persistence
spectra, the properties of interface motion in this deterministic, chaotic,
lattice system are found to ``interpolate'' between those of the two canonical
reference systems, the (probabilistic) Ising model, and the (deterministic),
space-continuous, time-dependent Ginzburg-Landau equation.Comment: 13 pages, to be published in Physica
Relevance of Metric-Free Interactions in Flocking Phenomena
We show that the collective properties of self-propelled particles aligning
with their "topological" (Voronoi) neighbors are qualitatively different from
those of usual models where metric interaction ranges are used. This relevance
of metric-free interactions, shown in a minimal setting, indicate that
realistic models for the cohesive motion of cells, bird flocks, and fish
schools may have to incorporate them, as suggested by recent observations.Comment: To appear on Physical Review Letter
Rare-event induced binding transition of heteropolymers
Sequence heterogeneity broadens the binding transition of a polymer onto a
linear or planar substrate. This effect is analyzed in a real-space
renormalization group scheme designed to capture the statistics of rare events.
In the strongly disordered regime, binding initiates at an exponentially rare
set of ``good contacts''. Renormalization of the contact potential yields a
Kosterlitz-Thouless type transition in any dimension. This and other
predictions are confirmed by extensive numerical simulations of a directed
polymer interacting with a columnar defect.Comment: 4 pages, 3 figure
Competing ferromagnetic and nematic alignment in self-propelled polar particles
We study a Vicsek-style model of self-propelled particles where ferromagnetic
and nematic alignment compete in both the usual "metric" version and in the
"metric-free" case where a particle interacts with its Voronoi neighbors. We
show that the phase diagram of this out-of-equilibrium XY model is similar to
that of its equilibrium counterpart: the properties of the fully-nematic model,
studied before in [F. Ginelli, F. Peruani, M. Baer, and H. Chat\'e, Phys. Rev.
Lett. 104, 184502 (2010)], are thus robust to the introduction of a modest bias
of interactions towards ferromagnetic alignment. The direct transitions between
polar and nematic ordered phases are shown to be discontinuous in the metric
case, and continuous, belonging to the Ising universality class, in the
metric-free version
From Phase to Micro-Phase Separation in Flocking Models: The Essential Role of Non-Equilibrium Fluctuations
We show that the flocking transition in the Vicsek model is best understood
as a liquid-gas transition, rather than an order-disorder one. The full phase
separation observed in flocking models with Z2 rotational symmetry is, however,
replaced by a microphase separation leading to a smectic arrangement of
traveling ordered bands. Remarkably, continuous deterministic descriptions do
not account for this difference, which is only recovered at the fluctuating
hydrodynamics level. Scalar and vectorial order parameters indeed produce
different types of number fluctuations, which we show to be essential in
selecting the inhomogeneous patterns. This highlights an unexpected role of
fluctuations in the selection of flock shapes.Comment: 5 p., 5 fig.. Supplementary material: 7 movie
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
Comment on ``Phase Transitions in Systems of Self-Propelled Agents and Related Network Models''
In this comment we show that the transition to collective motion in
Vicsek-like systems with angular noise remain discontinuous for large velocity
values. Thus, the networks studied by Aldana {\et al.} [Phys. Rev. Lett. {\bf
98}, 095702 (2007)] at best constitute a singular, large velocity limit of
these systems.Comment: To appear on Physical Review Letter
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