14 research outputs found
Quench dynamics of the 2d XY model
We investigate the out of equilibrium dynamics of the two-dimensional XY
model when cooled across the Berezinskii-Kosterlitz-Thouless (BKT) phase
transition using different protocols. We focus on the evolution of the growing
correlation length and the density of topological defects (vortices). By using
Monte Carlo simulations we first determine the time and temperature dependence
of the growing correlation length after an infinitely rapid quench from above
the transition temperature to the quasi-long range order region. The functional
form is consistent with a logarithmic correction to the diffusive law and it
serves to validate dynamic scaling in this problem. This analysis clarifies the
different dynamic roles played by bound and free vortices. We then revisit the
Kibble-Zurek mechanism in thermal phase transitions in which the disordered
state is plagued with topological defects. We provide a theory of quenching
rate dependence in systems with the BKT-type transition that goes beyond the
equilibrium scaling arguments. Finally, we discuss the implications of our
results to a host of physical systems with vortex excitations including planar
ferromagnets and liquid crystals as well as the Ginzburg-Landau approach to
bidimensional freely decaying turbulence.Comment: 28 pages, 14 figure
Silent Flocks
Experiments find coherent information transfer through biological groups on
length and time scales distinctly below those on which asymptotically correct
hydrodynamic theories apply. We present here a new continuum theory of
collective motion coupling the velocity and density fields of Toner and Tu to
the inertial spin field recently introduced to describe information propagation
in natural flocks of birds. The long-wavelength limit of the new equations
reproduces Toner-Tu theory, while at shorter wavelengths (or, equivalently,
smaller damping), spin fluctuations dominate over density fluctuations and
second sound propagation of the kind observed in real flocks emerges. We study
the dispersion relation of the new theory and find that when the speed of
second sound is large, a gap sharply separates first from second sound modes.
This gap implies the existence of `silent' flocks, namely medium-sized systems
across which neither first nor second sound can propagate
Nonsymmetric Interactions Trigger Collective Swings in Globally Ordered Systems
Many systems in nature, from ferromagnets to flocks of birds, exhibit ordering phenomena on the large scale. In condensed matter systems, order is statistically robust for large enough dimensions, with relative fluctuations due to noise vanishing with system size. Several biological systems, however, are less stable and spontaneously change their global state on relatively short time scales. Here we show that there are two crucial ingredients in these systems that enhance the effect of noise, leading to collective changes of state on finite time scales and off-equilibrium behavior: the nonsymmetric nature of interactions between individuals, and the presence of local heterogeneities in the topology of the network. Our results might explain what is observed in several living systems and are consistent with recent experimental data on bird flocks and other animal groups
Emergence of collective changes in travel direction of starling flocks from individual birds fluctuations
One of the most impressive features of moving animal groups is their ability
to perform sudden coherent changes in travel direction. While this collective
decision can be a response to an external perturbation, such as the presence of
a predator, recent studies show that such directional switching can also emerge
from the intrinsic fluctuations in the individual behaviour. However, the cause
and the mechanism by which such collective changes of direction occur are not
fully understood yet. Here, we present an experimental study of spontaneous
collective turns in natural flocks of starlings. We employ a recently developed
tracking algorithm to reconstruct three-dimensional trajectories of each
individual bird in the flock for the whole duration of a turning event. Our
approach enables us to analyze changes in the individual behavior of every
group member and reveal the emergent dynamics of turning. We show that
spontaneous turns start from individuals located at the elongated edges of the
flocks, and then propagate through the group. We find that birds on the edges
deviate from the mean direction of motion much more frequently than other
individuals, indicating that persistent localized fluctuations are the crucial
ingredient for triggering a collective directional change. Finally, we
quantitatively show that birds follow equal radius paths during turning
allowing the flock to change orientation and redistribute risky locations among
group members. The whole process of turning is a remarkable example of how a
self-organized system can sustain collective changes and reorganize, while
retaining coherence.Comment: 18 pages, 2 Videos adde
Flocking and turning: a new model for self-organized collective motion
Birds in a flock move in a correlated way, resulting in large polarization of
velocities. A good understanding of this collective behavior exists for linear
motion of the flock. Yet observing actual birds, the center of mass of the
group often turns giving rise to more complicated dynamics, still keeping
strong polarization of the flock. Here we propose novel dynamical equations for
the collective motion of polarized animal groups that account for correlated
turning including solely social forces. We exploit rotational symmetries and
conservation laws of the problem to formulate a theory in terms of generalized
coordinates of motion for the velocity directions akin to a Hamiltonian
formulation for rotations. We explicitly derive the correspondence between this
formulation and the dynamics of the individual velocities, thus obtaining a new
model of collective motion. In the appropriate overdamped limit we recover the
well-known Vicsek model, which dissipates rotational information and does not
allow for polarized turns. Although the new model has its most vivid success in
describing turning groups, its dynamics is intrinsically different from
previous ones in a wide dynamical regime, while reducing to the hydrodynamic
description of Toner and Tu at very large length-scales. The derived framework
is therefore general and it may describe the collective motion of any strongly
polarized active matter system.Comment: Accepted for the Special Issue of the Journal of Statistical Physics:
Collective Behavior in Biological Systems, 17 pages, 4 figures, 3 video
Time-delayed Follow-the-Leader model for pedestrians walking in line
International audienceWe use the results of a pedestrian tracking experiment to identify a follow-the-leader model for pedestrians walking-in-line. We demonstrate the existence of a time-delay between a subject's response and the predecessor's corresponding behavior. This time-delay induces an instability which can be damped out by a suitable relaxation. By comparisons with the experimental data, we show that the model reproduces well the emergence of large-scale structures such as congestions waves. The resulting model can be used either for modeling pedestrian queuing behavior or can be incorporated into bi-dimensional models of pedestrian traffic. Acknowledgements: This work has been supported by the french 'Agence Nationale pour la Recherche (ANR)' in the frame of the contract "Pedigree" (ANR-08-SYSC-015-01). JH acknowledges support of the ANR and the Institut de Mathématiques de Toulouse, where he conducted this research. AJ acknowledges support of the ANR and of the Laboratoire de physique t A c orique in Orsay where she conducted this research. PD is on leave from CNRS, Institut de Mat A c matiques de Toulouse, France
GReTA - a novel Global and Recursive Tracking Algorithm in three dimensions
Tracking multiple moving targets allows quantitative measure of the dynamic
behavior in systems as diverse as animal groups in biology, turbulence in fluid
dynamics and crowd and traffic control. In three dimensions, tracking several
targets becomes increasingly hard since optical occlusions are very likely,
i.e. two featureless targets frequently overlap for several frames. Occlusions
are particularly frequent in biological groups such as bird flocks, fish
schools, and insect swarms, a fact that has severely limited collective animal
behavior field studies in the past. This paper presents a 3D tracking method
that is robust in the case of severe occlusions. To ensure robustness, we adopt
a global optimization approach that works on all objects and frames at once. To
achieve practicality and scalability, we employ a divide and conquer
formulation, thanks to which the computational complexity of the problem is
reduced by orders of magnitude. We tested our algorithm with synthetic data,
with experimental data of bird flocks and insect swarms and with public
benchmark datasets, and show that our system yields high quality trajectories
for hundreds of moving targets with severe overlap. The results obtained on
very heterogeneous data show the potential applicability of our method to the
most diverse experimental situations.Comment: 13 pages, 6 figures, 3 tables. Version 3 was slightly shortened, and
new comprative results on the public datasets (thermal infrared videos of
flying bats) by Z. Wu and coworkers (2014) were included. in A. Attanasi et
al., "GReTA - A Novel Global and Recursive Tracking Algorithm in Three
Dimensions", IEEE Trans. Pattern Anal. Mach. Intell., vol.37 (2015
Flocking and turning: a new model for self-organized collective motion
Birds in a flock move in a correlated way, resulting in large polarization of velocities. A good understanding of this collective behavior exists for linear motion of the flock. Yet observing actual birds, the center of mass of the group often turns giving rise to more complicated dynamics, still keeping strong polarization of the flock. Here we propose novel dynamical equations for the collective motion of polarized animal groups that account for correlated turning including solely social forces. We exploit rotational symmetries and conservation laws of the problem to formulate a theory in terms of generalized coordinates of motion for the velocity directions akin to a Hamiltonian formulation for rotations. We explicitly derive the correspondence between this formulation and the dynamics of the individual velocities, thus obtaining a new model of collective motion. In the appropriate overdamped limit we recover the well-known Vicsek model, which dissipates rotational information and does not allow for polarized turns. Although the new model has its most vivid success in describing turning groups, its dynamics is intrinsically different from previous ones in a wide dynamical regime, while reducing to the hydrodynamic description of Toner and Tu at very large length-scales. The derived framework is therefore general and it may describe the collective motion of any strongly polarized active matter system.Instituto de Investigaciones FisicoquĂmicas TeĂłricas y Aplicada
Un modèle de suivi réaliste pour la simulation de foules
International audienc