81 research outputs found
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
Short-range interaction vs long-range correlation in bird flocks
Bird flocks are a paradigmatic example of collective motion. One of the
prominent experimental traits discovered about flocks is the presence of long
range velocity correlations between individuals, which allow them to influence
each other over the large scales, keeping a high level of group coordination. A
crucial question is to understand what is the mutual interaction between birds
generating such nontrivial correlations. Here we use the Maximum Entropy (ME)
approach to infer from experimental data of natural flocks the effective
interactions between birds. Compared to previous studies, we make a significant
step forward as we retrieve the full functional dependence of the interaction
on distance and find that it decays exponentially over a range of a few
individuals. The fact that ME gives a short-range interaction even though its
experimental input is the long-range correlation function, shows that the
method is able to discriminate the relevant information encoded in such
correlations and single out a minimal number of effective parameters. Finally,
we show how the method can be used to capture the degree of anisotropy of
mutual interactions.Comment: 21 pages, 7 figures, 1 tabl
Social interactions dominate speed control in driving natural flocks toward criticality
Flocks of birds exhibit a remarkable degree of coordination and collective
response. It is not just that thousands of individuals fly, on average, in the
same direction and at the same speed, but that even the fluctuations around the
mean velocity are correlated over long distances. Quantitative measurements on
flocks of starlings, in particular, show that these fluctuations are
scale-free, with effective correlation lengths proportional to the linear size
of the flock. Here we construct models for the joint distribution of velocities
in the flock that reproduce the observed local correlations between individuals
and their neighbors, as well as the variance of flight speeds across
individuals, but otherwise have as little structure as possible. These
minimally structured, or maximum entropy models provide quantitative,
parameter-free predictions for the spread of correlations throughout the flock,
and these are in excellent agreement with the data. These models are
mathematically equivalent to statistical physics models for ordering in
magnets, and the correct prediction of scale-free correlations arises because
the parameters - completely determined by the data - are in the critical
regime. In biological terms, criticality allows the flock to achieve maximal
correlation across long distances with limited speed fluctuations
Out-of-Equilibrium Non-Gaussian Behavior in Driven Granular Gases
The characterization of the distance from equilibrium is a debated problem in
particular in the treatment of experimental signals. If the signal is a
1-dimensional time-series, such a goal becomes challenging. A paradigmatic
example is the angular diffusion of a rotator immersed in a vibro-fluidized
granular gas. Here, we experimentally observe that the rotator's angular
velocity exhibits significative differences with respect to an equilibrium
process. Exploiting the presence of two relevant time-scales and non-Gaussian
velocity increments, we quantify the breakdown of time-reversal asymmetry,
which would vanish in the case of a 1d Gaussian process. We deduce a new model
for the massive probe, with two linearly coupled variables, incorporating both
Gaussian and Poissonian noise, the latter motivated by the rarefied collisions
with the granular bath particles. Our model reproduces the experiment in a
range of densities, from dilute to moderately dense, with a meaningful
dependence of the parameters on the density.Comment: 5 pages, 4 figure
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
Diffusion of individual birds in starling flocks
Flocking is a paradigmatic example of collective animal behaviour, where
decentralized interaction rules give rise to a globally ordered state. In the
emergence of order out of self-organization we find similarities between
biological systems, as bird flocks, and some physical systems, as ferromagnets.
In both cases, the tendency of individuals to align to their neighbours gives
rise to a polarized state. There is, however, one crucial difference: the
interaction network within an animal group is not necessarily fixed in time, as
each individual moves and may change its neighbours. Therefore, the dynamical
interaction mechanism in biological and physical system can be quite different,
not only due to the gross disparity in the complexity of the individual
entities, but also because of the potential role of inter-individual motion. To
assess the relevance of this mechanism it is necessary to gain quantitative
experimental information about how much individuals move with respect to each
other within the group. Here, by using data from field observations on
starlings, we study the diffusion properties of individual birds within a flock
and investigate the effect of diffusion on the dynamics of the interaction
network. We find that birds diffuse faster than Brownian particles
(superdiffusion) and in a strongly anisotropic way. We also find that
neighbours change in time exclusively as a consequence of diffusion, so that no
specific mechanism to keep one's neighbours seems to be enforced. Finally, we
study the diffusion properties of birds at the border of the flock. We find
that these individuals remain on the border significantly longer than what
would be expected on the basis of a purely diffusional model, suggesting that
there is a sort barrier a bird must cross to make the transition from border to
interior of the flock.Comment: 22 pages, 10 figure
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