936 research outputs found

### A question of scale

If you search for 'collective behaviour' with your web browser most of the
texts popping up will be about group activities of humans, including riots,
fashion and mass panic. Nevertheless, collective behaviour is also considered
to be an important aspect of observed phenomena in atoms and molecules, for
example, during spontaneous magnetization. In your web search, you might also
find articles on collectively migrating bacteria, insects or birds; or
phenomena where groups of organisms or non- living objects synchronize their
signals or motion (think of fireflies flashing in unison or people clapping in
phase during rhythmic applause).Comment: Concepts essay, published in Nature
http://www.nature.com/nature/journal/v411/n6836/full/411421a0.htm

### Synchronization of oscillators with long range interaction: phase transition and anomalous finite size effects

Synchronization in a lattice of a finite population of phase oscillators with
algebraically decaying, non-normalized coupling is studied by numerical
simulations. A critical level of decay is found, below which full locking takes
place if the population contains a sufficiently large number of elements. For
large number of oscillators and small coupling constant, numerical simulations
and analytical arguments indicate that a phase transition separating
synchronization from incoherence appears at a decay exponent value equal to the
number of dimensions of the lattice. In contrast with earlier results on
similar systems with normalized coupling, we have indication that for the decay
exponent less than the dimensions of the lattice and for large populations,
synchronization is possible even if the coupling is arbitarily weak. This
finding suggests that in organisms interacting through slowly decaying signals
like light or sound, collective oscillations can always be established if the
population is sufficiently large.Comment: 15 pages, 12 figures, submitted to Phys. Rev. E; Text slightly
changed; References added; Fig. 9 update

### Aggregation of magnetic holes in a rotating magnetic field

We have experimentally investigated field induced aggregation of nonmagnetic
particles confined in a magnetic fluid layer when rotating magnetic fields were
applied. After application of a magnetic field rotating in the plane of the
fluid layer, the single particles start to form two-dimensional (2D) clusters,
like doublets, triangels, and more complex structures. These clusters
aggregated again and again to form bigger clusters. During this nonequilibrium
process, a broad range of cluster sizes was formed, and the scaling exponents,
$z$ and $z'$, of the number of clusters $N(t)\sim t^{z'}$and average cluster
size $S(t)\sim t^{z}$ were calculated. The process could be characterized as
diffusion limited cluster-cluster aggregation. We have found that all sizes of
clusters that occured during an experiment, fall on a single curve as the
dynamic scaling theory predicts. Hovewer, the characteristic scaling exponents
$z',\: z$ and crossover exponents $\Delta$ were not universal. A particle
tracking method was used to find the dependence of the diffusion coefficients
$D_{s}$ on cluster size $s$. The cluster motions show features of
\textit{\emph{Brownian}} motion. The average diffusion coefficients $$
depend on the cluster sizes $s$ as a power law $\propto s^{\gamma}$
where values of $\gamma$ as different as $\gamma=-0.62\pm0.19$ and
$\gamma=-2.08\pm0. were found in two of the experiments

### Multifractal Network Generator

We introduce a new approach to constructing networks with realistic features.
Our method, in spite of its conceptual simplicity (it has only two parameters)
is capable of generating a wide variety of network types with prescribed
statistical properties, e.g., with degree- or clustering coefficient
distributions of various, very different forms. In turn, these graphs can be
used to test hypotheses, or, as models of actual data. The method is based on a
mapping between suitably chosen singular measures defined on the unit square
and sparse infinite networks. Such a mapping has the great potential of
allowing for graph theoretical results for a variety of network topologies. The
main idea of our approach is to go to the infinite limit of the singular
measure and the size of the corresponding graph simultaneously. A very unique
feature of this construction is that the complexity of the generated network is
increasing with the size. We present analytic expressions derived from the
parameters of the -- to be iterated-- initial generating measure for such major
characteristics of graphs as their degree, clustering coefficient and
assortativity coefficient distributions. The optimal parameters of the
generating measure are determined from a simple simulated annealing process.
Thus, the present work provides a tool for researchers from a variety of fields
(such as biology, computer science, biology, or complex systems) enabling them
to create a versatile model of their network data.Comment: Preprint. Final version appeared in PNAS

### Staggered and extreme localization of electron states in fractal space

We present exact analytical results revealing the existence of a countable
infinity of unusual single particle states, which are localized with a
multitude of localization lengths in a Vicsek fractal network with diamond
shaped loops as the 'unit cells'. The family of localized states form clusters
of increasing size, much in the sense of Aharonov-Bohm cages [J. Vidal et al.,
Phys. Rev. Lett. 81, 5888 (1998)], but now without a magnetic field. The length
scale at which the localization effect for each of these states sets in can be
uniquely predicted following a well defined prescription developed within the
framework of real space renormalization group. The scheme allows an exact
evaluation of the energy eigenvalue for every such state which is ensured to
remain in the spectrum of the system even in the thermodynamic limit. In
addition, we discuss the existence of a perfectly conducting state at the band
center of this geometry and the influence of a uniform magnetic field threading
each elementary plaquette of the lattice on its spectral properties. Of
particular interest is the case of extreme localization of single particle
states when the magnetic flux equals half the fundamental flux quantum.Comment: 9 pages, 8 figure

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