10,909 research outputs found
Gaussian model of explosive percolation in three and higher dimensions
The Gaussian model of discontinuous percolation, recently introduced by
Ara\'ujo and Herrmann [Phys. Rev. Lett., 105, 035701 (2010)], is numerically
investigated in three dimensions, disclosing a discontinuous transition. For
the simple-cubic lattice, in the thermodynamic limit, we report a finite jump
of the order parameter, . The largest cluster at the
threshold is compact, but its external perimeter is fractal with fractal
dimension . The study is extended to hypercubic lattices up
to six dimensions and to the mean-field limit (infinite dimension). We find
that, in all considered dimensions, the percolation transition is
discontinuous. The value of the jump in the order parameter, the maximum of the
second moment, and the percolation threshold are analyzed, revealing
interesting features of the transition and corroborating its discontinuous
nature in all considered dimensions. We also show that the fractal dimension of
the external perimeter, for any dimension, is consistent with the one from
bridge percolation and establish a lower bound for the percolation threshold of
discontinuous models with finite number of clusters at the threshold
An automata characterisation for multiple context-free languages
We introduce tree stack automata as a new class of automata with storage and
identify a restricted form of tree stack automata that recognises exactly the
multiple context-free languages.Comment: This is an extended version of a paper with the same title accepted
at the 20th International Conference on Developments in Language Theory (DLT
2016
Probing the Binary Black Hole Merger Regime with Scalar Perturbations
We present results obtained by scattering a scalar field off the curved
background of a coalescing binary black hole system. A massless scalar field is
evolved on a set of fixed backgrounds, each provided by a spatial hypersurface
generated numerically during a binary black hole merger. We show that the
scalar field scattered from the merger region exhibits quasinormal ringing once
a common apparent horizon surrounds the two black holes. This occurs earlier
than the onset of the perturbative regime as measured by the start of the
quasinormal ringing in the gravitational waveforms. We also use the scalar
quasinormal frequencies to associate a mass and a spin with each hypersurface,
and observe the compatibility of this measure with the horizon mass and spin
computed from the dynamical horizon framework.Comment: 10 Pages and 6 figure
Model for erosion-deposition patterns
We investigate through computational simulations with a pore network model
the formation of patterns caused by erosion-deposition mechanisms. In this
model, the geometry of the pore space changes dynamically as a consequence of
the coupling between the fluid flow and the movement of particles due to local
drag forces. Our results for this irreversible process show that the model is
capable to reproduce typical natural patterns caused by well known erosion
processes. Moreover, we observe that, within a certain range of porosity
values, the grains form clusters that are tilted with respect to the horizontal
with a characteristic angle. We compare our results to recent experiments for
granular material in flowing water and show that they present a satisfactory
agreement.Comment: 8 pages, 12 figures, submitted to Phys. Rev.
Gender gap in the ERASMUS mobility program
Studying abroad has become very popular among students. The ERASMUS mobility
program is one of the largest international student exchange programs in the
world, which has supported already more than three million participants since
1987. We analyzed the mobility pattern within this program in 2011-12 and found
a gender gap across countries and subject areas. Namely, for almost all
participating countries, female students are over-represented in the ERASMUS
program when compared to the entire population of tertiary students. The same
tendency is observed across different subject areas. We also found a gender
asymmetry in the geographical distribution of hosting institutions, with a bias
of male students in Scandinavian countries. However, a detailed analysis
reveals that this latter asymmetry is rather driven by subject and consistent
with the distribution of gender ratios among subject areas
Transport on exploding percolation clusters
We propose a simple generalization of the explosive percolation process
[Achlioptas et al., Science 323, 1453 (2009)], and investigate its structural
and transport properties. In this model, at each step, a set of q unoccupied
bonds is randomly chosen. Each of these bonds is then associated with a weight
given by the product of the cluster sizes that they would potentially connect,
and only that bond among the q-set which has the smallest weight becomes
occupied. Our results indicate that, at criticality, all finite-size scaling
exponents for the spanning cluster, the conducting backbone, the cutting bonds,
and the global conductance of the system, change continuously and significantly
with q. Surprisingly, we also observe that systems with intermediate values of
q display the worst conductive performance. This is explained by the strong
inhibition of loops in the spanning cluster, resulting in a substantially
smaller associated conducting backbone.Comment: 4 pages, 4 figure
Purification of Single-photon Entanglement
Single-photon entanglement is a simple form of entanglement that exists
between two spatial modes sharing a single photon. Despite its elementary form,
it provides a resource as useful as polarization-entangled photons and it can
be used for quantum teleportation and entanglement swapping operations. Here,
we report the first experiment where single-photon entanglement is purified
with a simple linear-optics based protocol. Besides its conceptual interest,
this result might find applications in long distance quantum communication
based on quantum repeaters.Comment: Main article: 5 pages, 4 figure
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