6,456 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
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
How dense can one pack spheres of arbitrary size distribution?
We present the first systematic algorithm to estimate the maximum packing
density of spheres when the grain sizes are drawn from an arbitrary size
distribution. With an Apollonian filling rule, we implement our technique for
disks in 2d and spheres in 3d. As expected, the densest packing is achieved
with power-law size distributions. We also test the method on homogeneous and
on empirical real distributions, and we propose a scheme to obtain
experimentally accessible distributions of grain sizes with low porosity. Our
method should be helpful in the development of ultra-strong ceramics and high
performance concrete.Comment: 5 pages, 5 figure
Periodic Neural Activity Induced by Network Complexity
We study a model for neural activity on the small-world topology of Watts and
Strogatz and on the scale-free topology of Barab\'asi and Albert. We find that
the topology of the network connections may spontaneously induce periodic
neural activity, contrasting with chaotic neural activities exhibited by
regular topologies. Periodic activity exists only for relatively small networks
and occurs with higher probability when the rewiring probability is larger. The
average length of the periods increases with the square root of the network
size.Comment: 4 pages, 5 figure
Theory of Andreev reflection in a two-orbital model of iron-pnictide superconductors
A recently developed theory for the problem of Andreev reflection between a
normal metal (N) and a multiband superconductor (MBS) assumes that the incident
wave from the normal metal is coherently transmitted through several bands
inside the superconductor. Such splitting of the probability amplitude into
several channels is the analogue of a quantum waveguide. Thus, the appropriate
matching conditions for the wave function at the N/MBS interface are derived
from an extension of quantum waveguide theory. Interference effects between the
transmitted waves inside the superconductor manifest themselves in the
conductance. We provide results for a FeAs superconductor, in the framework of
a recently proposed effective two-band model and two recently proposed gap
symmetries: in the sign-reversed s-wave () scenario
resonant transmission through surface Andreev bound states (ABS) at nonzero
energy is found as well as destructive interference effects that produce zeros
in the conductance; in the extended s-wave ()
scenario no ABS at finite energy are found.Comment: 4 pages, 5 figure
Invasion Percolation Between two Sites
We investigate the process of invasion percolation between two sites
(injection and extraction sites) separated by a distance r in two-dimensional
lattices of size L. Our results for the non-trapping invasion percolation model
indicate that the statistics of the mass of invaded clusters is significantly
dependent on the local occupation probability (pressure) Pe at the extraction
site. For Pe=0, we show that the mass distribution of invaded clusters P(M)
follows a power-law P(M) ~ M^{-\alpha} for intermediate values of the mass M,
with an exponent \alpha=1.39. When the local pressure is set to Pe=Pc, where Pc
corresponds to the site percolation threshold of the lattice topology, the
distribution P(M) still displays a scaling region, but with an exponent
\alpha=1.02. This last behavior is consistent with previous results for the
cluster statistics in standard percolation. In spite of these discrepancies,
the results of our simulations indicate that the fractal dimension of the
invaded cluster does not depends significantly on the local pressure Pe and it
is consistent with the fractal dimension values reported for standard invasion
percolation. Finally, we perform extensive numerical simulations to determine
the effect of the lattice borders on the statistics of the invaded clusters and
also to characterize the self-organized critical behavior of the invasion
percolation process.Comment: 7 pages, 11 figures, submited for PR
Theory and modeling of the magnetic field measurement in LISA PathFinder
The magnetic diagnostics subsystem of the LISA Technology Package (LTP) on
board the LISA PathFinder (LPF) spacecraft includes a set of four tri-axial
fluxgate magnetometers, intended to measure with high precision the magnetic
field at their respective positions. However, their readouts do not provide a
direct measurement of the magnetic field at the positions of the test masses,
and hence an interpolation method must be designed and implemented to obtain
the values of the magnetic field at these positions. However, such
interpolation process faces serious difficulties. Indeed, the size of the
interpolation region is excessive for a linear interpolation to be reliable
while, on the other hand, the number of magnetometer channels does not provide
sufficient data to go beyond the linear approximation. We describe an
alternative method to address this issue, by means of neural network
algorithms. The key point in this approach is the ability of neural networks to
learn from suitable training data representing the behavior of the magnetic
field. Despite the relatively large distance between the test masses and the
magnetometers, and the insufficient number of data channels, we find that our
artificial neural network algorithm is able to reduce the estimation errors of
the field and gradient down to levels below 10%, a quite satisfactory result.
Learning efficiency can be best improved by making use of data obtained in
on-ground measurements prior to mission launch in all relevant satellite
locations and in real operation conditions. Reliable information on that
appears to be essential for a meaningful assessment of magnetic noise in the
LTP.Comment: 10 pages, 8 figures, 2 tables, submitted to Physical Review
Magnetic and superconducting instabilities in the periodic Anderson model: an RPA stud
We study the magnetic and superconducting instabilities of the periodic
Anderson model with infinite Coulomb repulsion U in the random phase
approximation. The Neel temperature and the superconducting critical
temperature are obtained as functions of electronic density (chemical pressure)
and hybridization V (pressure). It is found that close to the region where the
system exhibits magnetic order the critical temperature T_c is much smaller
than the Neel temperature, in qualitative agreement with some T_N/T_c ratios
found for some heavy-fermion materials. In our study, all the magnetic and
superconducting physical behaviour of the system has its origin in the
fluctuating boson fields implementing the infinite on-site Coulomb repulsion
among the f-electrons.Comment: 9 pages, 2 figure
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