7,031 research outputs found
Critical Cooperation Range to Improve Spatial Network Robustness
A robust worldwide air-transportation network (WAN) is one that minimizes the
number of stranded passengers under a sequence of airport closures. Building on
top of this realistic example, here we address how spatial network robustness
can profit from cooperation between local actors. We swap a series of links
within a certain distance, a cooperation range, while following typical
constraints of spatially embedded networks. We find that the network robustness
is only improved above a critical cooperation range. Such improvement can be
described in the framework of a continuum transition, where the critical
exponents depend on the spatial correlation of connected nodes. For the WAN we
show that, except for Australia, all continental networks fall into the same
universality class. Practical implications of this result are also discussed
Enhancement of the critical temperature in iron-pnictide superconductors by finite size effects
Recent experiments have shown that, in agreement with previous theoretical
predictions, superconductivity in metallic nanostructures can be enhanced with
respect to the bulk limit. Motivated by these results we study finite size
effects (FSE) in an iron-pnictide superconductor. For realistic values of the
bulk critical temperature Tc ~ 20-50K, we find that, in the nanoscale region L
~ 10 nm, Tc(L) has a complicated oscillating pattern as a function of the
system size L. A substantial enhancement of Tc with respect to the bulk limit
is observed for different boundary conditions, geometries and two microscopic
models of superconductivity. Thermal fluctuations, which break long range
order, are still small in this region. Finally we show that the differential
conductance, an experimental observable, is also very sensitive to FSE.Comment: 4 pages, 3 figure
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
Breathing synchronization in interconnected networks
Global synchronization in a complex network of oscillators emerges from the
interplay between its topology and the dynamics of the pairwise interactions
among its numerous components. When oscillators are spatially separated,
however, a time delay appears in the interaction which might obstruct
synchronization. Here we study the synchronization properties of interconnected
networks of oscillators with a time delay between networks and analyze the
dynamics as a function of the couplings and communication lag. We discover a
new breathing synchronization regime, where two groups appear in each network
synchronized at different frequencies. Each group has a counterpart in the
opposite network, one group is in phase and the other in anti-phase with their
counterpart. For strong couplings, instead, networks are internally
synchronized but a phase shift between them might occur. The implications of
our findings on several socio-technical and biological systems are discussed.Comment: 7 pages, 3 figures + 3 pages of Supplemental Materia
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