12,389 research outputs found
Approximating the largest eigenvalue of network adjacency matrices
The largest eigenvalue of the adjacency matrix of a network plays an
important role in several network processes (e.g., synchronization of
oscillators, percolation on directed networks, linear stability of equilibria
of network coupled systems, etc.). In this paper we develop approximations to
the largest eigenvalue of adjacency matrices and discuss the relationships
between these approximations. Numerical experiments on simulated networks are
used to test our results.Comment: 7 pages, 4 figure
Comedia famosa. El mágico de Salerno : tercera parte / de Don Juan Salvo y Vela
Precede al tít.: "N. 283."Los datos de publicación tomados del colofónSign.: A-C4, D
The onset of synchronization in large networks of coupled oscillators
We study the transition from incoherence to coherence in large networks of
coupled phase oscillators. We present various approximations that describe the
behavior of an appropriately defined order parameter past the transition, and
generalize recent results for the critical coupling strength. We find that,
under appropriate conditions, the coupling strength at which the transition
occurs is determined by the largest eigenvalue of the adjacency matrix. We show
how, with an additional assumption, a mean field approximation recently
proposed is recovered from our results. We test our theory with numerical
simulations, and find that it describes the transition when our assumptions are
satisfied. We find that our theory describes the transition well in situations
in which the mean field approximation fails. We study the finite size effects
caused by nodes with small degree and find that they cause the critical
coupling strength to increase.Comment: To appear in PRE; Added an Appendix, a reference, modified two
figures and improved the discussion of the range of validity of perturbative
approache
On the local existence of maximal slicings in spherically symmetric spacetimes
In this talk we show that any spherically symmetric spacetime admits locally
a maximal spacelike slicing. The above condition is reduced to solve a
decoupled system of first order quasi-linear partial differential equations.
The solution may be accomplished analytical or numerically. We provide a
general procedure to construct such maximal slicings.Comment: 4 pages. Accepted for publication in Journal of Physics: Conference
Series, Proceedings of the Spanish Relativity Meeting ERE200
Twisted flux tube emergence from the convection zone to the corona
3D numerical simulations of a horizontal magnetic flux tube emergence with
different twist are carried out in a computational domain spanning the upper
layers of the convection zone to the lower corona. We use the Oslo Staggered
Code to solve the full MHD equations with non-grey and non-LTE radiative
transfer and thermal conduction along the magnetic field lines. The emergence
of the magnetic flux tube input at the bottom boundary into a weakly magnetized
atmosphere is presented. The photospheric and chromospheric response is
described with magnetograms, synthetic images and velocity field distributions.
The emergence of a magnetic flux tube into such an atmosphere results in varied
atmospheric responses. In the photosphere the granular size increases when the
flux tube approaches from below. In the convective overshoot region some 200km
above the photosphere adiabatic expansion produces cooling, darker regions with
the structure of granulation cells. We also find collapsed granulation in the
boundaries of the rising flux tube. Once the flux tube has crossed the
photosphere, bright points related with concentrated magnetic field, vorticity,
high vertical velocities and heating by compressed material are found at
heights up to 500km above the photosphere. At greater heights in the magnetized
chromosphere, the rising flux tube produces a cool, magnetized bubble that
tends to expel the usual chromospheric oscillations. In addition the rising
flux tube dramatically increases the chromospheric scale height, pushing the
transition region and corona aside such that the chromosphere extends up to 6Mm
above the photosphere. The emergence of magnetic flux tubes through the
photosphere to the lower corona is a relatively slow process, taking of order 1
hour.Comment: 53 pages,79 figures, Submitted to Ap
Gravitational Equilibrium in the Presence of a Positive Cosmological Constant
We reconsider the virial theorem in the presence of a positive cosmological
constant Lambda. Assuming steady state, we derive an inequality of the form rho
>= A (Lambda / 4 pi GN) for the mean density rho of the astrophysical object.
With a minimum at Asphere = 2, its value can increase by several orders of
magnitude as the shape of the object deviates from a spherically symmetric one.
This, among others, indicates that flattened matter distributions like e.g.
clusters or superclusters, with low density, cannot be in gravitational
equilibrium.Comment: 7 pages, no figure
Statistical Properties of Avalanches in Networks
We characterize the distributions of size and duration of avalanches
propagating in complex networks. By an avalanche we mean the sequence of events
initiated by the externally stimulated `excitation' of a network node, which
may, with some probability, then stimulate subsequent firings of the nodes to
which it is connected, resulting in a cascade of firings. This type of process
is relevant to a wide variety of situations, including neuroscience, cascading
failures on electrical power grids, and epidemology. We find that the
statistics of avalanches can be characterized in terms of the largest
eigenvalue and corresponding eigenvector of an appropriate adjacency matrix
which encodes the structure of the network. By using mean-field analyses,
previous studies of avalanches in networks have not considered the effect of
network structure on the distribution of size and duration of avalanches. Our
results apply to individual networks (rather than network ensembles) and
provide expressions for the distributions of size and duration of avalanches
starting at particular nodes in the network. These findings might find
application in the analysis of branching processes in networks, such as
cascading power grid failures and critical brain dynamics. In particular, our
results show that some experimental signatures of critical brain dynamics
(i.e., power-law distributions of size and duration of neuronal avalanches),
are robust to complex underlying network topologies.Comment: 11 pages, 7 figure
Dynamics and Pattern Formation in Large Systems of Spatially-Coupled Oscillators with Finite Response Times
We consider systems of many spatially distributed phase oscillators that
interact with their neighbors. Each oscillator is allowed to have a different
natural frequency, as well as a different response time to the signals it
receives from other oscillators in its neighborhood. Using the ansatz of Ott
and Antonsen (Ref. \cite{OA1}) and adopting a strategy similar to that employed
in the recent work of Laing (Ref. \cite{Laing2}), we reduce the microscopic
dynamics of these systems to a macroscopic partial-differential-equation
description. Using this macroscopic formulation, we numerically find that
finite oscillator response time leads to interesting spatio-temporal dynamical
behaviors including propagating fronts, spots, target patterns, chimerae,
spiral waves, etc., and we study interactions and evolutionary behaviors of
these spatio-temporal patterns
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