21,244 research outputs found
Small World Graphs by the iterated "My Friends are Your Friends'' Principle
We study graphs obtained by successive creation and destruction of edges into
small neighborhoods of the vertices. Starting with a circle graph of large
diameter we obtain small world graphs with logarithmic diameter, high
clustering coefficients and a fat tail distribution for the degree. Only local
edge formation processes are involved and no preferential attachment was used.
Furthermore we found an interesting phase transition with respect to the
initial conditions.Comment: Latex, 12 pages with 10 figure
Functional centrality in graphs
In this paper we introduce the functional centrality as a generalization of
the subgraph centrality. We propose a general method for characterizing nodes
in the graph according to the number of closed walks starting and ending at the
node. Closed walks are appropriately weighted according to the topological
features that we need to measure
The lowest singlet-triplet excitation energy of BN: a converged coupled cluster perspective
The notoriously small excitation energy of the BN
diatomic has been calculated using high-order coupled cluster methods.
Convergence has been established in both the 1-particle basis set and the
coupled cluster expansion. Explicit inclusion of connected quadruple
excitations is required for even semiquantitative agreement with
the limit value, while connected quintuple excitations still have
an effect of about 60 cm. Still higher excitations only account for
about 10 cm. Inclusion of inner-shell correlation further reduces
by about 60 cm at the CCSDT, and 85 cm at the CCSDTQ level. Our
best estimate, =18340 cm, is in excellent agreement with
earlier calculations and experiment, albeit with a smaller (and conservative)
uncertainty. The dissociation energy of BN() is =105.740.16
kcal/mol and =103.570.16 kcal/mol.Comment: J. Chem. Phys., in pres
Thermodynamic limit of the first-order phase transition in the Kuramoto model
In the Kuramoto model, a uniform distribution of the natural frequencies
leads to a first-order (i.e., discontinuous) phase transition from incoherence
to synchronization, at the critical coupling parameter . We obtain the
asymptotic dependence of the order parameter above criticality: . For a finite population, we demonstrate that the population
size may be included into a self-consistency equation relating and
in the synchronized state. We analyze the convergence to the thermodynamic
limit of two alternative schemes to set the natural frequencies. Other
frequency distributions different from the uniform one are also considered.Comment: 6 page
Quasi-Periodic Oscillations in Short Recurring Bursts of the magnetars SGR 1806-20 and SGR 1900+14 Observed With RXTE
Quasi-periodic oscillations (QPOs) observed in the giant flares of magnetars
are of particular interest due to their potential to open up a window into the
neutron star interior via neutron star asteroseismology. However, only three
giant flares have been observed. We therefore make use of the much larger data
set of shorter, less energetic recurrent bursts. Here, we report on a search
for QPOs in a large data set of bursts from the two most burst-active
magnetars, SGR 1806-20 and SGR 1900+14, observed with the Rossi X-ray Timing
Explorer (RXTE). We find a single detection in an averaged periodogram
comprising 30 bursts from SGR 1806-20, with a frequency of 57 Hz and a width of
5 Hz, remarkably similar to a giant flare QPO observed from SGR 1900+14. This
QPO fits naturally within the framework of global magneto-elastic torsional
oscillations employed to explain the giant flare QPOs. Additionally, we uncover
a limit on the applicability of Fourier analysis for light curves with low
background count rates and strong variability on short timescales. In this
regime, standard Fourier methodology and more sophisticated Fourier analyses
fail in equal parts by yielding an unacceptably large number of false positive
detections. This problem is not straightforward to solve in the Fourier domain.
Instead, we show how simulations of light curves can offer a viable solution
for QPO searches in these light curves.Comment: accepted for publication in ApJ; 12 pages, 7 figures; code +
instructions at https://github.com/dhuppenkothen/MagnetarQPOSearchPaper ;
associated data products at
http://figshare.com/articles/SGR_1900_14_RXTE_Data/1184101 (SGR 1900+14) and
http://figshare.com/articles/SGR_1806_20_Bursts_RXTE_data_set/1184427 (SGR
1806-20
A method for predicting full scale buffet response with rigid wind tunnel model fluctuating pressure data. Volume 1: Prediction method development and assessment
The method requires unsteady aerodynamic forces, natural airplane modes, and the measured pressure data as input. A gust response computer program is used to calculate buffet response due to the forcing function posed by the measured pressure data. By calculating both symmetric and antisymmetric solutions, upper and lower bounds on full-scale buffet response are formed. Comparisons of predictions with flight test results are made and the effects of horizontal tail loads and static aeroelasticity are shown. Discussions are also presented on the effects of primary wing torsion modes, chordwise and spanwise phase angles, and altitude
Neutron star glitches have a substantial minimum size
Glitches are sudden spin-up events that punctuate the steady spin down of
pulsars and are thought to be due to the presence of a superfluid component
within neutron stars. The precise glitch mechanism and its trigger, however,
remain unknown. The size of glitches is a key diagnostic for models of the
underlying physics. While the largest glitches have long been taken into
account by theoretical models, it has always been assumed that the minimum size
lay below the detectability limit of the measurements. In this paper we define
general glitch detectability limits and use them on 29 years of daily
observations of the Crab pulsar, carried out at Jodrell Bank Observatory. We
find that all glitches lie well above the detectability limits and by using an
automated method to search for small events we are able to uncover the full
glitch size distribution, with no biases. Contrary to the prediction of most
models, the distribution presents a rapid decrease of the number of glitches
below ~0.05 Hz. This substantial minimum size indicates that a glitch must
involve the motion of at least several billion superfluid vortices and provides
an extra observable which can greatly help the identification of the trigger
mechanism. Our study also shows that glitches are clearly separated from all
the other rotation irregularities. This supports the idea that the origin of
glitches is different to that of timing noise, which comprises the unmodelled
random fluctuations in the rotation rates of pulsars.Comment: 8 pages; 4 figures. Accepted for publication in MNRA
The Spread of Opinions and Proportional Voting
Election results are determined by numerous social factors that affect the
formation of opinion of the voters, including the network of interactions
between them and the dynamics of opinion influence. In this work we study the
result of proportional elections using an opinion dynamics model similar to
simple opinion spreading over a complex network. Erdos-Renyi, Barabasi-Albert,
regular lattices and randomly augmented lattices are considered as models of
the underlying social networks. The model reproduces the power law behavior of
number of candidates with a given number of votes found in real elections with
the correct slope, a cutoff for larger number of votes and a plateau for small
number of votes. It is found that the small world property of the underlying
network is fundamental for the emergence of the power law regime.Comment: 10 pages, 7 figure
Spreading and shortest paths in systems with sparse long-range connections
Spreading according to simple rules (e.g. of fire or diseases), and
shortest-path distances are studied on d-dimensional systems with a small
density p per site of long-range connections (``Small-World'' lattices). The
volume V(t) covered by the spreading quantity on an infinite system is exactly
calculated in all dimensions. We find that V(t) grows initially as t^d/d for
t>t^*$,
generalizing a previous result in one dimension. Using the properties of V(t),
the average shortest-path distance \ell(r) can be calculated as a function of
Euclidean distance r. It is found that
\ell(r) = r for r<r_c=(2p \Gamma_d (d-1)!)^{-1/d} log(2p \Gamma_d L^d), and
\ell(r) = r_c for r>r_c.
The characteristic length r_c, which governs the behavior of shortest-path
lengths, diverges with system size for all p>0. Therefore the mean separation s
\sim p^{-1/d} between shortcut-ends is not a relevant internal length-scale for
shortest-path lengths. We notice however that the globally averaged
shortest-path length, divided by L, is a function of L/s only.Comment: 4 pages, 1 eps fig. Uses psfi
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