4,122 research outputs found
Extreme events and event size fluctuations in biased random walks on networks
Random walk on discrete lattice models is important to understand various
types of transport processes. The extreme events, defined as exceedences of the
flux of walkers above a prescribed threshold, have been studied recently in the
context of complex networks. This was motivated by the occurrence of rare
events such as traffic jams, floods, and power black-outs which take place on
networks. In this work, we study extreme events in a generalized random walk
model in which the walk is preferentially biased by the network topology. The
walkers preferentially choose to hop toward the hubs or small degree nodes. In
this setting, we show that extremely large fluctuations in event-sizes are
possible on small degree nodes when the walkers are biased toward the hubs. In
particular, we obtain the distribution of event-sizes on the network. Further,
the probability for the occurrence of extreme events on any node in the network
depends on its 'generalized strength', a measure of the ability of a node to
attract walkers. The 'generalized strength' is a function of the degree of the
node and that of its nearest neighbors. We obtain analytical and simulation
results for the probability of occurrence of extreme events on the nodes of a
network using a generalized random walk model. The result reveals that the
nodes with a larger value of 'generalized strength', on average, display lower
probability for the occurrence of extreme events compared to the nodes with
lower values of 'generalized strength'
Level density of a Fermi gas and integer partitions: a Gumbel-like finite-size correction
We investigate the many-body level density of gas of non-interacting
fermions. We determine its behavior as a function of the temperature and the
number of particles. As the temperature increases, and beyond the usual
Sommerfeld expansion that describes the degenerate gas behavior, corrections
due to a finite number of particles lead to Gumbel-like contributions. We
discuss connections with the partition problem in number theory, extreme value
statistics as well as differences with respect to the Bose gas.Comment: 5 pages, 1 figure, one figure added, accepted for publication in
Phys. Rev.
The time-evolution of bias
We study the evolution of the bias factor b and the mass-galaxy correlation
coefficient r in a simple analytic model for galaxy formation and the
gravitational growth of clustering. The model shows that b and r can be
strongly time-dependent, but tend to approach unity even if galaxy formation
never ends as the gravitational growth of clustering debiases the older
galaxies. The presence of random fluctuations in the sites of galaxy formation
relative to the mass distribution can cause large and rapidly falling bias
values at high redshift.Comment: 4 pages, with 2 figures included. Typos corrected to match published
ApJL version. Color figure and links at http://www.sns.ias.edu/~max/bias.html
or from [email protected]
A low CMB variance in the WMAP data
We have estimated the CMB variance from the three-year WMAP data, finding a
value which is significantly lower than the one expected from Gaussian
simulations using the WMAP best-fit cosmological model, at a significance level
of 98.7 per cent. This result is even more prominent if we consider only the
north ecliptic hemisphere (99.8 per cent). Different analyses have been
performed in order to identify a possible origin for this anomaly. In
particular we have studied the behaviour of single radiometers and single year
data as well as the effect of residual foregrounds and 1/f noise, finding that
none of these possibilities can explain the low value of the variance. We have
also tested the effect of varying the cosmological parameters, finding that the
estimated CMB variance tends to favour higher values of than the one of
the WMAP best-fit model. In addition, we have also tested the consistency
between the estimated CMB variance and the actual measured CMB power spectrum
of the WMAP data, finding a strong discrepancy. A possible interpretation of
this result could be a deviation from Gaussianity and/or isotropy of the CMB.Comment: 13 pages, 5 figures. Some new tests added. Section 5 largely
modified. Accepted for publication in MNRA
A Counts-in-Cells Analysis of Lyman-break Galaxies at z~3
We have measured the counts-in-cells fluctuations of 268 Lyman-break galaxies
with spectroscopic redshifts in six 9 arcmin by 9 arcmin fields at z~3. The
variance of galaxy counts in cubes of comoving side length 7.7, 11.9, 11.4
h^{-1} Mpc is \sigma_{gal}^2 ~ 1.3\pm0.4 for \Omega_M=1, 0.2 open, 0.3 flat,
implying a bias on these scales of \sigma_{gal} / \sigma_{mass} = 6.0\pm1.1,
1.9\pm0.4, 4.0\pm0.7. The bias and abundance of Lyman-break galaxies are
surprisingly consistent with a simple model of structure formation which
assumes only that galaxies form within dark matter halos, that Lyman-break
galaxies' rest-UV luminosities are tightly correlated with their dark masses,
and that matter fluctuations are Gaussian and have a linear power-spectrum
shape at z~3 similar to that determined locally (\Gamma~0.2). This conclusion
is largely independent of cosmology or spectral normalization \sigma_8. A
measurement of the masses of Lyman-break galaxies would in principle
distinguish between different cosmological scenarios.Comment: Accepted for publication in ApJ, 16 pages including 4 figure
Computational Study of Turbulent-Laminar Patterns in Couette Flow
Turbulent-laminar patterns near transition are simulated in plane Couette
flow using an extension of the minimal flow unit methodology. Computational
domains are of minimal size in two directions but large in the third. The long
direction can be tilted at any prescribed angle to the streamwise direction.
Three types of patterned states are found and studied: periodic, localized, and
intermittent. These correspond closely to observations in large aspect ratio
experiments.Comment: 4 pages, 5 figure
Universal Asymptotic Statistics of Maximal Relative Height in One-dimensional Solid-on-solid Models
We study the probability density function of the maximum relative
height in a wide class of one-dimensional solid-on-solid models of finite
size . For all these lattice models, in the large limit, a central limit
argument shows that, for periodic boundary conditions, takes a
universal scaling form , with the width of the fluctuating interface and the Airy
distribution function. For one instance of these models, corresponding to the
extremely anisotropic Ising model in two dimensions, this result is obtained by
an exact computation using transfer matrix technique, valid for any .
These arguments and exact analytical calculations are supported by numerical
simulations, which show in addition that the subleading scaling function is
also universal, up to a non universal amplitude, and simply given by the
derivative of the Airy distribution function .Comment: 13 pages, 4 figure
Fluctuation Spectrum from a Scalar-Tensor Bimetric Gravity Theory
Predictions of the CMB spectrum from a bimetric gravity theory
(gr-qc/0101126) are presented. The initial inflationary period in BGT is driven
by a vanishingly small speed of gravitational waves v_g in the very early
universe. This initial inflationary period is insensitive to the choice of
scalar field potential and initial values of the scalar field. After this
initial period of inflation, v_g will increase rapidly and the effects of a
potential will become important. We show that a quadratic potential introduced
into BGT yields an approximately flat spectrum with inflation parameters:
n_s=0.98, n_t=-0.027, alpha_s=-3.2e-4 and alpha_t=-5.0e-4, with r >= 0.014.Comment: 14 pages, uses amsmath, amssym
Theory of Parabolic Arcs in Interstellar Scintillation Spectra
Our theory relates the secondary spectrum, the 2D power spectrum of the radio
dynamic spectrum, to the scattered pulsar image in a thin scattering screen
geometry. Recently discovered parabolic arcs in secondary spectra are generic
features for media that scatter radiation at angles much larger than the rms
scattering angle. Each point in the secondary spectrum maps particular values
of differential arrival-time delay and fringe rate (or differential Doppler
frequency) between pairs of components in the scattered image. Arcs correspond
to a parabolic relation between these quantities through their common
dependence on the angle of arrival of scattered components. Arcs appear even
without consideration of the dispersive nature of the plasma. Arcs are more
prominent in media with negligible inner scale and with shallow wavenumber
spectra, such as the Kolmogorov spectrum, and when the scattered image is
elongated along the velocity direction. The arc phenomenon can be used,
therefore, to constrain the inner scale and the anisotropy of scattering
irregularities for directions to nearby pulsars. Arcs are truncated by finite
source size and thus provide sub micro arc sec resolution for probing emission
regions in pulsars and compact active galactic nuclei. Multiple arcs sometimes
seen signify two or more discrete scattering screens along the propagation
path, and small arclets oriented oppositely to the main arc persisting for long
durations indicate the occurrence of long-term multiple images from the
scattering screen.Comment: 22 pages, 11 figures, submitted to the Astrophysical Journa
ExoMol molecular line lists XXXV: a rotation-vibration line list for hot ammonia
A new hot line list for NH is presented. The line list CoYuTe was
constructed using an accurate, empirically refined potential energy surface and
a CCSD(T)/aug-cc-pVQZ ab initio dipole moment surface of ammonia, previously
reported. The line list is an improvement of the ammonia line list BYTe
[Yurchenko et al., Mon. Not. R. Astron. Soc., 413, 1828 (2011)]. The CoYuTe
line list covers wavenumbers up to 20000 cm, i.e. wavelengths beyond 0.5
m for temperatures up to 1500 K. Comparisons with the high temperature
experimental data from the literature show excellent agrement for wavenumbers
below 6000 cm. The CoYuTe line list contains 16.9 billion transitions
and is available from the ExoMol website (www.exomol.com) and the CDS database
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