211 research outputs found
Weighted distances in scale-free preferential attachment models
We study three preferential attachment models where the parameters are such
that the asymptotic degree distribution has infinite variance. Every edge is
equipped with a non-negative i.i.d. weight. We study the weighted distance
between two vertices chosen uniformly at random, the typical weighted distance,
and the number of edges on this path, the typical hopcount. We prove that there
are precisely two universality classes of weight distributions, called the
explosive and conservative class. In the explosive class, we show that the
typical weighted distance converges in distribution to the sum of two i.i.d.
finite random variables. In the conservative class, we prove that the typical
weighted distance tends to infinity, and we give an explicit expression for the
main growth term, as well as for the hopcount. Under a mild assumption on the
weight distribution the fluctuations around the main term are tight.Comment: Revised version, results are unchanged. 30 pages, 1 figure. To appear
in Random Structures and Algorithm
Ultrametric Logarithm Laws, II
We prove positive characteristic versions of the logarithm laws of Sullivan
and Kleinbock-Margulis and obtain related results in Metric Diophantine
Approximation.Comment: submitted to Montasefte Fur Mathemati
Tunable-filter imaging of quasar fields at z~1. I. A cluster around MRC B0450-221
Using a combination of multicolour broad- and narrow-band imaging techniques
and follow-up spectroscopy, we have detected an overdensity of galaxies in the
field of quasar MRC B0450-221, whose properties are consistent with a cluster
at the quasar redshift z=0.9. An excess of red galaxies (V-I>2.2, I-K'>3.8) is
evident within 1' of the quasar, with the colours expected for galaxies at
z=0.9 that have evolved passively for 3 Gyr or more. A number of line-emitting
galaxies (nine candidates with equivalent widths EW>70A) are also detected in
the field using the TAURUS Tunable Filter (TTF). Three have been confirmed
spectroscopically to indeed lie at z=0.9. The TTF candidates with the strongest
[O II] line emission cluster in a group which lies 200-700 kpc away from the
quasar and the red galaxy excess, and therefore most likely on the outskirts of
the cluster. These observations are the first in a series probing quasar
environments at z~1 with TTF.Comment: Accepted for publication in AJ. 25 pages, 24 figs (large files in jpg
or gif format), uses emulateapj.st
Exact solution of a two-type branching process: Clone size distribution in cell division kinetics
We study a two-type branching process which provides excellent description of
experimental data on cell dynamics in skin tissue (Clayton et al., 2007). The
model involves only a single type of progenitor cell, and does not require
support from a self-renewed population of stem cells. The progenitor cells
divide and may differentiate into post-mitotic cells. We derive an exact
solution of this model in terms of generating functions for the total number of
cells, and for the number of cells of different types. We also deduce large
time asymptotic behaviors drawing on our exact results, and on an independent
diffusion approximation.Comment: 16 page
Renormalization group approach to multiscale modelling in materials science
Dendritic growth, and the formation of material microstructure in general,
necessarily involves a wide range of length scales from the atomic up to sample
dimensions. The phase field approach of Langer, enhanced by optimal asymptotic
methods and adaptive mesh refinement, copes with this range of scales, and
provides an effective way to move phase boundaries. However, it fails to
preserve memory of the underlying crystallographic anisotropy, and thus is
ill-suited for problems involving defects or elasticity. The phase field
crystal (PFC) equation-- a conserving analogue of the Hohenberg-Swift equation
--is a phase field equation with periodic solutions that represent the atomic
density. It can natively model elasticity, the formation of solid phases, and
accurately reproduces the nonequilibrium dynamics of phase transitions in real
materials. However, the PFC models matter at the atomic scale, rendering it
unsuitable for coping with the range of length scales in problems of serious
interest. Here, we show that a computationally-efficient multiscale approach to
the PFC can be developed systematically by using the renormalization group or
equivalent techniques to derive appropriate coarse-grained coupled phase and
amplitude equations, which are suitable for solution by adaptive mesh
refinement algorithms
CLTs and asymptotic variance of time-sampled Markov chains
For a Markov transition kernel P and a probability distribution
μ on nonnegative integers, a time-sampled Markov chain evolves according
to the transition kernel Pμ = Σkμ(k)Pk. In this note we obtain CLT
conditions for time-sampled Markov chains and derive a spectral formula
for the asymptotic variance. Using these results we compare efficiency of
Barker's and Metropolis algorithms in terms of asymptotic variance
Superconductivity in the SU(N) Anderson Lattice at U=\infty
We present a mean-field study of superconductivity in a generalized N-channel
cubic Anderson lattice at U=\infty taking into account the effect of a
nearest-neighbor attraction J. The condition U=\infty is implemented within the
slave-boson formalism considering the slave bosons to be condensed. We consider
the -level occupancy ranging from the mixed valence regime to the Kondo
limit and study the dependence of the critical temperature on the various model
parameters for each of three possible Cooper pairing symmetries (extended s,
d-wave and p-wave pairing) and find interesting crossovers. It is found that
the d- and p- wave order parameters have, in general, very similar critical
temperatures. The extended s-wave pairing seems to be relatively more stable
for electronic densities per channel close to one and for large values of the
superconducting interaction J.Comment: Seven Figures; one appendix. Accepted for publication in Phys. Rev.
Decay of correlations for maps with uniformly contracting fibers and logarithm law for singular hyperbolic attractors
We consider two dimensional maps preserving a foliation which is uniformly
contracting and a one dimensional associated quotient map having exponential
convergence to equilibrium (iterates of Lebesgue measure converge exponentially
fast to physical measure). We prove that these maps have exponential decay of
correlations over a large class of observables. We use this result to deduce
exponential decay of correlations for the Poincare maps of a large class of
singular hyperbolic flows. From this we deduce logarithm laws for these flows.Comment: 39 pages; 03 figures; proof of Theorem 1 corrected; many typos
corrected; improvements on the statements and comments suggested by a
referee. Keywords: singular flows, singular-hyperbolic attractor, exponential
decay of correlations, exact dimensionality, logarithm la
On the Spectral Index of Distant Radio Galaxies
The problems of using the spectral index of radio galaxies in various tests,
in particular, in selecting distant radio sources are considered. The history
of the question of choosing a criterion of searching for distant radio galaxies
based on the spectral index is presented. For a new catalog of 2442 radio
galaxies constructed from NED, SDSS, and CATS data, an analytical form of the
sp ectral index.redshift relation has been determined for the first time. The
spectral index.angular size and spectral index.flux density diagrams have also
been constructed. Peculiarities of the distribution of sources on these
diagrams are discussed.Comment: 7 pages,5 figure
VLT spectropolarimetry of two powerful radio galaxies at z~1.4: UV continuum, emission-line properties and the nature of high-redshift dust
(Abridged) Deep VLT spectropolarimetric observations are presented for two
powerful radio galaxies, 0850-206 and 1303+091. These observations cover the
rest-frame wavelength range ~ 1450 - 3750 A. New radio observations and
continuum images of the same sources are also presented. These galaxies are the
first two observed from a complete sample of nine radio sources with redshifts
in the range 1.3 < z < 1.5 (selected from the equatorial sample of powerful
radio sources of Best, Rottgering & Lehnert), as part of a project aimed to
investigate the multi-component nature of the UV continuum in radio galaxies
and any variations of the continuum properties with the radio source age.
The larger radio source of the two, 0850-206, presents a high continuum
fractional polarization, averaging 17% across the observed wavelength range and
reaching 24% at rest-frame wavelengths of <2000 A. The smaller radio source,
1303+091, shows a lower continuum polarization, averaging 8% and rising to 11%
for rest-frame wavelengths >3000 A. For both galaxies, the position angle of
the electric vector is generally constant with wavelength and within ~15
degrees of perpendicular to the radio axis. Both their total flux spectra and
polarized flux spectra reveal the 2200 A dust feature, and comparison with dust
scattering models suggests that the composition of the dust in these galaxies
is similar to that of Galactic dust. In 0850-206, scattered quasar radiation
dominates the UV continuum emission, with the nebular continuum accounting for
no more than ~22% and no requirement for any additional emission component such
as emission from young stars. By contrast, in 1303+091, unpolarized radiation
could be a major constituent of the UV continuum emission, with starlight
accounting for up to ~50% and the nebular continuum accounting for ~11%.Comment: 20 pages, including 14 figures. MNRAS accepte
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