2,689 research outputs found
Organized versus self-organized criticality in the abelian sandpile model
We define stabilizability of an infinite volume height configuration and of a
probability measure on height configurations. We show that for high enough
densities, a probability measure cannot be stabilized. We also show that in
some sense the thermodynamic limit of the uniform measures on the recurrent
configurations of the abelian sandpile model (ASM) is a maximal element of the
set of stabilizable measures. In that sense the self-organized critical
behavior of the ASM can be understood in terms of an ordinary transition
between stabilizable and non-stabilizableComment: 17 pages, appeared in Markov Processes and Related Fields 200
A note on the abelian sandpile in Z^d
We analyse the abelian sandpile model on \mathbbm{Z}^d for the starting
configuration of particles in the origin and particles otherwise. We
give a new short proof of the theorem of Fey, Levine and Peres \cite{FLP} that
the radius of the toppled cluster of this configuration is
Length correction for larval and early-juvenile Atlantic menhaden (Brevoortia tyrannus) after preservation in alcohol
Body length measurement is an important part of growth, condition, and mortality analyses of larval and juvenile fish. If the measurements are not accurate (i.e., do not reflect real fish length), results of subsequent analyses may be affected considerably (McGurk, 1985; Fey, 1999; Porter et al., 2001). The primary cause of error in fish length measurement is shrinkage related to collection and
preservation (Theilacker, 1980; Hay, 1981; Butler, 1992; Fey, 1999). The magnitude of shrinkage depends on many factors, namely the duration and speed of the collection tow, abundance of other planktonic organisms in the sample (Theilacker, 1980; Hay, 1981; Jennings, 1991), the type and
strength of the preservative (Hay, 1982), and the species of fish (Jennings, 1991; Fey, 1999). Further, fish size affects shrinkage (Fowler and Smith, 1983; Fey, 1999, 2001), indicating that live length should be modeled as a function of preserved length (Pepin et al., 1998; Fey, 1999)
Driving sandpiles to criticality and beyond
A popular theory of self-organized criticality relates driven dissipative
systems to systems with conservation. This theory predicts that the stationary
density of the abelian sandpile model equals the threshold density of the
fixed-energy sandpile. We refute this prediction for a wide variety of
underlying graphs, including the square grid. Driven dissipative sandpiles
continue to evolve even after reaching criticality. This result casts doubt on
the validity of using fixed-energy sandpiles to explore the critical behavior
of the abelian sandpile model at stationarity.Comment: v4 adds referenc
Bendings of radio jets in BL Lacertae objects I: EVN and MERLIN observations
Several blazars, and BL Lac objects in particular, show a misalignment
between the jet orientation on parsec and kiloparsec scales. Some authors (i.e.
Conway & Murphy, 1993) have attempted to explain this behaviour invoking
helical jets for misalignment angles around 90\degr, showing how in this case
there are interesting implications for the understanding of the medium into
which the jet is expanding. By comparing sensitive VLA observations (Cassaro et
al., 1999) with images available in the literature for the BL Lac objects from
the 1-Jy Sample (Stickel et al., 1991), it is clear that there is a wide range
of misalignments between the initial jet direction and the kpc-scale jet, when
detected. We have carried out VLBI observations of these BL Lac objects, in
order to investigate the spatial evolution of the radio jets from few tens to
hundreds of mas, and to search for helical jets in this class of sources. We
present here the first dataset obtained from EVN+MERLIN observations at 5 GHz
for seven objects. From these observations we never have a clear detection of
helical jets, we only have a possible signature of their presence in 2 objects.
In only one of the sources with a misalignment angle around 90\degr the
presence of helical jets can be ruled out. This implies that it is not possible
to invoke helical jets to explain the morphology of all the sources showing a
misalignment of about 90\degr between the parsec and the kiloparsec scale
jets.Comment: 12 pages, 9 figures, latex, accepted by Astronomy & Astrophysic
Current Results from the RRFID Kinematic Survey: Apparent Speeds from the First Five Years of Data
We present current results from our ongoing project to study the parsec-scale
relativistic jet kinematics of sources in the U.S. Naval Observatory's Radio
Reference Frame Image Database (RRFID). The RRFID consists of snapshot
observations using the VLBA plus up to 9 additional antennas at 8 and 2 GHz.
The Image Database currently contains about 3000 images of 450 sources from
1994 to 2004, with some sources having images at 20 epochs or more. We have now
completed analysis of the 8 GHz images for all sources observed at 3 or more
epochs from 1994 to 1998. The completed analysis comprises 966 images of 87
sources, or an average of 11 epochs per source. Apparent jet speeds have been
measured for these sources, and the resulting speed distribution has been
compared with results obtained by other large VLBI surveys. The measured
apparent speed distribution agrees with those found by the 2 cm survey and
Caltech-Jodrell Bank (CJ) survey; however, when a source-by-source comparison
is done with the 2 cm survey results, significant disagreement is found in the
apparent speed measurements for a number of sources. This disagreement can be
traced in most cases to either an insufficient time baseline for the current
RRFID results, or to apparent component mis-identification in the 2 cm survey
results caused by insufficient time sampling. These results emphasize the need
for long time baselines and dense time sampling for multi-epoch monitoring of
relativistic jets.Comment: 4 pages, To be published in the Proceedings of the 7th European VLBI
Network Symposiu
The Celestial Reference Frame at 24 and 43 GHz. II. Imaging
We have measured the sub-milli-arcsecond structure of 274 extragalactic
sources at 24 and 43 GHz in order to assess their astrometric suitability for
use in a high frequency celestial reference frame (CRF). Ten sessions of
observations with the Very Long Baseline Array have been conducted over the
course of 5 years, with a total of 1339 images produced for the 274
sources. There are several quantities that can be used to characterize the
impact of intrinsic source structure on astrometric observations including the
source flux density, the flux density variability, the source structure index,
the source compactness, and the compactness variability. A detailed analysis of
these imaging quantities shows that (1) our selection of compact sources from
8.4 GHz catalogs yielded sources with flux densities, averaged over the
sessions in which each source was observed, of about 1 Jy at both 24 and 43
GHz, (2) on average the source flux densities at 24 GHz varied by 20%-25%
relative to their mean values, with variations in the session-to-session flux
density scale being less than 10%, (3) sources were found to be more compact
with less intrinsic structure at higher frequencies, and (4) variations of the
core radio emission relative to the total flux density of the source are less
than 8% on average at 24 GHz. We conclude that the reduction in the effects due
to source structure gained by observing at higher frequencies will result in an
improved CRF and a pool of high-quality fiducial reference points for use in
spacecraft navigation over the next decade.Comment: 63 pages, 18 figures, 6 tables, accepted by the Astronomical Journa
Effect of type of otolith and preparation technique on age estimation of larval and juvenile spot (Leiostomus xanthurus)
Otoliths of larval and juvenile fish provide a record of age, size, growth, and development (Campana and Neilson,
1985; Thorrold and Hare, 2002). However, determining the time of first increment formation in otoliths (Campana, 2001) and assessing the accuracy (deviation from real age)
and precision (repeatability of increment counts from the same otolith) of increment counts are prerequisites for using otoliths to study the life history of fish (Campana and Moksness, 1991). For most fish species, first increment deposition occurs either at hatching, a day after hatching, or after first feeding and yolksac absorption (Jones, 1986; Thorrold and Hare, 2002). Increment deposition before
hatching also occurs (Barkmann and Beck, 1976; Radtke and Dean, 1982). If first increment deposition does not occur at hatching, the standard procedure is to add a predetermined number to increment counts to estimate fish age (Campana and Neilson, 1985)
Growth Rates and Explosions in Sandpiles
We study the abelian sandpile growth model, where n particles are added at
the origin on a stable background configuration in Z^d. Any site with at least
2d particles then topples by sending one particle to each neighbor. We find
that with constant background height h <= 2d-2, the diameter of the set of
sites that topple has order n^{1/d}. This was previously known only for h<d.
Our proof uses a strong form of the least action principle for sandpiles, and a
novel method of background modification.
We can extend this diameter bound to certain backgrounds in which an
arbitrarily high fraction of sites have height 2d-1. On the other hand, we show
that if the background height 2d-2 is augmented by 1 at an arbitrarily small
fraction of sites chosen independently at random, then adding finitely many
particles creates an explosion (a sandpile that never stabilizes).Comment: 19 pages, 4 figures, to appear in Journal of Statistical Physics. v2
corrects the proof of the outer bound of Theorem 4.1 of arXiv:0704.068
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