22,629 research outputs found
Transience and recurrence of random walks on percolation clusters in an ultrametric space
We study existence of percolation in the hierarchical group of order ,
which is an ultrametric space, and transience and recurrence of random walks on
the percolation clusters. The connection probability on the hierarchical group
for two points separated by distance is of the form , with , non-negative constants , and . Percolation was proved in Dawson and Gorostiza
(2013) for , with
. In this paper we improve the result for the critical case by
showing percolation for . We use a renormalization method of the type
in the previous paper in a new way which is more intrinsic to the model. The
proof involves ultrametric random graphs (described in the Introduction). The
results for simple (nearest neighbour) random walks on the percolation clusters
are: in the case the walk is transient, and in the critical case
, there exists a critical
such that the walk is recurrent for and transient for
. The proofs involve graph diameters, path lengths, and
electric circuit theory. Some comparisons are made with behaviours of random
walks on long-range percolation clusters in the one-dimensional Euclidean
lattice.Comment: 27 page
GDL: a model infrastructure for a regional digital library
This brief article describes the early days of the Glasgow Digital Library (GDL), when it was a cross-sectoral and city-wide collaborative initiative involving Strathclyde, Glasgow and Caledonian Universities, as well as Glasgow City Libraries and Archives and the Glasgow Colleges Group
Hierarchical equilibria of branching populations
The objective of this paper is the study of the equilibrium behavior of a
population on the hierarchical group consisting of families of
individuals undergoing critical branching random walk and in addition these
families also develop according to a critical branching process. Strong
transience of the random walk guarantees existence of an equilibrium for this
two-level branching system. In the limit (called the hierarchical
mean field limit), the equilibrium aggregated populations in a nested sequence
of balls of hierarchical radius converge to a backward
Markov chain on . This limiting Markov chain can be explicitly
represented in terms of a cascade of subordinators which in turn makes possible
a description of the genealogy of the population.Comment: 62 page
Mode-Coupling Theory of Colloids with Short-range Attractions
Within the framework of the mode-coupling theory of super-cooled liquids, we
investigate new phenomena in colloidal systems on approach to their glass
transitions. When the inter-particle potential contains an attractive part,
besides the usual repulsive hard core, two intersecting liquid-glass transition
lines appear, one of which extends to low densities, while the other one, at
high densities, shows a re-entrant behaviour. In the glassy region a new type
of transition appears between two different types of glasses. The complex
phenomenology can be described in terms of higher order glass transition
singularities. The various glass phases are characterised by means of their
viscoelastic properties. The glass driven by attractions has been associated to
particle gels, and the other glass is the well known repulsive colloidal glass.
These correspondences, in associations with the new predictions of glassy
behaviour mean that such phenomena may be expected in colloidal systems with,
for example, strong depletion or other short-ranged attractive potentials.Comment: 17 pages, 8 figure
Characterization of Mauritius parakeet (Psittacula eques) microsatellite loci and their cross-utility in other parrots (Psittacidae, Aves).
We characterized 21 polymorphic microsatellite loci in the endangered Mauritius parakeet (Psittacula eques). Loci were isolated from a Mauritius parakeet genomic library that had been enriched separately for eight different repeat motifs. Loci were characterized in up to 43 putatively unrelated Mauritius parakeets from a single population inhabiting the Black River Gorges National Park, Mauritius. Each locus displayed between three and nine alleles, with the observed heterozygosity ranging between 0.39 and 0.96. All loci were tested in 10 other parrot species. Despite testing few individuals, between seven and 21 loci were polymorphic in each of seven species tested
Scalar meson in dynamical and partially quenched two-flavor QCD: lattice results and chiral loops
This is an exploratory study of the lightest non-singlet scalar
state on the lattice with two dynamical quarks. Domain Wall fermions are used
for both sea and valence quarks on a 16^3*32 lattice with an inverse lattice
spacing of 1.7 GeV. We extract the scalar meson mass 1.58(34) GeV from the
exponential time-dependence of the dynamical correlators with
and N_f=2. Since this statistical error-bar from dynamical correlators is
rather large, we analyze also the partially quenched lattice correlators with
not equal . They are positive for and
negative for . In order to understand this striking effect of
partial quenching, we derive the scalar correlator within the Partially
Quenched ChPT and find it describes lattice correlators well. The leading
unphysical contribution in Partially Quenched ChPT comes from the exchange of
the two pseudoscalar fields and is also positive for and
negative for at large t. After the subtraction of this
unphysical contribution from the partially quenched lattice correlators, the
correlators are positive and exponentially falling. The resulting scalar meson
mass 1.51(19) GeV from the partially quenched correlators is consistent with
the dynamical result and has appreciably smaller error-bar.Comment: 23 pages, 8 figure
Abell 1033: birth of a radio phoenix
Extended steep-spectrum radio emission in a galaxy cluster is usually
associated with a recent merger. However, given the complex scenario of galaxy
cluster mergers, many of the discovered sources hardly fit into the strict
boundaries of a precise taxonomy. This is especially true for radio phoenixes
that do not have very well defined observational criteria. Radio phoenixes are
aged radio galaxy lobes whose emission is reactivated by compression or other
mechanisms. Here, we present the detection of a radio phoenix close to the
moment of its formation. The source is located in Abell 1033, a peculiar galaxy
cluster which underwent a recent merger. To support our claim, we present
unpublished Westerbork Synthesis Radio Telescope and Chandra observations
together with archival data from the Very Large Array and the Sloan Digital Sky
Survey. We discover the presence of two sub-clusters displaced along the N-S
direction. The two sub-clusters probably underwent a recent merger which is the
cause of a moderately perturbed X-ray brightness distribution. A steep-spectrum
extended radio source very close to an AGN is proposed to be a newly born radio
phoenix: the AGN lobes have been displaced/compressed by shocks formed during
the merger event. This scenario explains the source location, morphology,
spectral index, and brightness. Finally, we show evidence of a density
discontinuity close to the radio phoenix and discuss the consequences of its
presence.Comment: accepted MNRA
- …