16,552 research outputs found
Random graph asymptotics on high-dimensional tori. II. Volume, diameter and mixing time
For critical bond-percolation on high-dimensional torus, this paper proves
sharp lower bounds on the size of the largest cluster, removing a logarithmic
correction in the lower bound in Heydenreich and van der Hofstad (2007). This
improvement finally settles a conjecture by Aizenman (1997) about the role of
boundary conditions in critical high-dimensional percolation, and it is a key
step in deriving further properties of critical percolation on the torus.
Indeed, a criterion of Nachmias and Peres (2008) implies appropriate bounds on
diameter and mixing time of the largest clusters. We further prove that the
volume bounds apply also to any finite number of the largest clusters. The main
conclusion of the paper is that the behavior of critical percolation on the
high-dimensional torus is the same as for critical Erdos-Renyi random graphs.
In this updated version we incorporate an erratum to be published in a
forthcoming issue of Probab. Theory Relat. Fields. This results in a
modification of Theorem 1.2 as well as Proposition 3.1.Comment: 16 pages. v4 incorporates an erratum to be published in a forthcoming
issue of Probab. Theory Relat. Field
Anomalous Crossing Frequency in Odd Proton Nuclei
A generic explanation for the recently observed anomalous crossing
frequencies in odd proton rare earth nuclei is given. As an example, the proton
band in Ta is discussed in detail by using the
angular momentum projection theory. It is shown that the quadrupole pairing
interaction is decisive in delaying the crossing point and the changes in
crossing frequency along the isotope chain are due to the different neutron
shell fillings
Nuclear pairing and Coriolis effects in proton emitters
We introduce a Hartree-Fock-Bogoliubov mean-field approach to treat the
problem of proton emission from a deformed nucleus. By substituting a rigid
rotor in a particle-rotor-model with a mean-field we obtain a better
description of experimental data in Ho. The approach also elucidates
the softening of kinematic coupling between particle and collective rotation,
the Coriolis attenuation problem.Comment: 2 pages, 1 figur
The scaling limit of the incipient infinite cluster in high-dimensional percolation. II. Integrated super-Brownian excursion
For independent nearest-neighbour bond percolation on Z^d with d >> 6, we
prove that the incipient infinite cluster's two-point function and three-point
function converge to those of integrated super-Brownian excursion (ISE) in the
scaling limit. The proof is based on an extension of the new expansion for
percolation derived in a previous paper, and involves treating the magnetic
field as a complex variable. A special case of our result for the two-point
function implies that the probability that the cluster of the origin consists
of n sites, at the critical point, is given by a multiple of n^{-3/2}, plus an
error term of order n^{-3/2-\epsilon} with \epsilon >0. This is a strong
statement that the critical exponent delta is given by delta =2.Comment: 56 pages, 3 Postscript figures, in AMS-LaTeX, with graphicx, epic,
and xr package
Feeding behaviour and appetite in young children with non-organic failure to thrive
The study reported in this thesis was aimed at investigating taste preferences and caloric compensation in one to two year old children with non-organic failure to thrive (FTT) as compared to normally developing children of the same age. The sample studied included 28 cases with non-organic FTT, and 28 controls with normal growth. The study comprised two experiments. The first tested the child's relative preference for sucrose sweetened solutions versus water. The test session included six 60 second presentations of tastant at three levels of concentration n i.e. water, 0.2 Mol sucrose solution, and 0.4 Mol sucrose solution, with at least 30 second intervals between presentations. The second experiment measured caloric compensation, by testing the child's intake from a standard meal on two occasions, after a pre-load of no-calorie or high-calorie drink. In addition meal time behavioural observations were made, and information about the child’s feeding history was obtained from parent reports. All children regardless of whether they were failing to thrive or not preferred 0.2 Mol sucrose solution to 0.4 Mol sucrose and to water. The energy intake of children with FTT was lower than that of controls, and meal-time behaviours showed some differences between groups in both the child and parent behaviours. Unlike the controls the FTT children showed no caloric compensation, but showed a trend towards the opposite of compensation. Analysis of growth data showed that FTT in the sample studied was present from birth
Angular dependence of Josephson currents in unconventional superconducting junctions
Josephson effect in junctions between unconventional superconductors is
studied theoretically within the model describing the effects of interface
roughness. The particularly important issue of applicability of the frequently
used Sigrist-Rice formula for Josephson current in d-wave superconductor /
insulator / d-wave superconductor junctions is addressed. We show that although
the SR formula is not applicable in the ballistic case, it works well for rough
interfaces when the diffusive normal metal regions exist between the d-wave
superconductor and the insulator. It is shown that the SR approach only takes
into account the component of the d-wave pair potential symmetric with respect
to an inversion around the plane perpendicular to the interface. Similar
formula can be derived for general unconventional superconductors with
arbitrary angular momentum l.Comment: 4 pages, 4 figure
Scaling and data collapse for the mean exit time of asset prices
We study theoretical and empirical aspects of the mean exit time of financial
time series. The theoretical modeling is done within the framework of
continuous time random walk. We empirically verify that the mean exit time
follows a quadratic scaling law and it has associated a pre-factor which is
specific to the analyzed stock. We perform a series of statistical tests to
determine which kind of correlation are responsible for this specificity. The
main contribution is associated with the autocorrelation property of stock
returns. We introduce and solve analytically both a two-state and a three-state
Markov chain models. The analytical results obtained with the two-state Markov
chain model allows us to obtain a data collapse of the 20 measured MET profiles
in a single master curve.Comment: REVTeX 4, 11 pages, 8 figures, 1 table, submitted for publicatio
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