15,849 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
Magnetic characterization and switching of Co nano-rings in current-perpendicular-to-plane configuration
We fabricated Co nano-rings incorporated in the vertical pseudo-spin-valve
nanopillar structures with deep submicron lateral sizes. It is shown that the
current-perpendicular-to-plane giant magnetoresistance can be used to
characterize a very small magnetic nano-ring effectively. Both the onion state
and the flux-closure vortex state are observed. The Co nano-rings can be
switched between the onion states as well as between onion and vortex states
not only by the external field but also by the perpendicularly injected dc
current
On the Backbending Mechanism of Cr
The mechanism of backbending in Cr is investigated in terms of the
Projected Shell Model and the Generator Coordinate Method. It is shown that
both methods are reasonable shell model truncation schemes. These two quite
different quantum mechanical approaches lead to a similar conclusion that the
backbending is due to a band crossing involving an excited band which is built
on simultaneously broken neutron and proton pairs in the ``intruder'' subshell
. It is pointed out that this type of band crossing is usually known
to cause the second backbending in rare-earth nuclei.Comment: 4 pages, 4 figures, accepted for publication in Phys. Rev. Let
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
Suboptimal quantum-error-correcting procedure based on semidefinite programming
In this paper, we consider a simplified error-correcting problem: for a fixed
encoding process, to find a cascade connected quantum channel such that the
worst fidelity between the input and the output becomes maximum. With the use
of the one-to-one parametrization of quantum channels, a procedure finding a
suboptimal error-correcting channel based on a semidefinite programming is
proposed. The effectiveness of our method is verified by an example of the
bit-flip channel decoding.Comment: 6 pages, no figure, Some notations differ from those in the PRA
versio
Dual-camera system for high-speed imaging in particle image velocimetry
Particle image velocimetry is an important technique in experimental fluid
mechanics, for which it has been essential to use a specialized high-speed
camera. However, the high speed is at the expense of other performances of the
camera, i.e., sensitivity and image resolution. Here, we demonstrate that the
high-speed imaging is also possible with a pair of still cameras.Comment: 4 pages, accepted by Journal of Visualization (see
http://www.springerlink.com
New Lower Bounds on the Self-Avoiding-Walk Connective Constant
We give an elementary new method for obtaining rigorous lower bounds on the
connective constant for self-avoiding walks on the hypercubic lattice .
The method is based on loop erasure and restoration, and does not require exact
enumeration data. Our bounds are best for high , and in fact agree with the
first four terms of the expansion for the connective constant. The bounds
are the best to date for dimensions , but do not produce good results
in two dimensions. For , respectively, our lower bound is within
2.4\%, 0.43\%, 0.12\%, 0.044\% of the value estimated by series extrapolation.Comment: 35 pages, 388480 bytes Postscript, NYU-TH-93/02/0
Nonmonotonic temperature dependence of critical current in diffusive d-wave junctions
We study the Josephson effect in D/I/DN/I/D junctions, where I, DN and D
denote an insulator, a diffusive normal metal and a d-wave superconductor,
respectively.The Josephson current is calculated based on the quasiclassical
Green's function theory with a general boundary condition for unconventional
superconducting junctions. In contrast to s-wave junctions, the product of the
Josephson current and the normal state resistance is enhanced by making the
interface barriers stronger. The Josephson current has a nonmonotonic
temperature dependence due to the competition between the proximity effect and
the midgap Andreev resonant states.Comment: 5 pages, 4 figure
Reanalysis of Data Taken by the CANGAROO 3.8 Meter Imaging Atmospheric Cherenkov Telescope: PSR B1706-44, SN 1006, and Vela
We have reanalyzed data from observations of PSR B1706-44, SN 1006, and the
Vela pulsar region made with the CANGAROO 3.8 m imaging atmospheric Cherenkov
telescope between 1993 and 1998 in response to the results reported for these
sources by the H.E.S.S. collaboration. In our reanalysis, in which gamma-ray
selection criteria have been determined exclusively using gamma-ray simulations
and OFF-source data as background samples, no significant TeV gamma-ray signals
have been detected from compact regions around PSR B1706-44 or within the
northeast rim of SN 1006. We discuss reasons why the original analyses gave the
source detections. The reanalysis did result in a TeV gamma-ray signal from the
Vela pulsar region at the 4.5 sigma level using 1993, 1994, and 1995 data. The
excess was located at the same position, 0.13 deg. to the southeast of the Vela
pulsar, as that reported in the original analysis. We have investigated the
effect of the acceptance distribution in the field of view of the 3.8 m
telescope, which rapidly decreases toward the edge of the field of the camera,
on the detected gamma-ray morphology. The expected excess distribution for the
3.8 m telescope has been obtained by reweighting the distribution of HESS
J0835-455 measured by H.E.S.S. with the acceptance of the 3.8 m telescope. The
result is morphologically comparable to the CANGAROO excess distribution,
although the profile of the acceptance-reweighted H.E.S.S. distribution is more
diffuse than that of CANGAROO. The integral gamma-ray flux from HESS J0835-455
has been estimated for the same region as defined by H.E.S.S. from the
1993-1995 data of CANGAROO to be F(> 4.0 +/- 1.6 TeV) = (3.28 +/- 0.92) x
10^{-12} photons cm^{-2} s^{-1}, which is statistically consistent with the
integral flux obtained by H.E.S.S.Comment: Published in ApJ, minor improvement
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