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

A Calculation on the Self-field of a Point Charge and the Unruh Effect

Within the context of quantum field theory in curved spacetimes, Hacyan and Sarmiento defined the vacuum stress-energy tensor with respect to the accelerated observer. They calculated it for uniform acceleration and circular motion, and derived that the rotating observer perceives a flux. Mane related the flux to synchrotron radiation. In order to investigate the relation between the vacuum stress and bremsstrahlung, we estimate the stress-energy tensor of the electromagnetic field generated by a point charge, at the position of the charge. We use the retarded field as a self-field of the point charge. Therefore the tensor diverges if we evaluate it as it is. Hence we remove the divergent contributions by using the expansion of the tensor in powers of the distance from the point charge. Finally, we take an average for the angular dependence of the expansion. We calculate it for the case of uniform acceleration and circular motion, and it is found that the order of the vacuum stress multiplied by $\pi\alpha$ ($\alpha=e^2/\hbar c$ is the fine structure constant) is equal to that of the self-stress. In the Appendix, we give another trial approach with a similar result.Comment: 25 pages, Submitted to Prog. Theor. Phy

Perturbed Self-Similar Massless Scalar Field in Spherically Symmetric Spaceimes

In this paper, we investigate the linear perturbations of the spherically symmetric spacetimes with kinematic self-similarity of the second kind. The massless scalar field equations are solved which yield the background and an exact solutions for the perturbed equations. We discuss the boundary conditions of the resulting perturbed solutions. The possible perturbation modes turn out to be stable as well as unstable. The analysis leads to the conclusion that there does not exist any critical solution.Comment: 15 pages, accepted for publication Int. J. Mod. Phys.

On the Backbending Mechanism of 48^{48}Cr

The mechanism of backbending in $^{48}$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 $f_{7/2}$. 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

Pattern Matching and Discourse Processing in Information Extraction from Japanese Text

Information extraction is the task of automatically picking up information of interest from an unconstrained text. Information of interest is usually extracted in two steps. First, sentence level processing locates relevant pieces of information scattered throughout the text; second, discourse processing merges coreferential information to generate the output. In the first step, pieces of information are locally identified without recognizing any relationships among them. A key word search or simple pattern search can achieve this purpose. The second step requires deeper knowledge in order to understand relationships among separately identified pieces of information. Previous information extraction systems focused on the first step, partly because they were not required to link up each piece of information with other pieces. To link the extracted pieces of information and map them onto a structured output format, complex discourse processing is essential. This paper reports on a Japanese information extraction system that merges information using a pattern matcher and discourse processor. Evaluation results show a high level of system performance which approaches human performance.Comment: See http://www.jair.org/ for any accompanying file

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

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

Modelling of EIS spectrum drift from instrumental temperatures

An empirical model has been developed to reproduce the drift of the spectrum recorded by EIS on board Hinode using instrumental temperatures and relative motion of the spacecraft. The EIS spectrum shows an artificial drift in wavelength dimension in sync with the revolution of the spacecraft, which is caused by temperature variations inside the spectrometer. The drift amounts to 70 km s$^{-1}$ in Doppler velocity and introduces difficulties in velocity measurements. An artificial neural network is incorporated to establish a relationship between the instrumental temperatures and the spectral drift. This empirical model reproduces observed spectrum shift with an rms error of 4.4 km s$^{-1}$. This procedure is robust and applicable to any spectrum obtained with EIS, regardless of of the observing field. In addition, spectral curvatures and spatial offset in the North - South direction are determined to compensate for instrumental effects.Comment: 16 pages, 12 Figures, accepted for publication in Solar Physics. Added description of neural networ

On the Formation Age of the First Planetary System

Recently, it has been observed the extreme metal-poor stars in the Galactic halo, which must be formed just after Pop III objects. On the other hand, the first gas clouds of mass $\sim 10^6 M_{\odot}$ are supposed to be formed at $z \sim$ 10, 20, and 30 for the $1\sigma$, $2\sigma$ and $3\sigma$, where the density perturbations are assumed of the standard $\Lambda$CDM cosmology. If we could apply this gaussian distribution to the extreme small probability, the gas clouds would be formed at $z \sim$40, 60, and 80 for the $4\sigma$, $6\sigma$, and $8\sigma$. The first gas clouds within our galaxy must be formed around $z\sim 40$. Even if the gas cloud is metal poor, there is a lot of possibility to form the planets around such stars. The first planetary systems could be formed within $\sim 6\times 10^7$ years after the Big Bang in the universe. Even in our galaxies, it could be formed within $\sim 1.7\times 10^8$ years. It is interesting to wait the observations of planets around metal-poor stars. For the panspermia theory, the origin of life could be expected in such systems.Comment: 5 pages,Proceedings IAU Symposium No. 249, 2007, Exoplanets:Y-S. Sun, S. Ferraz-Mello and J.-L, Zhou, eds. (p325