An extension of Fourier analysis for the n-torus in the magnetic field and its application to spectral analysis of the magnetic Laplacian

We solved the Schr{\"o}dinger equation for a particle in a uniform magnetic field in the n-dimensional torus. We obtained a complete set of solutions for a broad class of problems; the torus T^n = R^n / {\Lambda} is defined as a quotient of the Euclidean space R^n by an arbitrary n-dimensional lattice {\Lambda}. The lattice is not necessary either cubic or rectangular. The magnetic field is also arbitrary. However, we restrict ourselves within potential-free problems; the Schr{\"o}dinger operator is assumed to be the Laplace operator defined with the covariant derivative. We defined an algebra that characterizes the symmetry of the Laplacian and named it the magnetic algebra. We proved that the space of functions on which the Laplacian acts is an irreducible representation space of the magnetic algebra. In this sense the magnetic algebra completely characterizes the quantum mechanics in the magnetic torus. We developed a new method for Fourier analysis for the magnetic torus and used it to solve the eigenvalue problem of the Laplacian. All the eigenfunctions are given in explicit forms.Comment: 32 pages, LaTeX, minor corrections are mad

An Easy-to-Construct Automated Winkler Titration System

The instrument described in this report is an updated version of the high precision, automated Winkler titration system described by Friederich et al.(1984). The original instrument was based on the work of Bryan et al. (1976) who developed a colorimetric endpoint detector and on the work of Williams and Jenkinson (1982) who produced an automated system that used this detector. The goals of our updated version of the device described by Friederich et al. (1984) were as follows: 1) Move control of the system to the MS-DOS environment because HP-85 computers are no longer in production and because more user-friendly programs could be written using the IBM XT or AT computers that control the new device. 2) Use more "off the shelf" components and reduce the parts count in the new system so that it could be easily constructed and maintained. This report describes how to construct and use the new automated Winkler titration device. It also includes information on the chemistry of the Winkler titration, and detailed instructions on how to prepare reagents, collect samples, standardize and perform the titrations (Appendix I: Codispoti, L.A. 1991 On the determination of dissolved oxygen in sea water, 15pp.). A disk containing the program needed to operate the new device is also included. (pdf contains 33 pages

Rotating Boson Star with Large Self-interaction in (2+1) dimensions

Solutions for rotating boson stars in (2+1) dimensional gravity with a negative cosmological constant are obtained numerically. The mass, particle number, and radius of the (2+1) dimensional rotating boson star are shown. Consequently we find the region where the stable boson star can exist.Comment: 14 pages, 6 figures, RevTe

Renormalization group for the probability distribution of magnetic impurities in a random-field ϕ4\phi^4 model

Extending the usual Ginzburg-Landau theory for the random-field Ising model, the possibility of dimensional reduction is reconsidered. A renormalization group for the probability distribution of magnetic impurities is applied. New parameters corresponding to the extra $\phi^4$ coupling constants in the replica Hamiltonian are introduced. Although they do not affect the critical phenomena near the upper critical dimension, they can when dimensions are lowered.Comment: 16 pages, 11 figures, revte

Large Area Crop Inventory Experiment (LACIE). USSR spring and winter wheat models, addendum

There are no author-identified significant results in this report

Probing the Structure of Gamma-Ray Burst Jets with Steep Decay Phase of their Early X-ray Afterglows

We show that the jet structure of gamma-ray bursts (GRBs) can be investigated with the tail emission of the prompt GRB. The tail emission which we consider is identified as a steep-decay component of the early X-ray afterglow observed by the X-ray Telescope onboard Swift. Using a Monte Carlo method, we derive, for the first time, the distribution of the decay index of the GRB tail emission for various jet models. The new definitions of the zero of time and the time interval of a fitting region are proposed. These definitions for fitting the light curve lead us an unique definition of the decay index, which is useful to investigate the structure of the GRB jet. We find that if the GRB jet has a core-envelope structure, the predicted distribution of the decay index of the tail has a wide scatter and has multiple peaks, which cannot be seen for the case of the uniform and the Gaussian jet. Therefore, the decay index distribution tells us the information on the jet structure. Especially, if we observe events whose decay index is less than about 2, both the uniform and the Gaussian jet models will be disfavored according to our simulation study.Comment: 21 pages, 10 figures, the paper with full resolution images is http://theo.phys.sci.hiroshima-u.ac.jp/~takami/research/achievements/papers/003_full.pd

Quantum Scattering in Two Black Hole Moduli Space

We discuss the quantum scattering process in the moduli space consisting of two maximally charged dilaton black holes. The black hole moduli space geometry has different structures for arbitrary dimensions and various values of dilaton coupling. We study the quantum effects of the different moduli space geometries with scattering process. Then, it is found that there is a resonance state on certain moduli spaces.Comment: 15 pages, 19 figures, RevTeX 3.