The Generation of Fullerenes

We describe an efficient new algorithm for the generation of fullerenes. Our implementation of this algorithm is more than 3.5 times faster than the previously fastest generator for fullerenes -- fullgen -- and the first program since fullgen to be useful for more than 100 vertices. We also note a programming error in fullgen that caused problems for 136 or more vertices. We tabulate the numbers of fullerenes and IPR fullerenes up to 400 vertices. We also check up to 316 vertices a conjecture of Barnette that cubic planar graphs with maximum face size 6 are hamiltonian and verify that the smallest counterexample to the spiral conjecture has 380 vertices.Comment: 21 pages; added a not

Detection of large scale intrinsic ellipticity-density correlation from the Sloan Digital Sky Survey and implications for weak lensing surveys

The power spectrum of weak lensing shear caused by large-scale structure is an emerging tool for precision cosmology, in particular for measuring the effects of dark energy on the growth of structure at low redshift. One potential source of systematic error is intrinsic alignments of ellipticities of neighbouring galaxies (II correlation) that could mimic the correlations due to lensing. A related possibility pointed out by Hirata and Seljak (2004) is correlation between the intrinsic ellipticities of galaxies and the density field responsible for gravitational lensing shear (GI correlation). We present constraints on both the II and GI correlations using 265 908 spectroscopic galaxies from the SDSS, and using galaxies as tracers of the mass in the case of the GI analysis. The availability of redshifts in the SDSS allows us to select galaxies at small radial separations, which both reduces noise in the intrinsic alignment measurement and suppresses galaxy- galaxy lensing (which otherwise swamps the GI correlation). While we find no detection of the II correlation, our results are nonetheless statistically consistent with recent detections found using the SuperCOSMOS survey. In contrast, we have a clear detection of GI correlation in galaxies brighter than L* that persists to the largest scales probed (60 Mpc/h) and with a sign predicted by theoretical models. This correlation could cause the existing lensing surveys at z~1 to underestimate the linear amplitude of fluctuations by as much as 20% depending on the source sample used, while for surveys at z~0.5 the underestimation may reach 30%. (Abridged.)Comment: 16 pages, matches version published in MNRAS (only minor changes in presentation from original version

Evolution of a spinor condensate: coherent dynamics, dephasing and revivals

We present measurements and a theoretical model for the interplay of spin dependent interactions and external magnetic fields in atomic spinor condensates. We highlight general features like quadratic Zeeman dephasing and its influence on coherent spin mixing processes by focusing on a specific coherent superposition state in a F=1 $^{87}$Rb Bose-Einstein condensate. In particular, we observe the transition from coherent spinor oscillations to thermal equilibration

Conformally Einstein Products and Nearly K\"ahler Manifolds

In the first part of this note we study compact Riemannian manifolds (M,g) whose Riemannian product with R is conformally Einstein. We then consider compact 6--dimensional almost Hermitian manifolds of type W_1+W_4 in the Gray--Hervella classification admitting a parallel vector field and show that (under some regularity assumption) they are obtained as mapping tori of isometries of compact Sasaki-Einstein 5-dimensional manifolds. In particular, we obtain examples of inhomogeneous locally (non-globally) conformal nearly K\"ahler compact manifolds

Revisiting algorithms for generating surrogate time series

The method of surrogates is one of the key concepts of nonlinear data analysis. Here, we demonstrate that commonly used algorithms for generating surrogates often fail to generate truly linear time series. Rather, they create surrogate realizations with Fourier phase correlations leading to non-detections of nonlinearities. We argue that reliable surrogates can only be generated, if one tests separately for static and dynamic nonlinearities.Comment: 5 pages, 4 figures, accepted for publication in PR

Investigation of the Spin-Peierls transition in CuGeO_3 by Raman scattering

Raman experiments on the spin-Peierls compound CuGeO$_3$ and the substituted (Cu$_{1- x}$,Zn$_x$)GeO$_3$ and Cu(Ge$_{1-x}$,Ga$_x$)O$_3$ compounds were performed in order to investigate the response of specific magnetic excitations of the one-dimensional spin-1/2 chain to spin anisotropies and substitution-induced disorder. In pure CuGeO$_3$, in addition to normal phonon scattering which is not affected at all by the spin-Peierls transition, four types of magnetic scattering features were observed. Below T$_{SP}$=14 K a singlet-triplet excitation at 30 cm$^{-1}$, two-magnon scattering from 30 to 227 cm$^{-1}$ and folded phonon modes at 369 and 819 cm$^{-1}$ were identified. They were assigned by their temperature dependence and lineshape. For temperatures between the spin-Peierls transition T$_{SP}$ and approximately 100 K a broad intensity maximum centered at 300 cm$^{-1}$ is observed.Comment: 7 pages, LaTex2e, including 3 figures (eps) to be published in Physica B (1996

Generalized Symmetries of Impulsive Gravitational Waves

We generalize previous \cite{AiBa2} work on the classification of ($C^\infty$) symmetries of plane-fronted waves with an impulsive profile. Due to the specific form of the profile it is possible to extend the group of normal-form-preserving diffeomorphisms to include non-smooth transformations. This extension entails a richer structure of the symmetry algebra generated by the (non-smooth) Killing vectors.Comment: 18 pages, latex2e, no figure

Temperature Dependence of the Cu(2) NQR Line Width in YBa2_2Cu3_3O7−y_{7-y}

Systematic measurements of the $^{63}$Cu(2) NQR line width were performed in underdoped YBa$_2$Cu$_3$O$_{7-y}$ samples over the temperature range 4.2 K $<T<300$ K. It was shown that the copper NQR line width monotonically increases upon lowering temperature in the below-critical region, resembling temperature behavior of the superconducting gap. The observed dependence is explained by the fact that the energy of a condensate of sliding charge-current states of the charge-density-wave type depends on the phase of order parameter. Calculations show that this dependence appears only at $T<T_c$. Quantitative estimates of the line broadening at $T<T_c$ agree with the measurement results.Comment: 4 pages, 2 figure

A Compact Supermassive Binary Black Hole System

We report on the discovery of a supermassive binary black hole system in the radio galaxy 0402+379, with a projected separation between the two black holes of just 7.3 pc. This is the closest black hole pair yet found by more than two orders of magnitude. These results are based upon recent multi-frequency observations using the Very Long Baseline Array (VLBA) which reveal two compact, variable, flat-spectrum, active nuclei within the elliptical host galaxy of 0402+379. Multi-epoch observations from the VLBA also provide constraints on the total mass and dynamics of the system. Low spectral resolution spectroscopy using the Hobby-Eberly Telescope indicates two velocity systems with a combined mass of the two black holes of ~1.5 x 10^8 solar masses. The two nuclei appear stationary while the jets emanating from the weaker of the two nuclei appear to move out and terminate in bright hot spots. The discovery of this system has implications for the number of close binary black holes that might be sources of gravitational radiation. Green Bank Telescope observations at 22 GHz to search for water masers in this interesting system are also presented.Comment: 34 pages, 7 figures, Accepted to The Astrophysical Journa

Revealing the obscured supernova remnant Kes 32 with Chandra

I report here on the analysis and interpretation of a Chandra observation of the supernova remnant Kes 32. Kes 32 is rather weak in X-rays due to a large interstellar absorption, which is found to be ~4E22 cm^-2, larger than previously reported. Spectral analysis indicates that the ionization age of this object is very young, with n_e t ~ 4E9 cm^-3s, and a temperature of kT_e ~ 1 keV. The X-ray emission peaks at a smaller radius than in the radio. The low ionization age suggests that Kes 32 is a young remnant. However, a young age is in contradiction with the relatively large apparent size, which indicates an age of several thousand years, instead of a few hundred years. This problem is discussed in connection with Kes 32's unknown distance and its possible association with the Norma galactic arm.Comment: Accepted for publication in the Astrophysical Journal. 7 pages, 7 figure