Noncommutative theories and general coordinate transformations

We study the class of noncommutative theories in $d$ dimensions whose spatial coordinates $(x_i)_{i=1}^d$ can be obtained by performing a smooth change of variables on $(y_i)_{i=1}^d$, the coordinates of a standard noncommutative theory, which satisfy the relation $[y_i, y_j] = i \theta_{ij}$, with a constant $\theta_{ij}$ tensor. The $x_i$ variables verify a commutation relation which is, in general, space-dependent. We study the main properties of this special kind of noncommutative theory and show explicitly that, in two dimensions, any theory with a space-dependent commutation relation can be mapped to another where that $\theta_{ij}$ is constant.Comment: 21 pages, no figures, LaTeX. v2: section 5 added, typos corrected. Version to appear in Physical Review

Edge of Chaos and Genesis of Turbulence

The edge of chaos is analyzed in a spatially extended system, modeled by the regularized long-wave equation, prior to the transition to permanent spatiotemporal chaos. In the presence of coexisting attractors, a chaotic saddle is born at the basin boundary due to a smooth-fractal metamorphosis. As a control parameter is varied, the chaotic transient evolves to well-developed transient turbulence via a cascade of fractal-fractal metamorphoses. The edge state responsible for the edge of chaos and the genesis of turbulence is an unstable travelling wave in the laboratory frame, corresponding to a saddle point lying at the basin boundary in the Fourier space

Lower Bounds in the Preprocessing and Query Phases of Routing Algorithms

In the last decade, there has been a substantial amount of research in finding routing algorithms designed specifically to run on real-world graphs. In 2010, Abraham et al. showed upper bounds on the query time in terms of a graph's highway dimension and diameter for the current fastest routing algorithms, including contraction hierarchies, transit node routing, and hub labeling. In this paper, we show corresponding lower bounds for the same three algorithms. We also show how to improve a result by Milosavljevic which lower bounds the number of shortcuts added in the preprocessing stage for contraction hierarchies. We relax the assumption of an optimal contraction order (which is NP-hard to compute), allowing the result to be applicable to real-world instances. Finally, we give a proof that optimal preprocessing for hub labeling is NP-hard. Hardness of optimal preprocessing is known for most routing algorithms, and was suspected to be true for hub labeling

The Star Formation History of the Hubble Sequence: Spatially Resolved Colour Distributions of Intermediate Redshift Galaxies in the Hubble Deep Field

We analyse the spatially resolved colours of distant galaxies of known redshift in the Hubble Deep Field, using a new technique based on matching resolved four-band internal colour data to the predictions of evolutionary synthesis models. We quantify the relative age, dispersion in age, ongoing star-formation rate, star-formation history, and dust content of these galaxies. To demonstrate the potential of the method, we study the near-complete sample of 32 I ~ 0.5 studied by Bouwens et al (1997). The dispersion of the internal colours of a sample of 0.4<z<1 early-type field galaxies in the HDF indicates that ~40% [4/11] show evidence of star formation which must have occurred within the past third of their ages at the epoch of observation. For a sample of well-defined spirals, we similarly exploit the dispersion in colour to analyse the relative histories of bulge and disc stars, in order to resolve the current controversy regarding the ages of galactic bulges. Dust and metallicity gradients are ruled out as major contributors to the colour dispersions we observe in these systems. The median ages of bulge stars are found to be signicantly older than those in galactic discs, and exhibit markedly different star-formation histories. This result is inconsistent with a secular growth of bulges from disc instabilities, but consistent with gradual disc formation by accretion of gas onto bulges, as predicted by hierarchical theories. We extend our technique in order to discuss the star formation history of the entire Bouwens et al sample in the context of earlier studies concerned with global star formation histories.Comment: 8 colour postscript figures plus LaTeX source; submitted to MNRAS. Uses the mnras.sty LaTeX style fil

Description of Atmospheric Conditions at the Pierre Auger Observatory Using Meteorological Measurements and Models

Atmospheric conditions at the site of a cosmic ray observatory must be known well for reconstructing observed extensive air showers, especially when measured using the fluorescence technique. For the Pierre Auger Observatory, a sophisticated network of atmospheric monitoring devices has been conceived. Part of this monitoring was a weather balloon program to measure atmospheric state variables above the Observatory. To use the data in reconstructions of air showers, monthly models have been constructed. Scheduled balloon launches were abandoned and replaced with launches triggered by high-energetic air showers as part of a rapid monitoring system. Currently, the balloon launch program is halted and atmospheric data from numerical weather prediction models are used. A description of the balloon measurements, the monthly models as well as the data from the numerical weather prediction are presented

Observing Lense-Thirring Precession in Tidal Disruption Flares

When a star is tidally disrupted by a supermassive black hole (SMBH), the streams of liberated gas form an accretion disk after their return to pericenter. We demonstrate that Lense-Thirring precession in the spacetime around a rotating SMBH can produce significant time evolution of the disk angular momentum vector, due to both the periodic precession of the disk and the nonperiodic, differential precession of the bound debris streams. Jet precession and periodic modulation of disk luminosity are possible consequences. The persistence of the jetted X-ray emission in the Swift J164449.3+573451 flare suggests that the jet axis was aligned with the spin axis of the SMBH during this event.Comment: 4 pages, 4 figures. Accepted for publication in Physical Review Letters. Minor changes made to match proof

Thickness dependent magnetotransport in ultra-thin manganite films

To understand the near-interface magnetism in manganites, uniform, ultra-thin films of La_{0.67}Sr_{0.33}MnO_3 were grown epitaxially on single crystal (001) LaAlO_3 and (110) NdGaO_3 substrates. The temperature and magnetic field dependent film resistance is used to probe the film's structural and magnetic properties. A surface and/or interface related dead-layer is inferred from the thickness dependent resistance and magnetoresistance. The total thickness of the dead layer is estimated to be $\sim 30 \AA$ for films on NdGaO_3 and $\sim 50 \AA$ for films on LaAlO_3.Comment: 11 pages, 4 figure

High-Redshift Galaxies: Their Predicted Size and Surface Brightness Distributions and Their Gravitational Lensing Probability

Direct observations of the first generation of luminous objects will likely become feasible over the next decade. The advent of the Next Generation Space Telescope (NGST) will allow imaging of numerous galaxies and mini-quasars at redshifts z>5. We apply semi-analytic models of structure formation to estimate the rate of multiple imaging of these sources by intervening gravitational lenses. Popular CDM models for galaxy formation yield a lensing optical depth of about 1% for sources at redshift 10. The expected slope of the luminosity function of the early sources implies an additional magnification bias of about 5, bringing the fraction of lensed sources at z=10 to about 5%. We estimate the angular size distribution of high-redshift disk galaxies and find that most of them are more extended than the resolution limit of NGST, roughly 0.06 arcseconds. We also show that there is only a modest redshift evolution in the mean surface brightness of galaxies at z>2. The expected increase by 1-2 orders of magnitude in the number of resolved sources on the sky, due to observations with NGST, will dramatically improve upon the statistical significance of existing weak lensing measurements. We show that, despite this increase in the density of sources, confusion noise from z>2 galaxies is expected to be small for NGST observations.Comment: 27 pages, 8 PostScript figures (of which two are new), revised version accepted for Ap