Augmented Homotopical Algebraic Geometry

We develop the framework for augmented homotopical algebraic geometry. This is an extension of homotopical algebraic geometry, which itself is a homotopification of classical algebraic geometry. To do so, we define the notion of augmentation categories, which are a special class of generalised Reedy categories. For an augmentation category, we prove the existence of a closed Quillen model structure on the presheaf category which is compatible with the Kan-Quillen model structure on simplicial sets. Moreover, we use the concept of augmented hypercovers to define a local model structure on the category of augmented presheaves. We prove that crossed simplicial groups, and the planar rooted tree category are examples of augmentation categories. Finally, we introduce a method for generating new examples from old via a categorical pushout construction.Comment: 36 pages, comments welcom

Ultraviolet/X-ray variability and the extended X-ray emission of the radio-loud broad absorption line quasar PG 1004+130

We present the results of recent Chandra, XMM-Newton, and Hubble Space Telescope observations of the radio-loud (RL), broad absorption line (BAL) quasar PG 1004+130. We compare our new observations to archival X-ray and UV data, creating the most comprehensive, high signal-to-noise, multi-epoch, spectral monitoring campaign of a RL BAL quasar to date. We probe for variability of the X-ray absorption, the UV BAL, and the X-ray jet, on month-year timescales. The X-ray absorber has a low column density of $N_{H}=8\times10^{20}-4\times10^{21}$ cm$^{-2}$ when it is assumed to be fully covering the X-ray emitting region, and its properties do not vary significantly between the 4 observations. This suggests the observed absorption is not related to the typical "shielding gas" commonly invoked in BAL quasar models, but is likely due to material further from the central black hole. In contrast, the CIV BAL shows strong variability. The equivalent width (EW) in 2014 is EW=11.24$\pm$0.56 \AA, showing a fractional increase of $\Delta EW / \langle EW \rangle$=1.16$\pm$0.11 from the 2003 observation, 3183 days earlier in the rest-frame. This places PG 1004+130 among the most highly variable BAL quasars. By combining Chandra observations we create an exposure 2.5 times deeper than studied previously, with which to investigate the nature of the X-ray jet and extended diffuse X-ray emission. An X-ray knot, likely with a synchrotron origin, is detected in the radio jet ~8 arcsec (30 kpc) from the central X-ray source with a spatial extent of ~4 arcsec (15 kpc). No similar X-ray counterpart to the counterjet is detected. Asymmetric, non-thermal diffuse X-ray emission, likely due to inverse Compton scattering of Cosmic Microwave Background photons, is also detected.Comment: 15 pages, 7 figures, 3 tables. Accepted for publication in Ap

Atmospheric Circulation of Brown Dwarfs and Jupiter and Saturn-like Planets: Zonal Jets, Long-term Variability, and QBO-type Oscillations

Brown dwarfs and directly imaged giant planets exhibit significant evidence for active atmospheric circulation, which induces a large-scale patchiness in the cloud structure that evolves significantly over time, as evidenced by infrared light curves and Doppler maps. These observations raise critical questions about the fundamental nature of the circulation, its time variability, and the overall relationship to the circulation on Jupiter and Saturn. Jupiter and Saturn themselves exhibit numerous robust zonal (east-west) jet streams at the cloud level; moreover, both planets exhibit long-term stratospheric oscillations involving perturbations of zonal wind and temperature that propagate downward over time on timescales of ~4 years (Jupiter) and ~15 years (Saturn). These oscillations, dubbed the Quasi Quadrennial Oscillation (QQO) for Jupiter and the Semi-Annual Oscillation (SAO) on Saturn, are thought to be analogous to the Quasi-Biennial Oscillation (QBO) on Earth, which is driven by upward propagation of equatorial waves from the troposphere. To investigate these issues, we here present global, three-dimensional, high-resolution numerical simulations of the flow in the stratified atmosphere--overlying the convective interior--of brown dwarfs and Jupiter-like planets. The effect of interior convection is parameterized by inducing small-scale, randomly varying perturbations in the radiative-convective boundary at the base of the model. In the simulations, the convective perturbations generate atmospheric waves and turbulence that interact with the rotation to produce numerous zonal jets. Moreover, the equatorial stratosphere exhibits stacked eastward and westward jets that migrate downward over time, exactly as occurs in the terrestrial QBO, Jovian QQO, and Saturnian SAO. This is the first demonstration of a QBO-like phenomenon in 3D numerical simulations of a giant planet.Comment: 27 pages, 15 figures, in press at ApJ; this is the revised (accepted) version, which includes a major new section providing detailed analysis of the types of wave modes present in the model, and characterizing the wave-mean-flow interactions by which they generate the QBO-like oscillation

Flux surface shaping effects on tokamak edge turbulence and flows

Shaping of magnetic flux surfaces is found to have a strong impact on turbulence and transport in tokamak edge plasmas. A series of axisymmetric equilibria with varying elongation and triangularity, and a divertor configuration are implemented into a computational gyrofluid turbulence model. The mechanisms of shaping effects on turbulence and flows are identified. Transport is mainly reduced by local magnetic shearing and an enhancement of zonal shear flows induced by elongation and X-point shaping.Comment: 10 pages, 11 figures. Submitted to Physics of Plasma

Effective Field Theory for Top Quark Physics

Physics beyond the standard model can affect top-quark physics indirectly. We describe the effective field theory approach to describing such physics, and contrast it with the vertex-function approach that has been pursued previously. We argue that the effective field theory approach has many fundamental advantages and is also simpler.Comment: 7 pages, 5 figures. To appear in the Proceedings of the International Workshop on Top Quark Physics (top2010), Bruges, Belgium, May 31 - June 4, 201