Lorentz-Zygmund Spaces and Interpolation of Weak Type Operators

The Lorentz-Zygmund spaces Lpa(log L)α are a class of function spaces containing as special cases the classical Lebesgue spaces Lp, the Lorentz spaces Lpa and the Zygmund spaces Lp(log L)α. It is shown here that the Lorentz-Zygmund spaces provide the correct framework for the interpolation theory of weak type operators. The interpolation principles established here unify many classical results in harmonic analysis. In particular, there are applications to the Fourier transform, the Hardy-Littlewood maximal operator, the Hilbert transform, and the Weyl fractional integrals

The Three-Dimensional Structure of Interior Ejecta in Cassiopeia A at High Spectral Resolution

We used the Spitzer Space Telescope's Infrared Spectrograph to create a high resolution spectral map of the central region of the Cassiopeia A supernova remnant, allowing us to make a Doppler reconstruction of its 3D structure. The ejecta responsible for this emission have not yet encountered the remnant's reverse shock or the circumstellar medium, making it an ideal laboratory for exploring the dynamics of the supernova explosion itself. We observe that the O, Si, and S ejecta can form both sheet-like structures as well as filaments. Si and O, which come from different nucleosynthetic layers of the star, are observed to be coincident in velocity space in some regions, and separated by 500 km/s or more in others. Ejecta traveling toward us are, on average, ~900 km/s slower than the material traveling away from us. We compare our observations to recent supernova explosion models and find that no single model can simultaneously reproduce all the observed features. However, models of different supernova explosions can collectively produce the observed geometries and structures of the interior emission. We use the results from the models to address the conditions during the supernova explosion, concentrating on asymmetries in the shock structure. We also predict that the back surface of Cassiopeia A will begin brightening in ~30 years, and the front surface in ~100 years.Comment: 35 pages, 16 figures, accepted to Ap

Spitzer Spectral Mapping of Supernova Remnant Cassiopeia A

We present the global distribution of fine structure infrared line emission in the Cassiopeia A supernova remnant using data from the Spitzer Space Telescope's Infrared Spectrograph. We identify emission from ejecta materials in the interior, prior to their encounter with the reverse shock, as well as from the post-shock bright ring. The global electron density increases by >~100 at the shock to ~10^4 cm^-3, providing evidence for strong radiative cooling. There is also a dramatic change in ionization state at the shock, with the fading of emission from low ionization interior species like [SiII], giving way to [SIV] and, at even further distances, high-energy X-rays from hydrogenic silicon. Two compact, crescent-shaped clumps with highly enhanced neon abundance are arranged symmetrically around the central neutron star. These neon crescents are very closely aligned with the "kick" direction of the compact object from the remnant's expansion center, tracing a new axis of explosion asymmetry. They indicate that much of the apparent macroscopic elemental mixing may arise from different compositional layers of ejecta now passing through the reverse shock along different directions.Comment: 9 pages, 8 figures, accepted by Ap

The Three-Dimensional Structure of Cassiopeia A

We used the Spitzer Space Telescope's Infrared Spectrograph to map nearly the entire extent of Cassiopeia A between 5-40 micron. Using infrared and Chandra X-ray Doppler velocity measurements, along with the locations of optical ejecta beyond the forward shock, we constructed a 3-D model of the remnant. The structure of Cas A can be characterized into a spherical component, a tilted thick disk, and multiple ejecta jets/pistons and optical fast-moving knots all populating the thick disk plane. The Bright Ring in Cas A identifies the intersection between the thick plane/pistons and a roughly spherical reverse shock. The ejecta pistons indicate a radial velocity gradient in the explosion. Some ejecta pistons are bipolar with oppositely-directed flows about the expansion center while some ejecta pistons show no such symmetry. Some ejecta pistons appear to maintain the integrity of the nuclear burning layers while others appear to have punched through the outer layers. The ejecta pistons indicate a radial velocity gradient in the explosion. In 3-D, the Fe jet in the southeast occupies a "hole" in the Si-group emission and does not represent "overturning", as previously thought. Although interaction with the circumstellar medium affects the detailed appearance of the remnant and may affect the visibility of the southeast Fe jet, the bulk of the symmetries and asymmetries in Cas A are intrinsic to the explosion.Comment: Accepted to ApJ. 54 pages, 21 figures. For high resolution figures and associated mpeg movie and 3D PDF files, see http://homepages.spa.umn.edu/~tdelaney/pape

Nucleosynthetic Layers in the Shocked Ejecta of Cassiopeia A

We present a three-dimensional analysis of the supernova remnant Cassiopeia A using high-resolution spectra from the Spitzer Space Telescope. We observe supernova ejecta both immediately before and during the shock-ejecta interaction. We determine that the reverse shock of the remnant is spherical to within 7%, although the center of this sphere is offset from the geometric center of the remnant by 810 km s^(–1). We determine that the velocity width of the nucleosynthetic layers is ~1000 km s^(–1) over 4000 arcsec^2 regions, although the velocity width of a layer along any individual line of sight is <250 km s^(–1). Si and O, which come from different nucleosynthetic layers in the progenitor star, are observed to be coincident in velocity space in some directions, but segregated by up to ~500 km s^(–1) in other directions. We compare these observations of the nucleosynthetic layers to predictions from supernova explosion models in an attempt to constrain such models. Finally, we observe small-scale, corrugated velocity structures that are likely caused during the supernova explosion itself, rather than hundreds of years later by dynamical instabilities at the remnant's reverse shock

Red Nuggets at z~1.5: Compact passive galaxies and the formation of the Kormendy Relation

We present the results of NICMOS imaging of a sample of 16 high mass passively evolving galaxies with 1.3<z<2, taken primarily from the Gemini Deep Deep Survey. Around 80% of galaxies in our sample have spectra dominated by stars with ages >1 Gyr. Our rest-frame R-band images show that most of these objects have compact regular morphologies which follow the classical R^1/4 law. These galaxies scatter along a tight sequence in the Kormendy relation. Around one-third of the massive red objects are extraordinarily compact, with effective radii under one kiloparsec. Our NICMOS observations allow the detection of such systems more robustly than is possible with optical (rest-frame UV) data, and while similar systems have been seen at z>2, this is the first time such systems have been detected in a rest-frame optical survey at 1.3<z<2. We refer to these compact galaxies as "red nuggets". Similarly compact massive galaxies are completely absent in the nearby Universe. We introduce a new "stellar mass Kormendy relation" (stellar mass density vs size) which isolates the effects of size evolution from those of luminosity and color evolution. The 1.1 < z < 2 passive galaxies have mass densities that are an order of magnitude larger then early type galaxies today and are comparable to the compact distant red galaxies at 2 < z < 3. We briefly consider mechanisms for size evolution in contemporary models focusing on equal-mass mergers and adiabatic expansion driven by stellar mass loss. Neither of these mechanisms appears able to transform the high-redshift Kormendy relation into its local counterpart. Comment: Accepted version (to appear in ApJ

The spatial distribution and annual cycle of upper ocean thermohaline structure

Author Posting. © American Geophysical Union, 2012. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 117 (2012): C02027, doi:10.1029/2011JC007033.Observations of the spatial distribution and persistence of thermohaline structure are presented, and show how advection and diffusion affect a passive tracer. More than two years of underwater glider observations in the central subtropical North Pacific showed thermohaline variability over horizontal scales from 5 to 1300 km. Thermohaline fluctuations along isopycnals (spice fluctuations) were elevated in layers throughout the water column with the largest fluctuations near the surface and subtropical frontal regions. Fluctuations were uncorrelated between the layers but stirred by the same velocity field. Spice variance had local extrema in the vertical because of differences in source water properties and the influence of neighboring water masses. Spice variance spanned about three orders of magnitude along deeper isopycnals with larger variance where different water masses met and where velocity and vorticity variance were elevated. Horizontal wave number spectra of spice had slopes of −2 everywhere in the upper 1000 m. Submesoscale spice fluctuations had slopes in physical space near the ratio of the Coriolis parameter to the buoyancy frequency (f/N), consistent with predictions of quasi-geostrophic theory. In the mixed layer, thermohaline structure had a significant annual cycle with smaller interannual differences. Thermohaline fluctuations left behind during restratification and isolated from the mixed layer decayed with time because of diffusion along isopycnals. Horizontal diffusivity estimates in the remnant mixed layer were 0.4 m2 s−1 at 15–28 km wavelengths and 0.9 m2 s−1 at 35–45 km wavelengths.We gratefully acknowledge the National Science Foundation for funding this work under grant number OCE0452574.2012-08-1

Rapid and High-Throughput pan-Orthopoxvirus Detection and Identification using PCR and Mass Spectrometry

The genus Orthopoxvirus contains several species of related viruses, including the causative agent of smallpox (Variola virus). In addition to smallpox, several other members of the genus are capable of causing human infection, including monkeypox, cowpox, and other zoonotic rodent-borne poxviruses. Therefore, a single assay that can accurately identify all orthopoxviruses could provide a valuable tool for rapid broad orthopovirus identification. We have developed a pan-Orthopoxvirus assay for identification of all members of the genus based on four PCR reactions targeting Orthopoxvirus DNA and RNA helicase and polymerase genes. The amplicons are detected using electrospray ionization-mass spectrometry (PCR/ESI-MS) on the Ibis T5000 system. We demonstrate that the assay can detect and identify a diverse collection of orthopoxviruses, provide sub-species information and characterize viruses from the blood of rabbitpox infected rabbits. The assay is sensitive at the stochastic limit of PCR and detected virus in blood containing approximately six plaque-forming units per milliliter from a rabbitpox virus-infected rabbit

Global Surveillance of Emerging Influenza Virus Genotypes by Mass Spectrometry

Effective influenza surveillance requires new methods capable of rapid and inexpensive genomic analysis of evolving viral species for pandemic preparedness, to understand the evolution of circulating viral species, and for vaccine strain selection. We have developed one such approach based on previously described broad-range reverse transcription PCR/electrospray ionization mass spectrometry (RT-PCR/ESI-MS) technology.Analysis of base compositions of RT-PCR amplicons from influenza core gene segments (PB1, PB2, PA, M, NS, NP) are used to provide sub-species identification and infer influenza virus H and N subtypes. Using this approach, we detected and correctly identified 92 mammalian and avian influenza isolates, representing 30 different H and N types, including 29 avian H5N1 isolates. Further, direct analysis of 656 human clinical respiratory specimens collected over a seven-year period (1999-2006) showed correct identification of the viral species and subtypes with >97% sensitivity and specificity. Base composition derived clusters inferred from this analysis showed 100% concordance to previously established clades. Ongoing surveillance of samples from the recent influenza virus seasons (2005-2006) showed evidence for emergence and establishment of new genotypes of circulating H3N2 strains worldwide. Mixed viral quasispecies were found in approximately 1% of these recent samples providing a view into viral evolution.Thus, rapid RT-PCR/ESI-MS analysis can be used to simultaneously identify all species of influenza viruses with clade-level resolution, identify mixed viral populations and monitor global spread and emergence of novel viral genotypes. This high-throughput method promises to become an integral component of influenza surveillance