Matrix Concentration for Products

This paper develops nonasymptotic growth and concentration bounds for a product of independent random matrices. These results sharpen and generalize recent work of Henriksen-Ward, and they are similar in spirit to the results of Ahlswede-Winter and of Tropp for a sum of independent random matrices. The argument relies on the uniform smoothness properties of the Schatten trace classes

Limits on Radio Continuum Emission from a Sample of Candidate Contracting Starless Cores

We used the NRAO Very Large Array to search for 3.6 cm continuum emission from embedded protostars in a sample of 8 nearby ``starless'' cores that show spectroscopic evidence for infalling motions in molecular emission lines. We detect a total of 13 compact sources in the eight observed fields to 5 sigma limiting flux levels of typically 0.09 mJy. None of these sources lie within 1' of the central positions of the cores, and they are all likely background objects. Based on an extrapolation of the empirical correlation between the bolometric luminosity and 3.6 cm luminosity for the youngest protostars, these null-detections place upper limits of ~0.1 L_sun (d/140pc)^2 on the luminosities of protostellar sources embedded within these cores. These limits, together with the extended nature of the inward motions inferred from molecular line mapping (Lee et al. 2001), are inconsistent with the inside-out collapse model of singular isothermal spheres and suggest a less centrally condensed phase of core evolution during the earliest stages of star formation.Comment: Accepted to the Astronomical Journal; 12 pages, 1 figur

Impact of major depression on cardiovascular outcomes for individuals with hypertension: prospective survival analysis in UK Biobank

Objectives: To assess whether a history of major depressive disorder (MDD) in middle-aged individuals with hypertension influences first-onset cardiovascular disease outcomes. Design: Prospective cohort survival analysis using Cox proportional hazards regression with a median follow-up of 63 months (702 902 person-years). Four mutually exclusive groups were compared: hypertension only (n=56 035), MDD only (n=15 098), comorbid hypertension plus MDD (n=12 929) and an unaffected (no hypertension, no MDD) comparison group (n=50 798). Setting: UK Biobank. Participants: UK Biobank participants without cardiovascular disease aged 39–70 who completed psychiatric questions relating International Classification of Diseases-10 Revision (ICD-10) diagnostic criteria on a touchscreen questionnaire at baseline interview in 2006–2010 (n=134 860). Primary and secondary outcome measures: First-onset adverse cardiovascular outcomes leading to hospital admission or death (ICD-10 codes I20–I259, I60–69 and G45–G46), adjusted in a stepwise manner for sociodemographic, health and lifestyle features. Secondary analyses were performed looking specifically at stroke outcomes (ICD-10 codes I60–69 and G45–G46) and in gender-separated models. Results: Relative to controls, adjusted HRs for adverse cardiovascular outcomes were increased for the hypertension only group (HR 1.36, 95% CI 1.22 to 1.52) and were higher still for the comorbid hypertension plus MDD group (HR 1.66, 95% CI 1.45 to 1.9). HRs for the comorbid hypertension plus MDD group were significantly raised compared with hypertension alone (HR 1.22, 95% CI 1.1 to 1.35). Interaction measured using relative excess risk due to interaction (RERI) and likelihood ratios (LRs) were identified at baseline (RERI 0.563, 95% CI 0.189 to 0.938; LR p=0.0116) but not maintained during the follow-up. Limitations: Possible selection bias in UK Biobank and inability to assess for levels of medication adherence. Conclusions: Comorbid hypertension and MDD conferred greater hazard than hypertension alone for adverse cardiovascular outcomes, although evidence of interaction between hypertension and MDD was inconsistent over time. Future cardiovascular risk prediction tools may benefit from the inclusion of questions about prior history of depressive disorders

The Ionization Fraction in Dense Molecular Gas II: Massive Cores

We present an observational and theoretical study of the ionization fraction in several massive cores located in regions that are currently forming stellar clusters. Maps of the emission from the J = 1-> O transitions of C18O, DCO+, N2H+, and H13CO+, as well as the J = 2 -> 1 and J = 3 -> 2 transitions of CS, were obtained for each core. Core densities are determined via a large velocity gradient analysis with values typically 10^5 cm^-3. With the use of observations to constrain variables in the chemical calculations we derive electron fractions for our overall sample of 5 cores directly associated with star formation and 2 apparently starless cores. The electron abundances are found to lie within a small range, -6.9 < log10(x_e) < -7.3, and are consistent with previous work. We find no difference in the amount of ionization fraction between cores with and without associated star formation activity, nor is any difference found in electron abundances between the edge and center of the emission region. Thus our models are in agreement with the standard picture of cosmic rays as the primary source of ionization for molecular ions. With the addition of previously determined electron abundances for low mass cores, and even more massive cores associated with O and B clusters, we systematically examine the ionization fraction as a function of star formation activity. This analysis demonstrates that the most massive sources stand out as having the lowest electron abundances (x_e < 10^-8).Comment: 35 pages (8 figures), using aaspp4.sty, to be published in Astrophysical Journa

Toward Real-Time Monitoring and Control of Single Nanoparticle Properties with a Microbubble Resonator Spectrometer

Optical microresonators have widespread application at the frontiers of nanophotonic technology, driven by their ability to confine light to the nanoscale and enhance light-matter interactions. Microresonators form the heart of a recently developed method for single-particle photothermal absorption spectroscopy, whereby the microresonators act as microscale thermometers to detect the heat dissipated by optically pumped, nonluminescent nanoscopic targets. However, translation of this technology to chemically dynamic systems requires a platform that is mechanically stable, solution compatible, and visibly transparent. We report microbubble absorption spectrometers as a versatile platform that meets these requirements. Microbubbles integrate a two-port microfluidic device within a whispering gallery mode microresonator, allowing for the facile exchange of chemical reagents within the resonator\u27s interior while maintaining a solution-free environment on its exterior. We first leverage these qualities to investigate the photoactivated etching of single gold nanorods by ferric chloride, providing a method for rapid acquisition of spatial and morphological information about nanoparticles as they undergo chemical reactions. We then demonstrate the ability to control nanorod orientation within a microbubble through optically exerted torque, a promising route toward the construction of hybrid photonic-plasmonic systems. Critically, the reported platform advances microresonator spectrometer technology by permitting room-temperature, aqueous experimental conditions, which may be used for time-resolved single-particle experiments on non-emissive, nanoscale analytes engaged in catalytically and biologically relevant chemical dynamics

A packaged whispering gallery resonator device based on an optical nanoantenna coupler

In this work, we present the design and fabrication of a packaged whispering gallery mode (WGM) device based on an optical nanoantenna as the coupler and a glass microsphere as the resonator. The microspheres were fabricated from SiO$_2$ fiber or Er$^{3+}$-doped fiber, the latter creating a WGM laser with a threshold of 93 $\mu$W at 1531 nm. The coupler-resonator WGM device is packaged in a glass capillary. The performance of the packaged microlaser is characterized, with lasing emission both excited in and collected from the WGM cavity via the nanoantenna. The packaged system provides isolation from environmental contamination, a small size, and unidirectional coupling while maintaining a high quality (Q-) factor ($\sim$10$^8$). It opens up new possibilities for practical applications of WGM microdevices in a variety of fields such as low threshold lasers, filters, and sensors

Transgranular Stress Corrosion Cracking of 304L Stainless Steel Pipe Clamps in Direct Use Geothermal Water Heating Applications

Direct use geothermal heating relies on heat extracted from naturally occurring geothermal water sources to provide heating needs for commercial and residential use. The city of Boise, Idaho maintains the largest district geothermal heating system in the United States, utilizing a source of geothermal water at 80 °C. 304 Stainless steel (UNS S30400) pipe clamps are used throughout the system as repair seals and for new service connections. Occasionally unexpected fracture of the stainless steel clamps occurs with time-in-service periods as short as 1 year. A failure analysis was conducted, including visual, microstructural, compositional, and mechanical characterization, to determine the cause and source of the degradation. Cracking of the clamps was limited to localized regions with the remainder of the clamp unaffected. Branched, brittle cracks were observed in the failure region and exhibited transgranular propagation. Based on the temperature, available moisture, stress level, and type of material used it was determined that the likely cause of failure was neutral pH, dilute chloride-induced stress corrosion cracking. Based on this failure analysis, geothermal or other buried heated water systems must consider protective measures or more SCC-resistant materials to prevent susceptible conditions from developing, compared to conventional water systems, to ensure maximum lifetime performance