Strichartz estimates for the Schr\"odinger equation on polygonal domains

We prove Strichartz estimates with a loss of derivatives for the Schr\"odinger equation on polygonal domains with either Dirichlet or Neumann homogeneous boundary conditions. Using a standard doubling procedure, estimates the on polygon follow from those on Euclidean surfaces with conical singularities. We develop a Littlewood-Paley squarefunction estimate with respect to the spectrum of the Laplacian on these spaces. This allows us to reduce matters to proving estimates at each frequency scale. The problem can be localized in space provided the time intervals are sufficiently small. Strichartz estimates then follow from a result of the second author regarding the Schr\"odinger equation on the Euclidean cone.Comment: 12 page

Observation of enhanced optical spring damping in a macroscopic mechanical resonator and application for parametric instability control in advanced gravitational-wave detectors

We show that optical spring damping in an optomechanical resonator can be enhanced by injecting a phase delay in the laser frequency-locking servo to rotate the real and imaginary components of the optical spring constant. This enhances damping at the expense of optical rigidity. We demonstrate enhanced parametric damping which reduces the Q factor of a 0.1-kg-scale resonator from 1.3×10^5 to 6.5×10^3. By using this technique adequate optical spring damping can be obtained to damp parametric instability predicted for advanced laser interferometer gravitational-wave detectors

Superconducting re-entrant cavity transducer for a resonant bar gravitational radiation antenna

Copyright @ American Institute of PhysicsA 10‐GHz superconducting niobium re‐entrant cavity parametric transducer was developed for use in a cryogenic 1.5‐tonne Nb resonant bar gravitational radiation antenna. The transducer has a very high electrical Q (6×105 at 4.2 K), and was operated at high cavity fields without degrading the Q. A very high electromechanical coupling between the antenna and the transducer was therefore achieved. The highest coupling attained, constrained by the available pump power, was 0.11. If the transducer were to be operated in conjunction with a wideband impedance matching element, an antenna bandwidth comparable to the frequency of the antenna would be attained. The temperature dependence of the Q of the transducer was in good agreement with theory. At temperatures above about 6 K the Q was degraded by the increase in the BCS surface resistance, while at lower temperatures the Q was limited by radiative losses

On the gravitational wave background from compact binary coalescences in the band of ground-based interferometers

This paper reports a comprehensive study on the gravitational wave (GW) background from compact binary coalescences. We consider in our calculations newly available observation-based neutron star and black hole mass distributions and complete analytical waveforms that include post-Newtonian amplitude corrections. Our results show that: (i) post-Newtonian effects cause a small reduction in the GW background signal; (ii) below 100 Hz the background depends primarily on the local coalescence rate $r_0$ and the average chirp mass and is independent of the chirp mass distribution; (iii) the effects of cosmic star formation rates and delay times between the formation and merger of binaries are linear below 100 Hz and can be represented by a single parameter within a factor of ~ 2; (iv) a simple power law model of the energy density parameter $\Omega_{GW}(f) ~ f^{2/3}$ up to 50-100 Hz is sufficient to be used as a search template for ground-based interferometers. In terms of the detection prospects of the background signal, we show that: (i) detection (a signal-to-noise ratio of 3) within one year of observation by the Advanced LIGO detectors (H1-L1) requires a coalescence rate of $r_0 = 3 (0.2) Mpc^{-3} Myr^{-1}$ for binary neutron stars (binary black holes); (ii) this limit on $r_0$ could be reduced 3-fold for two co-located detectors, whereas the currently proposed worldwide network of advanced instruments gives only ~ 30% improvement in detectability; (iii) the improved sensitivity of the planned Einstein Telescope allows not only confident detection of the background but also the high frequency components of the spectrum to be measured. Finally we show that sub-threshold binary neutron star merger events produce a strong foreground, which could be an issue for future terrestrial stochastic searches of primordial GWs.Comment: A few typos corrected to match the published version in MNRA

Support for Integrated Ecosystem Assessments of NOAA’s National Estuarine Research Reserves System (NERRS), Volume I: The Impacts of Coastal Development on the Ecology and Human Well-being of Tidal Creek Ecosystems of the US Southeast

A study was conducted, in association with the Sapelo Island and North Carolina National Estuarine Research Reserves (NERRs), to evaluate the impacts of coastal development on sentinel habitats (e.g., tidal creek ecosystems), including potential impacts to human health and well-being. Uplands associated with southeastern tidal creeks and the salt marshes they drain are popular locations for building homes, resorts, and recreational facilities because of the high quality of life and mild climate associated with these environments. Tidal creeks form part of the estuarine ecosystem characterized by high biological productivity, great ecological value, complex environmental gradients, and numerous interconnected processes. This research combined a watershed-level study integrating ecological, public health and human dimension attributes with watershed-level land use data. The approach used for this research was based upon a comparative watershed and ecosystem approach that sampled tidal creek networks draining developed watersheds (e.g., suburban, urban, and industrial) as well as undeveloped sites. The primary objective of this work was to clearly define the relationships between coastal development with its concomitant land use changes and non-point source pollution loading and the ecological and human health and well-being status of tidal creek ecosystems. Nineteen tidal creek systems, located along the southeastern United States coast from southern North Carolina to southern Georgia, were sampled during summer (June-August), 2005 and 2006. Within each system, creeks were divided into two primary segments based upon tidal zoning: intertidal (i.e., shallow, narrow headwater sections) and subtidal (i.e., deeper and wider sections), and watersheds were delineated for each segment. In total, we report findings on 24 intertidal and 19 subtidal creeks. Indicators sampled throughout each creek included water quality (e.g., dissolved oxygen concentration, salinity, nutrients, chlorophyll-a levels), sediment quality (e.g., characteristics, contaminants levels including emerging contaminants), pathogen and viral indicators, and abundance and genetic responses of biological resources (e.g., macrobenthic and nektonic communities, shellfish tissue contaminants, oyster microarray responses). For many indicators, the intertidally-dominated or headwater portions of tidal creeks were found to respond differently than the subtidally-dominated or larger and deeper portions of tidal creeks. Study results indicate that the integrity and productivity of headwater tidal creeks were impaired by land use changes and associated non-point source pollution, suggesting these habitats are valuable early warning sentinels of ensuing ecological impacts and potential public health threats. For these headwater creeks, this research has assisted the validation of a previously developed conceptual model for the southeastern US region. This conceptual model identified adverse changes that generally occurred in the physical and chemical environment (e.g., water quality indicators such as indicator bacteria for sewage pollution or sediment chemical contamination) when impervious cover levels in the watershed reach 10-20%. Ecological characteristics responded and were generally impaired when impervious cover levels exceed 20-30%. Estimates of impervious cover levels defining where human uses are impaired are currently being determined, but it appears that shellfish bed closures and the flooding vulnerability of headwater regions become a concern when impervious cover values exceed 10-30%. This information can be used to forecast the impacts of changing land use patterns on tidal creek environmental quality as well as associated human health and well-being. In addition, this study applied tools and technologies that are adaptable, transferable, and repeatable among the high quality NERRS sites as comparable reference entities to other nearby developed coastal watersheds. The findings herein will be of value in addressing local, regional and national needs for understanding multiple stressor (anthropogenic and human impacts) effects upon estuarine ecosystems and response trends in ecosystem condition with changing coastal impacts (i.e., development, climate change). (PDF contaions 88 pages

Sparticle Mass Spectrum in Grand Unified Theories

We carry out a detailed analysis of sparticle mass spectrum in supersymmetric grand unified theories. We consider the spectroscopy of the squarks and sleptons in SU(5) and SO(10) grand unified theories, and show how the underlying supersymmetry breaking parameters of these theories can be determined from a measurement of different sparticle masses. This analysis is done analytically by integrating the one-loop renormalization group equations with appropriate boundary conditions implied by the underlying grand unified gauge group. We also consider the impact of non-universal gaugino masses on the sparticle spectrum, especially the neutralino and chargino masses which arise in supersymmetric grand unified theories with non-minimal gauge kinetic function. In particular, we study the interrelationships between the squark and slepton masses which arise in grand unified theories at the one-loop level, which can be used to distinguish between the different underlying gauge groups and their breaking pattern to the Standard Model gauge group. We also comment on the corrections that can affect these one-loop results.Comment: 19 pages, 6 figure