Negative index Jacobi forms and quantum modular forms

In this paper, we consider the Fourier coefficients of a special class of meromorphic Jaocbi forms of negative index. Much recent work has been done on such coefficients in the case of Jacobi forms of positive index, but almost nothing is known for Jacobi forms of negative index. In this paper we show, from two different perspectives, that their Fourier coefficients have a simple decomposition in terms of partial theta functions. The first perspective uses the language of Lie super algebras, and the second applies the theory of elliptic functions. In particular, we find a new infinite family of rank-crank type PDEs generalizing the famous example of Atkin and Garvan. We then describe the modularity properties of these coefficients, showing that they are "mixed partial theta functions", along the way determining a new class of quantum modular partial theta functions which is of independent interest.Comment: 29 pages, minor correction

Observations of Backscatter from Sand and Gravel Seafloors Between 170-250 kHz

Interpreting observations of frequency-dependence in backscatter from the seafloor offers many challenges, either because multiple frequencies are used for different observations that will later be merged or simply because seafloor scattering models are not well-understood above 100 kHz. Hindering the understanding of these observations is the paucity of reported, calibratedacoustic measurements above 100 kHz. This manuscript seeks to help elucidate the linkages between seafloor properties and frequency-dependent seafloor backscatter by describing observations of backscatter collected from sand, gravel, and bedrock seafloors at frequencies between 170 and 250 kHz and at a grazing angle of 45°. Overall, the frequency dependence appeared weak for all seafloor types, with a slight increase in seafloor scattering strength with increasing frequency for an area with unimodal, very poorly to moderately well sorted, slightly granular to granular medium sand with significant amounts of shell debris and a slight decrease in all other locations

Considerations for Future IGS Receivers

Future IGS receivers are considered against the backdrop of GNSS signal modernization and the IGS’s goal of further improving the accuracy of its products. The purpose of this paper is to provide IGS members with a guide to making decisions about GNSS receivers. Modernized GNSS signals are analyzed with a view toward IGS applications. A schedule for minimum IGS receiver requirements is proposed. Features of idealized conceptual receivers are discussed. The prospects for standard commercial receivers and for software-defined GNSS receivers are examined. Recommendations are given for how the IGS should proceed in order to maximally benefit from the transformation in GNSS that will occur over the next decade.Aerospace Engineering and Engineering Mechanic

Advanced technology composite aircraft structures

Work performed during the 25th month on NAS1-18889, Advanced Technology Composite Aircraft Structures, is summarized. The main objective of this program is to develop an integrated technology and demonstrate a confidence level that permits the cost- and weight-effective use of advanced composite materials in primary structures of future aircraft with the emphasis on pressurized fuselages. The period from 1-31 May 1991 is covered

Status of the Pacific Mackerel resource during 1997 and management recommendations for the fishery

Based on a California Department of Fish and Game (CDFG) projected biomass estimate of 91,200 metric tons for July 1, 1997, the recommended commercial fishery quota for the 1997/98 fishing season is 22,000 metric tons. Age-specific abundance for 1996 was estimated using output from a stock assessment model called ADEPT and certain assumptions about growth and fishing mortality during the first half of 1997. In this year's assessment, abundance estimates made by ADEPT were expanded back in time to cover the 68-year period of 1929 through 1996. The commercial fishery quota recommendation is based upon the prescribed harvest formula for Pacific mackerel that is specified in the California Fish and Game Code. Several sources of information are available for the Pacific mackerel stock, all of which suggest a smaller biomass than was present in the 1980's. Landings from both California and Ensenada, Mexico have sharply decreased and catch rates from the southern California Commercial Passenger Fishing Vessel (CPFV) fleet have declined. Fishery-independent indices of abundance from aerial spotter observations and California Cooperative Oceanic Fisheries Investigations (CalCOFI) ichthyoplankton surveys show similar trends. The 1997 biomass estimate is higher than last year's estimate of 47,160 metric tons because data added to the model this year increased abundance for fish of 1994 and older year classes (age 2+). This year's results indicate there were more fish in the older year classes than estimated in previous assessments. (27pp.

Observations of High Frequency, Long Range Acoustic Propagation in a Harbor Environment

The positioning and navigation of AUV\u27s in harbor environments using underwater acoustics is complicated by shallow waters, long propagation distances, and complex oceanographic features. This paper reports on high frequency (40 kHz) acoustic measurements made in Portsmouth Harbor, NH, USA, which is an estuary containing several riverine inputs and a strong tidal flow (2+ knots). A one-way propagation experiment was conducted at the mouth of the harbor for propagation distances up to 100 water depths. Strong signatures of a variety of phenomenon were observed in the acoustic signal levels, including tidal heights and currents, turbulent mixing, and wind/wave action. The relative importance of each of these will be discussed in terms of signal to noise level and the associated constraints on acoustic positioning systems

Inflow and Loadings from Ground Water to the Great Bay Estuary, New Hampshire

This final report presents the results of a study to evaluate groundwater inflow and nutrient loadings to the Great Bay Estuary, New Hampshire. The evaluation of inflow was accomplished independently by two methods: one, used thermal imagery, and the other, piezometric mapping. The thermal imagery method assessed groundwater that was observed to discharge within the intertidal zone of an inland estuary. The groundwater piezometric mapping method used bedrock wells around the bay to create an overall piezometric map of the near-bay area. Groundwater discharge was evaluated with respect to flow, concentration, and ultimately nitrogen loading to coastal waters. The results represent a snapshot for these variables, examined by a thermal infrared aerial survey in the spring of 2000, and water quality, specific discharge, and piezometric surface maps in the summer of 2001. Monitoring wells upgradient of the Great Bay were analyzed for nitrogen as an indicator of potential discharge source waters. Total groundwater discharge to the estuary was calculated as 24.2 cubic feet per second (cfs) with an average of 0.81± 0.89 mg dissolved inorganic nitrogen (DIN)/L, with a maximum value of 2.7 mg DIN/L (n=20). Nutrient concentrations, averaging 0.83± 1.34 mg DIN/L, with a maximum value of 10.2 mg DIN/L, were observed in upgradient bedrock groundwater analyzed from 192 wells. Nutrient loading was calculated to be 19.3±21.2 tons of N per year for the total Great Bay Estuary, covering nearly 144 miles of shoreline. The groundwater derived nutrient loading accounts for approximately 5% of the total non-point source load to the estuary. The thermal imagery method was found to be an effective and affordable alternative to conventional groundwater exploration approaches

Gauge turbulence, topological defect dynamics, and condensation in Higgs models

The real-time dynamics of topological defects and turbulent configurations of gauge fields for electric and magnetic confinement are studied numerically within a 2+1D Abelian Higgs model. It is shown that confinement is appearing in such systems equilibrating after a strong initial quench such as the overpopulation of the infrared modes. While the final equilibrium state does not support confinement, metastable vortex defect configurations appear in the gauge field which are found to be closely related to the appearance of physically observable confined electric and magnetic charges. These phenomena are seen to be intimately related to the approach of a non-thermal fixed point of the far-from-equilibrium dynamical evolution, signalled by universal scaling in the gauge-invariant correlation function of the Higgs field. Even when the parameters of the Higgs action do not support condensate formation in the vacuum, during this approach, transient Higgs condensation is observed. We discuss implications of these results for the far-from-equilibrium dynamics of Yang-Mills fields and potential mechanisms how confinement and condensation in non-abelian gauge fields can be understood in terms of the dynamics of Higgs models. These suggest that there is an interesting new class of dynamics of strong coherent turbulent gauge fields with condensates.Comment: 16 pages, 14 figure

Acoustic sensing of gas seeps in the deep ocean with split-beam echosounders

When in the form of free gas in the water column, methane seeps emanating from the seabed are strong acoustic targets that are often detectable from surface vessels using echo sounders.In addition to detecting that a seep is present at some location, it is also desirable to characterize the nature of the seep in terms of its morphology and flux rates. Here, we examine how much we can learn about seeps in the deep (\u3e 1000 m) northern Gulf of Mexico using narrow-band split-beam echo sounders operating at fixed frequencies (18 kHz and 38 kHz).Methane seeps in this region are deeper than the methane hydrate stability zone, implying that bubbles of free gas form hydrate rinds that allow them to rise further in the water column than they otherwise would. While this behavior may aid in the classification of gas types in the seep, it is possible that the presence of hydrate rinds may also change the acoustic response of the bubbles and thereby make flux rate estimates more challenging. These and other aspects of seep characterization will be discussed