Observations of clustering inside oceanic bubble clouds and the effect on short-range acoustic propagation

It has recently been shown [Weber, T. C. et al. (Year: 2007). “Acoustic propagation through clustered bubble clouds,” IEEE J. Ocean. Eng.32, 513–523] that gas bubble clustering plays a role in determining the acoustic field characteristics of bubbly fluids. In particular, it has been shown that clustering changes the bubble-induced attenuation as well as the ping-to-ping variability in the acoustic field. The degree to which bubble clustering exists in nature, however, is unknown. This paper describes a method for quantifying bubble clustering using a high frequency (400kHz) multibeam sonar, and reports on observations of near-surface bubbleclustering during a storm ( 14.6m∕s wind speed) in the Gulf of Maine. The multibeam sonardata are analyzed to estimate the pair correlation function, a measure of bubble clustering. In order to account for clustering in the mean acoustic field, a modification to the effective mediumwave number is made. With this modification, the multibeam sonar observations are used to predict the effect of clustering on the attenuation of the mean field for short-range propagation (1 m) at frequencies between 10 and 350kHz . Results for this specific case show that clusteringcan cause the attenuation to change by 20%–80% over this frequency range

Twisted submanifolds of R^n

We propose a general procedure to construct noncommutative deformations of an embedded submanifold $M$ of $\mathbb{R}^n$ determined by a set of smooth equations $f^a(x)=0$. We use the framework of Drinfel'd twist deformation of differential geometry of [Aschieri et al., Class. Quantum Gravity 23 (2006), 1883]; the commutative pointwise product is replaced by a (generally noncommutative) $\star$-product determined by a Drinfel'd twist. The twists we employ are based on the Lie algebra $\Xi_t$ of vector fields that are tangent to all the submanifolds that are level sets of the $f^a$; the twisted Cartan calculus is automatically equivariant under twisted tangent infinitesimal diffeomorphisms. We can consistently project a connection from the twisted $\mathbb{R}^n$ to the twisted $M$ if the twist is based on a suitable Lie subalgebra $\mathfrak{e}\subset\Xi_t$. If we endow $\mathbb{R}^n$ with a metric then twisting and projecting to the normal and tangent vector fields commute, and we can project the Levi-Civita connection consistently to the twisted $M$, provided the twist is based on the Lie subalgebra $\mathfrak{k}\subset\mathfrak{e}$ of the Killing vector fields of the metric; a twisted Gauss theorem follows, in particular. Twisted algebraic manifolds can be characterized in terms of generators and polynomial relations. We present in some detail twisted cylinders embedded in twisted Euclidean $\mathbb{R}^3$ and twisted hyperboloids embedded in twisted Minkowski $\mathbb{R}^3$ [these are twisted (anti-)de Sitter spaces $dS_2,AdS_2$].Comment: Latex file, 48 pages, 1 figure. Slightly adapted version to the new preprint arXiv:2005.03509, where the present framework is specialized to quadrics and other algebraic submanifolds of R^n. Several typos correcte

Twist star products and Morita equivalence

We present a simple no-go theorem for the existence of a deformation quantization of a homogeneous space M induced by a Drinfel'd twist: we argue that equivariant line bundles on M with non-trivial Chern class and symplectic twist star products cannot both exist on the same manifold M. This implies, for example, that there is no symplectic star product on the complex projective spaces induced by a twist based on U(gl(n,C))[[h]] or any sub-bialgebra, for every n greater or equal than 2.Comment: 10 pages, no figure

A Method for Field Calibration of a Multibeam Echo Sounder

The use of multibeam echo sounders (MBES) has grown more frequent in applications like seafloor imaging, fisheries, and habitat mapping. Calibration of these instruments is important for understanding and validating the performance of MBES. For echo sounders in general, different calibration methodologies have been developed in controlled environments such as a fresh water tank and in the actual field of operation. While calibration in an indoor tank facility can bring excellent results in terms of accuracy, the amount of time required for a complete calibration can become prohibitively large. A field calibration can reveal the actual radiation beam pattern for shipmounted sonar systems, accounting for acoustic interferences which may be caused by objects around the installed transducers. The standard target method is a common practice for field calibration of split-beam echo sounders. However, when applied to a Mills Cross MBES, this method does not provide means to determine the alongship angle of the target, since the receiver transducer is a line array. A method to determine the combined transmit/receive radiation beam pattern for a ship-mounted multibeam system was developed and tested for a Reson Seabat 7125 MBES inside the fresh water calibration tank of the University of New Hampshire. This calibration methodology employs a tungsten carbide sphere of 38.1 mm diameter as target and a Simrad EK60 split-beam sonar system to provide athwartship and alongship angular information of the target sphere position. The multibeam sonar system was configured for 256 beams equi-angle mode at an operating frequency of 200 kHz; the split-beam system was set to work passively at the same frequency. A combined transmit/receive beam pattern was computed for an athwartship angular range between –6o and +6o and an alongship angular range between –1o and +3o . The limited angular range of the measurements is due to the –3 dB beamwidth of 7.1o in the athwartship and alongship directions of the split-beam sonar system coupled with the alongship offset of 1.6o between the maximum response axes (MRA) of the two sonar systems. Possible acoustic interferences caused by the monofilament line used to suspend the target sphere in the water column were found in the measurements for alongship angle values less than –1o . Beam pattern measurements for the combined transmit/receive beam pattern at a distance of 8 m show a –3 dB beamwidth of 1.1o in the athwartship direction and a –3 dB beamwidth of 2.0o in the alongship direction for the most inner beams. The dynamic range for the measurements was approximately of –40 dB

Calibration of multibeam echo sounders: a comparison between two methodologies

Multibeam echo sounders (MBES) are widely used in applications like seafloor imaging, fisheries, and habitat mapping. Calibration of acoustic backscatter is an important aspect of understanding and validating the performance of a MBES. Combined transmit/receive beampattern calibrations were performed on a 200 kHz Reson Seabat 7125 MBES in the acoustic tank of the University of New Hampshire utilizing two different methodologies. The first methodology employs fixed standard target spheres and a high accuracy/high resolution rotation mechanism. This method, similar to that proposed by Foote et al [ Protocols forcalibrating multibeam sonar , J. Acoust. Soc. Am. 117(4), 2005], is designed for a calibrationtank and provides accurate results but requires a large amount of operation time and cannot be performed in situ. The second methodology has been designed for field calibration of MBES. It employs a standard target sphere and a 200 kHz Simrad EK60 split-beam sonar system to provide athwartship and alongship angular information of the target sphere position. This method offers the possibility of field calibration for vessel mounted systems and a significantly reduced operation time, but has a potential reduction in accuracy. In this paper, results from these two methods applied to the same MBES are compared

High Resolution Calibration of a Multibeam Echo Sounder

Calibration can greatly increase the utility of collecting seafloor backscattering strength with multibeam echo sounders (MBES). A calibration procedure to determine high resolution, three dimensional transmit and receive beam patterns of a Reson SeaBat 7125 MBES was performed using the fresh water calibration tank at the University of New Hampshire. The measurements employed an omni-directional Reson TC4034 projector/hydrophone as a reference transducer at an acoustic distance of 13 m. The multibeam sonar system was configured for 256 beams equi-angle mode and operating frequency of 396 kHz. The transmit beam pattern was computed for across-track angular range between +/–90o in 0.1o increments and along-track angular range between +/–2.55o in 0.09o increments. Receive directional characteristics were measured for the across-track range of +/–120o in 0.1o increments with along-track angular range of +/–1.23o in 0.18o increments. With these measurements, a three-dimensional plot of the transmit beam pattern was computed for the entire range of angles, although for the receive beam pattern it was only determined for the 0o along-track angle. The reduced angular coverage of the receive beam pattern was due to discrepancies in the off-axis results that are thought to be related to receiver saturation. Measurements for the transmit beam pattern show a –3 dB beamwidth of 0.99o for across-track angle of 0o with side lobes below –17 dB. The results show an unexplained curvature in the transmit beam pattern that would have gone un-noticed during a two dimensional beam pattern measurement. An interference effect causing ripples and attenuation of the transmit beam pattern was also observed. This effect is thought to be caused by a second 200 kHz projector mounted parallel to the 396 kHz projector. This interference occurs at an across-track angular region between +30o and +75o with gradual decrease in amplitude of about 3 dB. The receive beam pattern measurements show a –3 dB beamwidth of approximately 0.62o for the most inner beams (beams 128 and 129) and of approximately 1.40o for the most outer beams (beams 1 and 256) at along-track angular position of 0o with side-lobes below –26 dB for the most inner beams and below –17 dB for the most outer beams

The Impact of Feedback Frequency on Risk Taking: How general is the Phenomenon?

In a recent QJE-article, Gneezy and Potters (1997) present experimental evidence for the impact of feedback frequency on individual risk taking behavior in repeated investment decisions. They find an increased willingness to invest into a risky asset if less frequent feedback about the outcome of previous investments is provided. The observed decision pattern is explained by myopic loss aversion, a combination of mental accounting and loss aversion. In this note, we argue that the findings of Gneezy and Potters on the relationship between feedback frequency and risk taking are not as general as they might seem. We provide theoretical arguments and experimental evidence to demonstrate that the reported phenomenon is not robust to changes in the risk profiles of the given investment options.

Tranching and Pricing in CDO-Transactions

This paper empirically investigates the tranching and tranche pricing of European securitization transactions of corporate loans and bonds. Tranching allows the originator to issue bonds with strong quality differences and thereby attract heterogeneous investors. We find that the number of differently rated tranches in a transaction is inversely related to the quality of the underlying asset pool. Credit spreads on tranches in a transaction are inversely related to the number of tranches. The average price for transferring a unit of expected default risk, paid in a transaction, is inversely related to the default probability of the underlying asset pool. The average price, paid for a tranche, increases with the rating of the tranche, it is higher for the lowest rated tranche and very high for AAA-tranches in true sale-transactions. It varies little across butterfly spreads obtained from rated tranches except for the most senior spread.Securitization, information asymmetries, tranching of asset portfolios, risk premiums of tranches

Constraints on the High-Density Nuclear Equation of State from Neutron Star Observables

Depending on the density reached in the cores of neutron stars, such objects may contain stable phases of novel matter found nowhere else in the Universe. This article gives a brief overview of these phases of matter and discusses astrophysical constraints on the high-density equation of state associated with ultra-dense nuclear matter.Comment: 16 pages, 11 figures, Contribution to Proceedings of the 3rd International Workshop on Astronomy and Relativistic Astrophysics (IWARA), 3-6 October 2007, Joao Pessoa, Brazi