Quantum integrability of quadratic Killing tensors

Quantum integrability of classical integrable systems given by quadratic Killing tensors on curved configuration spaces is investigated. It is proven that, using a "minimal" quantization scheme, quantum integrability is insured for a large class of classic examples.Comment: LaTeX 2e, no figure, 35 p., references added, minor modifications. To appear in the J. Math. Phy

Some Spacetimes with Higher Rank Killing-Stackel Tensors

By applying the lightlike Eisenhart lift to several known examples of low-dimensional integrable systems admitting integrals of motion of higher-order in momenta, we obtain four- and higher-dimensional Lorentzian spacetimes with irreducible higher-rank Killing tensors. Such metrics, we believe, are first examples of spacetimes admitting higher-rank Killing tensors. Included in our examples is a four-dimensional supersymmetric pp-wave spacetime, whose geodesic flow is superintegrable. The Killing tensors satisfy a non-trivial Poisson-Schouten-Nijenhuis algebra. We discuss the extension to the quantum regime

Designing Improved Sediment Transport Visualizations

Monitoring, or more commonly, modeling of sediment transport in the coastal environment is a critical task with relevance to coastline stability, beach erosion, tracking environmental contaminants, and safety of navigation. Increased intensity and regularity of storms such as Superstorm Sandy heighten the importance of our understanding of sediment transport processes. A weakness of current modeling capabilities is the ability to easily visualize the result in an intuitive manner. Many of the available visualization software packages display only a single variable at once, usually as a two-dimensional, plan-view cross-section. With such limited display capabilities, sophisticated 3D models are undermined in both the interpretation of results and dissemination of information to the public. Here we explore a subset of existing modeling capabilities (specifically, modeling scour around man-made structures) and visualization solutions, examine their shortcomings and present a design for a 4D visualization for sediment transport studies that is based on perceptually-focused data visualization research and recent and ongoing developments in multivariate displays. Vector and scalar fields are co-displayed, yet kept independently identifiable utilizing human perception\u27s separation of color, texture, and motion. Bathymetry, sediment grain-size distribution, and forcing hydrodynamics are a subset of the variables investigated for simultaneous representation. Direct interaction with field data is tested to support rapid validation of sediment transport model results. Our goal is a tight integration of both simulated data and real world observations to support analysis and simulation of the impact of major sediment transport events such as hurricanes. We unite modeled results and field observations within a geodatabase designed as an application schema of the Arc Marine Data Model. Our real-world focus is on the Redbird Artificial Reef Site, roughly 18 nautical miles offshor- Delaware Bay, Delaware, where repeated surveys have identified active scour and bedform migration in 27 m water depth amongst the more than 900 deliberately sunken subway cars and vessels. Coincidently collected high-resolution multibeam bathymetry, backscatter, and side-scan sonar data from surface and autonomous underwater vehicle (AUV) systems along with complementary sub-bottom, grab sample, bottom imagery, and wave and current (via ADCP) datasets provide the basis for analysis. This site is particularly attractive due to overlap with the Delaware Bay Operational Forecast System (DBOFS), a model that provides historical and forecast oceanographic data that can be tested in hindcast against significant changes observed at the site during Superstorm Sandy and in predicting future changes through small-scale modeling around the individual reef objects

Non-commutative oscillator with Kepler-type dynamical symmetry

A 3-dimensional non-commutative oscillator with no mass term but with a certain momentum-dependent potential admits a conserved Runge-Lenz vector, derived from the dual description in momentum space. The latter corresponds to a Dirac monopole with a fine-tuned inverse-square plus Newtonian potential, introduced by McIntosh, Cisneros, and by Zwanziger some time ago. The trajectories are (arcs of) ellipses, which, in the commutative limit, reduce to the circular hodographs of the Kepler problem. The dynamical symmetry allows for an algebraic determination of the bound-state spectrum and actually extends to the conformal algebra o(4,2).Comment: 10 pages, 3 figures. Published versio

A detailed seabed signature from Hurricane Sandy revealed in bedforms and scour

On 30 October 2012, Hurricane Sandy made landfall near Brigantine New Jersey bringing widespread erosion and damage to the coastline. We have obtained a unique set of high-resolution before and after storm measurements of seabed morphology and in situhydrodynamic conditions (waves and currents) capturing the impact of the storm at an inner continental shelf field site known as the “Redbird reef”. Understanding the signature of this storm event is important for identifying the impacts of such events and for understanding the role that such events have in the transport of sediment and marine debris on the inner continental shelf. As part of an ONR-sponsored program designed to understand and characterize the ripple dynamics and scour processes in an energetic, heterogeneous inner-shelf setting, a series of high-resolution geoacoustic surveys were conducted before and after Hurricane Sandy. Our overall goal is to improve our understanding of bedform dynamics and spatio-temporal length scales and defect densities through the application of a recently developed fingerprint algorithm technique. Utilizing high-resolution swath sonar collected by an AUV and from surface vessel sonars, our study focuses both on bedforms in the vicinity of manmade seabed objects and dynamic natural ripples on the inner shelf in energetic coastal settings with application to critical military operations such as mine countermeasures

Covariant analysis of Newtonian multi-fluid models for neutron stars: I Milne-Cartan structure and variational formulation

This is the first of a series of articles showing how 4 dimensionally covariant analytical procedures developed in the context of General Relativity can be usefully adapted for application in a purely Newtonian framework where they provide physical insights (e.g. concerning helicity currents) that are not so easy to obtain by the traditional approach based on a 3+1 space time decomposition. After an introductory presentation of the relevant Milne spacetime structure and the associated Cartan connection, the essential principles are illustrated by application to the variational formulation of simple barotropic perfect fluid models. This variational treatment is then extended to conservative multiconstituent self gravitating fluid models of the more general kind that is needed for treating the effects of superfluidity in neutron stars.Comment: 35 pages Latex, with typo corrections and updated reference

Tidal dissipation compared to seismic dissipation: in small bodies, in earths, and in superearths

While the seismic quality factor and phase lag are defined solely by the bulk properties of the mantle, their tidal counterparts are determined both by the bulk properties and self-gravitation of a body as a whole. For a qualitative estimate, we model the body with a homogeneous sphere and express the tidal phase lag through the lag in a sample of material. Although simplistic, our model is sufficient to understand that the lags are not identical. The difference emerges because self-gravitation pulls the tidal bulge down. At low frequencies, this reduces strain and makes tidal damping less efficient in larger bodies. At high frequencies, competition between self-gravitation and rheology becomes more complex, though for sufficiently large superearths the same rule works: the larger the body, the weaker tidal damping in it. Being negligible for small terrestrial planets and moons, the difference between the seismic and tidal lagging (and likewise between the seismic and tidal damping) becomes very considerable for superearths. In those, it is much lower than what one might expect from using a seismic quality factor. The tidal damping rate deviates from the seismic damping rate especially in the zero-frequency limit, and this difference takes place for bodies of any size. So the equal in magnitude but opposite in sign tidal torques, exerted on one another by the primary and the secondary, go smoothly through zero as the secondary crosses the synchronous orbit. We describe the mantle rheology with the Andrade model, allowing it to lean towards the Maxwell model at the lowest frequencies. To implement this additional flexibility, we reformulate the Andrade model by endowing it with a free parameter which is the ratio of the anelastic timescale to the viscoelastic Maxwell time of the mantle. Some uncertainty in this parameter's frequency-dependence does not influence our principal conclusions

Special Properties of Five Dimensional BPS Rotating Black Holes

Supersymmetric, rotating, asymptotically flat black holes with a regular horizon are rare configurations in String Theory. One example is known in five spacetime dimensions, within the toroidal compactification of type IIB string theory. Such special solution is allowed by the existence of a Chern-Simons coupling in the Supergravity theory and by the possibility of imposing a self duality condition on the `rotation 2-form'. We explore three peculiar features of such black holes: 1) Oxidising to D=10 the five dimensional configuration may be interpreted as a system of $D1-D5$ branes with a Brinkmann wave propagating along their worldvolume. Unlike its five dimensional Kaluza-Klein compactification, the universal covering space of this manifold has no causality violations. In other words, causal anomalies can be solved in higher dimensions. From the dual SCFT viewpoint, the causality bound for the compactified spacetime arises as the unitarity bound; 2) The vanishing of the scattering cross section for uncharged scalars and sufficiently high angular momentum of the background is shown still to hold at the level of charged interactions. The same is verified when a non-minimal coupling to the geometry is used. Therefore, the `repulson' behaviour previously found is universal for non accelerated observers; 3) The solutions are shown to have a non-standard gyromagnetic ratio of $g=3$. In contrast, the superpartners of a static, BPS, five dimensional black hole have $g=1$. At the semi-classical level, we find that a Dirac fermion propagating in the rotating hole background has $g=2\pm1$, depending on the spinor direction of the fermion being parallel to Killing or `anti-Killing' spinors.Comment: 29 pages,1 figure, LaTeX; minor changes, typos corrected, 3 references added; to appear in Nucl. Phys.

Quantum mechanics on noncommutative Riemann surfaces

We study the quantum mechanics of a charged particle on a constant curvature noncommutative Riemann surface in the presence of a constant magnetic field. We formulate the problem by considering quantum mechanics on the noncommutative AdS_2 covering space and gauging a discrete symmetry group which defines a genus-g surface. Although there is no magnetic field quantization on the covering space, a quantization condition is required in order to have single-valued states on the Riemann surface. For noncommutative AdS_2 and subcritical values of the magnetic field the spectrum has a discrete Landau level part as well as a continuum, while for overcritical values we obtain a purely noncommutative phase consisting entirely of Landau levels.Comment: 18 pages, 1 figure, final version to appear in Nucl.Phys.

The relation between dynamics and star formation in barred galaxies

We analyze optical and near-infrared data of a sample of 11 barred spiral galaxies, in order to establish a connection between star formation and bar/spiral dynamics. We find that 22 regions located in the bars, and 20 regions in the spiral arms beyond the end of the bar present azimuthal color/age gradients that may be attributed to star formation triggering. Assuming a circular motion dynamic model, we compare the observed age gradient candidates with stellar populations synthesis models. A link can then be established with the disk dynamics that allows us to obtain parameters like the pattern speed of the bar or spiral, as well as the positions of resonance radii. We subsequently compare the derived pattern speeds with those expected from theoretical and observational results in the literature (e.g., bars ending near corotation). We find a tendency to overestimate bar pattern speeds derived from color gradients in the bar at small radii, away from corotation; this trend can be attributed to non-circular motions of the young stars born in the bar region. In spiral regions, we find that ~ 50% of the color gradient candidates are "inverse", i.e., with the direction of stellar aging contrary to that of rotation. The other half of the gradients found in spiral arms have stellar ages that increase in the same sense as rotation. Of the 9 objects with gradients in both bars and spirals, six (67%) appear to have a bar and a spiral with similar Omega_p, while three (33%) do not.Comment: Accepted for publication in Ap