Entropy and scintillation analysis of acoustical beam propagation through ocean internal waves

Author Posting. © Acoustical Society of America, 2005. This article is posted here by permission of Acoustical Society of America for personal use, not for redistribution. The definitive version was published in Journal of the Acoustical Society of America 117 (2005): 1611-1623, doi:10.1121/1.1854571.Parabolic equation numerical simulations of waveguide acoustical beam propagation in an ocean of Garrett–Munk internal waves are used to examine the range evolution of beam properties such as beamwidth (both spectral and spatial), Shannon entropy, and scintillation index, as a function of beam angle. Simulations are carried out at 250- and 125-Hz acoustic frequencies. The ray trajectories associated with these beams are predominantly chaotic or exponentially sensitive to initial conditions and/or medium perturbations. At long range near saturation, the finite-frequency beams show a constant rate of change of Shannon entropy with range, independent of acoustic frequency. This full-wave rate of entropy is of the same order of magnitude as the average rate of entropy for the ray trajectories associated with this beam. Finite-range Lyapunov exponents provide the estimates of ray entropy rate or Kolmogorov–Siani entropy. The correspondence between full-wave and ray entropies suggests a full-wave manifestation of ray chaos, but only once statistical saturation is obtained. In spite of this correspondence, the simulated acoustical beams expand diffusively not exponentially (or explosively)

Spatially asymptotic S-matrix from general boundary formulation

We construct a new type of S-matrix in quantum field theory using the general boundary formulation. In contrast to the usual S-matrix the space of free asymptotic states is located at spatial rather than at temporal infinity. Hence, the new S-matrix applies to situations where interactions may remain important at all times, but become negligible with distance. We show that the new S-matrix is equivalent to the usual one in situations where both apply. This equivalence is mediated by an isomorphism between the respective asymptotic state spaces that we construct. We introduce coherent states that allow us to obtain explicit expressions for the new S-matrix. In our formalism crossing symmetry becomes a manifest rather than a derived feature of the S-matrix.Comment: 27 pages, LaTeX + revtex4; v2: various corrections, references update

Background independence in a nutshell

We study how physical information can be extracted from a background independent quantum system. We use an extremely simple `minimalist' system that models a finite region of 3d euclidean quantum spacetime with a single equilateral tetrahedron. We show that the physical information can be expressed as a boundary amplitude. We illustrate how the notions of "evolution" in a boundary proper-time and "vacuum" can be extracted from the background independent dynamics.Comment: 19 pages, 19 figure

Statistics of normal mode amplitudes in an ocean with random sound-speed perturbations : cross-mode coherence and mean intensity

Author Posting. © Acoustical Society of America, 2009. This article is posted here by permission of Acoustical Society of America for personal use, not for redistribution. The definitive version was published in Journal of the Acoustical Society of America 126 (2009): 1026-1035, doi:10.1121/1.3158818.In this paper Creamer's [(1996). J. Acoust. Soc. Am. 99, 2825–2838] transport equation for the mode amplitude coherence matrix resulting from coupled mode propagation through random fields of internal waves is examined in more detail. It is shown that the mode energy equations are approximately independent of the cross mode coherences, and that cross mode coherences and mode energy can evolve over very similar range scales. The decay of cross mode coherence depends on the relative mode phase randomization caused by coupling and adiabatic effects, each of which can be quantified by the theory. This behavior has a dramatic effect on the acoustic field second moments like mean intensity. Comparing estimates of the coherence matrix and mean intensity from Monte Carlo simulation, and the transport equations, good agreement is demonstrated for a 100-Hz deep-water example.This work was supported by the Office of Naval Research and the Naval Undersea Warfare Center’s (NUWC) Under- Sea Warfare (USW) chair at the Naval Postgraduate School

Three dimensional loop quantum gravity: coupling to point particles

We consider the coupling between three dimensional gravity with zero cosmological constant and massive spinning point particles. First, we study the classical canonical analysis of the coupled system. Then, we go to the Hamiltonian quantization generalizing loop quantum gravity techniques. We give a complete description of the kinematical Hilbert space of the coupled system. Finally, we define the physical Hilbert space of the system of self-gravitating massive spinning point particles using Rovelli's generalized projection operator which can be represented as a sum over spin foam amplitudes. In addition we provide an explicit expression of the (physical) distance operator between two particles which is defined as a Dirac observable.Comment: Typos corrected and references adde

Graviton propagator in loop quantum gravity

We compute some components of the graviton propagator in loop quantum gravity, using the spinfoam formalism, up to some second order terms in the expansion parameter.Comment: 41 pages, 6 figure

Physical boundary state for the quantum tetrahedron

We consider stability under evolution as a criterion to select a physical boundary state for the spinfoam formalism. As an example, we apply it to the simplest spinfoam defined by a single quantum tetrahedron and solve the associated eigenvalue problem at leading order in the large spin limit. We show that this fixes uniquely the free parameters entering the boundary state. Remarkably, the state obtained this way gives a correlation between edges which runs at leading order with the inverse distance between the edges, in agreement with the linearized continuum theory. Finally, we give an argument why this correlator represents the propagation of a pure gauge, consistently with the absence of physical degrees of freedom in 3d general relativity.Comment: 20 pages, 6 figure

Second-order amplitudes in loop quantum gravity

We explore some second-order amplitudes in loop quantum gravity. In particular, we compute some second-order contributions to diagonal components of the graviton propagator in the large distance limit, using the old version of the Barrett-Crane vertex amplitude. We illustrate the geometry associated to these terms. We find some peculiar phenomena in the large distance behavior of these amplitudes, related with the geometry of the generalized triangulations dual to the Feynman graphs of the corresponding group field theory. In particular, we point out a possible further difficulty with the old Barrett-Crane vertex: it appears to lead to flatness instead of Ricci-flatness, at least in some situations. The observation raises the question whether this difficulty remains with the new version of the vertex.Comment: 22 pages, 18 figure

Observations of sound-speed fluctuations on the New Jersey continental shelf in the summer of 2006

Author Posting. © Acoustical Society of America, 2012. This article is posted here by permission of Acoustical Society of America for personal use, not for redistribution. The definitive version was published in Journal of the Acoustical Society of America 131 (2012): 1733-1748, doi:10.1121/1.3666014.Environmental sensors moored on the New Jersey continental shelf tracked constant density surfaces (isopycnals) for 35 days in the summer of 2006. Sound-speed fluctuations from internal-wave vertical isopycnal displacements and from temperature/salinity variability along isopycnals (spiciness) are analyzed using frequency spectra and vertical covariance functions. Three varieties of internal waves are studied: Diffuse broadband internal waves (akin to waves fitting the deep water Garrett/Munk spectrum), internal tides, and, to a lesser extent, nonlinear internal waves. These internal-wave contributions are approximately distinct in the frequency domain. It is found that in the main thermocline spicy thermohaline structure dominates the root mean square sound-speed variability, with smaller contributions coming from (in order) nonlinear internal waves, diffuse internal waves, and internal tides. The frequency spectra of internal-wave displacements and of spiciness have similar form, likely due to the advection of variable-spiciness water masses by horizontal internal-wave currents, although there are technical limitations to the observations at high frequency. In the low-frequency, internal-wave band the internal-wave spectrum follows frequency to the −1.81 power, whereas the spice spectrum shows a −1.73 power. Mode spectra estimated via covariance methods show that the diffuse internal-wave spectrum has a smaller mode bandwidth than Garrett/Munk and that the internal tide has significant energy in modes one through three.This work was supported by the Office of Naval Research, and Professor Colosi gratefully acknowledges his additional support from the Naval Postgraduate School’s Undersea Warfare Chair that he holds

Simple model for quantum general relativity from loop quantum gravity

New progress in loop gravity has lead to a simple model of `general-covariant quantum field theory'. I sum up the definition of the model in self-contained form, in terms accessible to those outside the subfield. I emphasize its formulation as a generalized topological quantum field theory with an infinite number of degrees of freedom, and its relation to lattice theory. I list the indications supporting the conjecture that the model is related to general relativity and UV finite.Comment: 8 pages, 3 figure