Vacuum initial data, singularities, and cosmic censorship

The formation of a naked singularity in a vacuum, asymptotically flat spacetime would be a clear violation of cosmic censorship. We find initial value solutions to Einstein's field equations that may lead to this behavior. We construct two families of asymptotically flat, axisymmetric vaccum solutions at a moment of time symmetry. The limiting members of these families are singular. Our first family represents a linear string of Schwarzschild black holes. We study the divergence of the gravitational tidal field outside the holes as their number along the string is increased. Our second family consists of prolate Brill gravitational wave packets. We examine the tidal field strength as the characteristic width of the wave is reduced towards zero. In both cases we find that configurations can be constructed with arbitrarily large fields that are not clothed by apparent horizons. These configurations are characterized by long, prolate concentrations of mass energy. We analyze our results in the context of the hoop conjecture

Experimental observation of second-harmonic generation and diffusion inside random media

We have experimentally measured the distribution of the second-harmonic intensity that is generated inside a highly-scattering slab of porous gallium phosphide. Two complementary techniques for determining the distribution are used. First, the spatial distribution of second-harmonic light intensity at the side of a cleaved slab has been recorded. Second, the total second-harmonic radiation at each side of the slab has been measured for several samples at various wavelengths. By combining these measurements with a diffusion model for second-harmonic generation that incorporates extrapolated boundary conditions, we present a consistent picture of the distribution of the second-harmonic intensity inside the slab. We find that the ratio $\ell_{2\omega}/L_c$ of the mean free path at the second-harmonic frequency to the coherence length, which was suggested by some earlier calculations, cannot describe the second-harmonic yield in our samples. For describing the total second-harmonic yield, our experiments show that the scattering parameter at the fundamental frequency \k_{1\omega}\ell_{1\omega} is the most relevant parameter in our type of samples.Comment: 10 pages, 7 figure

Instabilities of waves in nonlinear disordered media

We develop a self-consistent theory of temporal fluctuations of a speckle pattern resulting from the multiple scattering of a coherent wave in a weakly nonlinear disordered medium. The speckle pattern is shown to become unstable if the nonlinearity exceeds a threshold value. The instability is due to a feedback provided by the multiple scattering and manifests itself in spontaneous fluctuations of the scattered intensity. The development of instability is independent of the sign of nonlinearity.Comment: 6 pages, 2 PostScript figures, accepted to Phys. Rev. Let

Weak localization of light by cold atoms: the impact of quantum internal structure

Since the work of Anderson on localization, interference effects for the propagation of a wave in the presence of disorder have been extensively studied, as exemplified in coherent backscattering (CBS) of light. In the multiple scattering of light by a disordered sample of thermal atoms, interference effects are usually washed out by the fast atomic motion. This is no longer true for cold atoms where CBS has recently been observed. However, the internal structure of the atoms strongly influences the interference properties. In this paper, we consider light scattering by an atomic dipole transition with arbitrary degeneracy and study its impact on coherent backscattering. We show that the interference contrast is strongly reduced. Assuming a uniform statistical distribution over internal degrees of freedom, we compute analytically the single and double scattering contributions to the intensity in the weak localization regime. The so-called ladder and crossed diagrams are generalized to the case of atoms and permit to calculate enhancement factors and backscattering intensity profiles for polarized light and any closed atomic dipole transition.Comment: 22 pages Revtex, 9 figures, to appear in PR

Temporal fluctuations of waves in weakly nonlinear disordered media

We consider the multiple scattering of a scalar wave in a disordered medium with a weak nonlinearity of Kerr type. The perturbation theory, developed to calculate the temporal autocorrelation function of scattered wave, fails at short correlation times. A self-consistent calculation shows that for nonlinearities exceeding a certain threshold value, the multiple-scattering speckle pattern becomes unstable and exhibits spontaneous fluctuations even in the absence of scatterer motion. The instability is due to a distributed feedback in the system "coherent wave + nonlinear disordered medium". The feedback is provided by the multiple scattering. The development of instability is independent of the sign of nonlinearity.Comment: RevTeX, 15 pages (including 5 figures), accepted for publication in Phys. Rev.

Autonomous and Lagrangian ocean observations for Atlantic tropical cyclone studies and forecasts

Author Posting. © The Oceanography Society, 2017. This article is posted here by permission of The Oceanography Society for personal use, not for redistribution. The definitive version was published in Oceanography 30, no. 2 (2017): 92–103, doi:10.5670/oceanog.2017.227.The tropical Atlantic basin is one of seven global regions where tropical cyclones (TCs) commonly originate, intensify, and affect highly populated coastal areas. Under appropriate atmospheric conditions, TC intensification can be linked to upper-ocean properties. Errors in Atlantic TC intensification forecasts have not been significantly reduced during the last 25 years. The combined use of in situ and satellite observations, particularly of temperature and salinity ahead of TCs, has the potential to improve the representation of the ocean, more accurately initialize hurricane intensity forecast models, and identify areas where TCs may intensify. However, a sustained in situ ocean observing system in the tropical North Atlantic Ocean and Caribbean Sea dedicated to measuring subsurface temperature, salinity, and density fields in support of TC intensity studies and forecasts has yet to be designed and implemented. Autonomous and Lagrangian platforms and sensors offer cost-effective opportunities to accomplish this objective. Here, we highlight recent efforts to use autonomous platforms and sensors, including surface drifters, profiling floats, underwater gliders, and dropsondes, to better understand air-sea processes during high-wind events, particularly those geared toward improving hurricane intensity forecasts. Real-time data availability is key for assimilation into numerical weather forecast models.The NOAA/AOML component of this work was originally funded by the Disaster Relief Appropriations Act of 2013, also known as the Sandy Supplemental, and is currently funded through NOAA research grant NA14OAR4830103 by AOML and CARICOOS, as well as NOAA’s Integrated Ocean Observing System (IOOS). The TEMPESTS component of this work is supported by NOAA through the Cooperative Institute for the North Atlantic Region (NA13OAR4830233) with additional analysis support from the WHOI Summer Student Fellowship Program, Nortek Student Equipment Grant, and the Rutgers University Teledyne Webb Graduate Student Fellowship Program. The drifter component of this work is funded through NOAA grant NA15OAR4320071(11.432) in support of the Global Drifter Program