The applications of satellites to communications, navigation and surveillance for aircraft operating over the contiguous United States. Volume 1 - Technical report

Satellite applications to aircraft communications, navigation, and surveillance over US including synthesized satellite network and aircraft equipment for air traffic contro

Time dependence of Bragg forward scattering and self-seeding of hard x-ray free-electron lasers

Free-electron lasers (FELs) can now generate temporally short, high power x-ray pulses of unprecedented brightness, even though their longitudinal coherence is relatively poor. The longitudinal coherence can be potentially improved by employing narrow bandwidth x-ray crystal optics, in which case one must also understand how the crystal affects the field profile in time and space. We frame the dynamical theory of x-ray diffraction as a set of coupled waves in order to derive analytic expressions for the spatiotemporal response of Bragg scattering from temporally short incident pulses. We compute the profiles of both the reflected and forward scattered x-ray pulses, showing that the time delay of the wave $\tau$ is linked to its transverse spatial shift $\Delta x$ through the simple relationship $\Delta x = c\tau \cot\theta$, where $\theta$ is the grazing angle of incidence to the diffracting planes. Finally, we apply our findings to obtain an analytic description of Bragg forward scattering relevant to monochromatically seed hard x-ray FELs.Comment: 11 pages, 6 figure

Laplacian Growth, Elliptic Growth, and Singularities of the Schwarz Potential

The Schwarz function has played an elegant role in understanding and in generating new examples of exact solutions to the Laplacian growth (or "Hele- Shaw") problem in the plane. The guiding principle in this connection is the fact that "non-physical" singularities in the "oil domain" of the Schwarz function are stationary, and the "physical" singularities obey simple dynamics. We give an elementary proof that the same holds in any number of dimensions for the Schwarz potential, introduced by D. Khavinson and H. S. Shapiro [17] (1989). A generalization is also given for the so-called "elliptic growth" problem by defining a generalized Schwarz potential. New exact solutions are constructed, and we solve inverse problems of describing the driving singularities of a given flow. We demonstrate, by example, how \mathbb{C}^n - techniques can be used to locate the singularity set of the Schwarz potential. One of our methods is to prolong available local extension theorems by constructing "globalizing families". We make three conjectures in potential theory relating to our investigation

Thick surface flows of granular materials: The effect of the velocity profile on the avalanche amplitude

A few years ago, Bouchaud al. introduced a phenomenological model to describe surface flows of granular materials [J. Phys. Fr. I, 4, 1383 (1994)]. According to this model, one can distinguish between a static phase and a rolling phase that are able to exchange grains through an erosion/accretion mechanism. Boutreux et al. [Phys. Rev. E, 58, 4692 (1998)] proposed a modification of the exchange term in order to describe thicker flows where saturation effects are present. However, these approaches assumed that the downhill convection velocity of the grains is constant inside the rolling phase, a hypothesis that is not verified experimentally. In this article, we therefore modify the above models by introducing a velocity profile in the flow, and study the physical consequences of this modification in the simple situation of an avalanche in an open cell. We present a complete analytical description of the avalanche in the case of a linear velocity profile, and generalize the results for a power-law dependency. We show, in particular, that the amplitude of the avalanche is strongly affected by the velocity profile.Comment: 7 figures, accepted for publication in Phys. Rev.

Metric fluctuations of an evaporating black hole from back reaction of stress tensor fluctuations

This paper delineates the first steps in a systematic quantitative study of the spacetime fluctuations induced by quantum fields in an evaporating black hole under the stochastic gravity program. The central object of interest is the noise kernel, which is the symmetrized two-point quantum correlation function of the stress tensor operator. As a concrete example we apply it to the study of the spherically-symmetric sector of metric perturbations around an evaporating black hole background geometry. For macroscopic black holes we find that those fluctuations grow and eventually become important when considering sufficiently long periods of time (of the order of the evaporation time), but well before the Planckian regime is reached. In addition, the assumption of a simple correlation between the fluctuations of the energy flux crossing the horizon and far from it, which was made in earlier work on spherically-symmetric induced fluctuations, is carefully scrutinized and found to be invalid. Our analysis suggests the existence of an infinite amplitude for the fluctuations when trying to localize the horizon as a three-dimensional hypersurface, as in the classical case, and, as a consequence, a more accurate picture of the horizon as possessing a finite effective width due to quantum fluctuations. This is supported by a systematic analysis of the noise kernel in curved spacetime smeared with different functions under different conditions, the details are collected in the appendices. This case study shows a pathway for probing quantum metric fluctuations near the horizon and understanding their physical meaning.Comment: 21 pages, REVTe

Uniqueness properties of the Kerr metric

We obtain a geometrical condition on vacuum, stationary, asymptotically flat spacetimes which is necessary and sufficient for the spacetime to be locally isometric to Kerr. Namely, we prove a theorem stating that an asymptotically flat, stationary, vacuum spacetime such that the so-called Killing form is an eigenvector of the self-dual Weyl tensor must be locally isometric to Kerr. Asymptotic flatness is a fundamental hypothesis of the theorem, as we demonstrate by writing down the family of metrics obtained when this requirement is dropped. This result indicates why the Kerr metric plays such an important role in general relativity. It may also be of interest in order to extend the uniqueness theorems of black holes to the non-connected and to the non-analytic case.Comment: 30 pages, LaTeX, submitted to Classical and Quantum Gravit

Effective Viscosity of Dilute Bacterial Suspensions: A Two-Dimensional Model

Suspensions of self-propelled particles are studied in the framework of two-dimensional (2D) Stokesean hydrodynamics. A formula is obtained for the effective viscosity of such suspensions in the limit of small concentrations. This formula includes the two terms that are found in the 2D version of Einstein's classical result for passive suspensions. To this, the main result of the paper is added, an additional term due to self-propulsion which depends on the physical and geometric properties of the active suspension. This term explains the experimental observation of a decrease in effective viscosity in active suspensions.Comment: 15 pages, 3 figures, submitted to Physical Biolog

Targeting neuroinflammation for therapeutic intervention in neurodegenerative pathologies: A role for the peptide analogue of thymulin (PAT)

Introduction: Inflammation has a vital task in protecting the organism, but when deregulated, it can have serious pathological consequences. The central nervous system (CNS) is capable of mounting immune and inflammatory responses, albeit different from that observed in the periphery. Neuroinflammation, however, can be a major contributor to neurodegenerative diseases and constitute a major challenge for medicine and basic research. Areas covered: Both innate and adaptive immune responses normally play an important role in homeostasis within the CNS. Microglia, astrocytes and neuronal cells express a wide array of toll-like receptors (TLR) that can be upregulated by infection, trauma, injuries and various exogenic or endogenic factors. Chronic hyper activation of brain immune cells can result in neurotoxic actions due to excessive production of several pro-inflammatory mediators. Several studies have recently described an important role for targeting receptors such as nicotinic receptors located on cells in the CNS or in other tissues for the control of inflammation. Expert opinion: Thymulin and its synthetic peptide analogue (PAT) appear to exert potent anti-inflammatory effects at the level of peripheral tissues as well as at the level of the brain. This effect involves, at least partially, the activation of cholinergic mechanisms. © 2012 Informa UK, Ltd

Does backreaction enforce the averaged null energy condition in semiclassical gravity?

The expected stress-energy tensor of quantum fields generically violates the local positive energy conditions of general relativity. However, may satisfy some nonlocal conditions such as the averaged null energy condition (ANEC), which would rule out traversable wormholes. Although ANEC holds in Minkowski spacetime, it can be violated in curved spacetimes if one is allowed to choose the spacetime and quantum state arbitrarily, without imposition of the semiclassical Einstein equation G_{ab} = 8 \pi . In this paper we investigate whether ANEC holds for solutions to this equation, by studying a free, massless scalar field with arbitrary curvature coupling in perturbation theory to second order about the flat spacetime/vacuum solution. We "reduce the order" of the perturbation equations to eliminate spurious solutions, and consider the limit in which the lengthscales determined by the incoming state are much larger than the Planck length. We also need to assume that incoming classical gravitational radiation does not dominate the first order metric perturbation. We find that although the ANEC integral can be negative, if we average the ANEC integral transverse to the geodesic with a suitable Planck scale smearing function, then a strictly positive result is obtained in all cases except for the flat spacetime/vacuum solution. This result suggests --- in agreement with conclusions drawn by Ford and Roman from entirely independent arguments --- that if traversable wormholes do exist as solutions to the semiclassical equations, they cannot be macroscopic but must be ``Planck scale''. A large portion of our paper is devoted to the analysis of general issues concerning the nature of the semiclassical Einstein equation and of prescriptions for extracting physically relevant solutions.Comment: 54 pages, 3 figures, uses revtex macros and epsf.tex, to appear in Phys Rev D. A new appendix has been added showing consistency of our results with recent results of Visser [gr-qc/9604008]. Some corrections were made to Appendix A, and several other minor changes to the body of the paper also were mad

Stress-energy tensor in the Bel-Szekeres space-time

In a recent work an approximation procedure was introduced to calculate the vacuum expectation value of the stress-energy tensor for a conformal massless scalar field in the classical background determined by a particular colliding plane wave space-time. This approximation procedure consists in appropriately modifying the space-time geometry throughout the causal past of the collision center. This modification in the geometry allows to simplify the boundary conditions involved in the calculation of the Hadamard function for the quantum state which represents the vacuum in the flat region before the arrival of the waves. In the present work this approximation procedure is applied to the non-singular Bel-Szekeres solution, which describes the head on collision of two electromagnetic plane waves. It is shown that the stress-energy tensor is unbounded as the killing-Cauchy horizon of the interaction is approached and its behavior coincides with a previous calculation in another example of non-singular colliding plane wave space-time.Comment: 17 pages, LaTex file, 2 PostScript figure