53,485 research outputs found

    Static solutions from the point of view of comparison geometry

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    We analyze (the harmonic map representation of) static solutions of the Einstein Equations in dimension three from the point of view of comparison geometry. We find simple monotonic quantities capturing sharply the influence of the Lapse function on the focussing of geodesics. This allows, in particular, a sharp estimation of the Laplacian of the distance function to a given (hyper)-surface. We apply the technique to asymptotically flat solutions with regular and connected horizons and, after a detailed analysis of the distance function to the horizon, we recover the Penrose inequality and the uniqueness of the Schwarzschild solution. The proof of this last result does not require proving conformal flatness at any intermediate step.Comment: 41 page

    Polynomial Cointegration among Stationary Processes with Long Memory

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    n this paper we consider polynomial cointegrating relationships among stationary processes with long range dependence. We express the regression functions in terms of Hermite polynomials and we consider a form of spectral regression around frequency zero. For these estimates, we establish consistency by means of a more general result on continuously averaged estimates of the spectral density matrix at frequency zeroComment: 25 pages, 7 figures. Submitted in August 200

    Peeling properties of lightlike signals in General Relativity

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    The peeling properties of a lightlike signal propagating through a general Bondi-Sachs vacuum spacetime and leaving behind another Bondi-Sachs vacuum space-time are studied. We demonstrate that in general the peeling behavior is the conventional one which is associated with a radiating isolated system and that it becomes unconventional if the asymptotically flat space-times on either side of the history of the light-like signal tend to flatness at future null infinity faster than the general Bondi-Sachs space-time. This latter situation occurs if, for example, the space-times in question are static Bondi-Sachs space- times.Comment: 14 pages, LaTeX2

    A procedure for assessing aircraft turbulence- penetration performance

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    Subsonic transport aircraft performance assessment during atmospheric turbulenc

    Math modeling for helicopter simulation of low speed, low altitude and steeply descending flight

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    A math model was formulated to represent some of the aerodynamic effects of low speed, low altitude, and steeply descending flight. The formulation is intended to be consistent with the single rotor real time simulation model at NASA Ames Research Center. The effect of low speed, low altitude flight on main rotor downwash was obtained by assuming a uniform plus first harmonic inflow model and then by using wind tunnel data in the form of hub loads to solve for the inflow coefficients. The result was a set of tables for steady and first harmonic inflow coefficients as functions of ground proximity, angle of attack, and airspeed. The aerodynamics associated with steep descending flight in the vortex ring state were modeled by replacing the steady induced downwash derived from momentum theory with an experimentally derived value and by including a thrust fluctuations effect due to vortex shedding. Tables of the induced downwash and the magnitude of the thrust fluctuations were created as functions of angle of attack and airspeed

    The moments of the PDF of concentration for gas clouds in the presence of fences

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    A team led by D. J. Hall has conducted many trials, each involving the instantaneous release of a heavy or neutrally buoyant gas in the presence of a fence aligned transverse to the mean flow, thus complementing earlier trials without fences. For each fence and for each Richardson Number Ri, at least 50 repetitions of each release were performed. This allowed estimates to be made of some statistical properties (mean concentration m, standard deviation s, skewness S, kurtosis K), and their variation with time. Typical results are presented and discussed. The strongest influence of the fences on the evolution of m and s with time is vertical mixing, but there are also interesting changes with fence height and type, and with Ri. The possibility of a relationship between m and s is discussed. However, the most remarkable result is, perhaps, that the estimates of S and K are such that, in all cases, the (K, S) plot collapses onto a quadratic curve; this extends the same finding earlier by Mole and Clarke for steady releases and, in particular, suggests strongly that the PDF of concentration is, in practice, determined by only three properties

    Non-invasive extraction of Cnidarian venom through the use of autotomised tentacles

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    The animals contained within the phylum Cnidaria have origins that can be dated back to around 750 million years ago (mya) and as such, they represent what is potentially the oldest known venomous lineage that is recognised today. The phylum Cnidaria, which includes Sea Anemones, Corals and Jellyfish are also one of the most under-studied as far as toxins go, likely a result of the constraints involved in obtaining samples. Over the last two decades there have been increased efforts to further our ability to obtain samples, however, the sampling techniques developed were invasive and generally required the dissection of tissues from the organism. Within recent years, there have been some developments in the chemical extraction of Cnidarian venom, using ethanol to trigger nematocyst firing. These developments have led to the formation of this research, which uses ethanol to elicit stimulation of nematocysts on naturally autotomised tentacles whilst being observed under light microscopy, before having protein content measured using microspectrophotometry. This paper focuses on a unique observation of Cnidaria that is unknown in any other animal taxa, passive autotomy of envenomation apparatus, the tentacles
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