8,181 research outputs found

    Quantification and prediction of extreme events in a one-dimensional nonlinear dispersive wave model

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    The aim of this work is the quantification and prediction of rare events characterized by extreme intensity in nonlinear waves with broad spectra. We consider a one-dimensional non- linear model with deep-water waves dispersion relation, the Majda-McLaughlin-Tabak (MMT) model, in a dynamical regime that is characterized by broadband spectrum and strong non- linear energy transfers during the development of intermittent events with finite-lifetime. To understand the energy transfers that occur during the development of an extreme event we perform a spatially localized analysis of the energy distribution along different wavenumbers by means of the Gabor transform. A stochastic analysis of the Gabor coefficients reveals i) the low-dimensionality of the intermittent structures, ii) the interplay between non-Gaussian statis- tical properties and nonlinear energy transfers between modes, as well as iii) the critical scales (or critical Gabor coefficients) where a critical amount of energy can trigger the formation of an extreme event. We analyze the unstable character of these special localized modes directly through the system equation and show that these intermittent events are due to the interplay of the system nonlinearity, the wave dispersion, and the wave dissipation which mimics wave breaking. These localized instabilities are triggered by random localizations of energy in space, created by the dispersive propagation of low-amplitude waves with random phase. Based on these properties, we design low-dimensional functionals of these Gabor coefficients that allow for the prediction of the extreme event well before the nonlinear interactions begin to occur.Comment: 21 pages, 14 figure

    Attitude control and damping system for spacecraft Patent

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    Utilization of momentum devices for forming attitude control and damping system for spacecraf

    Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations. V. Evidence for the strong equivalence principle to second post-Newtonian order

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    Using post-Newtonian equations of motion for fluid bodies valid to the second post-Newtonian order, we derive the equations of motion for binary systems with finite-sized, non-spinning but arbitrarily shaped bodies. In particular we study the contributions of the internal structure of the bodies (such as self-gravity) that would diverge if the size of the bodies were to shrink to zero. Using a set of virial relations accurate to the first post-Newtonian order that reflect the stationarity of each body, and redefining the masses to include 1PN and 2PN self-gravity terms, we demonstrate the complete cancellation of a class of potentially divergent, structure-dependent terms that scale as s^{-1} and s^{-5/2}, where s is the characteristic size of the bodies. This is further evidence of the Strong Equivalence Principle, and supports the use of post-Newtonian approximations to derive equations of motion for strong-field bodies such as neutron stars and black holes. This extends earlier work done by Kopeikin.Comment: 14 pages, submitted to Phys. Rev. D; small changes to coincide with published versio

    Mine water outbreak and stability risks : examples and challenges from England and Wales

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    Abstract Although their frequency of occurrence is rare, the sudden outbreak of mine water from abandoned mines, or collapse of waste rock stores can be environmentally significant and represent significant postclosure legacies. This paper reports on a national survey of abandoned non-coal mine sites where concerns over mine water outbreak or stability are apparent across England and Wales. A range of respondents across environmental regulators and local authorities were consulted to populate a geodatabase. Outbreak risk was highlighted as a documented or suspected concern at 19 mine sites. Typical issues were related to adit blockages and associated perched mine water alongside issues of sudden ingress of surface waters into mines under high flow conditions. The majority of the responses concerning stability issues (72 sites in total) were related to fluvial erosion of riparian waste rock heaps. While successful management of such issues is highlighted in some cases, these are generally isolated examples. In both cases, the fact that stability or outbreak issues are often caused or exacerbated by extreme rainfall events highlights a potential future management issue with the predicted effects of climate change in north west Europe
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