4,218 research outputs found

    The Classification of Zp\mathbb{Z}_p-Modules with Partial Decomposition Bases in L∞ωL_{\infty\omega}

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    Ulm's Theorem presents invariants that classify countable abelian torsion groups up to isomorphism. Barwise and Eklof extended this result to the classification of arbitrary abelian torsion groups up to L∞ωL_{\infty \omega}-equivalence. In this paper, we extend this classification to a class of mixed Zp\mathbb{Z}_p-modules which includes all Warfield modules and is closed under L∞ωL_{\infty\omega}-equivalence. The defining property of these modules is the existence of what we call a partial decomposition basis, a generalization of the concept of decomposition basis. We prove a complete classification theorem in L∞ωL_{\infty\omega} using invariants deduced from the classical Ulm and Warfield invariants

    Photogrammetry and ballistic analysis of a high-flying projectile in the STS-124 space shuttle launch

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    A method combining photogrammetry with ballistic analysis is demonstrated to identify flying debris in a rocket launch environment. Debris traveling near the STS-124 Space Shuttle was captured on cameras viewing the launch pad within the first few seconds after launch. One particular piece of debris caught the attention of investigators studying the release of flame trench fire bricks because its high trajectory could indicate a flight risk to the Space Shuttle. Digitized images from two pad perimeter high-speed 16-mm film cameras were processed using photogrammetry software based on a multi-parameter optimization technique. Reference points in the image were found from 3D CAD models of the launch pad and from surveyed points on the pad. The three-dimensional reference points were matched to the equivalent two-dimensional camera projections by optimizing the camera model parameters using a gradient search optimization technique. Using this method of solving the triangulation problem, the xyz position of the object's path relative to the reference point coordinate system was found for every set of synchronized images. This trajectory was then compared to a predicted trajectory while performing regression analysis on the ballistic coefficient and other parameters. This identified, with a high degree of confidence, the object's material density and thus its probable origin within the launch pad environment. Future extensions of this methodology may make it possible to diagnose the underlying causes of debris-releasing events in near-real time, thus improving flight safety.Comment: 26 pages, 11 figures, 3 table

    The emergence of classical behavior in magnetic adatoms

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    A wide class of nanomagnets shows striking quantum behavior, known as quantum spin tunneling (QST): instead of two degenerate ground states with opposite magnetizations, a bonding-antibonding pair forms, resulting in a splitting of the ground state doublet with wave functions linear combination of two classically opposite magnetic states, leading to the quenching of their magnetic moment. Here we study how QST is destroyed and classical behavior emerges in the case of magnetic adatoms, as the strength of their coupling, either to the substrate or to each other, is increased. Both spin-substrate and spin-spin coupling renormalize the QST splitting to zero allowing the environmental decoherence to eliminate superpositions between classical states, leading to the emergence of spontaneous magnetization.Comment: 5 pages, 4 figure
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