24,935 research outputs found

    On precessing flow in an oblate spheroid of arbitrary eccentricity

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    This is the author accepted manuscript. The final version is available from Cambridge University Press via the DOI in this record. Copyright © 2014 Cambridge University PressWe consider a homogeneous fluid of viscosity v confined within an oblate spheroidal cavity of arbitrary eccentricity E marked by the equatorial radius d and the polar radius d √1-E2 with 0<E<1. The spheroidal container rotates rapidly with an angular velocity Ω0 about its symmetry axis and precesses slowly with an angular velocity Ωp about an axis that is fixed in space. It is through both topographical and viscous effects that the spheroidal container and the viscous fluid are coupled together, driving precessing flow against viscous dissipation. The precessionally driven flow is characterized by three dimensionless parameters: the shape parameter E , the Ekman number Ek=v /(d2|Ω| 0 and the Poincaré number Po=±|Ωp|/ |Ω0|. We derive a time-dependent asymptotic solution for the weakly precessing flow in the mantle frame of reference satisfying the no-slip boundary condition and valid for a spheroidal cavity of arbitrary eccentricity at Ek≪1. No prior assumptions about the spatialoral structure of the precessing flow are made in the asymptotic analysis. We also carry out direct numerical simulation for both the weakly and the strongly precessing flow in the same frame of reference using a finite-element method that is particularly suitable for non-spherical geometry. A satisfactory agreement between the asymptotic solution and direct numerical simulation is achieved for sufficiently small Ekman and Poincaré numbers. When the nonlinear effect is weak with |Po| ≪ 1, the precessing flow in an oblate spheroid is characterized by an azimuthally travelling wave without having a mean azimuthal flow. Stronger nonlinear effects with increasing |Po| produce a large-amplitude, time-independent mean azimuthal flow that is always westward in the mantle frame of reference. Implications of the precessionally driven flow for the westward motion observed in the Earth's fluid core are also discussed. © 2014 Cambridge University Press.Science & Technology Facilities Council (STFC)NERCHong Kong RGCNSFCChinese Academy of SciencesK.Z. is supported by UK STFC and NERC grants, K.H.C. is supported by Hong Kong RGC grant/700310 and X.L. is supported by NSFC/11133004 and Chinese Academy of Sciences under grant number KZZD-EW-01-3. The numerical computation is supported by Shanghai Supercomputer Cente

    A Model Behind the Standard Model

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    In spite of its many successes, the Standard Model makes many empirical assumptions in the Higgs and fermion sectors for which a deeper theoretical basis is sought. Starting from the usual gauge symmetry u(1)×su(2)×su(3)u(1) \times su(2) \times su(3) plus the 3 assumptions: (A) scalar fields as vielbeins in internal symmetry space \cite{framevec}, (B) the ``confinement picture'' of symmetry breaking \cite{tHooft,Banovici}, (C) generations as ``dual'' to colour \cite{genmixdsm}, we are led to a scheme which offers: (I) a geometrical significance to scalar fields, (II) a theoretical criterion on what scalar fields are to be introduced, (III) a partial explanation of why su(2)su(2) appears broken while su(3)su(3) confines, (IV) baryon-lepton number (B - L) conservation, (V) the standard electroweak structure, (VI) a 3-valued generation index for leptons and quarks, and (VII) a dynamical system with all the essential features of an earlier phenomenological model \cite{genmixdsm} which gave a good description of the known mass and mixing patterns of quarks and leptons including neutrino oscillations. There are other implications the consistency of which with experiment, however, has not yet been systematically explored. A possible outcome is a whole new branch of particle spectroscopy from su(2)su(2) confinement, potentially as rich in details as that of hadrons from colour confinement, which will be accessible to experiment at high energy.Comment: 66 pages, added new material on phenomenology, and some new reference

    Dynamic Windows Scheduling with Reallocation

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    We consider the Windows Scheduling problem. The problem is a restricted version of Unit-Fractions Bin Packing, and it is also called Inventory Replenishment in the context of Supply Chain. In brief, the problem is to schedule the use of communication channels to clients. Each client ci is characterized by an active cycle and a window wi. During the period of time that any given client ci is active, there must be at least one transmission from ci scheduled in any wi consecutive time slots, but at most one transmission can be carried out in each channel per time slot. The goal is to minimize the number of channels used. We extend previous online models, where decisions are permanent, assuming that clients may be reallocated at some cost. We assume that such cost is a constant amount paid per reallocation. That is, we aim to minimize also the number of reallocations. We present three online reallocation algorithms for Windows Scheduling. We evaluate experimentally these protocols showing that, in practice, all three achieve constant amortized reallocations with close to optimal channel usage. Our simulations also expose interesting trade-offs between reallocations and channel usage. We introduce a new objective function for WS with reallocations, that can be also applied to models where reallocations are not possible. We analyze this metric for one of the algorithms which, to the best of our knowledge, is the first online WS protocol with theoretical guarantees that applies to scenarios where clients may leave and the analysis is against current load rather than peak load. Using previous results, we also observe bounds on channel usage for one of the algorithms.Comment: 6 figure

    The effect of 3He impurities on the nonclassical response to oscillation of solid 4He

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    We have investigated the influence of impurities on the possible supersolid transition by systematically enriching isotopically-pure 4He (< 1 ppb of 3He) with 3He. The onset of nonclassical rotational inertia is broadened and shifts monotonically to higher temperature with increasing 3He concentration, suggesting that the phenomenon is correlated to the condensation of 3He atoms onto the dislocation network in solid 4He.Comment: 4 page
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