1,120 research outputs found

    Bounds on solutions of the rotating, stratified, incompressible, non-hydrostatic, three-dimensional Boussinesq equations

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    We study the three-dimensional, incompressible, non-hydrostatic Boussinesq fluid equations, which are applicable to the dynamics of the oceans and atmosphere. These equations describe the interplay between velocity and buoyancy in a rotating frame. A hierarchy of dynamical variables is introduced whose members Ωm(t)\Omega_{m}(t) (1≤m<∞1 \leq m < \infty) are made up from the respective sum of the L2mL^{2m}-norms of vorticity and the density gradient. Each Ωm(t)\Omega_{m}(t) has a lower bound in terms of the inverse Rossby number, Ro−1Ro^{-1}, that turns out to be crucial to the argument. For convenience, the Ωm\Omega_{m} are also scaled into a new set of variables Dm(t)D_{m}(t). By assuming the existence and uniqueness of solutions, conditional upper bounds are found on the Dm(t)D_{m}(t) in terms of Ro−1Ro^{-1} and the Reynolds number ReRe. These upper bounds vary across bands in the {D1, Dm}\{D_{1},\,D_{m}\} phase plane. The boundaries of these bands depend subtly upon Ro−1Ro^{-1}, ReRe, and the inverse Froude number Fr−1Fr^{-1}. For example, solutions in the lower band conditionally live in an absorbing ball in which the maximum value of Ω1\Omega_{1} deviates from Re3/4Re^{3/4} as a function of Ro−1, ReRo^{-1},\,Re and Fr−1Fr^{-1}.Comment: 24 pages, 3 figures and 1 tabl

    Vlasov moments, integrable systems and singular solutions

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    The Vlasov equation for the collisionless evolution of the single-particle probability distribution function (PDF) is a well-known Lie-Poisson Hamiltonian system. Remarkably, the operation of taking the moments of the Vlasov PDF preserves the Lie-Poisson structure. The individual particle motions correspond to singular solutions of the Vlasov equation. The paper focuses on singular solutions of the problem of geodesic motion of the Vlasov moments. These singular solutions recover geodesic motion of the individual particles.Comment: 16 pages, no figures. Submitted to Phys. Lett.

    Ionic Capillary Evaporation in Weakly Charged Nanopores

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    Using a variational field theory, we show that an electrolyte confined to a neutral cylindrical nanopore traversing a low dielectric membrane exhibits a first-order ionic liquid-vapor pseudo-phase-transition from an ionic-penetration "liquid" phase to an ionic-exclusion "vapor" phase, controlled by nanopore-modified ionic correlations and dielectric repulsion. For weakly charged nanopores, this pseudotransition survives and may shed light on the mechanism behind the rapid switching of nanopore conductivity observed in experiments.Comment: This version is accepted for publication in PR

    Armies and Parties in Africa, by H. Bienen

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    Armies and Parties in Africa, by H. Bienen

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    Eliminating Trachoma in Areas with Limited Disease

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    The common wisdom is that a trachoma program cannot eliminate ocular chlamydia from a community, just reduce infection to a level where there would be minimal blindness. We describe the success of multiple mass antibiotic treatments, demonstrating that complete elimination of infection may be an attainable goal in an area with modest disease

    The structure of a resuscitation-promoting factor domain from Mycobacterium tuberculosis shows homology to lysozymes

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    Resuscitation-promoting factor (RPF) proteins reactivate stationary-phase cultures of (G+C)-rich Gram-positive bacteria including the causative agent of tuberculosis, Mycobacterium tuberculosis. We report the solution structure of the RPF domain from M. tuberculosis Rv1009 (RpfB) solved by heteronuclear multidimensional NMR. Structural homology with various glycoside hydrolases suggested that RpfB cleaved oligosaccharides. Biochemical studies indicate that a conserved active site glutamate is important for resuscitation activity. These data, as well as the presence of a clear binding pocket for a large molecule, indicate that oligosaccharide cleavage is probably the signal for revival from dormancy
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