Gravitational radiation from nonaxisymmetric spherical Couette flow in a neutron star

The gravitational wave signal generated by global, nonaxisymmetric shear flows in a neutron star is calculated numerically by integrating the incompressible Navier--Stokes equation in a spherical, differentially rotating shell. At Reynolds numbers \Rey \gsim 3 \times 10^{3}, the laminar Stokes flow is unstable and helical, oscillating Taylor--G\"ortler vortices develop. The gravitational wave strain generated by the resulting kinetic-energy fluctuations is computed in both $+$ and $\times$ polarizations as a function of time. It is found that the signal-to-noise ratio for a coherent, $10^{8}$-{\rm s} integration with LIGO II scales as $6.5 (\Omega_*/10^{4} {\rm rad} {\rm s}^{-1})^{7/2}$ for a star at 1 {\rm kpc} with angular velocity $\Omega_*$. This should be regarded as a lower limit: it excludes pressure fluctuations, herringbone flows, Stuart vortices, and fully developed turbulence (for \Rey \gsim 10^{6}).Comment: (1) School of Physics, University of Melbourne, Parkville, VIC 3010, Australia. (2) Departamento de Fisica, Escuela de Ciencias,Universidad de Oriente, Cumana, Venezuela, (3) Department of Mechanical Engineering, University of Melbourne, Parkville, VIC 3010, Australia. Accepted for publication in The Astrophysical Journal Letter

Convective flows of viscous fluid in spherical layers. Certain astrophysical applications

The convective stability of a viscous liquid in spherical layers is investigated taking into consideration rotation, the latitudinal temperature gradient, and shear flow. The results of calculating nonlinear convective motion in spherical layers are examined. A discussion is given of the applicability of the results obtained to studying convection in astrophysical objects

Nonlinear axisymmetric liquid currents in spherical annuli

A numerical analysis of non-linear axisymmetric viscous flows in spherical annuli of different gap sizes is presented. Only inner sphere was supposed to rotate at a constant angular velocity. The streamlines, lines of constant angular velocity, kinetic energy spectra, and spectra of velocity components are obtained. A total kinetic energy and torque needed to rotate the inner sphere are calculated as functions of Re for different gap sizes. In small-gap annulus nonuniqueness of steady solutions of Navier-Stokes equations is established and regions of different flow regime existences are found. Numerical solutions in a wide-gap annulus and experimental results are used in conclusions about flow stability in the considered range of Re. The comparison of experimental and numerical results shows close qualitative and quantitative agreement

Transitions between turbulent and laminar superfluid vorticity states in the outer core of a neutron star

We investigate the global transition from a turbulent state of superfluid vorticity to a laminar state, and vice versa, in the outer core of a neutron star. By solving numerically the hydrodynamic Hall-Vinen-Bekarevich-Khalatnikov equations for a rotating superfluid in a differentially rotating spherical shell, we find that the meridional counterflow driven by Ekman pumping exceeds the Donnelly-Glaberson threshold throughout most of the outer core, exciting unstable Kelvin waves which disrupt the rectilinear vortex array, creating a vortex tangle. In the turbulent state, the torque exerted on the crust oscillates, and the crust-core coupling is weaker than in the laminar state. This leads to a new scenario for the rotational glitches observed in radio pulsars: a vortex tangle is sustained in the differentially rotating outer core by the meridional counterflow, a sudden spin-up event brings the crust and core into corotation, the vortex tangle relaxes back to a rectilinear vortex array, then the crust spins down electromagnetically until enough meridional counterflow builds up to reform a vortex tangle. The turbulent-laminar transition can occur uniformly or in patches; the associated time-scales are estimated from vortex filament theory. We calculate numerically the global structure of the flow with and without an inviscid superfluid component, for Hall-Vinen and Gorter-Mellink forms of the mutual friction. We also calculate the post-glitch evolution of the angular velocity of the crust and its time derivative, and compare the results with radio pulse timing data, predicting a correlation between glitch activity and Reynolds number.Comment: (1) School of Physics, University of Melbourne, Parkville, VIC 3010, Australia. (2) Departamento de Fisica, Escuela de Ciencias,Universidad de Oriente, Cumana, Venezuela, (3) Department of Mechanical and Manufacturing Engineering, University of Melbourne, Parkville, VIC 3010, Australia. Accepted for publication in The Astrophysical Journal. 30 pages, 9 figures (in jpg format

Global three-dimensional flow of a neutron superfluid in a spherical shell in a neutron star

We integrate for the first time the hydrodynamic Hall-Vinen-Bekarevich-Khalatnikov equations of motion of a $^{1}S_{0}$-paired neutron superfluid in a rotating spherical shell, using a pseudospectral collocation algorithm coupled with a time-split fractional scheme. Numerical instabilities are smoothed by spectral filtering. Three numerical experiments are conducted, with the following results. (i) When the inner and outer spheres are put into steady differential rotation, the viscous torque exerted on the spheres oscillates quasiperiodically and persistently (after an initial transient). The fractional oscillation amplitude ($\sim 10^{-2}$) increases with the angular shear and decreases with the gap width. (ii) When the outer sphere is accelerated impulsively after an interval of steady differential rotation, the torque increases suddenly, relaxes exponentially, then oscillates persistently as in (i). The relaxation time-scale is determined principally by the angular velocity jump, whereas the oscillation amplitude is determined principally by the gap width. (iii) When the mutual friction force changes suddenly from Hall-Vinen to Gorter-Mellink form, as happens when a rectilinear array of quantized Feynman-Onsager vortices is destabilized by a counterflow to form a reconnecting vortex tangle, the relaxation time-scale is reduced by a factor of $\sim 3$ compared to (ii), and the system reaches a stationary state where the torque oscillates with fractional amplitude $\sim 10^{-3}$ about a constant mean value. Preliminary scalings are computed for observable quantities like angular velocity and acceleration as functions of Reynolds number, angular shear, and gap width. The results are applied to the timing irregularities (e.g., glitches and timing noise) observed in radio pulsars.Comment: 6 figures, 23 pages. Accepted for publication in Astrophysical Journa

Explicit Evidence Systems with Common Knowledge

Justification logics are epistemic logics that explicitly include justifications for the agents' knowledge. We develop a multi-agent justification logic with evidence terms for individual agents as well as for common knowledge. We define a Kripke-style semantics that is similar to Fitting's semantics for the Logic of Proofs LP. We show the soundness, completeness, and finite model property of our multi-agent justification logic with respect to this Kripke-style semantics. We demonstrate that our logic is a conservative extension of Yavorskaya's minimal bimodal explicit evidence logic, which is a two-agent version of LP. We discuss the relationship of our logic to the multi-agent modal logic S4 with common knowledge. Finally, we give a brief analysis of the coordinated attack problem in the newly developed language of our logic