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    The Anisotropic Two-Point Correlation Functions of the Nonlinear Traceless Tidal Field in the Principal-Axis Frame

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    Galaxies on the largest scales of the Universe are observed to be embedded in the filamentary cosmic web which is shaped by the nonlinear tidal field. As an efficient tool to quantitatively describe the statistics of this cosmic web, we present the anisotropic two-point correlation functions of the nonlinear traceless tidal field in the principal-axis frame, which are measured using numerical data from an N-body simulation. We show that both of the nonlinear density and traceless tidal fields are more strongly correlated along the directions perpendicular to the eigenvectors associated with the largest eigenvalues of the local tidal field. The correlation length scale of the traceless tidal field is found to be ~20 Mpc/h, which is much larger than that of the density field ~5 Mpc/h. We also provide analytic fitting formulae for the anisotropic correlation functions of the traceless tidal field, which turn out to be in excellent agreement with the numerical results. We expect that our numerical results and analytic formula are useful to disentangle cosmological information from the filamentary network of the large-scale structures.Comment: ApJ in press, accepted version, minor changes, discussion improve

    Surface r Modes and Burst Oscillations of Neutron Stars

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    We study the rr-modes propagating in steadily mass accreting, nuclear burning, and geometrically thin envelopes on the surface of rotating neutron stars. For the modal analysis, we construct the envelope models which are fully radiaitive or have a convective region. As the angular rotation frequency Ω\Omega is increased, the oscillation frequency ω\omega of the rr-modes in the thin envelopes deviates appreciably from the asymptotic frequency ω=2mΩ/l(l+1)\omega=2m\Omega/l^\prime(l^\prime+1) defined in the limit of Ω0\Omega\to 0, where ω\omega is the frequency observed in the corotating frame of the star, and mm and ll^\prime are the indices of the spherical harmonic function YlmY_{l^\prime}^m representing the angular dependence of the modes. We find that the fundamental rr-modes in the convective models are destabilized by strong nuclear burning in the convective region. Because of excessive heating by nuclear buring, the corotating-frame oscillation frequency ω\omega of the rr-modes in the convective models becomes larger, and hence the inertial-frame oscillation frequency σ|\sigma| becomes smaller, than those of the corresopnding rr-modes in the radiative models, where σ=ωmΩ\sigma=\omega-m\Omega is negative for the rr-modes of positive mm. We find that the relative frequency change f=(σconvσrad)/σradf=-(\sigma_{conv}-\sigma_{rad})/\sigma_{rad} is always positive and becomes less than \sim0.01 for the fundamental rr-modes of l>m+1l^\prime>|m|+1 at σrad/2π|\sigma_{rad}|/2\pi\sim300Hz for m=1m=1 or at σrad/2π|\sigma_{rad}|/2\pi\sim600Hz for m=2m=2, where σconv\sigma_{conv} and σrad\sigma_{rad} denote the oscillation frequencies for the convective and the radiative envelope models, respectively.Comment: 20 pages, 12 figure

    Spherical gauge fields

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    We introduce the spherical field formalism for free gauge fields. We discuss the structure of the spherical Hamiltonian for both general covariant gauge and radial gauge and point out several new features not present in the scalar field case. We then use the evolution equations to compute gauge-field and field-strength correlators