Multi-Zone Shell Model for Turbulent Wall Bounded Flows

We suggested a \emph{Multi-Zone Shell} (MZS) model for wall-bounded flows accounting for the space inhomogeneity in a "piecewise approximation", in which cross-section area of the flow, $S$, is subdivided into "$j$-zones". The area of the first zone, responsible for the core of the flow, $S_1\simeq S/2$, and areas of the next $j$-zones, $S_j$, decrease towards the wall like $S_j\propto 2^{-j}$. In each $j$-zone the statistics of turbulence is assumed to be space homogeneous and is described by the set of "shell velocities" $u_{nj}(t)$ for turbulent fluctuations of the scale $\propto 2^{-n}$. The MZS-model includes a new set of complex variables, $V_j(t)$, $j=1,2,... \infty$, describing the amplitudes of the near wall coherent structures of the scale $s_j\sim 2^{-j}$ and responsible for the mean velocity profile. Suggested MZS-equations of motion for $u_{nj}(t)$ and $V_j(t)$ preserve the actual conservations laws (energy, mechanical and angular momenta), respect the existing symmetries (including Galilean and scale invariance) and account for the type of the non-linearity in the Navier-Stokes equation, dimensional reasoning, etc. The MZS-model qualitatively describes important characteristics of the wall bounded turbulence, e.g., evolution of the mean velocity profile with increasing Reynolds number, \RE, from the laminar profile towards the universal logarithmic profile near the flat-plane boundary layer as \RE\to \infty.Comment: 27 pages, 17 figs, included, PRE, submitte

Classical/quantum integrability in non-compact sector of AdS/CFT

We discuss non-compact SL(2,R) sectors in N=4 SYM and in AdS string theory and compare their integrable structures. We formulate and solve the Riemann-Hilbert problem for the finite gap solutions of the classical sigma model and show that at one loop it is identical to the classical limit of Bethe equations of the spin (-1/2) chain for the dilatation operator of SYM.Comment: 27 pages, 1 figure; v2: unphysical windings around the time direction eliminated; v3: dicsussion of finite-size corrections remove

High accuracy binary black hole simulations with an extended wave zone

We present results from a new code for binary black hole evolutions using the moving-puncture approach, implementing finite differences in generalised coordinates, and allowing the spacetime to be covered with multiple communicating non-singular coordinate patches. Here we consider a regular Cartesian near zone, with adapted spherical grids covering the wave zone. The efficiencies resulting from the use of adapted coordinates allow us to maintain sufficient grid resolution to an artificial outer boundary location which is causally disconnected from the measurement. For the well-studied test-case of the inspiral of an equal-mass non-spinning binary (evolved for more than 8 orbits before merger), we determine the phase and amplitude to numerical accuracies better than 0.010% and 0.090% during inspiral, respectively, and 0.003% and 0.153% during merger. The waveforms, including the resolved higher harmonics, are convergent and can be consistently extrapolated to $r\to\infty$ throughout the simulation, including the merger and ringdown. Ringdown frequencies for these modes (to $(\ell,m)=(6,6)$) match perturbative calculations to within 0.01%, providing a strong confirmation that the remnant settles to a Kerr black hole with irreducible mass $M_{\rm irr} = 0.884355\pm20\times10^{-6}$ and spin $S_f/M_f^2 = 0.686923 \pm 10\times10^{-6}

Cauchy-perturbative matching and outer boundary conditions I: Methods and tests

We present a new method of extracting gravitational radiation from three-dimensional numerical relativity codes and providing outer boundary conditions. Our approach matches the solution of a Cauchy evolution of Einstein's equations to a set of one-dimensional linear wave equations on a curved background. We illustrate the mathematical properties of our approach and discuss a numerical module we have constructed for this purpose. This module implements the perturbative matching approach in connection with a generic three-dimensional numerical relativity simulation. Tests of its accuracy and second-order convergence are presented with analytic linear wave data.Comment: 13 pages, 6 figures, RevTe

Evidence of Quasi-linear Super-Structures in the Cosmic Microwave Background and Galaxy Distribution

Recent measurements of hot and cold spots on the cosmic microwave background (CMB) sky suggest a presence of super-structures on (>100 h^{-1}Mpc) scales. We develop a new formalism to estimate the expected amplitude of temperature fluctuations due to the integrated Sachs-Wolfe (ISW) effect from prominent quasi-linear structures. Applying the developed tools to the observed ISW signals from voids and clusters in catalogs of galaxies at redshifts z<1, we find that they indeed imply a presence of quasi-linear super-structures with a comoving radius 100~300 h^{-1}Mpc and a density contrast ~O(0.1). We find that the observed ISW signals are at odd with the concordant \Lambda cold dark matter (CDM) model that predicts Gaussian primordial perturbations at equal to or larger than 3 sigma level. We also confirm that the mean temperature around the CMB cold spot in the southern Galactic hemisphere filtered by a compensating top-hat filter deviates from a mean value at ~3 sigma level, implying that a quasi-linear supervoid or an underdensity region surrounded by a massive wall may reside at low redshifts z<0.3 and the actual angular size (16^\circ-17^\circ) may be larger than the apparent size (4^\circ-10^\circ) discussed in literature. Possible solutions are briefly discussed.Comment: 34 pages, 13 figures, a version accepted for publication in ApJ. A plot of non-linear PDF (Figure 7) is added. Error bars are added in figure

Relativistic Models for Binary Neutron Stars with Arbitrary Spins

We introduce a new numerical scheme for solving the initial value problem for quasiequilibrium binary neutron stars allowing for arbitrary spins. The coupled Einstein field equations and equations of relativistic hydrodynamics are solved in the Wilson-Mathews conformal thin sandwich formalism. We construct sequences of circular-orbit binaries of varying separation, keeping the rest mass and circulation constant along each sequence. Solutions are presented for configurations obeying an n=1 polytropic equation of state and spinning parallel and antiparallel to the orbital angular momentum. We treat stars with moderate compaction ((m/R) = 0.14) and high compaction ((m/R) = 0.19). For all but the highest circulation sequences, the spins of the neutron stars increase as the binary separation decreases. Our zero-circulation cases approximate irrotational sequences, for which the spin angular frequencies of the stars increases by 13% (11%) of the orbital frequency for (m/R) = 0.14 ((m/R) = 0.19) by the time the innermost circular orbit is reached. In addition to leaving an imprint on the inspiral gravitational waveform, this spin effect is measurable in the electromagnetic signal if one of the stars is a pulsar visible from Earth.Comment: 21 pages, 14 figures. A few explanatory sentences added and some typos corrected. Accepted for publication in Phys. Rev.

The 2D dynamics of radiative zones of low-mass stars

In the context of secular evolution, we describe the dynamics of the radiative core of low-mass stars to understand the internal transport of angular momentum in such stars which results in a solid rotation in the Sun from 0.7R_sun to 0.2R_sun and a weak radial core-envelope differential rotation in solar-type stars. This study requires at least a 2D description to capture the latitudinal variations of the differential rotation. We build 2D numerical models of a radiative core on the top of which we impose a latitudinal shear so as to reproduce a cylindrical differential rotation in a convective envelope. We perform a systematic study over the Rossby number measuring the latitudinal differential rotation at the radiative-convective interface. The imposed shear generates a geostrophic flow implying a cylindrical differential rotation. When compared to the baroclinic flow that arises from the stable stratification, we find that the geostrophic flow is dominant when the Rossby number is high enough with a cylindrical rotation profile. For low Rossby numbers, the baroclinic solution dominates with a quasi-shellular rotation profile. Using scaling laws from 3D simulations, we show that slow rotators are expected to have a cylindrical rotation profile. Fast rotators may have a shellular profile at the beginning of the main-sequence in stellar radiative zones. This study enables us to predict different types of differential rotation and emphasizes the need of a new generation of 2D rotating stellar models developed in synergy with 3D numerical simulations. The shear induced by a surface convective zone has a strong impact on the dynamics of the underlying radiative zone in low-mass stars. But, it cannot produce a flat internal rotation profile in a solar configuration calling for additional processes for the transport of angular momentum in both radial and latitudinal directions.Comment: 12 pages, 7 figures, accepted for publication in A&

Cooling Rates for Relativistic Electrons Undergoing Compton Scattering in Strong Magnetic Fields

For inner magnetospheric models of hard X-ray and gamma-ray emission in high-field pulsars and magnetars, resonant Compton upscattering is anticipated to be the most efficient process for generating continuum radiation. This is due in part to the proximity of a hot soft photon bath from the stellar surface to putative radiation dissipation regions in the inner magnetosphere. Moreover, because the scattering process becomes resonant at the cyclotron frequency, the effective cross section exceeds the classical Thomson value by over two orders of magnitude, thereby enhancing the efficiency of continuum production and the cooling of relativistic electrons. This paper presents computations of the electron cooling rates for this process, which are needed for resonant Compton models of non-thermal radiation from such highly-magnetized pulsars. The computed rates extend previous calculations of magnetic Thomson cooling to the domain of relativistic quantum effects, sampled near and above the quantum critical magnetic field of 44.13 TeraGauss. This is the first exposition of fully relativistic, quantum magnetic Compton cooling rates for electrons, and it employs both the traditional Johnson and Lippman cross section, and a newer Sokolov and Ternov (ST) formulation of Compton scattering in strong magnetic fields. Such ST formalism is formally correct for treating spin-dependent effects that are important in the cyclotron resonance, and has not been addressed before in the context of cooling by Compton scattering. The QED effects are observed to profoundly lower the rates below extrapolations of the familiar magnetic Thomson results, as expected, when recoil and Klein-Nishina reductions become important.Comment: 33 pages, 11 figures, accepted for publication in The Astrophysical Journa