4,932 research outputs found

    Unknotting numbers and triple point cancelling numbers of torus-covering knots

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    It is known that any surface knot can be transformed to an unknotted surface knot or a surface knot which has a diagram with no triple points by a finite number of 1-handle additions. The minimum number of such 1-handles is called the unknotting number or the triple point cancelling number, respectively. In this paper, we give upper bounds and lower bounds of unknotting numbers and triple point cancelling numbers of torus-covering knots, which are surface knots in the form of coverings over the standard torus TT. Upper bounds are given by using mm-charts on TT presenting torus-covering knots, and lower bounds are given by using quandle colorings and quandle cocycle invariants.Comment: 26 pages, 14 figures, added Corollary 1.7, to appear in J. Knot Theory Ramification

    Microlensing of collimated Gamma-Ray Burst afterglows

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    We investigate stellar microlensing of the collimated gamma-ray burst afterglows. A spherical afterglow appears on the sky as a superluminally expanding thin ring (``ring-like'' image), which is maximally amplified as it crosses the lens. We find that the image of the collimated afterglow becomes quite uniform (``disk-like'' image) after the jet break time (after the Lorentz factor of the jet drops below the inverse of the jet opening angle). Consequently, the amplification peak in the light curve after the break time is lower and broader. Therefore detailed monitoring of the amplification history will be able to test whether the afterglows are jets or not, i.e., ``disk-like'' or not, if the lensing occurs after the break time. We also show that some proper motion and polarization is expected, peaking around the maximum amplification. The simultaneous detection of the proper motion and the polarization will strengthen that the brightening of the light curve is due to microlensing.Comment: 16 pages, 6 figures, accepted for publication in Ap

    High frequency dynamics in liquid nickel: an IXS study

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    Owing to their large relatively thermal conductivity, peculiar, non-hydrodynamic features are expected to characterize the acoustic-like excitations observed in liquid metals. We report here an experimental study of collective modes in molten nickel, a case of exceptional geophysical interest for its relevance in Earth interior science. Our result shed light on previously reported contrasting evidences: in the explored energy-momentum region no deviation from the generalized hydrodynamic picture describing non conductive fluids are observed. Implications for high frequency transport properties in metallic fluids are discussed.Comment: 6 pages, 4 figures, to appear in "Journal of Chemical Physics

    Episodic excursions of low-mass protostars on the Hertzsprung-Russell diagram

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    Following our recent work devoted to the effect of accretion on the pre-main-sequence evolution of low-mass stars, we perform a detailed analysis of episodic excursions of low-mass protostars in the Hertzsprung-Russell (H-R) diagram triggered by strong mass accretion bursts typical of FU Orionis-type objects (FUors). These excursions reveal themselves as sharp increases in the stellar total luminosity and/or effective temperature of the protostar and can last from hundreds to a few thousands of years, depending on the burst strength and characteristics of the protostar. During the excursions, low-mass protostars occupy the same part of the H-R diagram as young intermediate-mass protostars in the quiescent phase of accretion. Moreover, the time spent by low-mass protostars in these regions is on average a factor of several longer than that spent by the intermediate-mass stars in quiescence. During the excursions, low-mass protostars pass close to the position of most known FUors in the H-R diagram, but owing to intrinsic ambiguity the model stellar evolutionary tracks are unreliable in determining the FUor properties. We find that the photospheric luminosity in the outburst state may dominate the accretion luminosity already after a few years after the onset of the outburst, meaning that the mass accretion rates of known FUors inferred from the bolometric luminosity may be systematically overestimated, especially in the fading phase.Comment: 15 pages, 12 figure

    Structural and dynamical properties of liquid Si. An orbital-free molecular dynamics study

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    Several static and dynamic properties of liquid silicon near melting have been determined from an orbital free {\em ab-initio} molecular dynamics simulation. The calculated static structure is in good agreement with the available X-ray and neutron diffraction data. The dynamical structure shows collective density excitations with an associated dispersion relation which closely follows recent experimental data. It is found that liquid silicon can not sustain the propagation of shear waves which can be related to the power spectrum of the velocity autocorrelation function. Accurate estimates have also been obtained for several transport coefficients. The overall picture is that the dynamic properties have many characteristics of the simple liquid metals although some conspicuous differences have been found.Comment: 12 pages, 11 figure

    Cosmological Growth History of Supermassive Black Holes and Demographics in the High-z Universe : Do Lyman-Break Galaxies Have Supermassive Black Holes?

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    We study the demographics of supermassive black holes (SMBHs) in the local and high-z universe with hard X-ray luminosity functions (HXLFs) of AGNs. First, we compare the mass accretion history at z>0 with optical luminosity functions (OLFs) and that with HXLFs. We consider the constraints on parameters of mass accretion (energy conversion efficiency and Eddington ratio) and conclude that the constraints based on HXLFs are more adequate rather than that based on OLFs. The sub-Eddington case is allowed only when we use HXLFs. Next, we estimate the upper limit of the cumulative mass density of SMBHs at any redshifts. For an application, we examine if Lyman-Break galaxies (LBGs) at z=3 already have SMBHs in their centers which is suggested by recent observations. If most of LBGs already has massive SMBHs at z=3, the resultant mass density of SMBHs at z=0 should exceed the observational estimate because such SMBHs should further grow by accretion. We show that the special conditions should be met in order that a large part of LBGs have SMBHs (for example, large energy conversion efficiency and frequent mergers and/or direct formations at z>3). The possibility that nearly all LBGs have SMBHs with large mass ratio, such as M_BH/M_stellar > 0.005, is reliably ruled out.(abridged)Comment: 30 pages including 5 figures, accepted for publication in Ap
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