164,083 research outputs found

    Biased random walk in positive random conductances on Zd\mathbb{Z}^{d}

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    We study the biased random walk in positive random conductances on Zd\mathbb {Z}^d. This walk is transient in the direction of the bias. Our main result is that the random walk is ballistic if, and only if, the conductances have finite mean. Moreover, in the sub-ballistic regime we find the polynomial order of the distance moved by the particle. This extends results obtained by Shen [Ann. Appl. Probab. 12 (2002) 477-510], who proved positivity of the speed in the uniformly elliptic setting.Comment: Published in at http://dx.doi.org/10.1214/13-AOP835 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Hidden Spoor, Ruan Xiaoxu, And His Treatise On Reclusion

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    In early medieval China great attention was paid to compiling accounts of men in reclusion, yet the prefaces to these compilations often contain only vague or stale reasoning concerning the nature of reclusion itself. A preface by Shen Yue (441-513) is a notable exception: Shen differentiated between disengagement and reclusion. A slightly later contemporary of Shen, Ruan Xiaoxu (479-536), took issue with him in a unique and tightly constructed disquisition on what Ruan saw as a basic dichotomy in the Way of man: the root and overt traces. Ruan\u27s overlooked treatise is examined here, as are some relevant facets of his life

    Relativistic stars with purely toroidal magnetic fields with realistic equations of state

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    We investigate equilibrium sequences of relativistic stars containing purely toroidal magnetic fields with four kinds of realistic equations of state (EOSs) of SLy (Douchin et al.), FPS (Pandharipande et al.), Shen (Shen et al.), and LS (Lattimer & Swesty). We numerically construct thousands of equilibrium configurations. Particularly we pay attention to the equilibrium sequences of constant baryon mass and/or constant magnetic flux, which model evolutions of an isolated neutron star. Important properties obtained in this study are summarized as follows ; (1) The dependence of the mass-shedding angular velocity on the EOSs is determined from that of the non-magnetized case. The stars with Shen(FPS) EOS reach the mass-shedding limit at the smallest(largest) angular velocity, while the stars with SLy or Lattimer-Swesty EOSs take the moderate values. (2) For the supramassive sequences, the equilibrium configurations are found to be generally oblate for the realistic EOSs in sharp contrast to the polytropic stars. For FPS(LS) EOS, the parameter region which permits the prolately deformed stars is widest(narrowest). For SLy and Shen EOS, it is in medium. Furthermore, the angular velocities Ωup\Omega_{\rm up}, above which the stars start to spin up as they lose angular momentum, are found to depend sharply on the realistic EOSs. Our analysis indicates that the hierarchy of this spin up angular velocity is Ωup,SLy>Ωup,FPS>Ωup,LS>Ωup,Shen\Omega_{\rm up,SLy} > \Omega_{\rm up,FPS} > \Omega_{\rm up,LS}>\Omega_{\rm up,Shen} and this relation holds even if the sequences have strong magnetic fields. Our results suggest the EOSs within the relativistic stars containing purely toroidal magnetic fields can be constrained by observing the angular velocity, the gravitational wave, and the signature of the spin up.Comment: Accepted to APJ, high-resolution figures will be appeared in published-versio

    Symmetry of the Gap in Bi2212 from Photoemission Spectroscopy

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    In a recent Letter, Shen et al have detected a large anisotropy of the superconducting gap in Bi2212, consistent with d-wave symmetry, from photoemission spectroscopy. Moreover, they claim that the change in their spectra as a function of aging is also consistent with such an intrepretation. In this Comment, I show that the latter statement is not entirely correct, in that the data as a function of aging are inconsistent with a d-wave gap but are consistent with an anisotropic s-wave gap.Comment: 3 pages (Plain TeX with macros), plus 1 postscript figur
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