5,945 research outputs found

    Approximate performance analysis of generalized join the shortest queue routing

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    In this paper we propose a highly accurate approximate performance analysis of a heterogeneous server system with a processor sharing service discipline and a general job-size distribution under a generalized join the shortest queue (GJSQ) routing protocol. The GJSQ routing protocol is a natural extension of the well-known join the shortest queue routing policy that takes into account the non-identical service rates in addition to the number of jobs at each server. The performance metrics that are of interest here are the equilibrium distribution and the mean and standard deviation of the number of jobs at each server. We show that the latter metrics are near-insensitive to the job-size distribution using simulation experiments. By applying a single queue approximation we model each server as a single server queue with a state-dependent arrival process, independent of other servers in the system, and derive the distribution of the number of jobs at the server. These state-dependent arrival rates are intended to capture the inherent correlation between servers in the original system and behave in a rather atypical way.Comment: 16 pages, 5 figures -- version 2 incorporates minor textual change

    What is the length of a knot in a polymer?

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    We give statistical definitions of the length, l, of a loose prime knot tied into a long, fluctuating ring macromolecule. Monte Carlo results for the equilibrium, good solvent regime show that ~ N^t, where N is the ring length and t ~ 0.75 is independent of the knot topology. In the collapsed regime below the theta temperature, length determinations based on the entropic competition of different knots within the same ring show delocalization (t~1).Comment: 9 pages, 5 Postscript figure

    Relativistic precession around rotating neutron stars: Effects due to frame-dragging and stellar oblateness

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    General relativity predicts that a rotating body produces a frame-dragging (or Lense-Thirring) effect: the orbital plane of a test particle in a non-equatorial orbit precesses about the body's symmetry axis. In this paper we compute the precession frequencies of circular orbits around rapidly rotating neutron stars for a variety of masses and equations of state. The precession frequencies computed are expressed as numerical functions of the orbital frequency observed at infinity. The post-Newtonian expansion of the exact precession formula is examined to identify the relative magnitudes of the precession caused by the Lense-Thirring effect, the usual Newtonian quadrupole effect and relativistic corrections. The first post-Newtonian correction to the Newtonian quadrupole precession is derived in the limit of slow rotation. We show that the post-Newtonian precession formula is a good approximation to the exact precession close to the neutron star in the slow rotation limit (up to \sim 400 Hz in the present context). The results are applied to recent RXTE observations of neutron star low-mass X-ray binaries, which display kHz quasi-periodic oscillations and, within the framework of beat frequency models, allow the measurement of both the neutron star spin frequency and the Keplerian frequency of the innermost ring of matter in the accretion disk around it. For a wide range of realistic equations of state, we find that the predicted precession frequency of this ring is close to one half of the low-frequency (\sim 20 - 35 Hz) quasi-periodic oscillations seen in several Atoll sources.Comment: 35 pages including 10 figures and 6 tables. To appear in the Astrophysical Journa

    GaP betavoltaic cells as a power source

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    Maximum power output for the GaP cells of this study was found to be on the order of 1 microW. This resulted from exposure to 200 and 40 KeV electrons at a flux of 2 x 10(exp 9) electrons/sq cm/s, equivalent to a 54 mCurie source. The efficiencies of the cells ranged from 5 to 9 percent for 200 and 40 KeV electrons respectively. The lower efficiency at higher energy is due to a substantial fraction of energy deposition in the substrate, further than a diffusion length from the depletion region of the cell. Radiation damage was clearly observed in GaP after exposure to 200 KeV electrons at a fluence of 2 x 10(exp 12) electrons/sq cm. No discernable damage was observed after exposure to 40 KeV electrons at the same fluence. Analysis indicates that a GaP betavoltaic system would not be practical if limited to low energy beta sources. The power available would be too low even in the ideal case. By utilizing high activity beta sources, such as Sr-90/Y-90, it may be possible to achieve performance that could be suitable for some space power applications. However, to utilize such a source the problem of radiation damage in the beta cell material must be overcome

    The Constitutionality of the Black Lung Interim Presumption

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    A scale-free network hidden in the collapsing polymer

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    We show that the collapsed globular phase of a polymer accommodates a scale-free incompatibility graph of its contacts. The degree distribution of this network is found to decay with the exponent γ=1/(2c)\gamma = 1/(2-c) up to a cut-off degree dcL2cd_c \propto L^{2-c}, where cc is the loop exponent for dense polymers (c=11/8c=11/8 in two dimensions) and LL is the length of the polymer. Our results exemplify how a scale-free network (SFN) can emerge from standard criticality.Comment: 4 pages, 3 figures, address correcte

    Steady-state analysis of shortest expected delay routing

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    We consider a queueing system consisting of two non-identical exponential servers, where each server has its own dedicated queue and serves the customers in that queue FCFS. Customers arrive according to a Poisson process and join the queue promising the shortest expected delay, which is a natural and near-optimal policy for systems with non-identical servers. This system can be modeled as an inhomogeneous random walk in the quadrant. By stretching the boundaries of the compensation approach we prove that the equilibrium distribution of this random walk can be expressed as a series of product-forms that can be determined recursively. The resulting series expression is directly amenable for numerical calculations and it also provides insight in the asymptotic behavior of the equilibrium probabilities as one of the state coordinates tends to infinity.Comment: 41 pages, 13 figure

    Anomalous scaling due to correlations: Limit theorems and self-similar processes

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    We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling forms, justify their universal character, and specify universality domains in the spaces of joint probability density functions of the summand variables. These density functions are assumed to be invariant under arbitrary permutations of their arguments. Examples from the theory of critical phenomena are discussed. The novel notion of stability implied by the limit theorems also allows us to define sequences of random variables whose sum satisfies anomalous scaling for any finite number of summands. If regarded as developing in time, the stochastic processes described by these variables are non-Markovian generalizations of Gaussian processes with uncorrelated increments, and provide, e.g., explicit realizations of a recently proposed model of index evolution in finance.Comment: Through text revision. 15 pages, 3 figure
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