87,183 research outputs found

    Universal scaling behavior at the upper critical dimension of non-equilibrium continuous phase transitions

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    In this work we analyze the universal scaling functions and the critical exponents at the upper critical dimension of a continuous phase transition. The consideration of the universal scaling behavior yields a decisive check of the value of the upper critical dimension. We apply our method to a non-equilibrium continuous phase transition. But focusing on the equation of state of the phase transition it is easy to extend our analysis to all equilibrium and non-equilibrium phase transitions observed numerically or experimentally.Comment: 4 pages, 3 figure

    Three-dimensional coating and rimming flow: a ring of fluid on a rotating horizontal cylinder

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    The steady three-dimensional flow of a thin, slowly varying ring of Newtonian fluid on either the outside or the inside of a uniformly rotating large horizontal cylinder is investigated. Specifically, we study “full-ring” solutions, corresponding to a ring of continuous, finite and non-zero thickness that extends all the way around the cylinder. In particular, it is found that there is a critical solution corresponding to either a critical load above which no full-ring solution exists (if the rotation speed is prescribed) or a critical rotation speed below which no full-ring solution exists (if the load is prescribed). We describe the behaviour of the critical solution and, in particular, show that the critical flux, the critical load, the critical semi-width and the critical ring profile are all increasing functions of the rotation speed. In the limit of small rotation speed, the critical flux is small and the critical ring is narrow and thin, leading to a small critical load. In the limit of large rotation speed, the critical flux is large and the critical ring is wide on the upper half of the cylinder and thick on the lower half of the cylinder, leading to a large critical load.\ud \ud We also describe the behaviour of the non-critical full-ring solution, and, in particular, show that the semi-width and the ring profile are increasing functions of the load but, in general, non-monotonic functions of the rotation speed. In the limit of large rotation speed, the ring approaches a limiting non-uniform shape, whereas in the limit of small load, the ring is narrow and thin with a uniform parabolic profile. Finally, we show that, while for most values of the rotation speed and the load the azimuthal velocity is in the same direction as the rotation of the cylinder, there is a region of parameter space close to the critical solution for sufficiently small rotation speed in which backflow occurs in a small region on the right-hand side of the cylinder

    Thermoviscous Coating and Rimming Flow

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    A comprehensive description is obtained of steady thermoviscous (i.e. with temperature-dependent viscosity) coating and rimming flow on a uniformly rotating horizontal cylinder that is uniformly hotter or colder than the surrounding atmosphere. It is found that, as in the corresponding isothermal problem, there is a critical solution with a corresponding critical load (which depends, in general, on both the Biot number and the thermoviscosity number) above which no ``full-film'' solutions corresponding to a continuous film of fluid covering the entire outside or inside of the cylinder exist. The effect of thermoviscosity on both the critical solution and the full-film solution with a prescribed load is described. In particular, there are no full-film solutions with a prescribed load M for any value of the Biot number when M is greater than or equal to M_{c0} divided by the square root of f for positive thermoviscosity number and when M is greater than M_{c0} for negative thermoviscosity number, where f is a monotonically decreasing function of the thermoviscosity number and M_{c0} = 4.44272 is the critical load in the constant-viscosity case. It is also found that when the prescribed load M is less than 1.50315 there is a narrow region of the Biot number - thermoviscosity number parameter plane in which backflow occurs

    The X-ray Emissions from the M87 Jet: Diagnostics and Physical Interpretation

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    We reanalyze the deep Chandra observations of the M87 jet, first examined by Wilson & Yang (2002). By employing an analysis chain that includes image deconvolution, knots HST-1 and I are fully separated from adjacent emission. We find slight but significant variations in the spectral shape, with values of αx\alpha_x ranging from 1.21.6\sim 1.2-1.6. We use VLA radio observations, as well as HST imaging and polarimetry data, to examine the jet's broad-band spectrum and inquire as to the nature of particle acceleration in the jet. As shown in previous papers, a simple continuous injection model for synchrotron-emitting knots, in which both the filling factor, faccf_{acc}, of regions within which particles are accelerated and the energy spectrum of the injected particles are constant, cannot account for the X-ray flux or spectrum. Instead, we propose that faccf_{acc} is a function of position and energy and find that in the inner jet, faccEγ0.4±0.2Ee0.2±0.1f_{acc} \propto E_\gamma^{-0.4 \pm 0.2} \propto E_e^{-0.2 \pm 0.1}, and in knots A and B, faccEγ0.7±0.2Ee0.35±0.1f_{acc} \propto E_\gamma^{-0.7 \pm 0.2} \propto E_e^{-0.35 \pm 0.1}, where EγE_\gamma is the emitted photon energy and and EeE_e is the emitting electron energy. In this model, the index pp of the injected electron energy spectrum (n(Ee)Eepn(E_{e}) \propto E_{e}^{-p}) is p=2.2p=2.2 at all locations in the jet, as predicted by models of cosmic ray acceleration by ultrarelativistic shocks. There is a strong correlation between the peaks of X-ray emission and minima of optical percentage polarization, i.e., regions where the jet magnetic field is not ordered. We suggest that the X-ray peaks coincide with shock waves which accelerate the X-ray emitting electrons and cause changes in the direction of the magnetic field; the polarization is thus small because of beam averaging.Comment: Accepted for publication in ApJ; 21 pages, 9 figures, 2 tables; abstract shortened for astro-ph; Figures 1, 7 and 8 at reduced resolutio

    Renormalization in Quantum Mechanics

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    We implement the concept of Wilson renormalization in the context of simple quantum mechanical systems. The attractive inverse square potential leads to a \b function with a nontrivial ultraviolet stable fixed point and the Hulthen potential exhibits the crossover phenomenon. We also discuss the implementation of the Wilson scheme in the broader context of one dimensional potential problems. The possibility of an analogue of Zamolodchikov's CC function in these systems is also discussed.Comment: 16 pages, UR-1310, ER-40685-760. (Additional references included.

    Functional renormalization for Bose-Einstein Condensation

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    We investigate Bose-Einstein condensation for interacting bosons at zero and nonzero temperature. Functional renormalization provides us with a consistent method to compute the effect of fluctuations beyond the Bogoliubov approximation. For three dimensional dilute gases, we find an upper bound on the scattering length a which is of the order of the microphysical scale - typically the range of the Van der Waals interaction. In contrast to fermions near the unitary bound, no strong interactions occur for bosons with approximately pointlike interactions, thus explaining the high quantitative reliability of perturbation theory for most quantities. For zero temperature we compute the quantum phase diagram for bosonic quasiparticles with a general dispersion relation, corresponding to an inverse microphysical propagator with terms linear and quadratic in the frequency. We compute the temperature dependence of the condensate and particle density n, and find for the critical temperature T_c a deviation from the free theory, Delta T_c/T_c = 2.1 a n^{1/3}. For the sound velocity at zero temperature we find very good agreement with the Bogoliubov result, such that it may be used to determine the particle density accurately.Comment: 21 pages, 16 figures. Reference adde
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