2,746 research outputs found

    Hydrodynamic Description of Granular Convection

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    We present a hydrodynamic model that captures the essence of granular dynamics in a vibrating bed. We carry out the linear stability analysis and uncover the instability mechanism that leads to the appearance of the convective rolls via a supercritical bifurcation of a bouncing solution. We also explicitly determine the onset of convection as a function of control parameters and confirm our picture by numerical simulations of the continuum equations.Comment: 14 pages, RevTex 11pages + 3 pages figures (Type csh

    Planetary Collisions outside the Solar System: Time Domain Characterization of Extreme Debris Disks

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    Luminous debris disks of warm dust in the terrestrial planet zones around solar-like stars are recently found to vary, indicative of ongoing large-scale collisions of rocky objects. We use Spitzer 3.6 and 4.5 {\mu}m time-series observations in 2012 and 2013 (extended to 2014 in one case) to monitor 5 more debris disks with unusually high fractional luminosities ("extreme debris disk"), including P1121 in the open cluster M47 (80 Myr), HD 15407A in the AB Dor moving group (80 Myr), HD 23514 in the Pleiades (120 Myr), HD 145263 in the Upper Sco Association (10 Myr), and the field star BD+20 307 (>1 Gyr). Together with the published results for ID8 in NGC 2547 (35 Myr), this makes the first systematic time-domain investigation of planetary impacts outside the solar system. Significant variations with timescales shorter than a year are detected in five out of the six extreme debris disks we have monitored. However, different systems show diverse sets of characteristics in the time domain, including long-term decay or growth, disk temperature variations, and possible periodicity.Comment: 50 pages, 14 figures, 9 tables; Accepted for publication in the Astrophysical Journa

    Traffic Equations and Granular Convection

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    We investigate both numerically and analytically the convective instability of granular materials by two dimensional traffic equations. In the absence of vibrations the traffic equations assume two distinctive classes of fixed bed solutions with either a spatially uniform or nonuniform density profile. The former one exists only when the function V(\rho) that monitors the relaxation of grains assumes a cut off at the closed packed density, \rho_c, with V(\rho_c)=0, while the latter one exists for any form of V. Since there is little difference between the uniform and nonuniform solution deep inside the bed, the convective instability of the bulk may be studied by focusing on the stability of the uniform solution. In the presence of vibrations, we find that the uniform solution bifurcates into a bouncing solution, which then undergoes a supercritical bifurcation to the convective instability. We determine the onset of convection as a function of control parameters and confirm this picture by solving the traffic equations numerically, which reveals bouncing solutions, two convective rolls, and four convective rolls. Further, convective patterns change as the aspect ratio changes: in a vertically long container, the rolls move toward the surface, and in a horizontally long container, the rolls move toward the walls. We compare these results with those reported previously with a different continuum model by Hayakawa, Yue and Hong[Phys. Rev. Lett. 75,2328, 1995]. Finally, we also present a derivation of the traffic equations from Enskoq equation.Comment: 34 pages, 10 figure
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