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The hydrodynamic simulation was done with the constitutive relations by Grossman et al., [10], more accurate at large densities. In addition, the gas-kinetic viscosity in the momentum equation was replaced in this simulation, as well as in the simulations [13,16], by a moderately large Stokes friction. Obviously, the Stokes friction does not affect hydrostatic steady states. However, it cannot provide a faithful description of the shear modes in a gas of hard spheres.
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Notice that, for large aspect ratios, hydrodynamic simulations are not expected to give a high accuracy for an entirely different reason. The density of the symmetry-broken cluster here approaches the close-packing density, while the accuracy of the interpolating constitutive relations [10] is not very high.
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44
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33645046259
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A single simulation such as those shown in Figs. 4(c), 4(d), or 4(e) requires about 350 h of the CPU time of a Pentium P4 at 1.4 GHz.
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Unfortunately, recent attempts to employ fluctuating hydrodynamics in the context of a freely evolving [35] and randomly driven [36] dilute granular gas are incomplete, as they do not account for an important additional Langevin term in the energy equation, arising because of the discreteness of the collisional energy losses.
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58
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33645071205
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See http://bioinf.charite.de/kies/giantfluctuations/
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