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Stationary States And Energy Cascades In Inelastic Gases, E. Ben-Naim, J. Machta
Stationary States And Energy Cascades In Inelastic Gases, E. Ben-Naim, J. Machta
Eli Ben-Naim
We find a general class of nontrivial stationary states in inelastic gases where, due to dissipation, energy is transfered from large velocity scales to small velocity scales. These steady-states exist for arbitrary collision rules and arbitrary dimension. Their signature is a stationary velocity distribution f(v) with an algebraic high-energy tail, f(v) ~ v^{-sigma}. The exponent sigma is obtained analytically and it varies continuously with the spatial dimension, the homogeneity index characterizing the collision rate, and the restitution coefficient. We observe these stationary states in numerical simulations in which energy is injected into the system by infrequently boosting particles to high …
Density Fluctuations In Vibrated Granular Materials , E.R. Nowak, J.B. Knight, E. Ben-Naim, H.M Jaeger, S.R. Nagel
Density Fluctuations In Vibrated Granular Materials , E.R. Nowak, J.B. Knight, E. Ben-Naim, H.M Jaeger, S.R. Nagel
Eli Ben-Naim
We report systematic measurements of the density of a vibrated granular material as a function of time. Monodisperse spherical beads were confined to a cylindrical container and shaken vertically. Under vibrations, the density of the pile slowly reaches a final steady-state value about which the density fluctuates. We have investigated the frequency dependence and amplitude of these fluctuations as a function of vibration intensity Γ. The spectrum of density fluctuations around the steady state value provides a probe of the internal relaxation dynamics of the system and a link to recent thermodynamic theories for the settling of granular material. In …