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      High-Energy Tail of the Velocity Distribution of Driven Inelastic Maxwell Gases

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          Abstract

          A model of homogeneously driven dissipative system, consisting of a collection of \(N\) particles that are characterized by only their velocities, is considered. Adopting a discrete time dynamics, at each time step, a pair of velocities is randomly selected. They undergo inelastic collision with probability \(p\). With probability \((1-p)\), energy of the system is changed by changing the velocities of both the particles independently according to \(v\rightarrow -r_w v +\eta\), where \(\eta\) is a Gaussian noise drawn independently for each particle as well as at each time steps. For the case \(r_w=- 1\), although the energy of the system seems to saturate (indicating a steady state) after time steps of \(O(N)\), it grows linearly with time after time steps of \(O(N^2)\), indicating the absence of a eventual steady state. For \( -1 <r_w \leq 1\), the system reaches a steady state, where the average energy per particle and the correlation of velocities are obtained exactly. In the thermodynamic limit of large \(N\), an exact equation is obtained for the moment generating function. In the limit of nearly elastic collisions and weak energy injection, the velocity distribution is shown to be a Gaussian. Otherwise, for \(|r_w| < 1\), the high-energy tail of the velocity distribution is Gaussian, with a different variance, while for \(r_w=+1\) the velocity distribution has an exponential tail.

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          Velocity distributions in homogeneous granular fluids: the free and the heated case

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            Velocity Fluctuations in a Homogeneous 2D Granular Gas in Steady State

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              The Granular Phase Diagram

              The kinetic energy distribution function satisfying the Boltzmann equation is studied analytically and numerically for a system of inelastic hard spheres in the case of binary collisions. Analytically, this function is shown to have a similarity form in the simple cases of uniform or steady-state flows. This determines the region of validity of hydrodynamic description. The latter is used to construct the phase diagram of granular systems, and discriminate between clustering instability and inelastic collapse. The molecular dynamics results support analytical results, but also exhibit a novel fluctuational breakdown of mean-field descriptions.
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                Author and article information

                Journal
                12 July 2013
                2014-01-29
                Article
                10.1209/0295-5075/104/54003
                1307.3564
                ef47148c-098c-4556-8d00-4bcf12ab9f04

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                EPL 104, 54003 (2013)
                6 pages, 5 figures
                cond-mat.stat-mech cond-mat.soft

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