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The exact nonequilibrium steady state solution of the nonlinear Boltzmann equation for a driven inelastic Maxwell model was obtained by Ben-Naim and Krapivsky [Phys. Rev. E 61, R5 (2000)] in the form of an infinite product for the Fourier transform of the distribution function $f(c)$. In this paper we have inverted the Fourier transform to express $f(c)$ in the form of an infinite series of exponentially decaying terms. The dominant high energy tail is exponential, $f(c)simeq A_0exp(-a|c|)$, where $aequiv 2/sqrt{1-alpha^2}$ and the amplitude $A_0$ is given in terms of a converging sum. This is explicitly shown in the totally inelastic limit ($alphato 0$) and in the quasi-elastic limit ($alphato 1$). In the latter case, the distribution is dominated by a Maxwellian for a very wide range of velocities, but a crossover from a Maxwellian to an exponential high energy tail exists for velocities $|c-c_0|sim 1/sqrt{q}$ around a crossover velocity $c_0simeq ln q^{-1}/sqrt{q}$, where $qequiv (1-alpha)/2ll 1$. In this crossover region the distribution function is extremely small, $ln f(c_0)simeq q^{-1}ln q$.
The nature of the velocity distribution of a driven granular gas, though well studied, is unknown as to whether it is universal or not, and if universal what it is. We determine the tails of the steady state velocity distribution of a driven inelasti
We discuss the exact solution for the properties of the recently introduced ``necklace model for reptation. The solution gives the drift velocity, diffusion constant and renewal time for asymptotically long chains. Its properties are also related to
Structural and thermodynamic properties of multicomponent hard-sphere fluids at odd dimensions have recently been derived in the framework of the rational function approximation (RFA) [Rohrmann and Santos, Phys. Rev. E textbf{83}, 011201 (2011)]. It
The Boltzmann equation for inelastic Maxwell models is considered to determine the rheological properties in a granular binary mixture in the simple shear flow state. The transport coefficients (shear viscosity and viscometric functions) are {em exac
The Boltzmann equation for d-dimensional inelastic Maxwell models is considered to analyze transport properties in spatially inhomogeneous states close to the simple shear flow. A normal solution is obtained via a Chapman--Enskog--like expansion arou