Shear-rate dependent transport coefficients for inelastic Maxwell models - Condensed Matter > Statistical Mechanics

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Abstract: The Boltzmann equation for d-dimensional inelastic Maxwell models isconsidered to analyze transport properties in spatially inhomogeneous statesclose to the simple shear flow. A normal solution is obtained via aChapman-Enskog-like expansion around a local shear flow distribution f^{(0)}that retains all the hydrodynamic orders in the shear rate. The constitutiveequations for the heat and momentum fluxes are obtained to first order in thedeviations of the hydrodynamic field gradients from their values in thereference state and the corresponding generalized transport coefficients are{\em exactly} determined in terms of the coefficient of restitution \alpha andthe shear rate a. Since f^{(0)} applies for arbitrary values of the shear rateand is not restricted to weak dissipation, the transport coefficients turn outto be nonlinear functions of both parameters a and \alpha. A comparison withprevious results obtained for inelastic hard spheres from a kinetic model ofthe Boltzmann equation is also carried out.

Autor: Vicente Garzo

Fuente: https://arxiv.org/