The direct simulation Monte Carlo method is used to study the homogeneous cooling state of a dilute granular gas composed of Gaussian and log-normal distributed particle sizes. The velocity distribution functions are extracted to determine if the hydrodynamic fields (the kinetic temperature) and the higher order moments (the fourth and sixth moments of velocity distribution function) follow an equivalent monodisperse theory. While the temperature is well approximated by Haff's law over a large range of inelasticity and size-variance, the fourth and sixth moments of the velocity distribution function deviate significantly from the predictions of an equivalent monodisperse theory for low restitution coefficients. The variation of the normalized temperature distribution as a function of the normalized particle sized is found to follow a master curve for a wide range of restitution coefficients.
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