  We consider a mean field model describing the free cooling process of a two
component granular mixture, a generalization of so called Maxwell model. The
cooling is viewed as an ordering process and the scaling behavior is attributed
to the presence of an attractive fixed point at $v=0$ for the dynamics. By
means of asymptotic analysis of the Boltzmann equation and of numerical
simulations we get the following results: 1)we establish the existence of two
different partial granular temperatures, one for each component, which violates
the Zeroth Law of Thermodynamics; 2) we obtain the scaling form of the two
distribution functions; 3) we prove the existence of a continuous spectrum of
exponents characterizing the inverse-power law decay of the tails of the
velocity, which generalizes the previously reported value 4 for the pure model;
4) we find that the exponents depend on the composition, masses and restitution
coefficients of the mixture; 5) we also remark that the reported distributions
represent a dynamical realization of those predicted by the Non Extensive
Statistical Mechanics, in spite of the fact that ours stem from a purely
dynamical approach.
