the former with respect the latter, the technical problem arises that the considered values of M/m are separated by intervals of the order of 10 or 15 units. Decreasing this interval would require to strongly increase the simulation time. In addition, some smoothing process should be used. Here, a different approach has been followed. The simulation data for L have been fitted by an analytical function of the mass ratio whose derivative has been afterwards computed. The trivial choice of a polynomial in m/M does not work so, motivated by the equilibrium elastic result, an expression of the form where A and B are two adjustable dimensionless parameters, was used. It turned out that it fits very well the results for all the values of α and α$_{P}$ considered here. Moreover, the values of the two fitting parameters are quite stable, in the sense that their value seem to converge very fast when the number of fitted data is increased. L = A g 0 mv 2 W ln ( 1 + Bm M ) , (A1) [1] H.M. Jaeger, S.R. Nagel, and R.P. Behringer, Rev. Mod. Phys. 68 , 1259 (1996). [2] J. Duran, Sands, Powers and Grains. An Introduction to the Physics of Granular Materials (Springer Verlag, New York, 2000). [3] I. Goldhirsch, Annu. Rev. Fluid Mech. 35 , 267 (2003). [4] N.V. Brilliantov and T. P¨ oschel, Kinetic Theory of Granular Gases (Oxford University Press, Oxford, 2004). [5] I.S. Aranson and L.S. Tsimring, Rev. Mod. Phys. 78 , 641 (2006). [6] J.J. Brey, M.I. Garc´ıa de Soria, P. Maynar, and M.J. Ruiz-Montero, Phys. Rev. E 70 , 011302 (2004). [7] P. Visco, A. Puglisi, A. Barrat, F. van Wijland, and E. Trizac, Eur. Phys. J. B 51 , 377 (2006). [8] M.P. Allen and D.J. Tildesley, Computer Simulations of Liquids (Clarendon Press, Oxford, 1987). [9] T. P¨ oschel and T. Schwager, Computational Granular Dynamics (Springer, Berlin 2005) [10] L.D. Landau and E.M. Lifschitz, Statistical Physics, Part 1 (Pergamon Press, Oxford, 1978). [11] A. Baldassarri, A. Barrat, G. D’Anna, V. Loreto, P. Mayor, and A. Puglisi, J. Phys.: Condens. Matter 17 , S2405 (2005). 20