 0  0.2  0.4  0.6  0.8  1  0  0.5  1  1.5  2 n (t) |  v$_{c}$  |  t  L = 1000, p = 0.25,  = 0.25,   = 0.60 = 1000, p = 0.25,  = 0.25,   = 0.70 = 1000, p = 0.25,  = 0.25,   = 0.80 = 1000, p = 0.25,  = 0.25,   = 0.90 = 5000, p = 0.25,  = 0.25,   = 0.60 = 5000, p = 0.25,  = 0.25,   = 0.70 = 5000, p = 0.25,  = 0.25,   = 0.80 = 5000, p = 0.25,  = 0.25,   = 0.90 = 10000, p = 0.25,  = 0.25,   = 0.60 = 10000, p = 0.25,  = 0.25,   = 0.70 = 10000, p = 0.25,  = 0.25,   = 0.80 = 10000, p = 0.25,  = 0.25,   = 0.90 7 function for the system density behaves as 1 − | v$_{c}$ t | /L with a finite support [ − L/ | v$_{c}$ | , L/ | v$_{c}$ | ], where v$_{c}$ is the collective velocity. For the case of v$_{max}$ = 1 an exact theoretical result is known for v$_{c}$ for all p ∈ [0 , 1]. When v$_{max}$ > 1 no rigorous results for v$_{c}$ are known, however we conjecture that the when p = 0 we simply have v$_{c}$ = v$_{max}$ in the low-density phase and v$_{c}$ = − 1 in the high-density phase. This result agrees with the exact result in the special case of v$_{max}$ = 1 and with numerical simulations for v$_{max}$ = 3 , 5. It seems reasonable to expect that it is valid for all v$_{max}$ for the deterministic NaSch model. This research was supported by the Australian Re- search Council. ZZ acknowledges support from the NSFC under Grant No. 10975127 and the NSF of Anhui under Grant No. 090416224. TMG would like to thank Alan Sokal for some useful comments. Acknowledgments FIG. 6: Color online. Finite-size scaling plot of ρ n ( t ) for p = 0 . 25 NaSch with v max = 3 in the high-density and low- density phases, for a variety of choices of α, β and L . The exact value of v c is unknown in this case but here we have set v c = 2 . 65. Straley, J. Phys. A: Math. Gen. 31 , 6911 (1998). [1] F. Spitzer, Adv. Math. 5 , 246 (1970). [2] J. de Gier and B. Nienhuis, Phys. Rev. E 59 , 4899 (1999). [14] R. H. Shumway and D. S. Stoffer, Time Series Analysis and Its Applications (Springer, New York, 2006), 2nd ed. [15] A. D. Sokal, in Functional Integration: Basics and Ap- plications , edited by C. DeWitt-Morette, P. Cartier, and A. Folacci (Plenum, New York, 1997), pp. 131–192. [16] J. de Gier and F. H. L. Essler, Phys. Rev. Lett. 95 , 240601 (2005). [17] J. de Gier and F. H. L. Essler, J. Stat. Mech. p. P12011 (2006). [3] M. R. Evans, N. Rajewsky, and E. R. Speer, J. Stat. Phys. 95 , 45 (1999). [4] B. Derrida, Physics Reports 301 , 65 (1998). [5] G. M. Sch¨ utz, Phase Transitions and Critical Phenom- ena , vol. 19 (Academic Press, London, 2001). [6] K. Nagel and M. Schreckenberg, Journal de Physique 2 , 2221 (1992). [7] D. Chowdhury, L. Santen, and A. Schadschneider, Phys. Rep. 329 , 199 (2000). [18] S. Cheybani, J. Kert´esz, and M. Schreckenberg, Phys. Rev. E 63 , 016107 (2000). [8] J. Esser and M. Schreckenberg, Internat. J. Modern Phys. C 8 , 1025 (1997). [9] M. Schreckenberg, L. Neubert, and J. Wahle, Future Generation Computer Systems 17 , 649 (2001). [10] N. Cetin, K. Nagel, B. Raney, and A. Voellmy, Comput. Phys. Comm. 147 , 559 (2002). [11] P. Pierobon, A. Parmeggiani, F. von Oppen, E. Frey, Phys. Rev. E 72 , 036123 (2005). [12] D. A. Adams, R. K. P. Zia, and B. Schmittmann, Phys. Rev. Lett. 99 , 020601 (2007). [13] A. B. Kolomeisky, G. Sch¨ utz, E. B. Kolomeisky, and J. P. [23] T. Neumann and P. Wagner, Phys. Rev. E 80 , 013101 (2009). [22] N. Jia and S. Ma, Phys. Rev. E 79 , 031115 (2009). [21] R. Barlovic, T. Huisinga, A. Schadschneider, and M. Schreckenberg, Phys. Rev. E 66 , 046113 (2002). [20] Ding-wei Huang, Phys. Rev. E 64 , 036108 (2001). [19] S. Cheybani, J. Kert´esz, and M. Schreckenberg, Phys. Rev. E 63 , 016108 (2000).