7 similar to the recent works for the colloidal systems 21 and Fe $^{24}$. J.A.P.R. acknowledges the support from Secretaria da Administra¸c˜ ao do Estado da Bahia. E.G. was supported by Funda¸c˜ ao de Amparo ` a Pesquisa do Estado de S˜ ao Paulo - FAPESP (Grant No. 07/08492-9). S.C.Y. also acknowledges FAPESP (Grant No. 09/01942-4) for sup- porting a visit to Instituto Nacional de Pesquisas Espa- ciais. This work has been supported in part also by the Academy of Finland through its COMP Center of Ex- cellence grant and by joint funding under EU STREP 016447 MagDot and NSF DMR Award No. 0502737. K. R. E. acknowledges support from NSF under Grant No. DMR-0906676. E.G. thanks Sami Majaniemi for many helpful discussions. for a PFC model with a pinning potential. The model describes a driven adsorbed layer as a continuous den- sity field, allowing for elastic and plastic deformations. The numerical results showed that at low temperatures, the velocity response of an initially commensurate layer shows hysteresis with dynamical melting and freezing transitions for increasing and decreasing applied forces at different critical values. The inclusion of both ther- mal fluctuations and inertial effects are crucial for a cor- rect description of these dynamical transitions. The main features of the nonlinear response, in particular the hys- teresis loop separating the static friction and sliding fric- tion thresholds are similar to the results obtained previ- ously with particle models. However, the details of the dynamical melting and freezing mechanisms are signifi- cantly different. In the PFC model considered here, they correspond to nucleation of stripes rather than closed do- mains found in particle models. It is possible to describe more realistic sliding adsorbed systems if the parameters of the model are adjusted to match experimental systems, Acknowledgments 14 J.A.P. Ramos, E. Granato, C.V. Achim, S.C. Ying, K.R. Elder, T. Ala-Nissila, Phys. Rev. E 78 , 031109 (2008). 15 C.V. Achim, J.A.P. Ramos, M. Karttunen, K.R. Elder, E. Granato, T. Ala-Nissila, and S.C. Ying, Phys. Rev. E 79 , 011606 (2009). 16 P.M. Chaikin and T.C. Lubensky, Principles of Condensed Matter Physics , Cambridge University Press, 1995. 17 G. Mazenko, Nonequilibrium Statistical Mechanics , Willey- VCH, 2006). 18 S. Ramaswamy and G.F. Mazenko, Phys. Rev. A 26 , 1735 (1982). 19 B.N.J. Persson and E. Tosatti, Phys. Rev. B 50 , 5590 (1994). 20 S. Majaniemi and M. Grant, Phys. Rev. B 75 , 054301, (2007). 21 Sven van Teeffelen, Rainer Backofen, Axel Voigt, and Hart- mut L¨ owen, Phys. Rev. E 79 , 051404 (2009). 22 P. Stefanovic, M. Haataja, and N. Provatas, Phys. Rev. Lett. 96 , 225504 (2006). 23 P. Galenko, D. Danilov, and V. Lebedev, Phys. Rev. E 79 , 051110 (2009). 24 A. Jaatinen, C. V. Achim, K. R. Elder, and T. Ala-Nissila, Phy. Rev. E, 80 , 031602 (2009). 13 C.V. Achim, M. Karttunen, K.R. Elder, E. Granato, T. Ala-Nissila, and S.C. Ying, Phys. Rev. E 74 , 021104 (2006); J. Phys.: Conf. Ser. 100 , 072001 (2008). 12 K.R. Elder, N. Provatas, J. Berry, P. Stefanovic, and M. Grant, Phys. Rev. B 75 , 064107 (2007). 11 K.R. Elder, and M. Grant, Phys. Rev. E 70 , 051605 (2004). 10 K.R. Elder, M. Katakowski, M. Haataja, and M. Grant, Phys. Rev. Lett. 88 , 245701 (2002). 9 D. S. Fisher, Phys. Rev. B 31 , 1396 (1985). 8 A. Carlin, L. Bruschi, M. Ferrari, and G. Mistura, Phys. Rev. B 68 , 045420 (2003). 7 J. Krim, D.H. Solina, and R. Chiarello, Phys. Rev. Lett. 66 , 181 (1991) 6 E. Granato and S.C. Ying, Phys. Rev. Lett. 85, 5368 (2000); Phys. Rev. B 69 , 125403 (2004). 5 E. Granato and S. C. Ying, Phys. Rev. B. 59 , 5154 (1999). 4 H. Yoshizawa, P. McGuiggan, and J. Israelachvili, Science 259 , 1305 (1993) 14), 109 (1992); Klafter, D. Gourdon, and J. Israelachvili, Nature 430 , 525 (2004). 3 B. N. J. Persson, Phys. Rev. Lett. 71 , 1212 (1993); J. Chem. Phys. 103 , 3449 (1995). 2 articles in Physics of Sliding Friction , edited by B.N. J. Persson and E. Tosatti (Kluwer, Dordrecht,1996). 1 B.N.J. Persson, Sliding Friction: Physical Principles and Applications (Springer, Heidelberg, 1998).