−5.0 −4.0 −3.0 −2.0 −1.0 log10(k) 2.0 4.0 6.0 8.0 10.0 12.0 log10(P(k)) Figure5:Averageofthepowerspectrumanalysisoverninefronts.Thebest ttedlinehasaslopeof 2:28= 1 2 , where is the roughness exponent. a creeping motion. Very high front velocities compared to the average crack speed are observed locally. We show that the dynamics of the fracture is controlled by local instabilities or bursts which give rise to a self-aÆne fracture front line with roughness exponent =0:60, and a dynamic exponent =1:2 . The slip along the front is found to be correlated on a length scale much larger than the asperity size. References [1] K. J. M al y, and J. Schmittbuhl, and K. J. M al y. Preprint, 2001 [2] B. B. Mandelbrot, D. E. Passoja, and A. J. Paullay. (1984) Nature, 308, 721. [3] S. R. Brown and C. H. Scholz.(1985) J. Geophys. Res., 90, 12575. [4] E. Bouchaud, G. Lapasset, and J. Plan es. (1990) Europhys. Lett., 13, 73. [5] J. Schmittbuhl, S. Gentier, and S. Roux. (1993) Geophys. Res. Lett., 20, 639. [6] B. L. Cox and J. S. Y. Wang. (1993) Fractals, 1, 87. [7] K. J. M al y, A. Hansen, E. L. Hinrichsen, and S. Roux. (1992) Phys. Rev. Lett., 68, 213. [8] J. Schmittbuhl, F. Schmitt, and C. H. Scholz. (1995) J. Geophys. Res., 100, 5953. [9] E. Bouchaud. (1997) J. Phys, 9, 4319. [10] H. Gao and J. R. Rice. (1989) ASME J. Appl. Mech, 56, 828. 5
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