0 50 100 150 V (mm/s) 100 102 104 106 108 N(V) Figure 2: The distribution of the velocity V. The velocity V are calculated on the basis of fronts separated with a time interval of Æt =20ms. The largest measured local speeds are about three order of magnitude larger than the average front speed Vf =68 m=s. It is important to note that the speeds V are average speeds within the time Æt =20ms.Thismeansthatevenmuchhigherspeed uctuations may be present with a higher resolution in space and time. them there are almost no evolution of the front position. Figure3:a)The gureshowsthespace(horizontal)andtime(vertical)diagram(5:12mm 8:7s) of the position uctuations h(x;t) hh(t)ix. The gray level represents h(x; t) hh(t)ix. Light gray corresponds to positive values of h(x; t) hh(t)ix, while dark gray corresponds to negative values of h(x; t) hh(t)ix. The dynamic scaling of the fracture front has been checked by calculating the power spectrumP(k;t) ofthepositiondi erence h(x;t) h(x;t = 0), where k is the wave-number and t is the time (t = 0 correspondstothe rstimage).TheFamily-Vicsekscaling[20]ofthepowerspectrumP(k;t) can be written as P(k; t)=t (1+2 )= G(kt 1= ) ; (1) where G(x) is constant for x<<1 and G(x) /x 1 2 for x>>1. The dynamic exponent gives the scaling with time of the horizontal correlation length x /t 1= . 3
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