Anomalous Roughness of Fracture Surfaces in 2D Fuse Models
Abstract
We study anomalous scaling and multiscaling of twodimensional crack profiles in the random fuse model using both periodic and open boundary conditions. Our large scale and extensively sampled numerical results reveal the importance of crack branching and coalescence of microcracks, which induce jumps in the solidonsolid crack profiles. Removal of overhangs (jumps) in the crack profiles eliminates the multiscaling observed in earlier studies and reduces anomalous scaling. We find that the probability density distribution $p(\Delta h(\ell))$ of the height differences $\Delta h(\ell) = [h(x+\ell)  h(x)]$ of the crack profile obtained after removing the jumps in the profiles has the scaling form $p(\Delta h(\ell)) = <\Delta h^2(\ell)>^{1/2} ~f(\frac{\Delta h(\ell)}{<\Delta h^2(\ell)>^{1/2}})$, and follows a Gaussian distribution even for small bin sizes $\ell$. The anomalous scaling can be summarized with the scaling relation $[\frac{<\Delta h^2(\ell)>^{1/2}}{<\Delta h^2(L/2)>^{1/2}}]^{1/\zeta_{loc}} + \frac{(\ellL/2)^2}{(L/2)^2} = 1$, where $<\Delta h^2(L/2)>^{1/2} \sim L^{\zeta}$.
 Publication:

arXiv eprints
 Pub Date:
 April 2008
 arXiv:
 arXiv:0804.2236
 Bibcode:
 2008arXiv0804.2236N
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Materials Science
 EPrint:
 9 pages, 10 figures