2008/04/14 by Phani K. V. V. Nukala, Nukala, Phani K. V. V., Stefano Zapperi +6
Engineering · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Geophysical Methods and Applications #Materials Science (cond-mat.mtrl-sci) #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.mtrl-sci #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.0804.2236
9 pages, 10 figures
arxiv created 2008/04/14 · openalex publication_date 2008/04/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study anomalous scaling and multiscaling of two-dimensional 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 solid-on-solid 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(Δh(ℓ)) of the height differences Δh(ℓ) = [h(x+ℓ) - h(x)] of the crack profile obtained after removing the jumps in the profiles has the scaling form p(Δh(ℓ)) = <Δh2(ℓ)>-1/2 ~f(\fracΔh(ℓ)<Δh2(ℓ)>1/2), and follows a Gaussian distribution even for small bin sizes ℓ. The anomalous scaling can be summarized with the scaling relation [\frac<Δh2(ℓ)>1/2<Δh2(L/2)>1/2]^1/ζloc + ((ℓ-L/2)2)/((L/2)2) = 1, where <Δh2(L/2)>1/2 ∼ Lζ.