2011/01/31 by E. A. Oliveira, Erneson A. Oliveira, K. J. Schrenk +5 · 36 citations
Decision Sciences · Engineering · Mathematics · Physics and Astronomy · #Computer network #Computer science #Mathematics #Numerical methods in engineering #Path (computing) #Physics #Probabilistic and Robust Engineering Design #Statistical physics #Statistics #Theoretical and Computational Physics #Uncorrelated #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.83.046113
published in Physical Review E 83(4), 046113 (American Physical Society) · 10 pages, 10 figures
arxiv created 2011/01/31 · openalex publication_date 2011/04/18 · arxiv updated 2015/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The optimal path crack model on uncorrelated surfaces, recently introduced by Andrade et al. [Phys. Rev. Lett. 103, 225503 (2009).], is studied in detail and its main percolation exponents computed. In addition to \ensuremathβ/\ensuremathν=0.46\ifmmode±\else\textpm\fi0.03, we report \ensuremathγ/\ensuremathν=1.3\ifmmode±\else\textpm\fi0.2 and \ensuremathτ=2.3\ifmmode±\else\textpm\fi0.2. The analysis is extended to surfaces with spatial long-range power-law correlations, where nonuniversal fractal dimensions are obtained when the degree of correlation is varied. The model is also considered on a three-dimensional lattice, where the main crack is found to be a surface with a fractal dimension of 2.46\ifmmode±\else\textpm\fi0.05.