A discrete time evolution model for fracture networks

摘要: We examine geological crack patterns using the mean field theory of convex mosaics. We assign the pair \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left({\overline{n } }^{*},{\overline{v } }^{*}\right)$$\end{document} of average corner degrees (Domokos et al. in A two-vertex theorem for normal tilings. Aequat Math https://doi.org/10.1007/s00010-022-00888-0, 2022) to each crack pattern and we define two local, random evolutionary steps R0 and R1, corresponding to secondary fracture and rearrangement of cracks, respectively. Random sequences of these steps result in trajectories on the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage …