A discrete time evolution model for fracture networks

Gábor Domokos; Krisztina Regős

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arXiv · 2207.00561

A discrete time evolution model for fracture networks

Gábor Domokos·Krisztina Regős

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Abstract

We examine geophysical crack patterns using the mean field theory of convex mosaics. We assign the pair $(\bar n^*,\bar v^*)$ of average corner degrees to each crack pattern and we define two local, random evolutionary steps $R_0$ and $R_1$, corresponding to secondary fracture and rearrangement of cracks, respectively. Random sequences of these steps result in trajectories on the $(\bar n^*,\bar v^*)$ plane. We prove the existence of limit points for several types of trajectories. Also, we prove that cell density $\rho = \bar v^*/\bar n^*$ increases monotonically under any admissible trajectory.

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Gábor Domokos, Krisztina Regős. 2022-07-01. A discrete time evolution model for fracture networks. https://arxiv.org/abs/2207.00561

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