论文标题
断裂网络的离散时间演变模型
A discrete time evolution model for fracture networks
论文作者
论文摘要
我们使用凸镶嵌的平均场理论检查地球物理裂纹模式。我们为每个裂纹模式分配了平均角度度的$（\ bar n^*，\ bar v^*）$，我们定义两个本地的，随机的进化步骤$ r_0 $和$ r_1 $，分别对应于二次裂缝和裂缝的重新排列。这些步骤的随机序列导致$（\ bar n^*，\ bar v^*）$ plane上的轨迹。我们证明了几种类型的轨迹的限制点。另外，我们证明单元密度$ρ= \ bar v^*/\ bar n^*$在任何可接受的轨迹下单调增加。
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 $ρ= \bar v^*/\bar n^*$ increases monotonically under any admissible trajectory.
