论文标题
入侵沙珀模型
Invasion Sandpile Model
论文作者
论文摘要
由储层中的多相流动，我们提出并研究了两个维度的两种砂模型。一堆颗粒变得不稳定，如果满足以下两个条件中的至少一个：1）桩中一个物种的颗粒数量超过给定阈值或2）堆中的颗粒总数超过第二个阈值。后一种机制导致通过以另一物种为主的区域侵袭了一个物种。我们以数字研究了雪崩的统计数据，并确定了两个不同的制度。对于大型雪崩，统计数据与普通的Bak-Tang-Weisenfeld模型一致。鉴于，对于小型雪崩，我们找到了一个具有不同指数的政权。尤其是，雪崩外部外周的分形维度为$ d_f = 1.47 \ pm 0.02 $，其大小分布指数的指数为$τ_s= 0.95 \ pm 0.03 $，与$ $ d_f = 1.25 \ pm 0.01 $ and $ d_f = 1.25 \ pm 0.01 $ and $τ_s= 1.26 $ = 1.26 $ 0.04 $ 04 $ 04 $ 04 $ 044 $ 04 $ 044 $ 04 $ 044 $ bal。
Motivated by multiphase flow in reservoirs, we propose and study a two-species sandpile model in two dimensions. A pile of particles becomes unstable and topples if, at least one of the following two conditions is fulfilled: 1) the number of particles of one species in the pile exceeds a given threshold or 2) the total number of particles in the pile exceeds a second threshold. The latter mechanism leads to the invasion of one species through regions dominated by the other species. We studied numerically the statistics of the avalanches and identified two different regimes. For large avalanches the statistics is consistent with ordinary Bak-Tang-Weisenfeld model. Whereas, for small avalanches, we find a regime with different exponents. In particular, the fractal dimension of the external perimeter of avalanches is $D_f=1.47\pm 0.02$ and the exponent of their size distribution exponent is $τ_s=0.95\pm 0.03$, which are significantly different from $D_f=1.25\pm 0.01$ and $τ_s=1.26\pm 0.04$, observed for large avalanches.
