关于力平衡渗流的研究
On the study of force-balance percolation
摘要：
我们研究模型的相关渗流有限制的网站，模仿力平衡的占领，即一个网站是稳定的，需要占领在两个维度的所有四个罗盘方向的相邻网站。我们严格证明了$p_c<1$的二维模型研究。数值数据表明，力平衡渗流过渡是不连续的交叉长度的增长，也许与堵塞渗流模型相同的形式，这表明在这两种情况下驱动过渡的相同的基本机制。换句话说，力平衡渗流和阻塞渗流可能确实属于同一普适类。我们发现一个下界的相关长度在连接阶段和关联函数不出现是一个幂律的过渡。最后，我们研究了动态的淘汰程序调用，以获得力平衡配置，并找到一个类似的动态指数，发现在沙堆模型。
英文摘要：
We study models of correlated percolation where there are constraints on the occupation of sites that mimic force-balance, i.e. for a site to be stable requires occupied neighboring sites in all four compass directions in two dimensions. We prove rigorously that $p_c<1$ for the two-dimensional models studied. Numerical data indicate that the force-balance percolation transition is discontinuous with a growing crossover length, with perhaps the same form as the jamming percolation models, suggesting the same underlying mechanism driving the transition in both cases. In other words, force-balance percolation and jamming percolation may indeed belong to the same universality class. We find a lower bound for the correlation length in the connected phase and that the correlation function does not appear to be a power law at the transition. Finally, we study the dynamics of the culling procedure invoked to obtain the force-balance configurations and find a dynamical exponent similar to that found in sandpile models.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
