有限随机多米诺自动机
Finite Random Domino Automaton
摘要：
随机多米诺自动机（FRDA）的有限版本-最近提出的玩具模型的地震-进行了研究。导出了描述FRDA定态的相应方程组，并与无限情况进行了比较。结果表明，对于大尺寸系统，这些方程与RDA方程是一致的。我们证明了一个不存在的精确方程的大小N大于4，并提出了适当的近似，其质量进行了研究，在马尔可夫链框架内获得的例子。我们推导出几个精确的公式描述的自动机的属性，包括时间方面。特别是，一种方法来实现准周期性的行为RDA。因此，基于相同的微观规则-产生指数和逆幂分布-我们将模型的适用性扩展到准周期现象。
英文摘要：
Finite version of Random Domino Automaton (FRDA) - recently proposed a toy model of earthquakes - is investigated. Respective set of equations describing stationary state of the FRDA is derived and compared with infinite case. It is shown that for the system of big size, these equations are coincident with RDA equations. We demonstrate a non-existence of exact equations for size N bigger then 4 and propose appropriate approximations, the quality of which is studied in examples obtained within Markov chains framework. We derive several exact formulas describing properties of the automaton, including time aspects. In particular, a way to achieve a quasi-periodic like behaviour of RDA is presented. Thus, based on the same microscopic rule - which produces exponential and inverse-power like distributions - we extend applicability of the model to quasi-periodic phenomena.
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