Phase diagram and critical behavior of a forest-fire model in a gradient of immunity
Phase diagram and critical behavior of a forest-fire model in a gradient of immunity
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DOI：
10.1103/physreve.83.011125
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发表时间：
2011-01-25
影响因子：
2.4
通讯作者：
Albano, Ezequiel V.
中科院分区：
文献类型：
--
作者：
Guisoni, Nara;Loscar, Ernesto S.;Albano, Ezequiel V.
带免疫树的森林火灾模型(FFMIT)是由Drossel和Schwabl[Physica A 199,183(1993)]最早提出的元胞自动机模型，其中格子的每个位置可以处于三种可能的状态：被树占据、空置或被燃烧的树(火)占据。树木以概率p生长在空地上，健康树以概率(1-g)从相邻的燃烧树上着火，其中g是免疫力，燃烧的树自发成为空地。本文用最近提出的梯度法(GM)研究了FFMIT，将免疫视为沿格子水平轴的均匀梯度。GM允许在同一模拟中同时处理模型的活动阶段和非活动阶段。这样，对单值界面的研究给出了有源-吸收相变的临界点，而对多值界面的研究则将渗流阈值带入了有源相。因此，我们给出了一个完整的FFMIT相图，对于p的所有范围，除了通常模型的有源-吸收相变外，我们还定位了有源渗流相和有源非渗流相之间的相变。两个界面的平均位置和宽度以及吸收和渗流团簇密度服从指数α=1/(1+nu)的标度行为，其中nu是合适的关联长度指数(对于定向渗流相变为nu(垂直于)，对于标准渗流相变为nu)。我们还表明，GM允许我们计算与吸收跃迁的序参数和多值界面中的粒子数有关的临界指数。此外，我们还证明了利用梯度方法，对于不同侧面的样品，在一条团簇密度曲线上坍塌是一种非常敏感的方法，以求取临界点和渗流阈值。
The forest-fire model with immune trees (FFMIT) is a cellular automaton early proposed by Drossel and Schwabl [Physica A 199, 183 (1993)], in which each site of a lattice can be in three possible states: occupied by a tree, empty, or occupied by a burning tree (fire). The trees grow at empty sites with probability p, healthy trees catch fire from adjacent burning trees with probability (1 - g), where g is the immunity, and a burning tree becomes an empty site spontaneously. In this paper we study the FFMIT by means of the recently proposed gradient method (GM), considering the immunity as a uniform gradient along the horizontal axis of the lattice. The GM allows the simultaneous treatment of both the active and the inactive phases of the model in the same simulation. In this way, the study of a single-valued interface gives the critical point of the active-absorbing transition, whereas the study of a multivalued interface brings the percolation threshold into the active phase. Therefore we present a complete phase diagram for the FFMIT, for all range of p, where, besides the usual active-absorbing transition of the model, we locate a transition between the active percolating and the active nonpercolating phases. The average location and the width of both interfaces, as well as the absorbing and percolating cluster densities, obey a scaling behavior that is governed by the exponent alpha = 1/(1 + nu), where nu is the suitable correlation length exponent (nu(perpendicular to) for the directed percolation transition and nu for the standard percolation transition). We also show that the GM allows us to calculate the critical exponents associated with both the order parameter of the absorbing transition and the number of particles in the multivalued interface. Besides, we show that by using the gradient method, the collapse in a single curve of cluster densities obtained for samples of different side is a very sensitive method in order to obtain the critical points and the percolation thresholds.