沙堆模型中的混沌
Chaos in Sandpile Models
摘要：
我们研究了“弱混沌”指数，看看它是否可以被认为是一个分类参数的不同沙堆模型。仿真结果表明，“弱混沌”指数可能是\textit{deterministic}模型吸引子的特征指数之一。我们证明了（阿贝尔）BTW沙堆模型和（非阿贝尔）Zhang模型具有不同的“弱混沌”指数，因而它们可能属于不同的普适类。我们还表明，\textit{stochasticity}破坏了“弱混沌”指数的有效性，因此它减缓了附近配置的发散。最后，我们表明，摆脱临界点破坏这种行为的确定性模型。
英文摘要：
We have investigated the "weak chaos" exponent to see if it can be considered as a classification parameter of different sandpile models. Simulation results show that "weak chaos" exponent may be one of the characteristic exponents of the attractor of \textit{deterministic} models. We have shown that the (abelian) BTW sandpile model and the (non abelian) Zhang model posses different "weak chaos" exponents, so they may belong to different universality classes. We have also shown that \textit{stochasticity} destroys "weak chaos" exponents' effectiveness so it slows down the divergence of nearby configurations. Finally we show that getting off the critical point destroys this behavior of deterministic models.
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