Critical phase transitions made self-organized : a dynamical system feedback mechanism for self-organized criticality
Critical phase transitions made self-organized : a dynamical system feedback mechanism for self-organized criticality
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自组织的关键相变：自组织临界的动态系统反馈机制
DOI：
10.1051/jp1:1992267
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发表时间：
1992
期刊：
影响因子：
--
通讯作者：
D. Sornette
中科院分区：
文献类型：
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作者：
D. Sornette
根据Kadanoff的说法，自组织临界性（SOC）意味着一种反馈机制的运行，该机制确保了系统对干扰的稳定状态。在这里，我们扩展了这一想法，并提出了一个图片，根据该图片的SOC依赖于控制参数的序参数的非线性反馈（S），这种反馈的幅度被调谐的空间相关长度λ。临界性的自组织性质源于极限λ ∞ +∞吸引非线性反馈动力学的事实。它适用于已知的自组织临界系统，如“沙堆”模型，以及一个简单的动力学概括的渗流模型。使用这种反馈机制，它是可能的，在原则上转换标准的“不稳定”的临界相变到自组织的临界动力学，从而大大增加了模型的数量提出SOC。这些想法被说明的二维伊辛模型和各种“雪崩”指数的值表示在静态和动态伊辛临界指数。
According to Kadanoff, self-organized criticality (SOC) implies the operation of a feedback mechanism that ensures a steady state in which the system is marginally stable against a disturbance. Here, we extend this idea and propose a picture according to which SOC relies on a non-linear feedback of the order parameter on the control parameter(s), the amplitude of this feedback being tuned by the spatial correlation length ξ. The self-organized nature of the criticality stems from the fact that the limit ξ↦+∞ is attracting the non-linear feedback dynamics. It is applied to known self-organized critical systems such as “sandpile” models as well as to a simple dynamical generalization of the percolation model. Using this feedback mechanism, it is possible in principle to convert standard “unstable” critical phase transitions into self-organized critical dynamics, thereby enlarging considerably the number of models presenting SOC. These ideas are illustrated on the 2D Ising model and the values of the various “avalanche” exponents are expressed in terms of the static and dynamic Ising critical exponents.