爆裂噪声系统和其他复杂系统中的点现自相似性
Point-occurrence self-similarity in crackling-noise systems and in other complex systems
摘要：
最近发现，一些显示噼啪声噪声的系统也表现出显着的行为，关于连续事件的时间发生与它们的大小：满足作为最小尺寸的函数的等待时间的概率分布的标度律，信号在这些系统上的存在时间大小的自相似性。这种特性也存在于一些无裂纹系统中。在这里，标度律的不寻常的字符说明了简单的显着的更新过程，建立的定义没有相关性。然而，具有有限平均等待时间的过程一般不满足标度律，并且在非常高的尺寸限制下倾向于泊松过程，而没有有限平均值的过程倾向于另一类分布，其特征在于双幂律等待时间密度。这在某种程度上让人想起了广义中心极限定理。具有短程相关性的模型无法摆脱这些极限分布的吸引力。在这些属性的建模开放的问题进行了讨论。
英文摘要：
It has been recently found that a number of systems displaying crackling noise also show a remarkable behavior regarding the temporal occurrence of successive events versus their size: a scaling law for the probability distributions of waiting times as a function of a minimum size is fulfilled, signaling the existence on those systems of self-similarity in time-size. This property is also present in some non-crackling systems. Here, the uncommon character of the scaling law is illustrated with simple marked renewal processes, built by definition with no correlations. Whereas processes with a finite mean waiting time do not fulfill a scaling law in general and tend towards a Poisson process in the limit of very high sizes, processes without a finite mean tend to another class of distributions, characterized by double power-law waiting-time densities. This is somehow reminiscent of the generalized central limit theorem. A model with short-range correlations is not able to escape from the attraction of those limit distributions. A discussion on open problems in the modeling of these properties is provided.
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。
