复杂系统中的波动缩放:泰勒定律及以后

IF 35 1区 物理与天体物理 Q1 PHYSICS, CONDENSED MATTER Advances in Physics Pub Date : 2007-08-15 DOI:10.1080/00018730801893043
Z. Eisler, I. Bartos, J. Kertész
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引用次数: 274

摘要

复杂系统由许多相互作用的元素组成,这些元素参与了一些动态过程。各种元素的活度往往是不同的,一个元素活度的波动随平均活度单调增长。这种关系通常为“波动≈常数×平均α”的形式,其中指数α主要在[1/ 2,1]范围内。这个幂律已经在很多学科中被观察到,从互联网的人口动态到股票市场,它通常被称为泰勒定律或波动缩放。这篇综述试图通过调查文献,以及通过报告一些新的经验数据和模型计算来显示上述比例关系的一般程度。我们还展示了一些基本原则,这些原则可以作为这种现象的普遍性的基础。接下来是基于随机变量和的平均场框架。在这种情况下,涨落标度的出现等价于一些相应的极限定理。在某些物理系统中,波动缩放与有限尺寸缩放有关。纪念l·r·泰勒(1924-2007)。
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Fluctuation scaling in complex systems: Taylor's law and beyond
Complex systems consist of many interacting elements which participate in some dynamical process. The activity of various elements is often different and the fluctuation in the activity of an element grows monotonically with the average activity. This relationship is often of the form ‘fluctuations ≈ constant × averageα’, where the exponent α is predominantly in the range [1/2, 1]. This power law has been observed in a very wide range of disciplines, ranging from population dynamics through the Internet to the stock market and it is often treated under the names Taylor's law or fluctuation scaling. This review attempts to show how general the above scaling relationship is by surveying the literature, as well as by reporting some new empirical data and model calculations. We also show some basic principles that can underlie the generality of the phenomenon. This is followed by a mean-field framework based on sums of random variables. In this context the emergence of fluctuation scaling is equivalent to some corresponding limit theorems. In certain physical systems fluctuation scaling can be related to finite size scaling. 1Dedicated to the memory of L. R. Taylor (1924–2007).
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来源期刊
Advances in Physics
Advances in Physics 物理-物理:凝聚态物理
CiteScore
67.60
自引率
0.00%
发文量
1
期刊介绍: Advances in Physics publishes authoritative critical reviews by experts on topics of interest and importance to condensed matter physicists. It is intended for motivated readers with a basic knowledge of the journal’s field and aims to draw out the salient points of a reviewed subject from the perspective of the author. The journal''s scope includes condensed matter physics and statistical mechanics: broadly defined to include the overlap with quantum information, cold atoms, soft matter physics and biophysics. Readership: Physicists, materials scientists and physical chemists in universities, industry and research institutes.
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