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Normalized entropy of rank distribution： a novel measure of heterogeneity of complex networks

Chinese Physics B 2007年第6期16卷 1576-1580页

作者：吴俊谭跃进邓宏钟朱大智 Natl Univ Def Technol Coll Informat Syst & Management Changsha 410073 Peoples R China

Many unique properties of complex networks result from heterogeneity. The measure and analysis of heterogeneity are important and desirable to the research of the properties and functions of complex networks. In this paper, the rank distribution is proposed as a new statistic feature of complex networks. Based on the rank distribution, a novel measure of the heterogeneity called a normalized entropy of rank distribution （NERD） is proposed. The NERD accords with the normal meaning of heterogeneity within the context of complex networks compared with conventional measures. The heterogeneity of scale-free networks is studied using the NERD. It is shown that scale-free networks become more heterogeneous as the scaling exponent decreases and the NERD of scale-free networks is independent of the number of vertices, which indicates that the NERD is a suitable and effective measure of heterogeneity for networks with different sizes.

关键词： complex networks heterogeneity rank distribution scale-free networks

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Assessment of the Elastic-Wave Well Treatment in Oil-Bearing Clastic and Carbonate Reservoirs

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Fluid Dynamics & Materials Processing 2023年第6期19卷 1495-1505页

作者： Vladimir Poplygin Chengzhi Qi Mikhail Guzev Evgenii Kozhevnikov Artem Kunitskikh Evgenii Riabokon Mikhail Turbakov Perm National Research Polytechnic University Perm614990Russian Beijing University of Civil Engineering and Architecture Beijing100049China Institute for Applied Mathematics FEB RAS Vladivostok690041Russian

A set of techniques for well treatment aimed to enhance oil recovery are considered in the present *** are based on the application of elastic waves of various types(dilation-wave,vibro-wave,or other acoustically induced effects).In such a context,a new technique is proposed to predict the effectiveness of the elastic-wave well treatment using the rank distribution according to Zipf’s *** is revealed that,when the results of elastic wave well treatments are analyzed,groups of wells exploiting various geological deposits can differ in terms of their slope coefficients and free *** the slope coefficient increases,the average increase in the well oil production rate(after the well treatment)becomes *** equation is obtained accordingly for estimating the slope coefficient in the Zipf’s equation from the frequency of the elastic *** obtained results demonstrate the applicability of the Zipf’s law in the analysis of the technological efficiency of elastic-wave well treatment methods.

关键词： Elastic wave well treatment oil well rate Zipf’s law rank distribution slope coefficient

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