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Long-range correlation: Difference between revisions
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These issues can be understood in the framework of [[Self-Organised Criticality]]. | These issues can be understood in the framework of [[Self-Organised Criticality]]. | ||
The mathematical modelling of such systems is based on the [[Continuous Time Random Walk]] and the Generalized Master Equation. | The mathematical modelling of such systems is based on the [[Continuous Time Random Walk]] and the Generalized Master Equation. | ||
<ref> | <ref>R. Sánchez, B.A. Carreras, and B.Ph. van Milligen, ''Fluid limit of nonintegrable continuous-time random walks in terms of fractional differential equations'', [[doi:10.1103/PhysRevE.71.011111|Phys. Rev. E '''71''' (2005) 011111]]</ref> | ||
=== Experimental determination === | === Experimental determination === | ||
It can be shown that determining the long-range behaviour of the correlation function directly from γ<sub>XY</sub> is not a good idea, due to its sensitivity to noise.<ref> | It can be shown that determining the long-range behaviour of the correlation function directly from γ<sub>XY</sub> is not a good idea, due to its sensitivity to noise.<ref>B.A. Carreras, D.E. Newman, B.Ph. van Milligen, and C. Hidalgo, ''Long-range time dependence in the cross-correlation function'', [[doi:10.1063/1.873192|Phys. Plasmas '''6''' (1999) 485]]</ref> | ||
Rather, techniques to determine the [[:Wikipedia:Hurst exponent|Hurst exponent]], such as the [[:Wikipedia:Rescaled range|Rescaled Range]]<ref> | Rather, techniques to determine the [[:Wikipedia:Hurst exponent|Hurst exponent]], such as the [[:Wikipedia:Rescaled range|Rescaled Range]]<ref>B.A. Carreras, B. van Milligen, M.A. Pedrosa, et al., ''Long-Range Time Correlations in Plasma Edge Turbulence'', [[doi:10.1103/PhysRevLett.80.4438|Phys. Rev. Lett. '''80''' (1998) 4438]]</ref><ref>B.A. Carreras, B.Ph. van Milligen, M.A. Pedrosa, et al., ''Experimental evidence of long-range correlations and self-similarity in plasma fluctuations'', [[doi:10.1063/1.873490|Phys. Plasmas 6 (1999) 1885]]</ref> or Structure Functions<ref>M. Gilmore, C.X. Yu, T.L. Rhodes, and W.A. Peebles, ''Investigation of rescaled range analysis, the Hurst exponent, and long-time correlations in plasma turbulence'', [[doi:10.1063/1.1459707|Phys. Plasmas '''9''' (2002) 1312]]</ref> should be used to determine long-range correlations in data series. | ||
In practice, long-range correlations may have various origins, and proper techniques are required to distinguish between those. | In practice, long-range correlations may have various origins, and proper techniques are required to distinguish between those. | ||