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Long-range correlation: Difference between revisions
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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>[[doi:10.1063/1.873192|B.A. Carreras, D.E. Newman, B.Ph. van Milligen, and C. Hidalgo, ''Long-range time dependence in the cross-correlation function'', Phys. Plasmas '''6''' (1999) 485]]</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>[[doi:10.1063/1.873192|B.A. Carreras, D.E. Newman, B.Ph. van Milligen, and C. Hidalgo, ''Long-range time dependence in the cross-correlation function'', 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>[[doi:10.1103/PhysRevLett.80.4438|B.A. Carreras, B. van Milligen, M.A. Pedrosa, et al., ''Long-Range Time Correlations in Plasma Edge Turbulence'', Phys. Rev. Lett. '''80''' (1998) 4438]]</ref><ref>[[doi:10.1063/1.873490|B.A. Carreras, B.Ph. van Milligen, M.A. Pedrosa, et al., ''Experimental evidence of long-range correlations and self-similarity in plasma fluctuations'', Phys. Plasmas 6 (1999) 1885]]</ref> or Structure Functions<ref>[[doi:10.1063/1.1459707|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'', Phys. Plasmas '''9''' (2002) 1312]]</ref> should be used to determine long-range correlations in data series. | Rather, techniques to determine the [[:Wikipedia:Hurst exponent|Hurst exponent]], such as the [[:Wikipedia:Rescaled range|Rescaled Range]]<ref>[[doi:10.1103/PhysRevLett.80.4438|B.A. Carreras, B. van Milligen, M.A. Pedrosa, et al., ''Long-Range Time Correlations in Plasma Edge Turbulence'', Phys. Rev. Lett. '''80''' (1998) 4438]]</ref><ref>[[doi:10.1063/1.873490|B.A. Carreras, B.Ph. van Milligen, M.A. Pedrosa, et al., ''Experimental evidence of long-range correlations and self-similarity in plasma fluctuations'', Phys. Plasmas 6 (1999) 1885]]</ref> or Structure Functions<ref>[[doi:10.1063/1.1459707|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'', 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. | |||
<ref>B.Ph. van Milligen et al, ''Parallel and perpendicular turbulence correlation length in the TJ-II Stellarator'', [[doi:10.1088/0029-5515/53/9/093025|Nucl. Fusion '''53''' (2013) 093025]]</ref> | |||
This is particularly important when trying to separate Zonal Flow contributions to the long-range correlation from other effects. | |||
<ref>B.Ph. van Milligen, E. Sánchez, A. Alonso, M.A. Pedrosa, C. Hidalgo, A. Martín de Aguilera, A. López Fraguas, ''The use of the Biorthogonal Decomposition for the identification of zonal flows at TJ-II'', [[doi:10.1088/0741-3335/57/2/025005|Plasma Phys. Control. Fusion '''57''', 2 (2015) 025005]]</ref> | |||
== See also == | == See also == | ||