Nonlinear scaling fields and corrections to scaling near criticality

1983 ◽  
Vol 27 (7) ◽  
pp. 4394-4400 ◽  
Author(s):  
Amnon Aharony ◽  
Michael E. Fisher
2003 ◽  
Vol 14 (04) ◽  
pp. 459-470 ◽  
Author(s):  
WEI-XING ZHOU ◽  
DIDIER SORNETTE ◽  
VLADILEN PISARENKO

We extend the analysis of Ref. 16 showing statistically significant log-periodic corrections to scaling in the moments of the energy dissipation rate in experiments at high Reynolds number (≈ 2500) of three-dimensional fully developed turbulence. First, we develop a simple variant of the canonical averaging method using a rephasing scheme between different samples based on pairwise correlations that confirms Zhou and Sornette's previous results. The second analysis uses a simpler local spectral approach and then performs averages over many local spectra. This yields stronger evidence of the existence of underlying log-periodic undulations, with the detection of more than 20 harmonics of a fundamental logarithmic frequency f = 1.434 ± 0.007 corresponding to the preferred scaling ratio γ = 2.008 ± 0.006.


1994 ◽  
Vol 367 ◽  
Author(s):  
Raphael Blumenfeld ◽  
Robin C. Ball

AbstractWe present a novel correlation scheme to characterize the morphology of fractal and hierarchical patterns beyond traditional scaling. The method consists of analysing correlations between more than two-points in logarithmic coordinates. This technique has several advantages: i) It can be used to quantify the currently vague concept of morphology; ii) It allows to distinguish between different signatures of structures with similar fractal dimension but different morphologies already for relatively small systems; iii) The method is sensitive to oscillations in logarithmic coordinates, which are both admissible solutions for renormalization equations and which appear in many branching patterns (e.g., noise-reduced diffusion-limited-aggregation and bronchial structures); iv) The methods yields information on corrections to scaling from the asymptotic behavior, which is very useful in finite size analysis. Markovian processes are calculated exactly and several structures are analyzed by this method to demonstrate its advantages.


1974 ◽  
Vol 9 (6) ◽  
pp. 2579-2581 ◽  
Author(s):  
Jack Swift ◽  
Morgan K. Grover

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