Nonlinear scaling fields and corrections to scaling near criticality

1983 ◽  
Vol 27 (7) ◽  
pp. 4394-4400 ◽  
Author(s):  
Amnon Aharony ◽  
Michael E. Fisher
Keyword(s):  
Corrections To Scaling ◽  
Scaling Fields

scholarly journals NEW EVIDENCE OF DISCRETE SCALE INVARIANCE IN THE ENERGY DISSIPATION OF THREE-DIMENSIONAL TURBULENCE: CORRELATION APPROACH AND DIRECT SPECTRAL DETECTION

2003 ◽  
Vol 14 (04) ◽  
pp. 459-470 ◽  
Author(s):  
WEI-XING ZHOU ◽  
DIDIER SORNETTE ◽  
VLADILEN PISARENKO
Keyword(s):  
Energy Dissipation ◽  
Three Dimensional ◽  
Energy Dissipation Rate ◽  
Corrections To Scaling ◽  
Developed Turbulence ◽  
Pairwise Correlations ◽  
Spectral Detection ◽  
Simple Variant ◽  
High Reynolds ◽  
New Evidence

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.

Characterizing Fractal and Hierarchical Morphologies Beyond the Fractal Dimension

1994 ◽  
Vol 367 ◽  
Author(s):  
Raphael Blumenfeld ◽  
Robin C. Ball
Keyword(s):  
Asymptotic Behavior ◽  
Fractal Dimension ◽  
Finite Size ◽  
Size Analysis ◽  
Corrections To Scaling ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited ◽  
Markovian Processes ◽  
Branching Patterns ◽  
Admissible Solutions

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.

Calculation of subcritical exponents for corrections to scaling

1974 ◽  
Vol 9 (6) ◽  
pp. 2579-2581 ◽  
Author(s):  
Jack Swift ◽  
Morgan K. Grover
Keyword(s):  
Corrections To Scaling
Sign in / Sign up

Export Citation Format

Share Document