Fractal Scaling of Earthquakes

2021 ◽  
pp. 399-405
Author(s):  
Simanchal Padhy ◽  
Vijay P. Dimri
Keyword(s):  
Fractal Scaling

The origin and loss of fractal scaling in simulated soil aggregates

1997 ◽  
Vol 48 (4) ◽  
pp. 643-650 ◽  
Author(s):  
J. W. CRAWFORD ◽  
S. VERRALL ◽  
I. M. YOUNG
Keyword(s):  
Soil Aggregates ◽  
Fractal Scaling

On the theory of the fractal scaling-law elasticity

Meccanica ◽  
2021 ◽  
Author(s):  
Xiao-Jun Yang ◽  
Jian-Gen Liu ◽  
Mahmoud Abdel-Aty
Keyword(s):  
Scaling Law ◽  
Fractal Scaling

Multi-fractal scaling law for split strength of concrete cubes

2016 ◽  
Vol 68 (3) ◽  
pp. 141-150 ◽  
Author(s):  
Ragip Ince ◽  
Mesut Gör ◽  
Kürşat Esat Alyamaç ◽  
Mehmet Esen Eren
Keyword(s):  
Scaling Law ◽  
Fractal Scaling

scholarly journals Evaluation of statistical methods for quantifying fractal scaling in water-quality time series with irregular sampling

2018 ◽  
Vol 22 (2) ◽  
pp. 1175-1192 ◽  
Author(s):  
Qian Zhang ◽  
Ciaran J. Harman ◽  
James W. Kirchner
Keyword(s):  
Water Quality ◽  
Time Series ◽  
Irregular Sampling ◽  
Quality Data ◽  
Sampled Data ◽  
Spectral Slope ◽  
Water Quality Data ◽  
Fractal Scaling ◽  
Wide Range ◽  
Irregularly Sampled Data

Abstract. River water-quality time series often exhibit fractal scaling, which here refers to autocorrelation that decays as a power law over some range of scales. Fractal scaling presents challenges to the identification of deterministic trends because (1) fractal scaling has the potential to lead to false inference about the statistical significance of trends and (2) the abundance of irregularly spaced data in water-quality monitoring networks complicates efforts to quantify fractal scaling. Traditional methods for estimating fractal scaling – in the form of spectral slope (β) or other equivalent scaling parameters (e.g., Hurst exponent) – are generally inapplicable to irregularly sampled data. Here we consider two types of estimation approaches for irregularly sampled data and evaluate their performance using synthetic time series. These time series were generated such that (1) they exhibit a wide range of prescribed fractal scaling behaviors, ranging from white noise (β  =  0) to Brown noise (β  =  2) and (2) their sampling gap intervals mimic the sampling irregularity (as quantified by both the skewness and mean of gap-interval lengths) in real water-quality data. The results suggest that none of the existing methods fully account for the effects of sampling irregularity on β estimation. First, the results illustrate the danger of using interpolation for gap filling when examining autocorrelation, as the interpolation methods consistently underestimate or overestimate β under a wide range of prescribed β values and gap distributions. Second, the widely used Lomb–Scargle spectral method also consistently underestimates β. A previously published modified form, using only the lowest 5 % of the frequencies for spectral slope estimation, has very poor precision, although the overall bias is small. Third, a recent wavelet-based method, coupled with an aliasing filter, generally has the smallest bias and root-mean-squared error among all methods for a wide range of prescribed β values and gap distributions. The aliasing method, however, does not itself account for sampling irregularity, and this introduces some bias in the result. Nonetheless, the wavelet method is recommended for estimating β in irregular time series until improved methods are developed. Finally, all methods' performances depend strongly on the sampling irregularity, highlighting that the accuracy and precision of each method are data specific. Accurately quantifying the strength of fractal scaling in irregular water-quality time series remains an unresolved challenge for the hydrologic community and for other disciplines that must grapple with irregular sampling.

scholarly journals Discriminating brain activity from task-related artifacts in functional MRI: Fractal scaling analysis simulation and application

NeuroImage ◽  
2008 ◽  
Vol 40 (1) ◽  
pp. 197-212 ◽  
Author(s):  
Jae-Min Lee ◽  
Jing Hu ◽  
Jianbo Gao ◽  
Bruce Crosson ◽  
Kyung K. Peck ◽  
...  
Keyword(s):  
Functional Mri ◽  
Brain Activity ◽  
Scaling Analysis ◽  
Fractal Scaling

scholarly journals Fractal scaling of C. elegans behavior is shaped by insulin signaling

2021 ◽  
Author(s):  
Yukinobu Arata ◽  
Itsuki Shiga ◽  
Yusaku Ikeda ◽  
Hiroshi Kimura ◽  
Peter Jurica ◽  
...  
Keyword(s):  
Residence Time ◽  
Insulin Signaling ◽  
Time Distribution ◽  
Animal Species ◽  
Power Law Distribution ◽  
Fractal Scaling ◽  
C Elegans ◽  
Fractal Analyses ◽  
Patients With Diabetes ◽  
Behavioral Activities

Abstract Fractal scaling governs the complex behavior of various animal species and, in humans, can be altered by neurodegenerative diseases and aging1. However, the mechanism underlying fractal scaling remains unknown. Here, we videorecorded C. elegans that had been cultured in a microfluidic device for 3 days and analyzed temporal patterns of C. elegans actions by fractal analyses. The residence-time distribution of C. elegans shared a common feature with those of human and mice2–4. Specifically, the residence-time power-law distribution of the active state changed to an exponential-like decline at a longer time scale, whereas this change did not occur in the inactive state. The exponential-like decline disappeared in starved C. elegans but was restored by culturing animals with glucose. The exponential-like decline similarly disappeared in insulin-signaling daf-2 and daf-16 mutants. Therefore, we conclude that insulin signaling regulates fractal scaling of C. elegans behavior. Our findings indicate that neurosensory modulation of C. elegans behavior by insulin signaling is achieved by regulation of fractal scaling. In humans, diabetes mellitus is associated with depression, bipolar disorder, and anxiety disorder5, which affect daily behavioral activities. We hypothesize that comorbid behavioral defects in patients with diabetes may be attributed to altered fractal scaling of human behavior.

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