scholarly journals Fractal statistics of brittle fragmentation

2013 ◽  
Vol 7 (24) ◽  
pp. 60-68 ◽  
Author(s):  
M. Davydova ◽  
S. Uvarov
Author(s):  
Natalia Bryksina ◽  
Norman Halden ◽  
Sergio Mejia
Keyword(s):  

2003 ◽  
Vol 17 (22n24) ◽  
pp. 4003-4012 ◽  
Author(s):  
Mogens H. Jensen ◽  
Anders Johansen ◽  
Ingve Simonsen

We consider inverse statistics in turbulence and financial data. By inverse statistics, also sometimes called exit time statistics, we "turn" the variables around such that the fluctuating variable becomes the fixed variable, while the fixed variable becomes fluctuating. In that sense we can probe distinct regimes of the data sets. In the case of turbulence, we obtain a new set of (multi)-scaling exponents which monitor the dissipation regime. In the case of economics, we obtain a distribution of waiting times needed to achieve a predefined level of return. Such a distribution typically goes through a maximum at a time called the optimal investment horizon[Formula: see text], since this defines the most likely waiting time for obtaining a given return ρ. By considering equal positive and negative levels of return, we report on a quantitative gain-loss asymmetry most pronounced for short horizons.


1990 ◽  
Vol 16 (6) ◽  
pp. 1117-1126 ◽  
Author(s):  
G. Sæther ◽  
K. Bendiksen ◽  
J. Müller ◽  
E. Frøland

Author(s):  
Bruce West ◽  
Damien West

AbstractAllometry relations (ARs) in physiology are nearly two hundred years old. In general if X ij is a measure of the size of the i th member of a complex host network from species j and Y ij is a property of a complex subnetwork embedded within the host network an intraspecies AR exists between the two when Y ij = aX ijb. We emphasize that the reductionist models of AR interpret X ij and Y ij as dynamic variables, albeit the ARs themselves are explicitly time independent. On the other hand, the phenomenological models of AR are based on the statistical analysis of data and interpret 〈X i〉 and 〈Y i〉 as averages over an ensemble of individuals to yields the interspecies AR 〈Y i〉 = a〈X i〉b. Modern explanations of AR begin with the application of fractal geometry and fractal statistics to scaling phenomena. The detailed application of fractal geometry to the explanation of intraspecies ARs is a little over a decade old and although well received it has not been universally accepted. An alternate perspective is given by the interspecies AR based on linear regression analysis of fluctuating data sets. We emphasize that the intraspecies and interspecies ARs are not the same and show that the interspecies AR can only be derived from the intraspecies one for a narrow distribution of fluctuations. This condition is not satisfied by metabolic data as is shown separately for aviary and mammal data sets. The empirical distribution of metabolic allometry coefficients is shown herein to be Pareto in form. A number of reductionist arguments conclude that the allometry exponent is universal, however herein we derive a deterministic relation between the allometry exponent and the allometry coefficient using the fractional calculus. The co-variation relation violates the universality assumption. We conclude that the interspecies physiologic AR is entailed by the scaling behavior of the probability density, which is derived using the fractional probability calculus.


Geophysics ◽  
2005 ◽  
Vol 70 (3) ◽  
pp. G59-G67 ◽  
Author(s):  
Alfonso Benavides I. ◽  
Mark E. Everett

Controlled-source electromagnetic-conductivity profiles and maps were obtained on the Brazos Valley, Texas, floodplain to study the fractal statistics of geologic noise and the effects of man-made conductive metal targets. Fourier transform, discrete wavelet transforms, and variogram analyses were used. Targets tend to flatten the power-law power spectrum at small wavenumbers and shift power to higher wavenumbers. Detection and localization of targets can be achieved using wavelet spectrogram techniques. Additionally, variograms from pure background conductivity maps show a power-law trend for all lags, whereas, in the presence of targets, a short power-law trend is followed by a sill corresponding to a loss in spatial correlation. A simple preprocessing step that combines responses from two perpendicular transmitter-receiver orientations enhances the localization of targets and rejects background signals in profiles and 2D apparent-conductivity maps. Finally, a field example shows how the use of wavelet filtering is able to separate target responses from the geologic background.


2000 ◽  
Vol 15 (31) ◽  
pp. 1931-1939 ◽  
Author(s):  
WELLINGTON DA CRUZ ◽  
ROSEVALDO DE OLIVEIRA

We introduce the notion of fractal index associated with the universal class h of particles or quasiparticles, termed fractons which obey specific fractal statistics. A connection between fractons and conformal field theory (CFT)-quasiparticles is established taking into account the central charge c[ν] and the particle-hole duality ν↔1/ν, for integer-value ν of the statistical parameter. In this way, we derive the Fermi velocity in terms of the central charge as [Formula: see text]. The Hausdorff dimension h which labeled the universal classes of particles and the conformal anomaly are therefore related. Following another route, we also established a connection between Rogers dilogarithm function, Farey series of rational numbers and the Hausdorff dimension.


2015 ◽  
Vol 103 ◽  
pp. 205-212 ◽  
Author(s):  
James D. Hogan ◽  
Charles El Mir ◽  
Jeffrey B. Plescia ◽  
K.T. Ramesh

2017 ◽  
Author(s):  
Nicolas Bouhier ◽  
Jean Tournadre ◽  
Frédérique Rémy ◽  
Rozenn Gourves-Cousin

Abstract. The evolution of the thickness and area of two large southern ocean icebergs, having drifted in open water for more than a year, is estimated through the combined analysis of altimeter data and visible satellite images. Most of the iceberg modelling studies uses two main melting formulations that are compared with the observed thickness evolution of our two icebergs, to test their validity in case of large icebergs. The first formulation, based on a fluid dynamics approach, would tend to underestimate basal melt rates, so that using the second one (using a thermodynamic budget consideration) may be more relevant. Fragmentation is, before melting, the major decay process of large icebergs, yet it is a complex and still poorly documented mechanism. A correlation analysis between the observed volume loss of our two icebergs and environmental parameters highlights those most likely to promote fragmentation. Consequently, a bulk model of fragmentation depending on ocean temperature and iceberg velocity is established and is shown to be able to reproduce well the observed volume variations. Finally, the size distribution of the calved pieces is estimated using both altimeter data and visible images and is found to be consistent with previous studies as typical of brittle fragmentation processes. These results are valuable to account for a more realistic representation of the freshwater flux constrained by large icebergs in models.


2016 ◽  
Vol 6 (2) ◽  
pp. 18
Author(s):  
Roselle Jardin Ranario

A recent innovation in the field of statistics is using fractal analysis where data sets are analyzed for anomaly detection, pattern analysis, and root cause analysis. In application of the fractal statistics, this paper examines the incidence of Philippine poverty from 2003 to 2012 based on its fractal dimension in the hope of providing policy makers a different approach in addressing sustained growth among the poor. Poverty is like a moving fractal where patterns simply repeat in various scales and variations.  What are the key implications of fractal poverty for policy and research? How can the fractal poverty provide an analytical foundation to make a pathway out of poverty accessible to Filipinos presently suffering in extreme poverty? The fractal model shows that poverty incidence is dictated by provinces whose poverty incidence are high. This means that if the poverty incidence of the province will be primarily addressed, it will affect the poverty scenario of the Philippines. Policy makers if looking for key indicators why Filipinos have some difficulty escaping poverty may focus on the province with the highest incidence. 


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