scholarly journals Power Law Size Distributions in Geoscience Revisited

2019 ◽  
Author(s):  
Álvaro Corral ◽  
Álvaro González
Keyword(s):  
Power Law ◽  
Size Distributions

Undersampling power-law size distributions: effect on the assessment of extreme natural hazards

2014 ◽  
Vol 72 (2) ◽  
pp. 565-595 ◽  
Author(s):  
Eric L. Geist ◽  
Tom Parsons
Keyword(s):  
Natural Hazards ◽  
Power Law ◽  
Size Distributions

Country Dependence on Company Size Distributions and a Numerical Model Based on Competition and Cooperation

Fractals ◽  
1998 ◽  
Vol 06 (01) ◽  
pp. 67-79 ◽  
Author(s):  
Hideki Takayasu ◽  
Kenji Okuyama
Keyword(s):  
Numerical Model ◽  
Power Law ◽  
Growth Rates ◽  
Company Size ◽  
Size Distributions ◽  
Competitive Growth ◽  
Small Companies ◽  
Power Law Distribution ◽  
Protection Effect ◽  
Competition And Cooperation

By analyzing international company data we find that company size distributions are not universal but clearly depend on country. In each country, the size distributions for different categories of business are quite similar. In order to understand the country dependence we introduce a numerical model of company size which is based on two effects: stochastic competitive growth by capital exchange, and deterministic protection of small companies by equi-partition of taxed wealth. A power law distribution is realized when the protection effect is negligible. The model is also consistent with the empirical laws for company's growth rates.

scholarly journals Semi-automated open water iceberg detection from Landsat applied to Disko Bay, West Greenland

2019 ◽  
Vol 65 (251) ◽  
pp. 468-480 ◽  
Author(s):  
JESSICA SCHEICK ◽  
ELLYN M. ENDERLIN ◽  
GORDON HAMILTON
Keyword(s):  
Machine Learning ◽  
Time Series ◽  
Power Law ◽  
Coastal Waters ◽  
Landsat Imagery ◽  
Open Water ◽  
Size Distributions ◽  
Negative Power ◽  
West Greenland ◽  
Cloud Mask

ABSTRACTChanges in Greenland's marine-terminating outlet glaciers have led to changes in the flux of icebergs into Greenland's coastal waters, yet icebergs remain a relatively understudied component of the ice-ocean system. We developed a simple iceberg delineation algorithm for Landsat imagery. A machine learning-based cloud mask incorporated into the algorithm enables us to extract iceberg size distributions from open water even in partially cloudy scenes. We applied the algorithm to the Landsat archive covering Disko Bay, West Greenland, to derive a time series of iceberg size distributions from 2000–02 and 2013–15. The time series captures a change in iceberg size distributions, which we interpret as a result of changes in the calving regime of the parent glacier, Sermeq Kujalleq (Jakobshavn Isbræ). The change in calving style associated with the disintegration and disappearance of Sermeq Kujalleq's floating ice tongue resulted in the production of more small icebergs. The increased number of small icebergs resulted in increasingly negative power law slopes fit to iceberg size distributions in Disko Bay, suggesting that iceberg size distribution time series provide useful insights into changes in calving dynamics.

scholarly journals Investigating the Diurnal Evolution of the Cloud Size Distribution of Continental Cumulus Convection Using Multiday LES

2019 ◽  
Vol 76 (3) ◽  
pp. 729-747 ◽  
Author(s):  
Thirza W. van Laar ◽  
Vera Schemann ◽  
Roel A. J. Neggers
Keyword(s):  
Power Law ◽  
Cloud Cover ◽  
Large Scale ◽  
Correlation Coefficients ◽  
Scale Model ◽  
Cloud Base ◽  
Size Distributions ◽  
Total Cloud Cover ◽  
Surface Precipitation ◽  
Shallow Cumulus

Abstract The diurnal dependence of cumulus cloud size distributions over land is investigated by means of an ensemble of large-eddy simulations (LESs). A total of 146 days of transient continental shallow cumulus are selected and simulated, reflecting a low midday maximum of total cloud cover, weak synoptic forcing, and the absence of strong surface precipitation. The LESs are semi-idealized, forced by large-scale model output but using an interactive surface. This multitude of cases covers a large parameter space of environmental conditions, which is necessary for identifying any diurnal dependencies in cloud size distributions. A power-law exponential function is found to describe the shape of the cloud size distributions for these days well, with the exponential component capturing the departure from power-law scaling at the larger cloud sizes. To assess what controls the largest cloud size in the distribution, the correlation coefficients between the maximum cloud size and various candidate variables reflecting the boundary layer state are computed. The strongest correlation is found between total cloud cover and maximum cloud size. Studying the size density of the cloud area revealed that larger clouds contribute most to a larger total cloud cover, and not the smaller ones. Besides cloud cover, cloud-base and cloud-top height are also found to weakly correlate with the maximum cloud size, suggesting that the classic idea of deeper boundary layers accommodating larger convective thermals still holds for shallow cumulus. Sensitivity tests reveal that the results are only minimally affected by the representation of microphysics and the output resolution.

Relations between the scaling exponents, entropies, and energies of fracture networks

2013 ◽  
Vol 184 (4-5) ◽  
pp. 373-382 ◽  
Author(s):  
Agust Guđmundsson ◽  
Nahid Mohajeri
Keyword(s):  
Power Law ◽  
Scaling Laws ◽  
Plate Boundary ◽  
Normal Faults ◽  
Scaling Exponent ◽  
Size Distributions ◽  
Fracture Networks ◽  
Scaling Exponents ◽  
The Holocene ◽  
Arithmetic Average

Abstract Fracture networks commonly show power-law length distributions. Thermodynamic principles form the basis for understanding fracture initiation and growth, but have not been easily related to the power-law size distributions. Here we present the power-law scaling exponents and the calculated entropies of fracture networks from the Holocene part of the plate boundary in Iceland. The total number of tension fractures and normal faults used in these calculations is 565 and they range in length by five orders of magnitude. Each network can be divided into populations based on ‘breaks’ (abrupt changes) in the scaling exponents. The breaks, we suggest, are related to the comparatively long and deep fractures changing from tension fractures into normal faults and penetrating the contacts between the Holocene lava flows and the underlying and mechanically different Quaternary rocks. The results show a strong linear correlation (r = 0.84) between the population scaling exponents and entropies. The correlation is partly explained by the entropy (and the scaling exponent) varying positively with the arithmetic average and the length range (the difference between the longest and the shortest fracture) of the populations in each network. We show that similar scaling laws apply to other lineaments, such as streets. We propose that the power-law size distributions of fractures are a consequence of energy requirements for fracture growth.

Comparing Three Environmental Particle Size Distributions: Power Law (FED-STD-209D), Lognormal, Approximate Lognormal (MIL-STD-1246B)

1991 ◽  
Vol 34 (1) ◽  
pp. 21-24
Author(s):  
Douglas Cooper
Keyword(s):  
Particle Size ◽  
Power Law ◽  
Lognormal Distribution ◽  
Cumulative Distribution ◽  
Size Distributions ◽  
Power Law Distribution ◽  
Particle Size Distributions ◽  
Contamination Control ◽  
Control Programs ◽  
Power Law Distributions

Particle size strongly influences particle behavior. To summarize the distribution of particle sizes, a distribution function can be used. The characteristics of the particle size distributions chosen are important for two specification documents currently under revision: (1) FED-STD-209D, concerning air-cleanliness in manufacturing, which uses cumulative particle size distributions that are linear when plotted on log-log axes; these are power law distributions. (2) MIL-STD-1246B, "Product Cleanliness Levels and Contamination Control Programs," primarily concerning surface cleanliness, which uses cumulative particle size distributions that are linear when plotted as the logarithm of the cumulative distribution versus the square of the logarithm of the particle size, log2x, A third distribution, the lognormal, is commonly found in aerosol science, especially where there is a single particle source. The distributions are compared and discussed. The FED-STD-209D power law distribution can approximate a lognormal distribution over only a limited size range. The MIL-STD-1246B distribution is an asymptotic approximation to the lognormal distribution.

scholarly journals Cluster size distributions: signatures of self–organization in spatial ecologies

2002 ◽  
Vol 357 (1421) ◽  
pp. 657-666 ◽  
Author(s):  
Mercedes Pascual ◽  
Manojit Roy ◽  
Frédéric Guichard ◽  
Glenn Flierl
Keyword(s):  
Power Law ◽  
Cluster Size ◽  
Environmental Variability ◽  
Size Distributions ◽  
Ecological Interactions ◽  
Positive Slope ◽  
Predator Prey ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Recovery Dynamics

Three different lattice–based models for antagonistic ecological interactions, both nonlinear and stochastic, exhibit similar power–law scalings in the geometry of clusters. Specifically, cluster size distributions and perimeter–area curves follow power–law scalings. In the coexistence regime, these patterns are robust: their exponents, and therefore the associated Korcak exponent characterizing patchiness, depend only weakly on the parameters of the systems. These distributions, in particular the values of their exponents, are close to those reported in the literature for systems associated with self–organized criticality (SOC) such as forest–fire models; however, the typical assumptions of SOC need not apply. Our results demonstrate that power–law scalings in cluster size distributions are not restricted to systems for antagonistic interactions in which a clear separation of time–scales holds. The patterns are characteristic of processes of growth and inhibition in space, such as those in predator–prey and disturbance–recovery dynamics. Inversions of these patterns, that is, scalings with a positive slope as described for plankton distributions, would therefore require spatial forcing by environmental variability.

FROM LOGNORMAL DISTRIBUTION TO POWER LAW: A NEW CLASSIFICATION OF THE SIZE DISTRIBUTIONS

2006 ◽  
Vol 17 (10) ◽  
pp. 1429-1436 ◽  
Author(s):  
LUCIEN BENGUIGUI ◽  
EFRAT BLUMENFELD-LIEBERTHAL
Keyword(s):  
Normal Distribution ◽  
Power Law ◽  
Lognormal Distribution ◽  
Size Distributions ◽  
New Classification ◽  
Multiplicative Process ◽  
Random Multiplicative Process ◽  
Log Normal ◽  
Log Normal Distribution

We propose a new classification of the size distributions of entities based on an exponent α defined from the shape of the log–log Rank Size plot. From an inspection of a large number of cases in different fields, one finds three possibilities: α = 1 giving a power law, α > 1 (parabola like curve) and 0 < α < 1 (analogous to a log normal distribution). A fourth possibility that can be defined when α < 0 was never observed. We present a modified version of models based on a random multiplicative process and an introduction of new entities during the growth. We recover all three kinds of distributions and show that the type of a distribution is conditioned by the rate of the introduction of new entities.

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