POWER-LAW DISTRIBUTION OF RIVER BASIN SIZES

Fractals ◽  
1993 ◽  
Vol 01 (03) ◽  
pp. 521-528 ◽  
Author(s):  
HIDEKI TAKAYASU
Keyword(s):  
Size Distribution ◽  
River Basin ◽  
Power Law ◽  
Point Of View ◽  
The Self ◽  
General Point ◽  
Size Distributions ◽  
Power Law Distribution ◽  
River Models ◽  
River Pattern

River models are reviewed with emphasis on the power-law nature of basin size distributions. From a general point of view, the whole river pattern on a surface can be regarded as a kind of tiling by random self-affine branches. Applying the idea of stable distributions, we show that the self-affinity and tiling condition naturally derive the power-law basin size distribution.

scholarly journals On reconciling disparate studies of the sea-ice floe size distribution

Elem Sci Anth ◽  
2018 ◽  
Vol 6 ◽  
Author(s):  
Harry L. Stern ◽  
Axel J. Schweiger ◽  
Jinlun Zhang ◽  
Michael Steele
Keyword(s):  
Sea Ice ◽  
Size Distribution ◽  
Power Law ◽  
Goodness Of Fit ◽  
Accurate Method ◽  
Spatial And Temporal Variability ◽  
Size Distributions ◽  
Power Law Model ◽  
Power Law Distribution ◽  
Goodness Of Fit Test

The size distribution of sea-ice floes is an important descriptor of the sea-ice cover. Most studies report that floe sizes follow a power-law distribution over some size range, but the power-law exponents often differ substantially. Other studies report two power-law regimes over different size ranges, or more complicated behavior. We review the construction of power-law floe size distributions and compare the results of previous studies. Differences between studies may be due to spatial and temporal variability of the floe size distribution, sampling variability, inadequacy of the power-law model, or flaws in the mathematical analysis. For a power-law model, the most accurate method for determining the exponent from data is Maximum Likelihood Estimation; least-squares methods based on log-log plots of the data yield biased estimates. After calculating the power-law exponent from data, a goodness-of-fit test should be applied to determine whether or not the power-law model actually describes the distribution of the data. These analysis principles have been described in the literature but have not generally been applied to floe size distributions. Numerical ice-ocean models are beginning to simulate the floe size distribution, which should give further insight into the interpretation of observational studies.

Power Law Distributions and the Size Distribution of Strikes

2017 ◽  
Vol 48 (3) ◽  
pp. 561-587 ◽  
Author(s):  
Michele Campolieti
Keyword(s):  
Size Distribution ◽  
Power Law ◽  
Model Fit ◽  
Power Law Distribution ◽  
Policy Perspective ◽  
Methodological Research ◽  
Canadian Data ◽  
Alternative Measures ◽  
Power Law Distributions ◽  
Research And Policy

Using Canadian data from 1976 to 2014, I study the size distribution of strikes with three alternative measures of strike size: the number of workers on strike, strike duration in calendar days, and the number of person calendar days lost to a strike. I use a maximum likelihood framework that provides a way to estimate distributions, evaluate model fit, and also test against alternative distributions. I consider a few theories that can create power law distributions in strike size, such as the joint costs model that posits strike size is inversely proportional to dispute costs. I find that the power law distribution fits the data for the number of lost person calendar days relatively well and is also more appropriate than the lognormal distribution. I also discuss the implications of my findings from a methodological, research, and policy perspective.

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 Characterizing the movement patterns of minibus taxis in Kampala's paratransit system

2020 ◽  
Author(s):  
Innocent Ndibatya ◽  
MJ Booysen
Keyword(s):  
Power Law ◽  
Search Strategies ◽  
The Self ◽  
Power Law Distribution ◽  
Floating Car Data ◽  
Movement Characteristics ◽  
System P ◽  
Heavy Tailed ◽  
Self Organizing

Urban travelers in Africa depend on minibus taxis for their daily social and business commuting. This paratransit system is loosely regulated, self-organizing, and evolves organically in response to demand. Our study used floating car data to analyze and describe the movement characteristics of the minibus taxis in Kampala, Uganda. We made three intriguing ?findings. Firstly, in searching for, picking up and transporting passengers, minibus taxi trajectories followed a heavy-tailed power-law distribution similar to a Levy walk. Secondly, their routes gradually evolved. Thirdly, the extraordinary winding (expressed in terms of tortuosity) of the paths suggested the extreme determination of the drivers' search for passengers. Overall, we found that the passenger search strategies used by the taxis were signi?ficantly inefficient. Our fi?ndings could help city planners to build on the self-organizing characteristics of the minibus taxi system, and improve the mobility of travelers, by optimizing routes and the distribution of public amenities.

scholarly journals Transition from Self-Organized Criticality into Self-Organization during Sliding Si3N4 Balls against Nanocrystalline Diamond Films

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1055
Author(s):  
Bogatov ◽  
Podgursky ◽  
Vagiström ◽  
Yashin ◽  
Shaikh ◽  
...  
Keyword(s):  
Friction Force ◽  
Power Law ◽  
Early Stage ◽  
Nanocrystalline Diamond ◽  
The Self ◽  
Self Organization ◽  
Power Law Distribution ◽  
Reciprocating Sliding ◽  
Self Organized ◽  
Self Organized Criticality

The paper investigates the variation of friction force (Fx) during reciprocating sliding tests on nanocrystalline diamond (NCD) films. The analysis of the friction behavior during the run-in period is the focus of the study. The NCD films were grown using microwave plasma-enhanced chemical vapor deposition (MW-PECVD) on single-crystalline diamond SCD(110) substrates. Reciprocating sliding tests were conducted under 500 and 2000 g of normal load using Si3N4 balls as a counter body. The friction force permanently varies during the test, namely Fx value can locally increase or decrease in each cycle of sliding. The distribution of friction force drops (dFx) was extracted from the experimental data using a specially developed program. The analysis revealed a power-law distribution f-µ of dFx for the early stage of the run-in with the exponent value (µ) in the range from 0.6 to 2.9. In addition, the frequency power spectrum of Fx time series follows power-law distribution f-α with α value in the range of 1.0–2.0, with the highest values (1.6–2.0) for the initial stage of the run-in. No power-law distribution of dFx was found for the later stage of the run-in and the steady-state periods of sliding with the exception for periods where a relatively extended decrease of coefficient of friction (COF) was observed. The asperity interlocking leads to the stick-slip like sliding at the early stage of the run-in. This tribological behavior can be related to the self-organized criticality (SOC). The emergence of dissipative structures at the later stages of the run-in, namely the formation of ripples, carbonaceous tribolayer, etc., can be associated with the self-organization (SO).

scholarly journals Size distribution of particles in Saturn’s rings from aggregation and fragmentation

2015 ◽  
Vol 112 (31) ◽  
pp. 9536-9541 ◽  
Author(s):  
Nikolai Brilliantov ◽  
P. L. Krapivsky ◽  
Anna Bodrova ◽  
Frank Spahn ◽  
Hisao Hayakawa ◽  
...  
Keyword(s):  
Size Distribution ◽  
Power Law ◽  
Momentum Conservation ◽  
Power Law Distribution ◽  
Water Ice ◽  
Flat Disk ◽  
Cutoff Radius ◽  
Saturn’S Rings ◽  
Saturn's Rings ◽  
Interparticle Collisions

Saturn’s rings consist of a huge number of water ice particles, with a tiny addition of rocky material. They form a flat disk, as the result of an interplay of angular momentum conservation and the steady loss of energy in dissipative interparticle collisions. For particles in the size range from a few centimeters to a few meters, a power-law distribution of radii, ∼r−q with q≈3, has been inferred; for larger sizes, the distribution has a steep cutoff. It has been suggested that this size distribution may arise from a balance between aggregation and fragmentation of ring particles, yet neither the power-law dependence nor the upper size cutoff have been established on theoretical grounds. Here we propose a model for the particle size distribution that quantitatively explains the observations. In accordance with data, our model predicts the exponent q to be constrained to the interval 2.75≤q≤3.5. Also an exponential cutoff for larger particle sizes establishes naturally with the cutoff radius being set by the relative frequency of aggregating and disruptive collisions. This cutoff is much smaller than the typical scale of microstructures seen in Saturn’s rings.

The Size Distribution of Particles Released by Garments During Helmke Drum Tests

2001 ◽  
Vol 44 (4) ◽  
pp. 24-27 ◽  
Author(s):  
David Ensor ◽  
Jenni Elion ◽  
Jan Eudy
Keyword(s):  
Particle Size ◽  
Size Distribution ◽  
Power Law ◽  
High Performance ◽  
Fine Particles ◽  
Particle Diameter ◽  
Test Method ◽  
Power Law Distribution ◽  
Controlled Environments ◽  
Size Distribution Of Particles

The Helmke Drum test method to measure particles shed from garments was developed twenty years ago. It consists of a tumbling drum containing the garment under test. A probe connected to an optical particle counter is used to transport the sample from the drum. Dilution air is drawn into the drum from the surrounding cleanroom. The optical particle counters at the time of development were limited in resolution to 0.5 μm diameter. This particle size requirement is still in the current version of IEST-RP-CC003.2, Garment Systems Considerations for Cleanrooms and Other Controlled Environments. A question was raised in the current IEST Contamination Control Working Group 003, "Garment System Considerations for Cleanrooms and Other Controlled Environments," as to whether the method could be extended to smaller particle diameters. The method would benefit by including measurements of smaller particle diameters for two reasons: the higher particle counts expected for sub-0.5 μm particles might improve the statistics of the method; and there is a growing need to consider contamination by ultra-fine particles during the manufacture of high performance products. We hypothesized that the size distribution of particles released by garments follows a power law similar to that for cleanroom classes. The form of the power law distribution is N(d) = Ad(-B), where N(d) is the cumulative concentration greater to or equal to d, d is the particle diameter, and A and B are statistically determined coefficients. The size distributions from a number of Helmke Drum tests were analyzed and were found to be highly correlated to the power law equation. However, the slopes appeared to vary depending on the type of garment tested. These results support including guidance with respect to particle size in the Helmke Drum test section in the upcoming revision of IEST-RP-CC003.2.

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 Raindrop size distributions and radar reflectivity–rain rate relationships for radar hydrology

2001 ◽  
Vol 5 (4) ◽  
pp. 615-628 ◽  
Author(s):  
R. Uijlenhoet
Keyword(s):  
Size Distribution ◽  
Power Law ◽  
Rain Rate ◽  
Radar Reflectivity ◽  
Size Distributions ◽  
Raindrop Size Distribution ◽  
Special Cases ◽  
Fundamental Reason ◽  
Radar Measurements ◽  
Raindrop Size

Abstract. The conversion of the radar reflectivity factor Z(mm6m-3) to rain rate R(mm h-1 ) is a crucial step in the hydrological application of weather radar measurements. It has been common practice for over 50 years now to take for this conversion a simple power law relationship between Z and R. It is the purpose of this paper to explain that the fundamental reason for the existence of such power law relationships is the fact that Z and R are related to each other via the raindrop size distribution. To this end, the concept of the raindrop size distribution is first explained. Then, it is demonstrated that there exist two fundamentally different forms of the raindrop size distribution, one corresponding to raindrops present in a volume of air and another corresponding to those arriving at a surface. It is explained how Z and R are defined in terms of both these forms. Using the classical exponential raindrop size distribution as an example, it is demonstrated (1) that the definitions of Z and R naturally lead to power law Z–R relationships, and (2) how the coefficients of such relationships are related to the parameters of the raindrop size distribution. Numerous empirical Z–R relationships are analysed to demonstrate that there exist systematic differences in the coefficients of these relationships and the corresponding parameters of the (exponential) raindrop size distribution between different types of rainfall. Finally, six consistent Z–R relationships are derived, based upon different assumptions regarding the rain rate dependence of the parameters of the (exponential) raindrop size distribution. An appendix shows that these relationships are in fact special cases of a general Z–R relationship that follows from a recently proposed scaling framework for describing raindrop size distributions and their properties. Keywords: radar hydrology, raindrop size distribution, radar reflectivity–rain rate relationship

BUSINESS CYCLE FLUCTUATIONS AND FIRMS' SIZE DISTRIBUTION DYNAMICS

2004 ◽  
Vol 07 (02) ◽  
pp. 223-240 ◽  
Author(s):  
DOMENICO DELLI GATTI ◽  
CORRADO DI GUILMI ◽  
EDOARDO GAFFEO ◽  
GIANFRANCO GIULIONI ◽  
MAURO GALLEGATI ◽  
...  
Keyword(s):  
Size Distribution ◽  
Power Law ◽  
Power Law Distribution ◽  
Distribution Dynamics ◽  
Size Change ◽  
Empirical Distributions ◽  
Straight Line ◽  
Distribution Shifts ◽  
Time Invariant ◽  
Power Law Distributions

Power law behavior is an emerging property of many economic models. In this paper we emphasize the fact that power law distributions are persistent but not time invariant. In fact, the scale and shape of the firms' size distribution fluctuate over time. In particular, on a log–log space, both the intercept and the slope of the power law distribution of firms' size change over the cycle: during expansions (recessions) the straight line representing the distribution shifts up and becomes less steep (steeper). We show that the empirical distributions generated by simulations of the model presented in Ref. 11 mimic real empirical distributions remarkably well.

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