Cluster growth poised on the edge of break-up: Size distributions with small exponent power-laws

2008 ◽  
Vol 387 (11) ◽  
pp. 2504-2510 ◽  
Author(s):  
I.T. Koponen ◽  
K.A. Riekki
Keyword(s):  
Power Laws ◽  
Cluster Growth ◽  
Size Distributions ◽  
Break Up

scholarly journals Power laws, demography and entrepreneurship in selected South African regions

2018 ◽  
Vol 114 (5/6) ◽  
Author(s):  
Daan Toerien
Keyword(s):  
South Africa ◽  
Economic Development ◽  
South African ◽  
Local Economic Development ◽  
Power Laws ◽  
Development Planning ◽  
Size Distributions ◽  
Skewed Distributions ◽  
Enterprise Growth ◽  
Different Parts

Statistically significant Pareto-like log-log rank-size distributions were recorded for population and enterprise agglomeration in the towns of three different regions of South Africa, and are indicative of skewed distributions of population and enterprise numbers in regional towns. There were no distinct differences between groups of towns of regions from different parts of the country. However, the regional agglomerations differed from those of groups of towns randomly selected from a database. Regions, therefore, appear to have some uniqueness regarding such agglomerations. The identification of Zipf-like links between population and enterprise growth in regional towns still does not fully explain why some towns grow large and others stay small and there is a need to further explore these issues. The extreme skewness in population and enterprise numbers of different towns’ distributions should, however, be considered in local economic development planning and execution.

Dynamic Break-Up and Drop Formation From a Liquid Jet Spun From a Rotating Orifice: Part I — Experimental

2003 ◽  
Author(s):  
David Wong ◽  
Mark Simmons ◽  
Andrew King ◽  
Stephen Decent ◽  
Emilian Parau
Keyword(s):  
Dynamic Viscosity ◽  
Rotation Rate ◽  
Nonlinear Effects ◽  
Size Distributions ◽  
Strong Function ◽  
Highly Nonlinear ◽  
Experimental Parameters ◽  
Break Up ◽  
Drop Size Distributions ◽  
Viscous Solutions

The dynamics of the break-up of curved jets produced by the prilling process were studied. The effects of liquid dynamic viscosity, rotation rate and orifice size upon the surface tension driven instabilities were investigated. Liquid dynamic viscosity was varied by using mixtures of glycerol and water which gave dynamic viscosities ranging from 0.001 to 0.081 Pa.s at 20°C. Over the range of experimental parameters studied, four different break-up modes were identified. For each mode, considerable differences in the break-up mechanism and in the drop size distributions produced were observed. Dimensional analysis has shown that the break-up modes can be predicted from a plot of Reynolds number against Weber number. The break-up mode observed is a strong function of viscosity and highly nonlinear effects were observed with the most viscous solutions used. The effect of rotation rate on the jet break-up length was inconclusive from the experiment.

scholarly journals Glitch time series and size distributions in eight prolific pulsars

2019 ◽  
Vol 630 ◽  
pp. A115 ◽  
Author(s):  
J. R. Fuentes ◽  
C. M. Espinoza ◽  
A. Reisenegger
Keyword(s):  
Waiting Time ◽  
Power Laws ◽  
Strong Positive Correlation ◽  
Crab Pulsar ◽  
Size Distributions ◽  
Normal Functions ◽  
Vela Pulsar ◽  
The Times ◽  
Log Normal ◽  
Trigger Mechanisms

Context. Glitches are rare spin-up events that punctuate the smooth slow-down of the rotation of pulsars. For the Vela pulsar and PSR J0537−6910, their large glitch sizes and the times between consecutive events have clear preferred scales (Gaussian distributions), contrary to the handful of other pulsars with enough glitches for such a study. Moreover, PSR J0537−6910 is the only pulsar that shows a strong positive correlation between the size of each glitch and the waiting time until the following one. Aims. We attempt to understand this behaviour through a detailed study of the distributions and correlations of glitch properties for the eight pulsars with at least ten detected glitches. Methods. We modelled the distributions of glitch sizes and of the times between consecutive glitches for the eight pulsars with at least ten detected events. We also looked for possible correlations between these parameters and used Monte Carlo simulations to explore two hypotheses that could explain why the correlation so clearly seen in PSR J0537−6910 is absent in other pulsars. Results. We confirm the above results for Vela and PSR J0537−6910, and verify that the latter is the only pulsar with a strong correlation between glitch size and waiting time to the following glitch. For the remaining six pulsars, the waiting time distributions are best fitted by exponentials, and the size distributions are best fitted by either power laws, exponentials, or log-normal functions. Some pulsars in the sample yield significant Pearson and Spearman coefficients (rp and rs) for the aforementioned correlation, confirming previous results. Moreover, for all except the Crab pulsar, both coefficients are positive. For each coefficient taken separately, the probability of this happening is 1/16. Our simulations show that the weaker correlations in pulsars other than PSR J0537−6910 cannot be due to missing glitches that are too small to be detected. We also tested the hypothesis that each pulsar may have two kinds of glitches, namely large, correlated ones and small, uncorrelated ones. The best results are obtained for the Vela pulsar, which exhibits a correlation with rp = 0.68 (p-value = 0.003) if its two smallest glitches are removed. The other pulsars are harder to accommodate under this hypothesis, but their glitches are not consistent with a pure uncorrelated population either. We also find that all pulsars in our sample, except the Crab pulsar, are consistent with the previously found constant ratio between glitch activity and spin-down rate, ν̇g/|ν̇| = 0.010±0.001, even though some of them have not shown any large glitches. Conclusions. To explain these results, we speculate except in the case of the Crab pulsar, that all glitches draw their angular momentum from a common reservoir (presumably a neutron superfluid component containing ≈1% of the star’s moment of inertia). However, two different trigger mechanisms could be active, a more deterministic one for larger glitches and a more random one for smaller ones.

scholarly journals The variability of tidewater-glacier calving: Origin of event-size and interval distributions

2014 ◽  
Vol 60 (222) ◽  
pp. 622-634 ◽  
Author(s):  
Anne Chapuis ◽  
Tom Tetzlaff
Keyword(s):  
Size Distribution ◽  
Power Laws ◽  
Size Distributions ◽  
Event Data ◽  
Model Data ◽  
Small Perturbations ◽  
Tidewater Glaciers ◽  
Glacier Terminus ◽  
Wide Range ◽  
Parameter Measuring

AbstractCalving activity at the termini of tidewater glaciers produces a wide range of iceberg sizes at irregular intervals. We present calving-event data obtained from continuous observations of the termini of two tidewater glaciers on Svalbard, and show that the distributions of event sizes and inter-event intervals can be reproduced by a simple calving model, focusing on the mutual interplay between calving and the destabilization of the glacier terminus. The event-size distributions of both the field and the model data extend over several orders of magnitude and resemble power laws. The distributions of inter-event intervals are broad, but have a less pronounced tail. In the model, the width of the size distribution increases with the calving susceptibility of the glacier terminus, a parameter measuring the effect of calving on the stress in the local neighborhood of the calving region. Inter-event interval distributions, in contrast, are insensitive to the calving susceptibility. Above a critical susceptibility, small perturbations of the glacier result in ongoing self-sustained calving activity. The model suggests that the shape of the event-size distribution of a glacier is informative about its proximity to this transition point. Observations of rapid glacier retreats can be explained by supercritical self-sustained calving.

scholarly journals The effect of reported high-velocity small raindrops on inferred drop size distributions and derived power laws

2010 ◽  
Vol 10 (4) ◽  
pp. 9121-9151 ◽  
Author(s):  
H. Leijnse ◽  
R. Uijlenhoet
Keyword(s):  
High Velocity ◽  
Drop Size ◽  
Doppler Radar ◽  
Probability Distributions ◽  
Power Laws ◽  
Size Distributions ◽  
Optical Links ◽  
Gamma Distributions ◽  
Raindrop Size Distribution ◽  
Drop Size Distributions

Abstract. It has recently been shown that at high rainfall intensities, small raindrops may fall with much larger velocities than would be expected from their diameters. These were argued to be fragments of recently broken-up larger drops. In this paper we quantify the effect of this phenomenon on raindrop size distribution measurements from a Joss-Waldvogel disdrometer, a 2-D Video Distrometer, and a vertically-pointing Doppler radar. Probability distributions of fall velocities have been parameterized, where the parameters are functions of both rainfall intensity and drop size. These parameterizations have been used to correct Joss-Waldvogel disdrometer measurements for this phenomenon. The effect of these corrections on fitted scaled drop size distributions are apparent but not major. Fitted gamma distributions for three different types of rainfall have been used to simulate drop size measurements. The effect of the high-velocity small drops is shown to be minor. Especially for the purpose of remote sensing of rainfall using radar, microwave links, or optical links, the errors caused by using the slightly different retrieval relations will be masked completely by other error sources.

scholarly journals Experimental evidence for inherent Lévy search behaviour in foraging animals

2015 ◽  
Vol 282 (1807) ◽  
pp. 20150424 ◽  
Author(s):  
Andrea Kölzsch ◽  
Adriana Alzate ◽  
Frederic Bartumeus ◽  
Monique de Jager ◽  
Ellen J. Weerman ◽  
...  
Keyword(s):  
Experimental Evidence ◽  
Power Laws ◽  
Size Distributions ◽  
New Paradigm ◽  
Landscape Complexity ◽  
Search Behaviour ◽  
Multi Scale ◽  
Behavioural Strategy ◽  
Lévy Walks ◽  
Set Up

Recently, Lévy walks have been put forward as a new paradigm for animal search and many cases have been made for its presence in nature. However, it remains debated whether Lévy walks are an inherent behavioural strategy or emerge from the animal reacting to its habitat. Here, we demonstrate signatures of Lévy behaviour in the search movement of mud snails ( Hydrobia ulvae ) based on a novel, direct assessment of movement properties in an experimental set-up using different food distributions. Our experimental data uncovered clusters of small movement steps alternating with long moves independent of food encounter and landscape complexity. Moreover, size distributions of these clusters followed truncated power laws. These two findings are characteristic signatures of mechanisms underlying inherent Lévy-like movement. Thus, our study provides clear experimental evidence that such multi-scale movement is an inherent behaviour rather than resulting from the animal interacting with its environment.

SCALING PARAMETERS FOR GOLD AND COPPER CLUSTER GROWTH ON AN ALUMINA SINGLE CRYSTAL SURFACE

2001 ◽  
Vol 08 (06) ◽  
pp. 693-697 ◽  
Author(s):  
C. WINKLER ◽  
A. CAREW ◽  
R. RAVAL ◽  
J. LEDIEU ◽  
R. McGRATH
Keyword(s):  
Single Crystal ◽  
Crystal Surface ◽  
Scaling Law ◽  
Cluster Growth ◽  
Size Distributions ◽  
Single Crystal Surface ◽  
Particle Size Distributions ◽  
Metal Vapour ◽  
Scaling Parameters ◽  
Log Scaling

The growth of gold and copper nanoparticles on a γ- Al 2 O 3 single crystal surface has been investigated using LEED and STM. The clusters were grown on the sample by exposing the substrate to a metal vapour. The particle size distributions are determined as a function of the metal vapour dosage and, furthermore, the Volmer–Weber growth mechanism and a semi-log scaling law are deduced from these data.

scholarly journals The effect of reported high-velocity small raindrops on inferred drop size distributions and derived power laws

2010 ◽  
Vol 10 (14) ◽  
pp. 6807-6818 ◽  
Author(s):  
H. Leijnse ◽  
R. Uijlenhoet
Keyword(s):  
High Velocity ◽  
Drop Size ◽  
Doppler Radar ◽  
Probability Distributions ◽  
Power Laws ◽  
Size Distributions ◽  
Optical Links ◽  
Gamma Distributions ◽  
Raindrop Size Distribution ◽  
Drop Size Distributions

Abstract. It has recently been shown that at high rainfall intensities, small raindrops may fall with much larger velocities than would be expected from their diameters. These were argued to be fragments of recently broken-up larger drops. In this paper we quantify the effect of this phenomenon on raindrop size distribution measurements from a Joss-Waldvogel disdrometer, a 2-D Video Distrometer, and a vertically-pointing Doppler radar. Probability distributions of fall velocities have been parameterized, where the parameters are functions of both rainfall intensity and drop size. These parameterizations have been used to correct Joss-Waldvogel disdrometer measurements for this phenomenon. The effect of these corrections on fitted scaled drop size distributions are apparent but not major. Fitted gamma distributions for three different types of rainfall have been used to simulate drop size measurements. The effect of the high-velocity small drops is shown to be minor. Especially for the purpose of remote sensing of rainfall using radar, microwave links, or optical links, the errors caused by using the slightly different retrieval relations will be masked completely by other error sources.

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