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.

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.

Physical properties of Saturn's rings

1984 ◽  
Vol 75 ◽  
pp. 211-217 ◽  
Author(s):  
Jeffrey N. Cuzzi
Keyword(s):  
Particle Size ◽  
Radio Occultation ◽  
Particle Density ◽  
Bulk Material ◽  
Small Particles ◽  
Water Ice ◽  
Saturn’S Rings ◽  
Saturn's Rings ◽  
Classical Ring ◽  
Sharp Cutoff

A review is given of important features of the rings, touching only lightly on aspects covered by other speakers (Spokes, E ring). This extended abstract will only convey the high points of the talk.Most of the material in Saturn's rings is concentrated in the B ring, with a lesser amount in the A ring and only small amounts in the C ring and Cassini Division. There is a very different character to these classical ring regions; the C and Cassini particles are darker and more neutral in color; (Smith et al. 1981, 1982). The A and B regions contain nearly all of the “small” particles, from microns to millimeters. Overall, however, the particles are fairly well characterized by Voyager radio occultation results as roughly following an r-3powerlaw between about 1 cm and a few meters (Tyler et al. 1982, Marouf et al. 1982). A fairly sharp cutoff in the size distribution is seen at radii varying with location from about 1 to about 5 meters. The material of the ring particles is probably mostly water ice (see e.g., Pollack 1975) but the redness of the rings requires the presence of minor constitutents. Combinations of ground-based radar and radio emission observations (Pollack 1975, Cuzzi and Pollack 1978; Pettengill, this issue) strongly indicate that the non-icy component comprises a small fraction of the total bulk material. In fact, mass densities derived from density waves (e.g. Holberg et al. 1982) and CRAND measurements (Cooper et al. 1982) combined with Voyager particle size measurements indicate a particle density more like that of snow or frost than that of pure ice.

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.

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.

Voyager UVS observations of Saturn's rings and the ring atmosphere

1984 ◽  
Vol 75 ◽  
pp. 263
Author(s):  
J.B. Holbelg
Keyword(s):  
Reflectance Spectrum ◽  
Neutral Hydrogen ◽  
Hydrogen Atmosphere ◽  
Electrostatic Discharges ◽  
Water Ice ◽  
Upper Limits ◽  
Saturn’S Rings ◽  
Far Ultraviolet ◽  
Ionic States ◽  
Saturn's Rings

During the Voyager 1 and 2 Saturn encounters the Voyager ultraviolet spectrometers (UVS) made numerous observations of Saturn's rings in the extreme and far ultraviolet. HI Lyman a (1216 Å) observations of the rings from a number of different aspects are used to define the extent and density of the neutral hydrogen “atmosphere” associated with the rings. Voyager 2 observations of the 520 to 1700 Å spectrum of the rings (~20 Å resolution) are used to derive the albedo of particles in the B ring at these wavelengths. These albedo measurements are compared with the laboratory reflectance spectrum of water ice longward of 1200 Å. The significance of the lack of ring reflectance in the Voyager 1 UVS data is also discussed. Finally, UVS spectra of the rings obtained in Saturn's shadow are used to establish upper limits on the presence of any emission from the neutral and ionic states of oxygen possibly associated with the Saturn electrostatic discharges (SED) discovered by the Voyager Planetary Radio Astronomy experiment.

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 Size distribution of function-based human gene sets and the split–merge model

2016 ◽  
Vol 3 (8) ◽  
pp. 160275 ◽  
Author(s):  
Wentian Li ◽  
Oscar Fontanelli ◽  
Pedro Miramontes
Keyword(s):  
Size Distribution ◽  
Power Law ◽  
Common Property ◽  
Target Genes ◽  
Human Gene ◽  
Beta Function ◽  
Gene Families ◽  
Rank Function ◽  
Power Law Distribution ◽  
Gene Sets

The sizes of paralogues—gene families produced by ancestral duplication—are known to follow a power-law distribution. We examine the size distribution of gene sets or gene families where genes are grouped by a similar function or share a common property. The size distribution of Human Gene Nomenclature Committee (HGNC) gene sets deviate from the power-law, and can be fitted much better by a beta rank function. We propose a simple mechanism to break a power-law size distribution by a combination of splitting and merging operations. The largest gene sets are split into two to account for the subfunctional categories, and a small proportion of other gene sets are merged into larger sets as new common themes might be realized. These operations are not uncommon for a curator of gene sets. A simulation shows that iteration of these operations changes the size distribution of Ensembl paralogues and could lead to a distribution fitted by a rank beta function. We further illustrate application of beta rank function by the example of distribution of transcription factors and drug target genes among HGNC gene families.

Spatial Distribution of Tourism Activities: A Polya Urn Process Model of Rank-Size Distribution

2019 ◽  
Vol 59 (2) ◽  
pp. 231-246 ◽  
Author(s):  
Pong Lung Lau ◽  
Tay T. R. Koo ◽  
Cheng-Lung Wu
Keyword(s):  
Size Distribution ◽  
Power Law ◽  
Process Model ◽  
Word Of Mouth ◽  
Preferential Attachment ◽  
Power Law Distribution ◽  
Habit Persistence ◽  
Pólya Urn ◽  
Polya Urn ◽  
Attachment Process

The power law is considered one of the most enduring regularities in human geography. This article aims to develop an understanding of the circumstances that may result in the power law distribution in the geography of tourism activities. The finite Polya urn process is adopted as a device to model the preferential attachment process in the flow of tourists. The model generates a rank-size distribution of tourism regions along with intuitively appealing parameters. Empirically examined using two independent sets of Australian inbound and outbound tourism data, results show that the rank-size distribution emerging from the finite Polya urn process is a superior fit to the conventional power law curve. This rank-size distribution (termed the Polya urn process model of visitor distribution) is compatible with tourist behaviors such as habit persistence and word-of-mouth effects, and can be adopted by tourism modelers to predict and efficiently summarize the spatiality of tourism.

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