Moments of Particle Size Distributions under Sequential Breakage with Applications to Species Abundance.

1981 ◽  
Author(s):  
Andrew F. Siegel ◽  
George Sugihara
Keyword(s):  
Particle Size ◽  
Species Abundance ◽  
Size Distributions ◽  
Particle Size Distributions

Moments of particle size distributions under sequential breakage with applications to species abundance

1983 ◽  
Vol 20 (01) ◽  
pp. 158-164 ◽  
Author(s):  
Andrew F. Siegel ◽  
George Sugihara
Keyword(s):  
Particle Size ◽  
Species Abundance ◽  
Binary Trees ◽  
Particle Sizes ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Underlying Distribution ◽  
Path Lengths ◽  
Stick Model ◽  
Random Binary Trees

The sequential broken stick model has appeared in numerous contexts, including biology, physics, engineering and geology. Kolmogorov showed that under appropriate conditions, sequential breakage processes often yield a lognormal distribution of particle sizes. Of particular interest to ecologists is the observed variance of the logarithms of the sizes, which characterizes the evenness of an assemblage of species. We derive the first two moments for the logarithms of the sizes in terms of the underlying distribution used to determine the successive breakages. In particular, for a process yielding n pieces, the expected sample variance behaves asymptotically as log(n). These results also yield a new identity for moments of path lengths in random binary trees.

Moments of particle size distributions under sequential breakage with applications to species abundance

1983 ◽  
Vol 20 (1) ◽  
pp. 158-164 ◽  
Author(s):  
Andrew F. Siegel ◽  
George Sugihara
Keyword(s):  
Particle Size ◽  
Species Abundance ◽  
Binary Trees ◽  
Particle Sizes ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Underlying Distribution ◽  
Path Lengths ◽  
Stick Model ◽  
Random Binary Trees

The sequential broken stick model has appeared in numerous contexts, including biology, physics, engineering and geology. Kolmogorov showed that under appropriate conditions, sequential breakage processes often yield a lognormal distribution of particle sizes. Of particular interest to ecologists is the observed variance of the logarithms of the sizes, which characterizes the evenness of an assemblage of species. We derive the first two moments for the logarithms of the sizes in terms of the underlying distribution used to determine the successive breakages. In particular, for a process yielding n pieces, the expected sample variance behaves asymptotically as log(n). These results also yield a new identity for moments of path lengths in random binary trees.

254. A Comparison of the Particle Size Distributions for Aerosols Generated During Wet Grinding and Dry Deburring of Beryllium

1999 ◽  
Author(s):  
K.K. Ellis ◽  
R. Buchan ◽  
M. Hoover ◽  
J. Martyny ◽  
B. Bucher-Bartleson ◽  
...  
Keyword(s):  
Particle Size ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Wet Grinding

Measurements of Mineral Particle Size Distributions by a Buoyancy Weighing Method

2010 ◽  
Vol 126 (10/11) ◽  
pp. 577-582 ◽  
Author(s):  
Katsuhiko FURUKAWA ◽  
Yuichi OHIRA ◽  
Eiji OBATA ◽  
Yutaka YOSHIDA
Keyword(s):  
Particle Size ◽  
Mineral Particle ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Weighing Method

Certain Problems with the Application of Stochastic Diffusion Processes for the Description of Chemical Engineering Phenomena. Diffusional Change of Solid Particle Size

1996 ◽  
Vol 61 (4) ◽  
pp. 536-563
Author(s):  
Vladimír Kudrna ◽  
Pavel Hasal
Keyword(s):  
Particle Size ◽  
Solid Particle ◽  
Chemical Engineering ◽  
Diffusion Processes ◽  
Granular Systems ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Diffusion Term ◽  
Population Balances ◽  
And Diffusion

To the description of changes of solid particle size in population, the application was proposed of stochastic differential equations and diffusion equations adequate to them making it possible to express the development of these populations in time. Particular relations were derived for some particle size distributions in flow and batch equipments. It was shown that it is expedient to complement the population balances often used for the description of granular systems by a "diffusion" term making it possible to express the effects of random influences in the growth process and/or particle diminution.

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