On the lengths of the pieces of a stick broken at random

Holst, Lars

doi:10.1017/s0021900200033738

Cited by 36 publications

(43 citation statements)

References 11 publications

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“…In this paper, the spatial distribution of fiber breaks in a 2-D array of glass fibers is compared with break locations observed from SFFT specimens. In both cases, the break locations in each fiber were found to evolve to a uniform distribution, thereby confirming that the ordered fragment lengths from the repeated fracture process conforms for both SFFT and multi-fiber fragmentation test (MFFT) specimens to a cumulative distribution function (CDF) derived by Whitworth [2][3][4][5]. The array break density was also observed to be less than the break density in isolated fibers, and break locations across array fibers were observed to be highly coordinated and mostly aligned.…”

supporting

confidence: 53%

The fiber break evolution process in a 2-D epoxy/glass multi-fiber array

McCarthy

Kim

Heckert

et al. 2015

Composites Science and Technology

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The mechanical integrity of a structural composite is strongly affected by the strength and toughness of the fiber-matrix interface/interphase [1], with interfacial shear strength (IFSS) being generally accepted as the best quantifying metric. The value of the IFSS is not directly measurable, but it can be approximated by several micromechanics based test methods with the value obtained being dependent on the choice of the model. The most popular of these test methods is the embedded single fiber fragmentation test (SFFT) which provides the experimental data needed to estimate the IFSS: (a) mean fragment length at saturation and (b) fiber strength at the critical fragment length.Because the IFSS is used in unidirectional composite models to predict strength and failure behavior, where the interaction between fibers can be important, the validity of extrapolating from test results based upon the repeated failure of a single isolated fiber has often been questioned. In this paper, the spatial distribution of fiber breaks in a 2-D array of glass fibers is compared with break locations observed from SFFT specimens. In both cases, the break locations in each fiber were found to evolve to a uniform distribution, thereby confirming that the ordered fragment lengths from the repeated fracture process conforms for both SFFT and multi-fiber fragmentation test (MFFT) specimens to a cumulative distribution function (CDF) derived by Whitworth [2][3][4][5]. The array break density was also observed to be less than the break density in isolated fibers, and break locations across array fibers were observed to be highly coordinated and mostly aligned.

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supporting

confidence: 53%

The fiber break evolution process in a 2-D epoxy/glass multi-fiber array

McCarthy

Kim

Heckert

et al. 2015

Composites Science and Technology

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“…For each fitness set we generated a random initial allele-frequency vector,

\overset{true˜}{p} = (p_{1}, p_{2}, \dots, p_{n}),

using the broken stick method (Holst 1980). Since any n -allele polymorphism is also globally stable (Bürger 2000), the system will iterate to this equilibrium should it exist.…”

Section: Methodsmentioning

confidence: 99%

The Selective Maintenance of Allelic Variation Under Generalized Dominance

Spencer

Mitchell

2016

G3 Genes|Genomes|Genetics

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Simple models of viability selection acting on variation at a single diploid locus only maintain multiple alleles for very restricted sets of fitnesses. Most of these models assume that fitnesses are independent, even if the genotypes share alleles. Here, we extend this result to a model with generalized dominance interactions, in which fitnesses are strongly affected by what we call the “primary effects” of the genotype’s component alleles, so that genotypes with shared alleles have correlated fitnesses. Nevertheless, in keeping with previously reported results, we also show that such fitness sets are easily constructed over time if recurrent mutation is occurring simultaneously. We find that such models maintain less variation over time than do (previous) models with independently sampled fitnesses, especially when the effects of genetic drift are taken into account. We also show that there is a weak tendency for greater weighting of primary effects to evolve over time.

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“…In this case the division of the known sales among the known stores could be represented as a stochastic sharing or breakage process, analogous to ecological models in which resources, niches, or John S. Pipkin / 183 space are split among species or individuals (Pielou 1969; Ord, Patil, and Taillie 1980). The broken stick model would be one straightforward way to represent the process (Holst 1980).…”

Section: / Geographic01mentioning

confidence: 99%

A Partitioning Model of Urban Retail Structure

Pipkin¹

1993

Geographical Analysis

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On the lengths of the pieces of a stick broken at random

Cited by 36 publications

References 11 publications

The fiber break evolution process in a 2-D epoxy/glass multi-fiber array

The fiber break evolution process in a 2-D epoxy/glass multi-fiber array

The Selective Maintenance of Allelic Variation Under Generalized Dominance

A Partitioning Model of Urban Retail Structure

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