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Planar Line Processes for Void and Density Statistics in Thin Stochastic Fibre Networks

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Abstract

Using results for the distribution of perimeters of random polygons arising from random lines in a plane, we obtain new analytic approximations to the distributions of areas and local line densities for random polygons and compute various limiting properties of random polygons. Using simulation, we show that the lengths of adjacent sides of polygons generated by random line processes in the plane are correlated with ρ=0.616±0.001.

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Authors and Affiliations

  1. School of Mathematics, University of Manchester, Manchester, M60 1QD, UK

    C. T. J. Dodson

  2. School of Materials, University of Manchester, Manchester, M60 1QD, UK

    W. W. Sampson

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  1. C. T. J. Dodson
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  2. W. W. Sampson
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Correspondence to W. W. Sampson.

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Dodson, C.T.J., Sampson, W.W. Planar Line Processes for Void and Density Statistics in Thin Stochastic Fibre Networks. J Stat Phys 129, 311–322 (2007). https://doi.org/10.1007/s10955-007-9379-9

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  • DOI: https://doi.org/10.1007/s10955-007-9379-9

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