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Non-uniform breakage-mechanism branching processes and degradation of long-chain polymers

Published online by Cambridge University Press:  14 July 2016

William H. Olson
William H. Olson*
Affiliation:
University of Tennessee and Oak Ridge National Laboratory, Tennessee
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Abstract

We consider the problem of number and weight distributions for breakage-mechanism branching processes whose break distributions are general. We derive a recursive relation between the expected empirical distribution after (n + 1) breaks and after n breaks, making use of length-biased sampling. Using this relation and the strong law of large numbers, we derive integro-differential equations for the asymptotic expected empirical distribution and its associated weight distribution. The mean of the asymptotic number distribution is derived using the integro-differential equation. We then provide approximate solutions to these equations and the moments of these approximations. Finally we apply these results to the case where the break distribution is a symmetric beta distribution.

Keywords

MARKOV PROCESSBRANCHING PROCESSPOPULATION PROCESSBREAKAGE-MECHANISMDEGRADATIONPOLYMERLENGTH-BIASED SAMPLINGEMPIRICAL DISTRIBUTIONASYMPTOTIC EMPIRICAL DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 1 , March 1977 , pp. 1 - 13
Copyright
Copyright © Applied Probability Trust 1977 

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