Theoretical Analysis on the Spectral Densities of Random Slivers and Its Applications. Part 2

概要

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In this paper, we calculate some examples of the spectral densities of random slivers by using the fundamental formula proposed in Part 1 of this series, and induce the distribution functions of variance σ2 with respect to wave length. When fibre length is constant, the distribution function X(p) is given by the following equation : X(p)=a2N⁄π2L(1−cos 2πL⁄p) where p : wave length a : denier of single fibre N : average number of fibres in the cross-section L : fibre length Where the fibre length is uniformly distributed from zero to the maximum value, the X (p) is given as follows: X(p)=a2N⁄π2L(1−p⁄4πL sin 4πL⁄p) where L : average f fibre length which is equal to half of the maximum length.
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