A Stochastic Differential Equation Model for Cotton Fiber Breakage

摘要

A stochastic differential equation model is derived for cotton fibers that are experiencing breakage. The model provides greater understanding of the fiber breakage phenomenon and the origination of different fiber-length distributions. In the stochastic model, the fibers are grouped by length. In this manner, the cotton fiber distribution can be considered as a population distribution. An Ito stochastic differential equation model is derived by carefully considering the population process and breakage possibilities over a short time interval. Comparisons between the stochastic model and Monte Carlo calculations indicate that a stochastic differential equation can accurately model fiber-length distributions. In addition, the stochastic model generalizes classic deterministic integro-differential equation models for fiber breakage.