Mathematical Aspects of Cotton Fiber Length Distribution under Various Breakage Models

Abstract

Mathematical models of cotton fiber length distribution under various breakage models are discussed. Theoretical analyses are given, including the demonstration of certain factors, capable of measurement. which afford the possibility for numerical con firmation of the respective models. For example, the model for random fiber breakage independent of length shows that where μ F and μ G are the means and γ F and γ G are the absolute second moments about the origin of the parent and daughter populations, respectively. In addition, mathematical models, somewhat more complicated, are given when breakage is proportional to length and for the case where the fibers are held and then subjected to breakage.