The Fragmentation Kernel in Multinary/Multicomponent Fragmentation

TL;DR

This paper extends the concept of the fragmentation kernel from binary to multinary/multicomponent fragmentation, providing new mathematical expressions for special cases of fragmentation processes.

Contribution

It introduces a generalized fragmentation kernel framework for multinary/multicomponent fragmentation and derives specific expressions for certain cases.

Findings

Extended the fragmentation kernel to multinary/multicomponent cases

Derived expressions for special cases of fragmentation

Provided a mathematical foundation for complex fragmentation processes

Abstract

The fragmentation equation is commonly expressed in terms of two functions, the rate of fragmentation and the mean number of fragments. In the case of binary fragmentation an alternative description is possible based on the fragmentation kernel, a function from which the rate of fragmentation and the mean distribution of fragments can be obtained. We extend the fragmentation kernel to multinary/multicomponent fragmentation and derive expressions for certain special cases of random and non random fragmentation.