The nonlinear fragmentation equation

TL;DR

This paper investigates the nonlinear fragmentation process driven by particle interactions, develops solutions for the equations, and analyzes conditions leading to shattering or scaling states, providing a comprehensive phase diagram of the phenomena.

Contribution

It introduces a detailed analysis of nonlinear fragmentation equations, including initial and scaling solutions, and establishes criteria for shattering transitions across various models.

Findings

Identification of conditions for shattering transitions.

Construction of initial and scaling solutions.

Development of a phase diagram for model parameters.

Abstract

We study the kinetics of nonlinear irreversible fragmentation. Here fragmentation is induced by interactions/collisions between pairs of particles, and modelled by general classes of interaction kernels, and for several types of breakage models. We construct initial value and scaling solutions of the fragmentation equations, and apply the "non-vanishing mass flux "criterion for the occurrence of shattering transitions. These properties enable us to determine the phase diagram for the occurrence of shattering states and of scaling states in the phase space of model parameters.