# The nonlinear fragmentation equation

Source: [The nonlinear fragmentation equation](<https://www.sota2.com/research/paper/68fa20d57a2b558e29333945>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-23T23:10:32.577Z

Authors: M. H. Ernst, I. Pagonabarraga

Published: 2007-03-22T08:57:18.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/0703571>)

[PDF](<https://arxiv.org/pdf/cond-mat/0703571.pdf>)