Fragmentation of fractal random structures

Breakup phenomena are ubiquitous in nature and technology. They span a vast range of time and length scales, including polymer degradation as well as collision induced fragmentation of asteroids. In geology, fragmentation results in the distribution of grain sizes observed in soils; fluids break up into droplets and fluid structures such as eddies undergo fragmentation. On the subatomic scale, excited atomic nuclei break up into fragments. Practical applications, such as mineral processing, ask for optimizations according to technological requirements and efficiency considerations. More generally, a wide range of structures from transport systems to social connections are described by complex networks, whose degree of resilience against fragmentation is a recent subject of intense scrutiny. In this talk I will give an introduction to fragmentation phenomena and show how they can be described in mean-field theory using a rate equation. Going beyond mean-field theory, I will analyze the fragmentation behavior of random clusters on the lattice. Using a combination of analytical and numerical techniques allows for a complete understanding of the critical properties of this system. Dynamical fragmentation with a size cut-off leads to broad distributions of fragment sizes, where the fragment size distribution encodes characteristic fingerprints of the fragmented objects.

References
[1] E. M. Elci, M.Weigel, and N. G. Fytas, Fragmentation of random fractal structures, Phys. Rev. Lett. 114, 115701 (2015).
[2] E. M. Elci, M. Weigel, and N. G. Fytas, Bridges in the random-cluster model, Nucl. Phys. B 903, 19 (2016).