Abstract for the talk on 25.10.2016 (16:00 h)Colloquium of the Faculty of Physics and Geosciences
Martin Weigel (Applied Mathematics Research Centre, Coventry University)
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.
 E. M. Elci, M.Weigel, and N. G. Fytas, Fragmentation of random fractal structures, Phys. Rev. Lett. 114, 115701 (2015).
 E. M. Elci, M. Weigel, and N. G. Fytas, Bridges in the random-cluster model, Nucl. Phys. B 903, 19 (2016).