Fragmentation of Fractal Random Structures

Eren Metin Elçi, Martin Weigel, and Nikolaos G. Fytas
Phys. Rev. Lett. 114, 115701 – Published 20 March 2015

Abstract

We analyze the fragmentation behavior of random clusters on the lattice under a process where bonds between neighboring sites are successively broken. Modeling such structures by configurations of a generalized Potts or random-cluster model allows us to discuss a wide range of systems with fractal properties including trees as well as dense clusters. We present exact results for the densities of fragmenting edges and the distribution of fragment sizes for critical clusters in two dimensions. Dynamical fragmentation with a size cutoff leads to broad distributions of fragment sizes. The resulting power laws are shown to encode characteristic fingerprints of the fragmented objects.

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  • Received 7 November 2014

DOI:https://doi.org/10.1103/PhysRevLett.114.115701

© 2015 American Physical Society

Authors & Affiliations

Eren Metin Elçi1,*, Martin Weigel1,2,†, and Nikolaos G. Fytas1,‡

  • 1Applied Mathematics Research Centre, Coventry University, Coventry CV1 5FB, England
  • 2Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 7, D-55099 Mainz, Germany

  • *eren.metin.elci@gmail.com
  • martin.weigel@coventry.ac.uk
  • nikolaos.fytas@coventry.ac.uk

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Vol. 114, Iss. 11 — 20 March 2015

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