Fragmentation of a sheet by propagating, branching and merging cracks

Dhar, Deepak (2015) Fragmentation of a sheet by propagating, branching and merging cracks Journal of Physics A: Mathematical and Theoretical, 48 (17). Article ID 175001. ISSN 1751-8113

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Official URL: http://iopscience.iop.org/article/10.1088/1751-811...

Related URL: http://dx.doi.org/10.1088/1751-8113/48/17/175001

Abstract

We consider a model of the fragmentation of a sheet by cracks that move with a velocity in a preferred direction but which undergo random transverse displacements as they move. There is a non-zero probability of crack-splitting and the split cracks move independently. If two cracks meet, they merge, and move as a single crack. In the steady state, there is non-zero density of cracks and the sheet left behind by the moving cracks is broken into a large number of fragments of different sizes. The evolution operator for this model reduces to the Hamiltonian of a quantum XY spin chain, which is exactly integrable. This allows us to determine the steady state and to also determine the distribution of the sizes of the fragments.

Item Type:Article
Source:Copyright of this article belongs to Institute of Physics.
ID Code:112296
Deposited On:31 Jan 2018 04:29
Last Modified:31 Jan 2018 04:29

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