Elastic lines on splayed columnar defects studied numerically

Petäjä, Viljo; Sarjala, Matti; Alava, Mikko J.; Rieger, Heiko

doi:10.1103/physrevb.73.094517

Cited by 3 publications

(1 citation statement)

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“…These structures can result from some global optimization problem that has connections with graph theory. For example, Dijkstra's shortest path algorithm [1,2] can be used to find the lowest energy path of a vortex line in a disordered superconductor [3,4], and these paths are self-affine. Excitations in a disordered XY model in two dimensions [5,6], domain walls in spin glasses [7], and boundaries between drainage basins [8] are examples of physical objects with fractal dimension that are found by global optimization.…”

Section: Introduction To the Problemmentioning

confidence: 99%

Minimal spanning trees at the percolation threshold: A numerical calculation

Sweeney

Middleton²

2013

Phys. Rev. E

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The fractal dimension of minimal spanning trees on percolation clusters is estimated for dimensions d up to d=5. A robust analysis technique is developed for correlated data, as seen in such trees. This should be a robust method suitable for analyzing a wide array of randomly generated fractal structures. The trees analyzed using these techniques are built using a combination of Prim's and Kruskal's algorithms for finding minimal spanning trees. This combination reduces memory usage and allows for simulation of larger systems than would otherwise be possible. The path length fractal dimension d_{s} of MSTs on critical percolation clusters is found to be compatible with the predictions of the perturbation expansion developed by T. S. Jackson and N. Read [Phys. Rev. E 81, 021131 (2010)].

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