Cut-out sets, fractal voids and cosmic structure
| dc.creator | Gaite, Jose | |
| dc.date | 2006-03-21 | |
| dc.date.accessioned | 2026-07-07T11:57:21Z | |
| dc.date.available | 2026-07-07T11:57:21Z | |
| dc.description | "Cut-out sets" are fractals that can be obtained by removing a sequence of disjoint regions from an initial region of d-dimensional euclidean space. Conversely, a description of some fractals in terms of their void complementary set is possible. The essential property of a sequence of fractal voids is that their sizes decrease as a power law, that is, they follow Zipf's law. We prove the relation between the box dimension of the fractal set (in d <= 3) and the exponent of the Zipf law for convex voids; namely, if the Zipf law exponent e is such that 1 < e < d/(d-1) and, in addition, we forbid the appearance of degenerate void shapes, we prove that the corresponding cut-out set has box dimension d/e (d-1 < d/e < d). We explore the application of this result to the large scale distribution of matter in cosmology, in connection with ``cosmic foam'' models. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/astro-ph/0603572 | |
| dc.identifier | http://arxiv.org/abs/astro-ph/0603572 | |
| dc.identifier | PhysicaD223:248-255,2006 | |
| dc.identifier | doi:10.1016/j.physd.2006.09.021 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/205850 | |
| dc.subject | Astrophysics | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Mathematical Physics | |
| dc.title | Cut-out sets, fractal voids and cosmic structure | |
| dc.type | text |