Title: Logarithmic fractals and hierarchical deposition of debris
Authors: Indekeu, Joseph ×
Fleerackers, Gunther #
Issue Date: 1998
Series Title: Physica. A: Statistical and theoretical physics vol:261 issue:3-4 pages:294-308
Conference: date:Katholieke Univ Leuven, Vaste Stof Fys & Magnetisme Lab, B-3001 Louvain, Belgium
Abstract: We study geometrical objects on the borderline between standard Euclidean forms and fractals. The length (or area) increases with an additive rather than multiplicative constant, upon reducing the ruler length by a fixed rescaling factor. This leads to a logarithmic law instead of the usual power law for fractals. The fractal dimension D-F equals the topological dimension D-T and a fractal amplitude. A(F) is proposed for characterizing the objects. We introduce a model for the random deposition of debris consisting of a hierarchy of fragments with a hyperbolic size distribution (similar to meteors in space) that fall onto a D-dimensional surface (D = 1 or 2). The deposition takes place in air or another Viscous medium so that the fragments hit the surface in order of size, the large ones first. Employing both numerical simulation and analytic solution we verify that the rough landscape after impact is a logarithmic fractal for both D = 1 and 2, and determine the amplitude A(F) as a function of the probabilities P for piling up hills, and Q for digging holes, with P + Q less than or equal to 1. (C) 1998 Elsevier Science B.V. All rights reserved.
ISSN: 0378-4371
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Solid State Physics and Magnetism Section
× corresponding author
# (joint) last author

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