Lacunarity exponents. (14th February 2019)

• Record Type: Journal Article
• Authors: Wilkinson, Michael; Pradas, Marc; Huber, Greg; Pumir, Alain
• Is Part Of: Journal of physics. Volume 52:Number 11(2019)
• Publication Date: 2019-02-14
• Subjects: chaos -- fractals -- lacunarity; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ab0349
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: Many physical processes result in very uneven, apparently random, distributions of matter, characterised by fluctuations of the local density varying over orders of magnitude. The density of matter in the sparsest regions can have a power-law distribution, with an exponent that we term the lacunarity exponent. We discuss a mechanism which explains the wide occurrence of these power laws, and give analytical expressions for the exponent in some simple models.