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Self-referential order

Aste, T; Butler, P; Di Matteo, T; (2013) Self-referential order. PHILOSOPHICAL MAGAZINE , 93 (31-33) 3983 - 3992. 10.1080/14786435.2013.835495. Green open access

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Abstract

We introduce the concept of self-referential order which provides a way to quantify structural organization in non-crystalline materials. The key idea consists in the observation that, in a disordered system, where there is no ideal, reference, template structure, each sub-portion of the whole structure can be taken as reference for the rest and the system can be described in terms of its parts in a self-referential way. Some parts carry larger information about the rest of the structure and they are identified as motifs. We discuss how this method can efficiently reduce the amount of information required to describe a complex disordered structure by encoding it in a set of motifs and matching rules. We propose an information-theoretic approach to define a self-referential-order-parameter and we show that, by means of entropic measures, such a parameter can be quantified explicitly. A proof of concept application to equal disk packing is presented and discussed.

Type: Article
Title: Self-referential order
Open access status: An open access version is available from UCL Discovery
DOI: 10.1080/14786435.2013.835495
Publisher version: http://dx.doi.org/10.1080/14786435.2013.835495
Additional information: © 2013 The Author(s). Published by Taylor & Francis This is an Open Access article distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0/, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The moral rights of the named author(s) have been asserted.
Keywords: self-referential order, disordered structure, information theory, order, structural encoding
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/1395681
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