Discrete rearranging disordered patterns, part I: Robust statistical tools in two or three dimensions View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2008-04

AUTHORS

F. Graner, B. Dollet, C. Raufaste, P. Marmottant

ABSTRACT

Discrete rearranging patterns include cellular patterns, for instance liquid foams, biological tissues, grains in polycrystals; assemblies of particles such as beads, granular materials, colloids, molecules, atoms; and interconnected networks. Such a pattern can be described as a list of links between neighbouring sites. Performing statistics on the links between neighbouring sites yields average quantities (hereafter "tools") as the result of direct measurements on images. These descriptive tools are flexible and suitable for various problems where quantitative measurements are required, whether in two or in three dimensions. Here, we present a coherent set of robust tools, in three steps. First, we revisit the definitions of three existing tools based on the texture matrix. Second, thanks to their more general definition, we embed these three tools in a self-consistent formalism, which includes three additional ones. Third, we show that the six tools together provide a direct correspondence between a small scale, where they quantify the discrete pattern's local distortion and rearrangements, and a large scale, where they help describe a material as a continuous medium. This enables to formulate elastic, plastic, fluid behaviours in a common, self-consistent modelling using continuous mechanics. Experiments, simulations and models can be expressed in the same language and directly compared. As an example, a companion paper (P. Marmottant, C. Raufaste, and F. Graner, this issue, 25 (2008) DOI 10.1140/epje/i2007-10300-7) provides an application to foam plasticity. More... »

PAGES

349-369

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1140/epje/i2007-10298-8

DOI

http://dx.doi.org/10.1140/epje/i2007-10298-8

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1025563246

PUBMED

https://www.ncbi.nlm.nih.gov/pubmed/18446271


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