Title: Order parameters from image analysis: a honeycomb example
Authors: Kaatz, Forrest ×
Bultheel, Adhemar
Egami, Takeshi #
Issue Date: Nov-2008
Publisher: Springer
Series Title: Die Naturwissenschaften vol:95 issue:11 pages:1033-1040
Abstract: Honeybee combs have aroused interest in the ability of honeybees to form regular hexagonal geometric constructs since ancient times. Here we use a real space technique based on the pair distribution function (PDF) and radial distribution function (RDF), and a reciprocal space method utilizing the Debye-Waller Factor (DWF) to quantify the order for a range of honeycombs made by Apis mellifera. The PDFs and RDFs are fit with a series of Gaussian curves. We characterize the order in the honeycomb using a real space order parameter, OP3, to describe the order in the combs and a twodimensional Fourier transform from which a Debye-Waller order parameter u, is derived. Both OP3 and u take values from [0, 1] where the value one represents perfect order. The analyzed combs have values of OP3 from 0.33 to 0.60 and values of u from 0.83 to 0.98. RDF fits of honeycomb histograms show that naturally made comb can be crystalline in a 2D ordered structural sense, yet is more 'liquid-like' than cells made on foundation wax. We show that with the assistance of man-made foundation wax, honeybees can manufacture highly ordered arrays of hexagonal cells.
ISSN: 0028-1042
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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