| Order parameters from image analysis: a honeycomb example. | |
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MedLine Citation:
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PMID: 18633584 Owner: NLM Status: MEDLINE |
Abstract/OtherAbstract:
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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 ligustica. 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, OP ( 3 ), to describe the order in the combs and a two-dimensional Fourier transform from which a Debye-Waller order parameter, u, is derived. Both OP ( 3 ) and u take values from [0, 1] where the value one represents perfect order. The analyzed combs have values of OP ( 3 ) from 0.33 to 0.60 and values of u from 0.59 to 0.69. 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. This is the first description of honeycomb utilizing the Debye-Waller Factor, and provides a complete analysis of the order in comb from a real-space order parameter and a reciprocal space order parameter. It is noted that the techniques used are general in nature and could be applied to any digital photograph of an ordered array. |
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Authors:
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Forrest H Kaatz; Adhemar Bultheel; Takeshi Egami |
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Publication Detail:
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Type: Journal Article Date: 2008-07-17 |
Journal Detail:
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Title: Die Naturwissenschaften Volume: 95 ISSN: 0028-1042 ISO Abbreviation: Naturwissenschaften Publication Date: 2008 Nov |
Date Detail:
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Created Date: 2008-10-13 Completed Date: 2009-03-24 Revised Date: - |
Medline Journal Info:
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Nlm Unique ID: 0400767 Medline TA: Naturwissenschaften Country: Germany |
Other Details:
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Languages: eng Pagination: 1033-40 Citation Subset: IM |
Affiliation:
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Department of Mathematics and Life/Natural Sciences, Owens Community College, Toledo, OH 43699, USA. fhkaatz@yahoo.com |
Export Citation:
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| MeSH Terms | |
Descriptor/Qualifier:
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Animals Bees / physiology* Computer Simulation Ecosystem Honey Housing, Animal* Nesting Behavior* |
From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine
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