Mathematical model of honeycomb construction |
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| Authors: | M R Belić V Škarka J L Deneubourg M Lax |
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| Institution: | (1) Institute of Physics, P.O. Box 57, 11001 Belgrade, Yugoslavia;(2) Faculté des Sciences, Université Libre de Bruxelles, Bruxelles, Belgique;(3) Physics Department of the City College, The Graduate Center of the City University of New York, 10031, NY;(4) AT&T Bell Laboratories, 07974 Murray Hill, NJ, USA;(5) Present address: Max-Planck-Institut für Quantenoptik, D-8046 Garching, Federal Republic of Germany |
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| Abstract: | We developed a mathematical model and an algorithm for numerical treatment of a model of honeycomb construction in a beehive. The model contains essential features of the bee-bee and bee-wax interactions, and in a qualitative way captures the dynamics of parallel comb construction. The construction is represented by a set of dynamical coupled partial differential equations for the density of bees situated on the hive ceiling, and the quantity of wax distributed by the bees. A spectral algorithm is invented for treatment of these equations, based on a modified thin-sheet gain scheme and a fast Fourier transform technique.Work at City College supported in part by the Army Research Office and the Department of Energy |
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| Keywords: | Comb building Self-organization Gain-sheet fast Fourier procedure |
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