TY - JOUR
T1 - Optimal shape of an anthill dome
T2 - Bejan's constructal law revisited
AU - Kasimova, R. G.
AU - Obnosov, Yu V.
AU - Baksht, F. B.
AU - Kacimov, A. R.
N1 - Funding Information:
This work has been supported by the Russian Foundation of Basic Research Grant no. 12-01-97015-r_povolgh’e_a . Helpful comments by two anonymous referees are highly appreciated.
PY - 2013/2
Y1 - 2013/2
N2 - An anthill is modelled as a paraboloid of revolution, whose surface (dome) dissipates heat from the interior of the nest to the ambient air according to the Robin boundary condition, which involves a constant coefficient, given temperature jump and dome's area. The total heat loss of the net is one (integral) component of ants' colony expenditures of energy. Ants, populating the paraboloid, spend also energy individually, by hoisting the load from the ground surface to a certain elevation within the paraboloid and by overcoming a Coulombian resistance, proportional to the trajectory length. In order to count the gross colony expenditures for these mechanical activities all trajectories are integrated over the volume. Ants are assumed to move along the shortest straight lines of their regular sorties between the nest and forest. The three-component energy is mathematically expressed as a closed-form function of only one variable, the paraboloid height-to-width ratio. The minimum of this function is found by a routine of computer algebra. The proposed model amalgamates into a single and relatively simple function, tractable by standard calculus, the property of the whole structure (dome area) with labouring of insects-comrades. The ants are sociobiologically analogized with Bejan's builders of ancient pyramids and contemporary designers of man-made "dream-houses" or "dream-prisons".
AB - An anthill is modelled as a paraboloid of revolution, whose surface (dome) dissipates heat from the interior of the nest to the ambient air according to the Robin boundary condition, which involves a constant coefficient, given temperature jump and dome's area. The total heat loss of the net is one (integral) component of ants' colony expenditures of energy. Ants, populating the paraboloid, spend also energy individually, by hoisting the load from the ground surface to a certain elevation within the paraboloid and by overcoming a Coulombian resistance, proportional to the trajectory length. In order to count the gross colony expenditures for these mechanical activities all trajectories are integrated over the volume. Ants are assumed to move along the shortest straight lines of their regular sorties between the nest and forest. The three-component energy is mathematically expressed as a closed-form function of only one variable, the paraboloid height-to-width ratio. The minimum of this function is found by a routine of computer algebra. The proposed model amalgamates into a single and relatively simple function, tractable by standard calculus, the property of the whole structure (dome area) with labouring of insects-comrades. The ants are sociobiologically analogized with Bejan's builders of ancient pyramids and contemporary designers of man-made "dream-houses" or "dream-prisons".
KW - Ant nest
KW - Constructal design
KW - Global minimum
KW - Heat transfer
KW - Mathematical modelling
KW - Social insects
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U2 - 10.1016/j.ecolmodel.2012.11.021
DO - 10.1016/j.ecolmodel.2012.11.021
M3 - Article
AN - SCOPUS:84872384100
SN - 0304-3800
VL - 250
SP - 384
EP - 390
JO - Ecological Modelling
JF - Ecological Modelling
ER -