### Abstract

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".

Original language | English |
---|---|

Pages (from-to) | 384-390 |

Number of pages | 7 |

Journal | Ecological Modelling |

Volume | 250 |

DOIs | |

Publication status | Published - Feb 2013 |

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### Keywords

- Ant nest
- Constructal design
- Global minimum
- Heat transfer
- Mathematical modelling
- Social insects

### ASJC Scopus subject areas

- Ecological Modelling

### Cite this

*Ecological Modelling*,

*250*, 384-390. https://doi.org/10.1016/j.ecolmodel.2012.11.021

**Optimal shape of an anthill dome : Bejan's constructal law revisited.** / Kasimova, R. G.; Obnosov, Yu V.; Baksht, F. B.; Kacimov, A. R.

Research output: Contribution to journal › Article

*Ecological Modelling*, vol. 250, pp. 384-390. https://doi.org/10.1016/j.ecolmodel.2012.11.021

}

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.

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

UR - http://www.scopus.com/inward/record.url?scp=84872384100&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84872384100&partnerID=8YFLogxK

U2 - 10.1016/j.ecolmodel.2012.11.021

DO - 10.1016/j.ecolmodel.2012.11.021

M3 - Article

VL - 250

SP - 384

EP - 390

JO - Ecological Modelling

JF - Ecological Modelling

SN - 0304-3800

ER -