title: Ant mound as an optimal shape in constructal design: solar irradiation and circadian brood/fungi-warming sorties.
abstract: Sizes, shapes, ambient and in-dome temperature, incoming solar radiation and illumination are measured on a Formica rufa anthill in a mixed forest of the Volga-Kama National Reserve in Russia. These data are used in a conceptual model of insolation of a right conical surface by direct-beam, descending atmospheric and ascending ground-reflected radiation. Unlike a standard calculation of the energy flux intercepted by a solar panel, the anthill is a 3-D structure and double-integration of the cosine of the angle between the solar beams and normal to the surface is carried out for a "cozy trapezium", where the insects expose themselves and the brood to "morning" sunbathing pulses (Jones and Oldroyd, 2007). Several constructal design problems are formulated with the criteria involving either a pure solar energy gained by the dome or this energy, as a mathematical criterion, penalized by additive terms of mechanical energy (potential and friction) lost by the ants in their diurnal forays from a "heartland" of the nest to the sun-basking zone on the surface. The unique and global optima are analytically found, with the optimal tilt angle of the cone explicitly expressed through the zenith angle of the Sun and meteorological constants for the isotropic sky model.
authors.affiliation: German University of Technology in Oman, Sultanate of Oman, Oman. Electronic address: rouzalia.kasimova@gutech.edu.om.
authors.forename: R G
authors.initials: RG
authors.lastname: Kasimova
authors.affiliation: Department of General Ecology, Kazan Federal University, Russia.
authors.forename: D
authors.initials: D
authors.lastname: Tishin
authors.affiliation: Department of Differential Equations, Kazan Federal University, Russia. Electronic address: yurii.obnosov@gmail.com.
authors.forename: Yu V
authors.initials: YV
authors.lastname: Obnosov
authors.affiliation: Department of Biological Evolution, Moscow State University, Russia.
authors.forename: G M
authors.initials: GM
authors.lastname: Dlussky
authors.affiliation: Department of Geology, Tomsk Polytechnic University, Russia.
authors.forename: F B
authors.initials: FB
authors.lastname: Baksht
authors.affiliation: Department of Soils, Water and Agricultural Engineering, Sultan Qaboos University, Oman. Electronic address: anvar@squ.edu.om.
authors.forename: A R
authors.initials: AR
authors.lastname: Kacimov
mesh_terms: D000818:Animals; D001000:Ants / Q000502:physiology*; D057906:Circadian Clocks / Q000502:physiology*; D008954:Models, Biological; D012993:Solar Energy
keywords: Adaptive ant-mound; Direct-diffuse-reflected radiation on non-flat surfaces; Insolation; Optimal slope; Social insects