Symmetry analysis of an equation for constrained optimal transport, modelling the distribution of ants round a nest

E. Momoniat; H. Laurie

doi:10.1016/j.amc.2003.08.067

Symmetry analysis of an equation for constrained optimal transport, modelling the distribution of ants round a nest

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Abstract

A second-order nonlinear partial differential equation modelling the optimal transport of food into an ant nest is derived. The Lie group method is used to determine group invariant solutions admitted by the model equation. Two classes of solutions are obtained. In the first case we are able to impose zero ant density on a circle which yields physically relevant solutions. Here, the optimal transport of food into the ant nest occurs when the foraging region has a circular boundary. In the second case we are only able to impose zero ant density at a point.

Original language	English
Pages (from-to)	111-120
Number of pages	10
Journal	Applied Mathematics and Computation
Volume	158
Issue number	1
DOIs	https://doi.org/10.1016/j.amc.2003.08.067
Publication status	Published - 25 Oct 2004
Externally published	Yes

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2003.08.067

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abstract = "A second-order nonlinear partial differential equation modelling the optimal transport of food into an ant nest is derived. The Lie group method is used to determine group invariant solutions admitted by the model equation. Two classes of solutions are obtained. In the first case we are able to impose zero ant density on a circle which yields physically relevant solutions. Here, the optimal transport of food into the ant nest occurs when the foraging region has a circular boundary. In the second case we are only able to impose zero ant density at a point.",

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Symmetry analysis of an equation for constrained optimal transport, modelling the distribution of ants round a nest

Abstract

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