J Austral Math Soc Ser B 34 pp274--281, 1993.

Variational principles, duality, Legendre transformations and mine shaft ventilation

A. M. Watts

(Received 11 September 1991; revised 17 January 1992)

Abstract

The calculation of flows in pipe networks and in networks of mine shafts and the calculations of the currents in electrical circuits can be represented as variational problems. There are two approaches: the nodal method and the loop method. There is a variational representation for each of these. This paper describes the relationship between the two representations and in particular shows that the loop formulation is the Wolfe dual of the nodal formulation after the application of Legendre transformations to the variables and to the objective function.

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Author

A. M. Watts: Centre for Industrial and Applied Mathematics and Parallel Computing, Mathematics Department, The University of Queensland, Qld 4072.

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Last Modified: Mon Jun 26 12:52:04 2000