Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-23T11:13:59.118Z Has data issue: false hasContentIssue false
  • English
  • Français

Variational principles, duality, Legendre transformations and mine shaft ventilation

Published online by Cambridge University Press:  17 February 2009

A. M. Watts
A. M. Watts
Affiliation:
Centre for Industrial and Applied Mathematics and Parallel Computing, Mathematics Department, The University of Queensland, Qld 4072.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
Information
The ANZIAM Journal , Volume 34 , Issue 3 , January 1993 , pp. 274 - 281
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Brooks, A., Kendrick, D., and Meeraus, A., GAMS A User's Guide (The Scientific Press, San Francisco, 1988).Google Scholar
[2]Fletcher, R., Practical Methods of Optimization, Vol. 2 (John Wiley & Sons, 1981).Google Scholar
[3]Osiadacz, A. J., Simulation and Analysis of Gas Networks (E. & F. N. Spon Ltd., London, 1987).Google Scholar
[4]Wang, Y. J., “Solving mine vertilation networks with fixed and non-fixed branches”, Mining Engineering (1990) 1342–1346.Google Scholar