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Conference Papers Year : 2015

Geometric Methods for the Study of Electrical Networks

Philippe Durand
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  • PersonId : 961915
Alain Reineix
OSA

Abstract

The methods developed by Gabriel Kron, for the tensor approach of networks (TAN), offers a great source of applications for the geometrical and topo-logical study of electrical networks. The language of tensorial analysis is well adapted to the description of networks. Tools about discrete com-binatorial topology are well adapted specifically to the study of graphs, for example, the Euler-Poincaré characteristic, the simplest invariant in to-pology is connected to a formula obtained by Kron connecting the nodes of the graphs, edges, mesh currents and node pairs. Extensions using toolsof algebraic topology are possible in larger dimension. We thus find the node law and the law of mesh The addition of differential geometry is used toconnect discrete data obtained from circuit and continuous phenomena for example, transmission problems via antenna.
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Dates and versions

hal-01185017 , version 1 (26-08-2015)

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  • HAL Id : hal-01185017 , version 1

Cite

Philippe Durand, Olivier Maurice, Alain Reineix. Geometric Methods for the Study of Electrical Networks. ICIAM, Aug 2015, Beijing, China. ⟨hal-01185017⟩
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