HAL : hal-00089022, version 3

arXiv : cond-mat/0608208

DOI : 10.1103/PhysRevLett.98.088701

Fiche détaillée

Récupérer au format BibTeX - EndNote - TEI - RefWorks -

Physical Review Letters 98 (2007) 088701

Versions disponibles :

v1 (09-08-2006)

v2 (27-09-2006)

v3 (07-09-2010)

Structure of Optimal Transport Networks Subject to a Global Constraint

Marc Durand 1

(21/02/2007)

The structure of pipe networks minimizing the total energy dissipation rate is studied analytically. Among all the possible pipe networks that can be built with a given total pipe volume (or pipe lateral surface area), the network which minimizes the dissipation rate is shown to be loopless. Furthermore, such an optimal network is shown to contain at most N-2 nodes in addition to the N sources plus sinks that it connects. These results are valid whether the possible locations for the additional nodes are chosen freely or from a set of nodes (such as points of a grid). Applications of these results to various physical situations and to the efficient computation of optimal pipe networks are also discussed.

1 :	Matière et Systèmes Complexes (MSC)
	CNRS : UMR7057 – Université Paris VII - Paris Diderot

Domaine

:

Physique/Matière Condensée/Systèmes désordonnés et réseaux de neurones Physique/Matière Condensée/Mécanique statistique Mathématiques/Optimisation et contrôle Science non linéaire/Adaptation et Systèmes auto-organisés

Mots Clés : networks – optimization – resistance – dissipative energy – Steiner tree – spanning tree – optimal mass transport – weighted networks – transport – irrigation – pipe networks – channel networks

hal-00089022, version 3

http://hal.archives-ouvertes.fr/hal-00089022

oai:hal.archives-ouvertes.fr:hal-00089022

Contributeur : Marc Durand <>

Soumis le : Mardi 7 Septembre 2010, 17:16:30

Dernière modification le : Mardi 7 Septembre 2010, 21:11:02