The structure of branched transportation networks
The transportation problem can be formalized as the problem of finding the optimal paths to transport a measure μ + onto a measure μ − with the same mass. In contrast with the Monge–Kantorovich formalization, recent approaches model the branched structure of such supply networks by an energy funct...
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Veröffentlicht in: | Calculus of variations and partial differential equations 2008-07, Vol.32 (3), p.279-317 |
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Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
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Zusammenfassung: | The transportation problem can be formalized as the problem of finding the optimal paths to transport a measure
μ
+
onto a measure
μ
−
with the same mass. In contrast with the Monge–Kantorovich formalization, recent approaches model the branched structure of such supply networks by an energy functional whose essential feature is to favor wide roads. Given a flow
s
in a road or a tube or a wire, the transportation cost per unit length is supposed to be proportional to
s
α
with 0 |
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ISSN: | 0944-2669 1432-0835 |
DOI: | 10.1007/s00526-007-0139-0 |