Optimal Transportation Networks

Models and Theory
2009
ISBN: 978-3-540-69314-7
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1955, 200 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 341 g

Reihe: Lecture Notes in Mathematics

The transportation problem can be formalized as the problem of ?nding + ? the optimal paths to transport a measure ? onto a measure ? 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 ?ow ? in a tube or a road or a wire, the transportation cost per unit length ? is supposed to be proportional to ? with 0

Zielgruppe

Research

Autoren/Hrsg.

Bernot, Marc

Morel, Jean-Michel

Caselles, Vicent

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung
• Wirtschaftswissenschaften Betriebswirtschaft Unternehmensforschung
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Wirtschaftswissenschaften Betriebswirtschaft Bereichsspezifisches Management Produktionsmanagement, Qualitätskontrolle
• Mathematik | Informatik Mathematik Operations Research

Inhaltsverzeichnis

Introduction: The Models.- The Mathematical Models.- Traffic Plans.- The Structure of Optimal Traffic Plans.- Operations on Traffic Plans.- Traffic Plans and Distances between Measures.- The Tree Structure of Optimal Traffic Plans and their Approximation.- Interior and Boundary Regularity.- The Equivalence of Various Models.- Irrigability and Dimension.- The Landscape of an Optimal Pattern.- The Gilbert-Steiner Problem.- Dirac to Lebesgue Segment: A Case Study.- Application: Embedded Irrigation Networks.- Open Problems.