Optimal transportation networks : models and theory

Author(s)

Bibliographic Information

Optimal transportation networks : models and theory

Marc Bernot, Vicent Caselles, Jean-Michel Morel

(Lecture notes in mathematics, 1955)

Springer, c2009

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Note

Includes bibliographical references (p. 193-197) and index

Description and Table of Contents

Description

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

Table of Contents

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.

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Details

  • NCID
    BA87343338
  • ISBN
    • 9783540693147
  • LCCN
    2008931162
  • Country Code
    gw
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Berlin
  • Pages/Volumes
    x, 200 p.
  • Size
    24 cm
  • Parent Bibliography ID
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