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
Rezensionen / Stimmen
From the reviews:
"The book aims to give a unified mathematical theory of branched transportation (or irrigation) networks. . The logical structure of the book makes it easy to learn the theory. . this book, in addition to being a great source of references is also extremely suitable for a study from scratch. The theory is presented while avoiding useless complications and keeping the language simple. I would also suggest this book to graduate students who want to enter this very interesting research field." (Luigi De Pascale, Mathematical Reviews, Issue 2010 e)
Reihe
Auflage
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für Beruf und Forschung
Research
Illustrationen
53
5 farbige Abbildungen, 53 s/w Abbildungen
X, 200 p. 58 illus., 5 illus. in color.
Maße
Höhe: 235 mm
Breite: 155 mm
Dicke: 13 mm
Gewicht
ISBN-13
978-3-540-69314-7 (9783540693147)
DOI
10.1007/978-3-540-69315-4
Schweitzer Klassifikation
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.
