Del 1955 - Lecture Notes in Mathematics

Optimal Transportation Networks

Models and Theory

Häftad, Engelska, 2008

Av Marc Bernot, Vicent Caselles, Jean-Michel Morel

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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

Produktinformation

Utgivningsdatum2008-09-23
Mått155 x 235 x 13 mm
Vikt341 g
FormatHäftad
SpråkEngelska
SerieLecture Notes in Mathematics
Antal sidor200
Upplaga2009
FörlagSpringer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN9783540693147

Tillhör följande kategorier

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.

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)