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Lecture Notes in Mathematics

Optimal Transportation Networks

Models and Theory

Authors: Bernot, Marc, Caselles, Vicent, Morel, Jean-Michel

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About this book

The transportation problem can be formalized as the problem of finding the optimal way to transport a given measure into another with the same mass. In contrast to the Monge-Kantorovitch problem, recent approaches model the branched structure of such supply networks as minima of an energy functional whose essential feature is to favour wide roads. Such a branched structure is observable in ground transportation networks, in draining and irrigation systems, in electrical power supply systems and in natural counterparts such as blood vessels or the branches of trees.
These lectures provide mathematical proof of several existence, structure and regularity properties empirically observed in transportation networks. The link with previous discrete physical models of irrigation and erosion models in geomorphology and with discrete telecommunication and transportation models is discussed. It will be mathematically proven that the majority fit in the simple model sketched in this volume.

Reviews

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)

Table of contents (15 chapters)

Buy this book

eBook $44.99
price for USA in USD (gross)
  • ISBN 978-3-540-69315-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
  • ISBN 978-3-540-69314-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Optimal Transportation Networks
Book Subtitle
Models and Theory
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1955
Copyright
2009
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-69315-4
DOI
10.1007/978-3-540-69315-4
Softcover ISBN
978-3-540-69314-7
Series ISSN
0075-8434
Edition Number
1
Number of Pages
X, 200
Number of Illustrations
53 b/w illustrations, 5 illustrations in colour
Topics