Lecture Notes in Mathematics
              Volume              19552009
Optimal Transportation NetworksModels and TheoryAuthors:

• Marc Bernot,
• Vicent Caselles,
• Jean-Michel Morel
• …show all 3hide
  

ISBN: 978-3-540-69314-7 (Print) 978-3-540-69315-4  (Online)



Models and Theory

Series: Lecture Notes in Mathematics, Vol. 1955

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

X, 200 p. 58 illus., 5 in color.

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)