ENGLISH

Optimal transportation networks: Models and theory

By Jean-Michel Morel (auth.) , Marc Bernot , Vicent Caselles

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2009
ISBN
3540693149, 9783540693147
DOI
10.1007/978-3-540-69315-4
Language
english
Format
PDF
Filesize
2 MB (1934827 bytes)
Series
Lecture Notes in Mathematics 1955
Edition
1
Pages
200\0
Library
Kolxo3
Time added
2009-07-20 03:45:11
Calculus of Variations and Optimal Control; OptimiLogisticsMarketing; Operations Research/Decision Theory; ApMathematical Programming; Engineering EconomicsOrganization

Description

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.

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