Optimal Transportation Networks

Marc Bernot

ISBN 10: 3540693149 / ISBN 13: 9783540693147

Published by Springer, Springer Vieweg Sep 2008, 2008

About this Item

This item is printed on demand - Print on Demand Titel. Neuware -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 0Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 220 pp. Englisch.

Seller Inventory # 9783540693147

Bibliographic Details

• Title: Optimal Transportation Networks
• Publisher: Springer, Springer Vieweg Sep 2008
• Publication Date: 2008
• Language: English
• ISBN 10: 3540693149
• ISBN 13: 9783540693147
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 13D millimeters 235 millimeters width by 155 millimeters height by 13 millimeters depth
• Weight: 341 grams

About this title

Synopsis

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.