TY  - GEN
AU  - Bernot, Marc
AU  - Morel, Jean-Michel
AU  - Caselles, Vicent 
TI  - Optimal transportation networks: models and theory
SN  - 9783540693147
U1  - 515.64 
PY  - 2009///
CY  - Berlin
PB  - Springer
KW  - Transportation Engineering
KW  - Mathematical Models
KW  - Transportation  Mathematical Models
KW  - Traffic Engineering
KW  - Equivalence of Various Models
KW  - Optimal Pattern
KW  -  Irrigation Networks
KW  - Flows in Tubes
N1  - Including Index
N2  - 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." --Book Jacket
ER  -