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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.
Submodular Functions and Optimization Автор: Satoru Fujishige Год: 2005 |
Discrete Cosine and Sine Transforms: General Properties, Fast Algorithms and Integer Approximations Автор: Britanak V., Rao K. R., Yip P. C. Год: 2006 |
Dynamic economic models in discrete time Автор: Ferguson B.S., Lim G.C. Год: 2003 |
Introduction to Modern Traffic Flow Theory and Control Автор: Kerner B.S. Год: 2009 |
The Derivation of a Time-Harmonic Adjoint Method Автор: Mihai Constantin Duta Год: 2010 |