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Optimal Transportation Networks : Models and Theory / by Marc Bernot, Vicent Caselles, Jean-Michel Morel.
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View onlineMath/Physics/Astronomy Library QA3 .L28 v.1-999 470,523,830,849:2nd ed. v.1000-1722,1762,1781,1799-2099,2100-2218 2219-2223-2258,2260-2271,2273-2274-2277,2279-2281,2283-2289,2291,2293-2294,2296,2298-2299,2300-2311,2313-2379,2380-2384 2385-2389,2392
Mixed Availability
LIBRA QA3 .L28 Scattered vols.
Mixed Availability
- Format:
- Book
- Author/Creator:
- Bernot, Marc, author.
- Caselles, Vicent, 1960- author.
- Morel, Jean-Michel, 1953- author.
- Series:
- Lecture Notes in Mathematics, 0075-8434 ; 1955.
- Lecture Notes in Mathematics, 0075-8434 ; 1955
- Language:
- English
- Subjects (All):
- Mathematical optimization.
- Engineering economy.
- Operations research.
- Mathematics.
- Calculus of Variations and Optimal Control; Optimization.
- Operations Research, Management Science.
- Engineering Economics, Organization, Logistics, Marketing.
- Operations Research/Decision Theory.
- Applications of Mathematics.
- Local Subjects:
- Calculus of Variations and Optimal Control; Optimization.
- Operations Research, Management Science.
- Engineering Economics, Organization, Logistics, Marketing.
- Operations Research/Decision Theory.
- Applications of Mathematics.
- Physical Description:
- 1 online resource (X, 200 pages 58 illustrations, 5 illustrations in color).
- Contained In:
- Springer eBooks
- Place of Publication:
- Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
- System Details:
- text file PDF
- Summary:
- 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.
- Contents:
- Introduction: The Models
- The Mathematical Models
- Traffic Plans
- The Structure of Optimal Traffic Plans
- Operations on Traffic Plans
- Traffic Plans and Distances between Measures
- The Tree Structure of Optimal Traffic Plans and their Approximation
- Interior and Boundary Regularity
- The Equivalence of Various Models
- Irrigability and Dimension
- The Landscape of an Optimal Pattern
- The Gilbert-Steiner Problem
- Dirac to Lebesgue Segment: A Case Study
- Application: Embedded Irrigation Networks
- Open Problems.
- Other Format:
- Printed edition:
- ISBN:
- 9783540693154
- Access Restriction:
- Restricted for use by site license.
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