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024 7 $a10.1007/978-3-540-69315-4
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035   $a(DE-He213)978-3-540-69315-4
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100   $a20100301d2009      u|             0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aOptimal Transportation Networks$b[electronic resource] $eModels and Theory /$fby Marc Bernot, Vicent Caselles, Jean-Michel Morel
205   $a1st ed. 2009.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2009.
215   $a1 online resource (X, 200 p. 58 illus., 5 illus. in color.)
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1955
300   $aISSN 0075-8434 for print edition.
311   $a3-540-69314-9 
320   $aIncludes bibliographical references and index.
327   $aIntroduction: 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.
330   $aThe transportation problem can be formalized as the problem of finding the optimal way to transport a given measure into another with the same mass. In contrast to the Monge-Kantorovitch problem, recent approaches model the branched structure of such supply networks as minima of an energy functional whose essential feature is to favour wide roads. Such a branched structure is observable in ground transportation networks, in draining and irrigation systems, in electrical power supply systems and in natural counterparts such as blood vessels or the branches of trees. These lectures provide mathematical proof of several existence, structure and regularity properties empirically observed in transportation networks. The link with previous discrete physical models of irrigation and erosion models in geomorphology and with discrete telecommunication and transportation models is discussed. It will be mathematically proven that the majority fit in the simple model sketched in this volume.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v1955
606   $aCalculus of variations
606   $aOperations research
606   $aManagement science
606   $aEngineering economics
606   $aEngineering economy
606   $aDecision making
606   $aApplied mathematics
606   $aEngineering mathematics
606   $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016
606   $aOperations Research, Management Science$3https://scigraph.springernature.com/ontologies/product-market-codes/M26024
606   $aEngineering Economics, Organization, Logistics, Marketing$3https://scigraph.springernature.com/ontologies/product-market-codes/T22016
606   $aOperations Research/Decision Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/521000
606   $aApplications of Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M13003
615  0$aCalculus of variations.
615  0$aOperations research.
615  0$aManagement science.
615  0$aEngineering economics.
615  0$aEngineering economy.
615  0$aDecision making.
615  0$aApplied mathematics.
615  0$aEngineering mathematics.
615 14$aCalculus of Variations and Optimal Control; Optimization.
615 24$aOperations Research, Management Science.
615 24$aEngineering Economics, Organization, Logistics, Marketing.
615 24$aOperations Research/Decision Theory.
615 24$aApplications of Mathematics.
676   $a515.64
700   $aBernot$b Marc$4aut$4http://id.loc.gov/vocabulary/relators/aut$0472371
702   $aCaselles$b Vicent$4aut$4http://id.loc.gov/vocabulary/relators/aut
702   $aMorel$b Jean-Michel$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a996466512203316
996   $aOptimal Transportation Networks$92831258
997   $aUNISA