04866nam 22008055 450 99646651220331620200630171733.03-540-69315-710.1007/978-3-540-69315-4(CKB)1000000000546316(SSID)ssj0000447013(PQKBManifestationID)11314939(PQKBTitleCode)TC0000447013(PQKBWorkID)10505016(PQKB)10797610(DE-He213)978-3-540-69315-4(MiAaPQ)EBC3063516(PPN)13111851X(EXLCZ)99100000000054631620100301d2009 u| 0engurnn#008mamaatxtccrOptimal Transportation Networks[electronic resource] Models and Theory /by Marc Bernot, Vicent Caselles, Jean-Michel Morel1st ed. 2009.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2009.1 online resource (X, 200 p. 58 illus., 5 illus. in color.)Lecture Notes in Mathematics,0075-8434 ;1955ISSN 0075-8434 for print edition.3-540-69314-9 Includes bibliographical references and index.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.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.Lecture Notes in Mathematics,0075-8434 ;1955Calculus of variationsOperations researchManagement scienceEngineering economicsEngineering economyDecision makingApplied mathematicsEngineering mathematicsCalculus of Variations and Optimal Control; Optimizationhttps://scigraph.springernature.com/ontologies/product-market-codes/M26016Operations Research, Management Sciencehttps://scigraph.springernature.com/ontologies/product-market-codes/M26024Engineering Economics, Organization, Logistics, Marketinghttps://scigraph.springernature.com/ontologies/product-market-codes/T22016Operations Research/Decision Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/521000Applications of Mathematicshttps://scigraph.springernature.com/ontologies/product-market-codes/M13003Calculus of variations.Operations research.Management science.Engineering economics.Engineering economy.Decision making.Applied mathematics.Engineering mathematics.Calculus of Variations and Optimal Control; Optimization.Operations Research, Management Science.Engineering Economics, Organization, Logistics, Marketing.Operations Research/Decision Theory.Applications of Mathematics.515.64Bernot Marcauthttp://id.loc.gov/vocabulary/relators/aut472371Caselles Vicentauthttp://id.loc.gov/vocabulary/relators/autMorel Jean-Michelauthttp://id.loc.gov/vocabulary/relators/autBOOK996466512203316Optimal Transportation Networks2831258UNISA