Optimal Transportation Networks [[electronic resource] ] : Models and Theory / / by Marc Bernot, Vicent Caselles, Jean-Michel Morel

• Autore: Bernot Marc
• Pubblicazione: Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2009
• Edizione: 1st ed. 2009.
• Descrizione fisica: 1 online resource (X, 200 p. 58 illus., 5 illus. in color.)
• Disciplina: 515.64
• Soggetto topico: Calculus 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
• Persona (resp. second.): CasellesVicent; MorelJean-Michel
• Note generali: ISSN 0075-8434 for print edition.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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.
• Sommario/riassunto: 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.
• Titolo autorizzato: Optimal Transportation Networks
• ISBN: 3-540-69315-7
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996466512203316
• Lo trovi qui: Univ. di Salerno
• Serie: Lecture Notes in Mathematics, . 0075-8434 ; ; 1955