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020 _a9783540693154
_9978-3-540-69315-4
024 7 _a10.1007/978-3-540-69315-4
_2doi
050 4 _aQA315-316
050 4 _aQA402.3
050 4 _aQA402.5-QA402.6
072 7 _aPBKQ
_2bicssc
072 7 _aMAT005000
_2bisacsh
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082 0 4 _a515.64
_223
100 1 _aBernot, Marc.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aOptimal Transportation Networks
_h[electronic resource] :
_bModels and Theory /
_cby Marc Bernot, Vicent Caselles, Jean-Michel Morel.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2009.
300 _aX, 200 p. 58 illus., 5 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1955
505 0 _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.
520 _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.
650 0 _aMathematical optimization.
650 0 _aEngineering economy.
650 0 _aOperations research.
650 0 _aMathematics.
650 1 4 _aCalculus of Variations and Optimal Control; Optimization.
_0http://scigraph.springernature.com/things/product-market-codes/M26016
650 2 4 _aOperations Research, Management Science.
_0http://scigraph.springernature.com/things/product-market-codes/M26024
650 2 4 _aEngineering Economics, Organization, Logistics, Marketing.
_0http://scigraph.springernature.com/things/product-market-codes/T22016
650 2 4 _aOperations Research/Decision Theory.
_0http://scigraph.springernature.com/things/product-market-codes/521000
650 2 4 _aApplications of Mathematics.
_0http://scigraph.springernature.com/things/product-market-codes/M13003
700 1 _aCaselles, Vicent.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aMorel, Jean-Michel.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540865308
776 0 8 _iPrinted edition:
_z9783540693147
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1955
856 4 0 _uhttps://doi.org/10.1007/978-3-540-69315-4
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c11335
_d11335