Optimal transportation networks : models and theory
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...
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| Autors principals: | , , |
|---|---|
| Format: | Livre numérique |
| Idioma: | Anglais |
| Publicat: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Edició: | 1st ed. 2009. |
| Col·lecció: | Lecture Notes in Mathematics
1955 |
| Matèries: | |
| Accés en línia: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
Description d'apès consultation du 23 janvier 2012 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Optimal transportation networks, models and theory, Marc Bernot, Vicent Caselles, Jean-Michel Morel, Berlin, Springer, 2009, 1 vol. (X-200 p.), Lecture notes in mathematics, 978-3-540-69314-7 • Optimal Transportation Networks, Texte imprimé, 9783540865308 • Optimal transportation networks, models and theory, Marc Bernot, Vicent Caselles, Jean-Michel Morel, Berlin, Springer, 2009, 1 vol. (X-200 p.), Lecture notes in mathematics, 978-3-540-69314-7 |
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| 100 | 1 | |a Bernot, Marc, |d 1978- | |
| 245 | 1 | 0 | |a Optimal transportation networks : |b models and theory |c Marc Bernot, Vicent Caselles, Jean-Michel Morel. |
| 250 | |a 1st ed. 2009. | ||
| 260 | |a Berlin, Heidelberg : |b Springer Berlin Heidelberg. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 1 | |a Lecture Notes in Mathematics |v 1955 |x 1617-9692 | |
| 500 | |a Description d'apès consultation du 23 janvier 2012 | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 505 | 1 | |a 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. | |
| 505 | 0 | |a 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 | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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 | ||
| 650 | |a Modèles mathématiques | ||
| 650 | |a Réseaux (mathématiques) | ||
| 650 | |a Recherche opérationnelle | ||
| 650 | |a Mathématiques | ||
| 650 | |a Calcul des variations | ||
| 700 | 1 | |a Morel, Jean-Michel, |d 1953- |4 aut | |
| 700 | 1 | |a Caselles, Vicent, |d 1960-2013. |4 aut | |
| 776 | 0 | |0 12835318X |t Optimal transportation networks |o models and theory |f Marc Bernot, Vicent Caselles, Jean-Michel Morel |c Berlin |n Springer |d 2009 |p 1 vol. (X-200 p.) |s Lecture notes in mathematics |z 978-3-540-69314-7 | |
| 776 | 0 | |t Optimal Transportation Networks |b Texte imprimé |z 9783540865308 | |
| 776 | 0 | |0 12835318X |t Optimal transportation networks |o models and theory |f Marc Bernot, Vicent Caselles, Jean-Michel Morel |c Berlin |n Springer |d 2009 |p 1 vol. (X-200 p.) |s Lecture notes in mathematics |z 978-3-540-69314-7 | |
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