Optimal Transportation Networks
Bernot, Marc.
Optimal Transportation Networks Models and Theory / [electronic resource] : by Marc Bernot, Vicent Caselles, Jean-Michel Morel. - X, 200 p. 58 illus., 5 illus. in color. online resource. - Lecture Notes in Mathematics, 1955 0075-8434 ; . - Lecture Notes in Mathematics, 1955 .
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.
9783540693154
10.1007/978-3-540-69315-4 doi
Mathematical optimization.
Engineering economy.
Operations research.
Mathematics.
Calculus of Variations and Optimal Control; Optimization.
Operations Research, Management Science.
Engineering Economics, Organization, Logistics, Marketing.
Operations Research/Decision Theory.
Applications of Mathematics.
QA315-316 QA402.3 QA402.5-QA402.6
515.64
Optimal Transportation Networks Models and Theory / [electronic resource] : by Marc Bernot, Vicent Caselles, Jean-Michel Morel. - X, 200 p. 58 illus., 5 illus. in color. online resource. - Lecture Notes in Mathematics, 1955 0075-8434 ; . - Lecture Notes in Mathematics, 1955 .
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.
9783540693154
10.1007/978-3-540-69315-4 doi
Mathematical optimization.
Engineering economy.
Operations research.
Mathematics.
Calculus of Variations and Optimal Control; Optimization.
Operations Research, Management Science.
Engineering Economics, Organization, Logistics, Marketing.
Operations Research/Decision Theory.
Applications of Mathematics.
QA315-316 QA402.3 QA402.5-QA402.6
515.64