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Minicourse on "Branched transport theory"
Speakers: Jean Michel Morel and Filippo Santambrogio (ENS Cachan)

Location: WPI Seminarroom C714 Mon, 18. Jun (Opening: 9:50) - Wed, 20. Jun 07
Organisation(s)
Wolfgang Pauli Institut
Organiser(s)
Marco Di Francesco (U. L'Aquila)
Remark: Click HERE for lecture notes.

A branched structure is observable in most practical transportation systems such as draining and irrigation systems, electric power supply systems and natural objects like the blood vessels, the river basins, or the trees. Recent approaches of these transportation networks derive their branched structure from an energy functional whose essential feature is to favor wide routes. Given a flow $s$ in a river, a road, a tube or a wire, the transportation cost per unit length is supposed in these models to be proportional to s^alpha with 0 < alpha < 1.

The aim of these talks is to compare various (actually equivalent) variational models for these phenomena, and to make the usual work: feasibility, existence of weak solutions, regularity, structure properties, subjacent PDE, open problems and their connections to geophysical models of optimal river networks. Among the open problems are the fractal properties of the infinite irrigation trees, and the existence and regularity of river basins.

Talks in the framework of this event


Morel, Jean Michel WPI, Seminarroom C714 Mon, 18. Jun 07, 10:00
Branched transport theory (2h)

A branched structure is observable in most practical transportation systems such as draining and irrigation systems, electric power supply systems and natural objects like the blood vessels, the river basins, or the trees. Recent approaches of these transportation networks derive their branched structure from an energy functional whose essential feature is to favor wide routes. Given a flow $s$ in a river, a road, a tube or a wire, the transportation cost per unit length is supposed in these models to be proportional to s^alpha with 0 < alpha < 1.

The aim of these talks is to compare various (actually equivalent) variational models for these phenomena, and to make the usual work: feasibility, existence of weak solutions, regularity, structure properties, subjacent PDE, open problems and their connections to geophysical models of optimal river networks. Among the open problems are the fractal properties of the infinite irrigation trees, and the existence and regularity of river basins.

  • Event: Minicourse on "Branched transport theory"; Speakers: Jean Michel Morel and Filippo Santambrogio (ENS Cachan) (2007)

Morel, Jean Michel WPI, Seminarroom C714 Tue, 19. Jun 07, 10:00
Branched transport theory (2h)

A branched structure is observable in most practical transportation systems such as draining and irrigation systems, electric power supply systems and natural objects like the blood vessels, the river basins, or the trees. Recent approaches of these transportation networks derive their branched structure from an energy functional whose essential feature is to favor wide routes. Given a flow $s$ in a river, a road, a tube or a wire, the transportation cost per unit length is supposed in these models to be proportional to s^alpha with 0 < alpha < 1.

The aim of these talks is to compare various (actually equivalent) variational models for these phenomena, and to make the usual work: feasibility, existence of weak solutions, regularity, structure properties, subjacent PDE, open problems and their connections to geophysical models of optimal river networks. Among the open problems are the fractal properties of the infinite irrigation trees, and the existence and regularity of river basins.

  • Event: Minicourse on "Branched transport theory"; Speakers: Jean Michel Morel and Filippo Santambrogio (ENS Cachan) (2007)

Morel, Jean Michel and Santambrogio, Filippo WPI, Seminarroom C714 Wed, 20. Jun 07, 10:00
Branched transport theory (2h)

A branched structure is observable in most practical transportation systems such as draining and irrigation systems, electric power supply systems and natural objects like the blood vessels, the river basins, or the trees. Recent approaches of these transportation networks derive their branched structure from an energy functional whose essential feature is to favor wide routes. Given a flow $s$ in a river, a road, a tube or a wire, the transportation cost per unit length is supposed in these models to be proportional to s^alpha with 0 < alpha < 1.

The aim of these talks is to compare various (actually equivalent) variational models for these phenomena, and to make the usual work: feasibility, existence of weak solutions, regularity, structure properties, subjacent PDE, open problems and their connections to geophysical models of optimal river networks. Among the open problems are the fractal properties of the infinite irrigation trees, and the existence and regularity of river basins.

  • Event: Minicourse on "Branched transport theory"; Speakers: Jean Michel Morel and Filippo Santambrogio (ENS Cachan) (2007)

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