Numerical enclosures of the optimal cost of the Kantorovitch’s mass transportation problem

International audience

A mass-transportation approach to a one dimensional fluid mechanics model with nonlocal velocity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Problems of optimal transportation on the circle and their mechanical applications

We consider a mechanical problem concerning a 2D axisymmetric body moving forward on the plane and making slow turns of fixed magnitude about its axis of symmetry. The body moves through a medium of non-interacting particles at rest, and collisions of particles with the body's boundary are perfectly elastic (billiard-like). The body has a blunt nose: a line segment orthogonal to the symmetry axis. It is required to make small cavities with special shape on the nose so as to minimize its aerodynamic resistance. This problem of optimizing the shape of the cavities amounts to a special case of the optimal mass transfer problem on the circle with the transportation cost being the squared Euclidean distance. We find the exact solution for this problem when the amplitude of rotation is smaller than a fixed critical value, and give a numerical solution otherwise. As a by-product, we get explicit description of the solution for a class of optimal transfer problems on the circle.

National urban mass transportation statistics. First annual report, section 15 reporting system.

Urban Mass Transportation Administration, Washington, D.C.

National urban mass transportation statistics. Second annual report, section 15 reporting system.

Urban Mass Transportation Administration, Washington, D.C.

National urban mass transportation statistics. [Third annual report]. 1981, section 15 report.

Urban Mass Transportation Administration, Washington, D.C.

National urban mass transportation statistics. [Fourth annual report]. 1982, section 15 report.

Urban Mass Transportation Administration, Washington, D.C.

Guidelines for assessing the environmental impact of public mass transportation projects: executive summary.

Transportation Department, Office of Environment and Safety, Washington, D.C.

Alternative mass transportation technologies technical data. Interim report.

Texas State Department of Highways and Public Transportaion, Transportation Planning Division, Austin

Guidelines for assessing the environmental impact of public mass transportation projects. Notebook 1: purpose and procedures. Final report.

Transportation Department, Office of Environment and Safety, Washington, D.C.

Guidelines for assessing the environmental impact of public mass transportation projects. Notebook 2: social impacts. Final report.

Transportation Department, Office of Environment and Safety, Washington, D.C.

Guidelines for assessing the environmental impact of public mass transportation projects. Notebook 4: physical impacts. Final report.

Transportation Department, Office of Environment and Safety, Washington, D.C.

Guidelines for assessing the environmental impact of public mass transportation projects. Notebook 5: environmental assessment reference book. Final report.

Transportation Department, Office of Environment and Safety, Washington, D.C.

A guide to innovative financing mechanisms for mass transportation: an update. Revised edition.

Urban Mass Transportation Administration, Washington, D.C.

Guidelines for assessing the environmental impact of public mass transportation projects. Notebook 3: economic impacts. Final report.

Transportation Department, Office of Environment and Safety, Washington, D.C.