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Title: Problems of optimal transportation on the circle and their mechanical applications
Author: Plakhov, Alexander
Tchemisova, Tatiana
Keywords: Problems of minimal resistance
Monge-Kantorovich problem
Optimal mass transportation
Shape optimization
Issue Date: 5-Feb-2017
Publisher: Elsevier
Abstract: 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.
Peer review: yes
ISSN: 0022-0396
Appears in Collections:CIDMA - Artigos
DMat - Artigos
OGTCG - Artigos

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