PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Federico Rodriguez Hertz, Stephanie Zerby, Anatole Katok, Boris Kalinin, Dmitri Burago.

Title:Problems of optimal resistance in Newtonian aerodynamics
Seminar:Center for Dynamics and Geometry Seminars
Speaker:Alexandre Plakhov, University of Aveiro, Portugal and Institute for Information Transmission Problems, Russia
Abstract:
A rigid body moves in a rarefied medium of resting particles and at the same time very slowly rotates (somersaults). Each particle of the medium is reflected elastically when hitting the body boundary (multiple reflections are possible). The resulting resistance force acting on the body is time-dependent; we consider the time-averaged value of resistance. The problem is: given a convex body, find a roughening of its surface that minimizes or maximizes its resistance. (The problem includes mathematical definition of roughening.) This problem is solved using the methods of billiard theory and optimal mass transportation. Surprisingly, the minimum and maximum depend only on the dimension of the ambient Euclidean space and do not depend on the original body. In particular, the resistance of a 3-dimensional convex body can be decreased by (approx.) 3.05% at most and can be increased at most twice by roughening.

Room Reservation Information

Room Number:MB114
Date:04 / 17 / 2013
Time:03:35pm - 04:35pm