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Two-dimensional body of maximum mean resistance
A two-dimensional body, exhibiting a slight rotational movement, moves in a
rarefied medium of particles which collide with it in a perfectly elastic way.
In previously realized investigations by the first two authors, Plakhov &
Gouveia (2007, Nonlinearity, 20), shapes of nonconvex bodies were sought which
would maximize the braking force of the medium on their movement. Giving
continuity to this study, new investigations have been undertaken which
culminate in an outcome which represents a large qualitative advance relative
to that which was achieved earlier. This result, now presented, consists of a
two-dimensional shape which confers on the body a resistance which is very
close to its theoretical supremum value. But its interest does not lie solely
in the maximization of Newtonian resistance; on regarding its characteristics,
other areas of application are seen to begin to appear which are thought to be
capable of having great utility. The optimal shape which has been encountered
resulted from numerical studies, thus it is the object of additional study of
an analytical nature, where it proves some important properties which explain
in great part its effectiveness.Comment: Accepted (April 16, 2009) for publication in the journal "Applied
Mathematics and Computation
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