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Optimal Roughening of Convex Bodies

  Published:2011-11-03
 Printed: Oct 2012
  • Alexander Plakhov,
    University of Aveiro, Department of Mathematics, Aveiro 3810-193, Portugal
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Abstract

A body moves in a rarefied medium composed of point particles at rest. The particles make elastic reflections when colliding with the body surface, and do not interact with each other. We consider a generalization of Newton's minimal resistance problem: given two bounded convex bodies $C_1$ and $C_2$ such that $C_1 \subset C_2 \subset \mathbb{R}^3$ and $\partial C_1 \cap \partial C_2 = \emptyset$, minimize the resistance in the class of connected bodies $B$ such that $C_1 \subset B \subset C_2$. We prove that the infimum of resistance is zero; that is, there exist "almost perfectly streamlined" bodies.
Keywords: billiards, shape optimization, problems of minimal resistance, Newtonian aerodynamics, rough surface billiards, shape optimization, problems of minimal resistance, Newtonian aerodynamics, rough surface
MSC Classifications: 37D50, 49Q10 show english descriptions Hyperbolic systems with singularities (billiards, etc.)
Optimization of shapes other than minimal surfaces [See also 90C90]
37D50 - Hyperbolic systems with singularities (billiards, etc.)
49Q10 - Optimization of shapes other than minimal surfaces [See also 90C90]
 

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