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Optimal Roughening of Convex Bodies

Published online by Cambridge University Press:  20 November 2018

Alexander Plakhov
Alexander Plakhov*
Affiliation:
University of Aveiro, Department of Mathematics, Aveiro 3810-193, Portugal email: plakhov@ua.pt Institute for Information Transmission Problems, Moscow 127994, Russia
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Abstract

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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}}\,=\,\varnothing $ , 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

37D5049Q10billiardsshape optimizationproblems of minimal resistanceNewtonian aerodynamicsrough surface

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 64 , Issue 5 , 01 October 2012 , pp. 1058 - 1074
Copyright
Copyright © Canadian Mathematical Society 2012

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