location:  Publications → journals → CJM
Abstract view

# Optimal Roughening of Convex Bodies

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

## 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
 MSC Classifications: 37D50 - Hyperbolic systems with singularities (billiards, etc.) 49Q10 - Optimization of shapes other than minimal surfaces [See also 90C90]

 top of page | contact us | privacy | site map |