Bodies invisible in one direction and bodies of zero total cross section

TL;DR

This paper demonstrates the existence of bodies that are either invisible or exert zero resistance in a flow of particles, with implications for understanding particle-body interactions in rarefied flows.

Contribution

It introduces the concepts of bodies of zero resistance and invisible bodies, proving their existence within the context of elastic particle flows.

Findings

Bodies of zero resistance exist.

Invisible bodies in particle flows exist.

Theoretical proof of such bodies' existence.

Abstract

We consider a body in a parallel flow of non-interacting particles. One can imagine that the flow is highly rarefied or consists of light rays. The interaction of particles with the body is perfectly elastic. We introduce the notions of a body of zero resistance and an invisible body and prove that all such bodies do exist.