Exterior Billiards: Systems with Impacts Outside Bounded Domains

ISBN-13: 9781489999139 / Angielski / Miękka / 2014 / 286 str.

Plakhov, Alexander

Opis

A billiard is a dynamical system in which a point particle alternates between free motion and specular reflections from the boundary of a domain. Exterior Billiards presents billiards in the complement of domains and their applications in aerodynamics and geometrical optics. This book distinguishes itself from existing literature by presenting billiard dynamics outside bounded domains, including scattering, resistance, invisibility and retro-reflection. It begins with an overview of the mathematical notations used throughout the book and a brief review of the main results. Chapters 2 and 3 are focused on problems of minimal resistance and Newton's problem in media with positive temperature. In chapters 4 and 5, scattering of billiards by nonconvex and rough domains is characterized and some related special problems of optimal mass transportation are studied. Applications in aerodynamics are addressed next and problems of invisibility and retro-reflection within the framework of geometric optics conclude the text. The book will appeal to mathematicians working in dynamical systems and calculus of variations. Specialists working in the areas of applications discussed will also find it useful.

Recenzje

From the reviews:

"The book under review is a very nice presentation of several problems related to the aerodynamics of bodies in highly rarefied media. ... The book is very pleasant to read; the various mathematical models are clearly presented, and even a nonspecialist in the field can follow the presentation of the problems. Several pictures that are included greatly help the reader ... ." (Giuseppe Buttazzo, SIAM Review, Vol. 56 (1), March, 2014)

Spis treści

​​ ​-Notation and synopsis of main results. -Problem of minimum resistance to translational motion of bodies. -Newton’s problem in media with positive temperature. -Scattering in billiards. -Problems of optimal mass transportation. -Problems on optimization of mean resistance. -Magnus effect and dynamics of a rough disc. -On invisible bodies. –Retroreflectors.​