The N-Vortex Problem: Analytical Techniques: 145 (Applied Mathematical Sciences, 145) - Hardcover

Newton, Paul K.

Hardcover

ISBN 10: 0387952268 ISBN 13: 9780387952260

Publisher: Springer, 2001

Synopsis

For applied mathematicians, physicists, and engineers interested in either nonlinear dynamics or classical mechanics and fluid dynamics. Describes the Hamiltonian aspects of vortex dynamics so that it may serve as an entry into the large literature on integrable and non-integrable vortex problems.

About this title

Review

From the reviews:

ZENTRALBLATT MATH

"Exercises given at the end of each chapter could be very useful to the readers to enhance their knowledge...the first three chapters deal with the basic classical two-dimensional point vortex theory, and the rest of the book takes care of the recent applications and extensions of the basic theory. The references are adequate for further study. Many open problems associated with N-vortex motion are also listed. The book is a welcome addition to the book shelves of researchers pursuing the N-vortex problem."

MATHEMATICAL REVIEWS

"Although several other books on vortex dynamics have appeared in recent years, none have the level of detail on these discrete vortex models that Newton achieves. The book is sure to be a key reference work on this area for many years to come. Students of fluid mechanics will find much valuable material here on modern dynamics applied to problems of interest to them. Applied mathematicians will find an entree to frontline problems of fluid mechanics using tools with which they are eminently familiar."

"This is a very timely addition to the literature. ... Exercises are scattered throughout the book, many of them quite substantial. ... A massive bibliography - a treasure in itself - concludes the text. Although several other books on vortex dynamics have appeared in recent years, none have the level of detail on these discrete vortex models that Newton achieves. The book is sure to be a key reference work on this area for many years to come." (Hassan Aref, Mathematical Reviews, Issue 2002 f)

"The goal of this book is to describe the Hamilton aspects of vortex dynamics in such a way that graduate students and researchers can use this book as an entry level text to the rather large literature on integrable and non-integrable vortex problems ... . The book is well written with each chapter containing useful biographical notes and exercises. Of particular note is the extensive list of seven hundred and seventy four references." (Ernie Kalnins, New Zealand Mathematical Society Newsletter, Issue 85, 2002)

"The author describes Hamiltonian aspects of vortex dynamics, enabling graduate students and researchers to use this book as an entry point into large literature on integrable and nonintegrable vortex problems. ... Exercises given at the end of each chapter could be very useful to the readers to enhance their knowledge. ... The references are adequate for further study. ... The book is a welcome addition to book shelves of researchers pursuing the N-vortex problem." (Adabala Ramachandra Rao, Zentralblatt MATH, Vol. 981, 2002)

Synopsis

This book is an introduction to current research on the N- vortex problem of fluid mechanics. Its goal is to describe the Hamiltonian aspects of vortex dynamics so that graduate students and researchers can use the book as an entry point into the rather large literature on integrable and non-integrable vortex problems within the broader context of dynamical systems. It is as self-contained as possible: the only training required of the reader is a good background in advanced calculus and ordinary and partial differential equations at the level of a typical undergraduate engineering, physics, or applied mathematics major. Exercises of varying difficulty are found at the end of each chapter which often require the reader to fill in details of proofs or complete examples.

Edition details

• Publisher: Springer
• Publication date: 2001
• Language: English
• ISBN 10: 0387952268
• ISBN 13: 9780387952260
• Binding: Hardcover
• Number of pages: 438