The N-Vortex Problem
Subtitle: Analytical Techniques
By: by Paul K. Newton
Series: Applied Mathematical Sciences -- 145; Applied mathematical sciences (Springer-Verlag New York Inc.) -- 145.
Publisher: Springer New York
Published: 2001
Place of publication: New York, NY
Language: eng
Format: [electronic resource] :
Number of pages: 415
ISBN-13: 9781441929167; 9781468492903
Subjects: Mathematics; Cell aggregation; Physics; Engineering
Description: 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.
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Mode of access: World Wide Web.
Table of contents: title: N-Vortices in the Plane; title: Domains with Boundaries; title: Vortex Motion on a Sphere; title: Geometric Phases; title: Statistical Point Vortex Theories; title: Vortex Patch Models; title: Vortex Filament Models; title: References.