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Rene Denfeld: IMG Powell’s Q&A: Rene Denfeld



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    The Enchanted

    Rene Denfeld 9780062285508

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Applied Mathematical Sciences #125: Topological Methods in Hydrodynamics

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Applied Mathematical Sciences #125: Topological Methods in Hydrodynamics Cover

 

Synopses & Reviews

Publisher Comments:

Topological hydrodynamics is a young branch of mathematics studying topological features of flows with complicated trajectories, as well as their applications to fluid motions. It is situated at the crossroad of hyrdodynamical stability theory, Riemannian and symplectic geometry, magnetohydrodynamics, theory of Lie algebras and Lie groups, knot theory, and dynamical systems. Applications of this approach include topological classification of steady fluid flows, descriptions of the Korteweg-de Vries equation as a geodesic flow, and results on Riemannian geometry of diffeomorphism groups, explaining, in particular, why longterm dynamical weather forecasts are not reliable. Topological Methods in Hydrodynamics is the first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics for a unified point of view. The necessary preliminary notions both in hydrodynamics and pure mathematics are described with plenty of examples and figures. The book is accessible to graduate students as well as to both pure and applied mathematicians working in the fields of hydrodynamics, Lie groups, dynamical systems and differential geometry.

Synopsis:

This book describes the general approach to hydrodynamics with its applications to such problems as hydrodynamical stability and fast kinematic dynamo problem, helicity and asymptotic Hopf invariant, to the topology of the stationary solutions of the Euler equations and to integral invariants of ideal fluid hydrodynamics and magnet-hydrodynamics.

Synopsis:

The first to examine topological, group-theoretic and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified viewpoint, this book describes preliminary notions in hydrodynamics and pure mathematics with numerous examples and figures.

Synopsis:

The first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. The book is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry.

Description:

Includes bibliographical references (p. [345]-369) and index.

Table of Contents

Group and Hamiltonian Structures of Fluid Dynamics.- Topology of Steady Fluid Flows.- Topological Properties of Magnetic and Vorticity Fields.- Differential Geometry of Diffeomorphism Groups.- Kinematic Fast Dynamo Problems.- Dynamical Systems with Hydrodynamical Background.- References.- Index.

Product Details

ISBN:
9780387949475
With:
Khesin, Boris
Author:
Arnol'd, V. I.
Author:
Arnol'd, Vladimir I.
Author:
Arnold, V. I.
Author:
Khesin, Boris A.
Author:
Khesin, Boris
Publisher:
Springer
Location:
New York, NY
Subject:
Physics
Subject:
Applied
Subject:
Hydraulics
Subject:
Topology
Subject:
Hydrodynamics
Subject:
General Mathematics
Subject:
Mathematics - General
Subject:
Fluid- and Aerodynamics
Subject:
Statistical Physics, Dynamical Systems and Complexity
Subject:
Computational intelligence
Subject:
Mathematics-Applied
Subject:
Mathematics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Subject:
Engineering
Copyright:
Edition Number:
2
Edition Description:
1st ed. 1998. Corr. 2nd printing
Series:
Applied Mathematical Sciences
Series Volume:
v. 125
Publication Date:
19980431
Binding:
HARDCOVER
Language:
English
Illustrations:
Yes
Pages:
391
Dimensions:
235 x 155 mm 1610 gr

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Related Subjects

Engineering » Civil Engineering » General
Reference » Science Reference » Technology
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Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry
Science and Mathematics » Physics » Fluid Mechanics
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Applied Mathematical Sciences #125: Topological Methods in Hydrodynamics New Hardcover
0 stars - 0 reviews
$140.25 In Stock
Product details 391 pages Springer-Verlag - English 9780387949475 Reviews:
"Synopsis" by , This book describes the general approach to hydrodynamics with its applications to such problems as hydrodynamical stability and fast kinematic dynamo problem, helicity and asymptotic Hopf invariant, to the topology of the stationary solutions of the Euler equations and to integral invariants of ideal fluid hydrodynamics and magnet-hydrodynamics.
"Synopsis" by , The first to examine topological, group-theoretic and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified viewpoint, this book describes preliminary notions in hydrodynamics and pure mathematics with numerous examples and figures.
"Synopsis" by , The first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. The book is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry.
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