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An Introduction to the Geometry and Topology of Fluid Flows by H. Keith Moffatt (auth.), Renzo L. Ricca (eds.)

By H. Keith Moffatt (auth.), Renzo L. Ricca (eds.)

Leading specialists current a different, valuable advent to the learn of the geometry and typology of fluid flows. From simple motions on curves and surfaces to the hot advancements in knots and hyperlinks, the reader is progressively ended in discover the attention-grabbing global of geometric and topological fluid mechanics.
Geodesics and chaotic orbits, magnetic knots and vortex hyperlinks, continuous flows and singularities develop into alive with greater than a hundred and sixty figures and examples.
within the commencing article, H. okay. Moffatt units the speed, providing 8 amazing difficulties for the twenty first century. The booklet is going directly to supply suggestions and methods for tackling those and lots of different attention-grabbing open problems.

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Additional resources for An Introduction to the Geometry and Topology of Fluid Flows

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American Mathematical Society. 7. S. (1994) Topology for Physicists. Springer. 8. Smoller, J. (1994) Shock Waves and Reaction-Diffusion equations. Springer. 1. 2. ch Abstract. The aim of this article is to present an elementary introduction to classical knot theory. The word classical means two things. First, it means the study of knots in the usual 3D space R3 or S3. It also designates knot theory before 1984. In section 1 we describe the basic facts: curves in 3D space, isotopies, knots, links and knot types.

Vp E cvpn, 1r-l(p) ~ circle {e ifJ I 0 ~ () < 21r}. This is the Hopf fibration of s2n+l over

11. F. (1968) Some integral formulas for space curves and their generalization. Am. J. Math. 40(4), 1321-1345. 12. F. (1968) The self-linking number of a closed space curve. J. Math. & Mech. 17,975-985. 13. Rolfsen, D. (1976) Knots and Links. Publish or Perish, Wilmington, USA. 14. Rudin, W. (1970) Real and Complex Analysis. Mac Graw Hill. 15. H. (1969) Self-linking and the Gauss integral in higher dimensions. Am. J. Math. 91, 693-728. P. 8888, succ. ca Abstract. This is a transcription of a series of 4 lectures presented at the Newton Institute in December 2000 to an audience of fluid dynamicists and an astrophysicist.

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