The Kinematics of Mixing: Stretching, Chaos, and Transport

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Cambridge University Press, 1989 - Mathematics - 364 pages
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In spite of its universality, mixing is poorly understood and generally speaking, mixing problems are attacked on a case-by-case basis. This is the first book to present a unified treatment of the mixing of fluids from a kinematical viewpoint. The author's aim is to provide a conceptually clear basis from which to launch analysis and to facilitate an understanding of the numerous mixing problems encountered in nature and technology. After presenting the necessary background in kinematics and fluid dynamics, Professor Ottino considers various examples of dealing with necessary background in dynamical systems and chaos. The book assumes little previous knowledge of fluid dynamics and dynamical systems and can be used as a textbook by final-year undergraduates, graduate students and researchers in applied mathematics, engineering science, geophysics and physics who have an interest in fluid dynamics, continuum mechanics and dynamical systems. It is profusely illustrated in colour, with many line diagrams and half-tones. Systems which illustrate the most important concepts, many exercises and examples are included.
 

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Contents

Introduction
1
Applications and geometrical structure
9
Flow trajectories and deformation
18
Conservation equations change of frame and vorticity
42
Computation of stretching and efficiency
64
Chaos in dynamical systems
96
Chaos in Hamiltonian systems
130
Mixing and chaos in twodimensional timeperiodic flows
154
Mixing and chaos in threedimensional and open flows
220
diffusion and reaction in lamellar structures
273
Cartesian rectors and tensors
319
Lisf of frequently used symbols
342
Author index
355
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