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　　分類: 图书,进口原版书,科学与技术 Science & Techology ,

作者： Rob Sturman著

出 版 社：

出版时间： 2006-10-1字数：版次： 1页数： 281印刷时间： 2006/10/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780521868136包装： 精装编辑推荐

作者介绍：Rob Sturnan

Rob Sturnan gained his PhD from University College London in 2000. He is currently carrying out research on mixing in microfluidics at the University of Bristol.

内容简介

Mixing processes occur in many technological and natural applications, with length and time scales ranging from the very small to the very large. The diversity of problems can give rise to a diversity of approaches. Are there concepts that are central to all of them? Are there tools that allow for prediction and quantification? The authors show how a variety of flows in very different settings possess the characteristic of streamline crossing. This notion can be placed on firm mathematical footing via Linked Twist Maps (LTMs), which is the central organizing principle of this book. The authors discuss the definition and construction of LTMs, provide examples of specific mixers that can be analyzed in the LTM framework and introduce a number of mathematical techniques which are then brought to bear on the problem of fluid mixing. In a final chapter, they present a number of open problems and new directions.

目录

Acknowledgments

1Mixing: physical issues

1.1Length and time scales

1.2Stretching and folding, chaotic mixing

1.3Reorientation

1.4Diffusion and scaling

1.5Examples

1.5.1The Aref blinking vortex flow

1.5.2Samelson's tidal vortex advection model

1.5.3Chaotic stirring in tidal systems

1.5.4Cavity flows

1.5.5An electro-osmotic driven micromixer blinking flow

1.5.6Egg beater flows

1.5.7A blinking flow model of mixing of granular materials

1.5.8Mixing in DNA microarrays

1.6Mixing at the microscale

2Linked twist maps: definition, construction and the relevance to mixing

2.1Introduction

2.2Linked twist maps on the torus

2.2.1Geometry of mixing for toral LTMs

2.3Linked twist maps on the plane

2.3.1Geometry of mixing for LTMs on the plane

2.4Constructing a LTM from a blinking flow

2.5Constructing a LTM from a duct flow

2.6More examples of mixers that can be analysed in the LTM framework

3The ergodic hierarchy

3.1Introduction

3.2Mathematical ideas for describing and quantifying the flow domain, and a 'blob' of dye in the flow

3.2.1Mathematical structure of spaces

3.2.2Describing sets of points

3.2.3Compactness and connectedness

3.2.4Measuring the 'size' of sets

3.3Mathematical ideas for describing the movement of blobs in the flow domain

3.4Dynamical systems terminology and concepts

3.4.1Terminology for general fluid kinematics

3.4.2Specific types of orbits

3.4.3Behaviour near a specific orbit

3.4.4Sets of fluid particles that give rise to 'flow structures'

3.5Fundamental results for measure-preserving dynamical systems

3.6Ergodicity

3.6.1A typical scheme for proving ergodicity

3.7Mixing

3.8The K-property

3.9The Bernoulli property

3.9.1The space of (bi-intinite) symbol sequences, [Sigma superscript N]

3.9.2The shift map

3.9.3What it means for a map to have the Bernoulli property

3.10Summary

4Existence of a horseshoe for the linked twist map

4.1Introduction

4.2The Smale horseshoe in dynamical systems

4.2.1The standard horseshoe

4.2.2Symbolic dynamics

4.2.3Generalized horseshoes

4.2.4The Conley-Moser conditions

……

5Hyperbolicity

6The ergodic partition for toral linked twist maps

7Ergodicity and the Bernoulli property for toral linked twist maps

8Linked twist maps on the plane

9Further directions and open problems

References

Index

 

 

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