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分形几何与流体PDF|Epub|txt|kindle电子书版本网盘下载
- 瞿波著 著
- 出版社： 上海：上海社会科学院出版社
- ISBN：9787552004748
- 出版时间：2014
- 标注页数：387页
- 文件大小：53MB
- 文件页数：399页
- 主题词：分形几何
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图书目录
序1
自序1
分形几何介绍19
博士论文19
The Use of Fractional Brownian Motion in the Modelling of the Dispersion of Contaminants in Fluids19
List of Symbols19
Chapter 1 Outline of Project23
1.Introduction23
2.Fractals and Fractional Brownian Motion23
3.Aim and Objectives24
4.Structure of Thesis25
Chapter 2 Diffusion and Dispersion in Fluids26
1.Introduction26
2.Molecular Diffusion： Fick’s Law and the Diffusion Equation27
3.Statistical Theory of Diffusion： Brownian Motion29
4.Turbulent Diffusion32
4.1 Introduction32
4.2 Eddies33
4.3 Taylor’s Theorem33
4.4 The Relationship Between Lagrangian and Eulerian Measurement36
4.5 Relative Diffusion and Richardson’s Law37
4.6 Okubo’s Oceanic Diffusion Diagrams38
5.Shear Dispersion41
5.1 Introduction41
5.2 Taylor and Elder’s Shear Dispersion Results42
5.3 Dispersion in Rivers43
5.4 Dispersion in the Sea48
6.Numerical Model of Dispersion55
6.1 Solution of the Advection-Diffusion Equation55
6.2 The Disadvantage of Solving the Advection-Diffusion Equation57
7.Traditional Particle Tracking Methods58
8.Summary62
Chapter 3 Brownian Motion， Fractional Brownian Motion and Fractal Geometry64
1.Brownian Motion64
1.1 The Definition of Brownian Motion64
1.2 Two Simple Random Walks65
1.3 Brownian Motion Generation67
1.4 The Properties of a One-Dimensional Brownian Motion Time Trace70
1.5 The Skewness and Kurtosis of Random Walks73
1.6 Random Walks in Two Dimensions75
1.7 The Last Steps of the Random Walks in Two Dimensions77
2.Fractional Brownian Motion77
2.1 Introduction77
2.2 FBM Model85
2.3 FBMINC Model90
2.4 The Comparison of the FBM and FBMINC Models93
2.5 FBM Plots in One Dimension98
2.6 The Relationship Between Memory， M， Number of Steps， NSTEP， and Number of Particles， P104
2.7 Fractional Brownian Motion in Two Dimensions107
2.8 Projection of Two-Dimensional Fractional Brownian Motion109
2.9 The Use of Simpler Probability Distributions to Reduce CPU Time111
2.10 Long Term Fickian Behaviour115
3.fBm as a Random Fractal Function117
3.1Fractal Geometry and Fractal Curves117
3.2 Fractal Dimension119
3.3 Fractal Properties of fBm120
3.4 Methods for Determining H from Real Data125
4.Summary129
Chapter 4 Coastal Bay Modelling130
1.Introduction130
2.New Particle Tracking Method Using in the Bay130
2.1 Advection132
2.2 Diffusion133
2.3 Choosing a Time Interval136
2.4 Choosing a Diffusion Coefficient140
2.5 Boundary Reflection142
2.6 The Particle Tracking Model144
2.7 Particle Clouds155
2.8 Concentration Calculation and Plots162
2.9 Further Reported Results163
3.Shear Dispersion169
3.1 Simple Shear Dispersion （Brownian Motion）169
3.2 Shear Dispersion with Fractional Brownian Motion174
3.3 Shear Dispersion in the Coastal Bay Model Recirculation Zone178
4.Summary186
Chapter 5 Simulation of Observed Coastal Dispersion189
1.Introduction189
2.Northumbrian Coastal Water Data Sets190
3.Three Methods for Calculating the Standard Deviation of the Dye Patch Concentrations197
3.1 The SQ-Method210
3.2 The R-Method211
3.3 The SR-Method213
3.4 Estimation of the Direction of the Mean Advective Velocity Vector for Each Patch213
4.Comparison of the Three Methods215
4.1 The Reason for Introducing the SR-Method215
4.2 Comparison of the Results Using the Three Methods216
5.Accuracy of the Results218
5.1 Sensitivity of the Centre218
5.2 The Concentration Function Calculation220
6.Simulation of the Observed Dye Patches Using an fBm Based Particle Tracking Model220
6.1 The Accelerated Fractional Brownian Motion （AFBM） Model223
6.2 Simulation Using the FBMINC and AFBM Models227
6.3 Concentration Calculations236
6.4 Contour Plots237
7.Summary239
Chapter 6 Conclusions， Discussion and Recommendations241
1.Introduction241
2.Achievement of Objectives241
3.Discussion244
4.Recommendations for Future Work246
Appendix249
brown.for249
fbm.for252
fbminc.for256
bayflu.for260
baycloud.for266
concent.for271
srb1.for273
srbb1.for282
sruvb1.for285
afbm.for287
References292
分形应用论文选317
分数布朗运动的简化和应用317
从分形维数到海洋表面漂浮物轨迹的模拟328
流体中污染物扩散的分形模拟335
用分数型布朗运动模拟海湾的剪切湍流分散343
Development of FBMINC model for particle diffusion in fluids354
加速分数型布朗运动粒子追踪模型在水面污染扩散中的应用377
后记387