Elementary Introduction to Spatial and Temporal Fractals
Elementary Introduction to Spatial and Temporal Fractals
Fractals play an important role in modeling natural phenomena and engineering processes. And fractals have a close connection to the concepts of chaotic dynamics. This monograph presents definitions, concepts, notions and methodologies of both spatial and temporal fractals. It addresses students and researchers in chemistry and in chemical engineering. The authors present the concepts and methodologies in sufficient detail for uninitiated readers. They include many simple examples and graphical illustrations. They outline some examples in more detail: Perimeter fractal dimension of char particles, surface fractal dimension of charcoal; fractal analysis of pressure fluctuation in multiphase flow systems. Readers who master the concepts in this book, can confidently apply them to their fields of interest.
3. Examples of Fractal Geometry
3.1 Cantor Set (0 < dF < 1)
3.2 Rugged Lines (1 < dF ? 2)
3.3 Irregular Surface (2 < dF ? 3)
3.4 Growth Processes
4. Fractals in Time
4.1 Change of Commodity Prices
4.2 Fractional Brownian Motion
4.3 Fractal Stochastic Processes
5. Fractals in Chaos
5.1 Quantification of Chaos
6. Epilog
A1. Appendix 1: Perimeter Fractal Dimension of Char Particles from a Downdraft Gasifier Through Image Analysis
A1.1 Theoretical
A1.1.1 Perimeter Fractal Dimension
Al.1.2 Geometrical Bases for Measurement
A1.2 Experimental
A1.2.1 Sample Generation
A1.2.2 Sample Preparation
A1.2.3 Measurement of Feret Diameter
A1.2.4 Evaluation of Perimeter Fractal Dimension
A1.3 Results and Discussion
A1.3.1 Comparison with Other Methods
A1.3.2 Evaluation of Various Methods
A2. Appendix 2: Surface Fractal Dimension of Rice Hull-Derived Charcoal from a Fluidized-Bed Reactor
A2.1 Theoretical
A2.2 Experimental
A2.3 Results and Discussion
A3. Appendix 3: Fractal Analysis of Pressure Fluctuations in Multiphase Flow Systems
A3.1 Theoretical
A3.1.1 Discrete-time Fractional Noise
A3.1.2 Rescaled Range Analysis
A3.2 Experimental
A3.2.1 Facilities
A3.2.2 Measurements and Computations
A3.3 Results and Discussion
Nomenclature
Literature Cited
Author Index.
1. Introduction
2. Fundamental Concepts and Definitions3. Examples of Fractal Geometry
3.1 Cantor Set (0 < dF < 1)
3.2 Rugged Lines (1 < dF ? 2)
3.3 Irregular Surface (2 < dF ? 3)
3.4 Growth Processes
4. Fractals in Time
4.1 Change of Commodity Prices
4.2 Fractional Brownian Motion
4.3 Fractal Stochastic Processes
5. Fractals in Chaos
5.1 Quantification of Chaos
6. Epilog
A1. Appendix 1: Perimeter Fractal Dimension of Char Particles from a Downdraft Gasifier Through Image Analysis
A1.1 Theoretical
A1.1.1 Perimeter Fractal Dimension
Al.1.2 Geometrical Bases for Measurement
A1.2 Experimental
A1.2.1 Sample Generation
A1.2.2 Sample Preparation
A1.2.3 Measurement of Feret Diameter
A1.2.4 Evaluation of Perimeter Fractal Dimension
A1.3 Results and Discussion
A1.3.1 Comparison with Other Methods
A1.3.2 Evaluation of Various Methods
A2. Appendix 2: Surface Fractal Dimension of Rice Hull-Derived Charcoal from a Fluidized-Bed Reactor
A2.1 Theoretical
A2.2 Experimental
A2.3 Results and Discussion
A3. Appendix 3: Fractal Analysis of Pressure Fluctuations in Multiphase Flow Systems
A3.1 Theoretical
A3.1.1 Discrete-time Fractional Noise
A3.1.2 Rescaled Range Analysis
A3.2 Experimental
A3.2.1 Facilities
A3.2.2 Measurements and Computations
A3.3 Results and Discussion
Nomenclature
Literature Cited
Author Index.
Fan, L. T.
Neogi, D.
Yashima, M.
| ISBN | 978-3-540-54212-4 |
|---|---|
| Medientyp | Buch |
| Copyrightjahr | 1991 |
| Verlag | Springer, Berlin |
| Umfang | IX, 168 Seiten |
| Abbildungen | IX, 168 p. |
| Sprache | Englisch |
