Elementary Introduction to Spatial and Temporal Fractals: 55 - Brossura

D. Neogi, L. T. Fan

Brossura

ISBN 10: 3540542124 ISBN 13: 9783540542124

Casa editrice: Springer Berlin Heidelberg, 1991

Riassunto

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.

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Contenuti

1. Introduction.- 2. Fundamental Concepts and Definitions.- 3. Examples of Fractal Geometry.- 3.1 Cantor Set (0 < dF < 1).- 3.2 Rugged Lines (1 < dF ? 2).- 3.2.1 Koch Curve and Lake.- 3.2.2 Fractal Dimension of a Rugged Profile.- 3.2.3 Multi-fractal Dimensions.- 3.3 Irregular Surface (2 < dF ? 3).- 3.3.1 Monolayers of Different Adsorbates.- 3.3.2 Monolayers on Adsorbent Particles of Different Sizes.- 3.3.3 Pore-size Distribution.- 3.4 Growth Processes.- 3.4.1 Eden (Surface Growth) Model.- 3.4.2 Diffusion-limited Aggregation (DLA).- 4. Fractals in Time.- 4.1 Change of Commodity Prices.- 4.1.1 Stable (Levy) Distribution.- 4.2 Fractional Brownian Motion.- 4.2.1 Self-affinity.- 4.2.2 Discrete-time Fractional Noise.- 4.2.3 Rescaled Range Analysis.- 4.3 Fractal Stochastic Processes.- 4.3.1 Bernoulli’s Scaling and the St. Petersburg Paradox.- 4.3.2 Fractal Random Walk.- 4.3.3 Fractal Time.- 5. Fractals in Chaos.- 5.1 Quantification of Chaos.- 5.1.1 Stochastic or Chaotic.- 5.1.2 Calculation of Attractor Dimension from a Time Series.- 5.1.3 Lyapunov Exponent and Limits of Predictability.- 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.

Product Description

Book by Fan LT Neogi D Yashima M

Dettagli dell'edizione

• Editore: Springer Berlin Heidelberg
• Data di pubblicazione: 1991
• Lingua: Inglese
• ISBN 10: 3540542124
• ISBN 13: 9783540542124
• Rilegatura: Copertina flessibile
• Numero di pagine: 184
• Contatto del produttore: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Germania