Elementary Introduction to Spatial and Temporal Fractals

ISBN-13: 9783540542124 / Angielski / Miękka / 1991 / 168 str.

L. T. Fan; D. Neogi; M. Yashima

Opis

This monograph presents the definitions, concepts, notions and methodologies of both spatial and temporal fractals. Simple examples and illustrations are used to illustrate the text, and all concepts are applied to various scientific and engineering problems.

Spis treści

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.

O autorze

The concepts of spatial and temporal fractals are applied to many scientific and engineering problems. The authors are professors in chemical engineering and statistics. They introduce fractals without mathematical rigor for students and practitioners. Many simple examples illustrate the book.