Chapter 13 - Davidson Physics

CHAPTER 14. FRACTALS AND KINETIC GROWTH MODELS 557Fereydoon Family and David P. Landau, editors, Kinetics of Aggregation and Gelation, North-Holland (1984). A collection of research papers that give a wealth of information, pictures,and references on a variety of growth models.Fereydoon Family, Daniel E. Platt, and Tamás Vicsek, “Deterministic growth model of patternformation in dendritic solidification,” J. Phys. A 20, L1177–L1183 (1987). The authors discussthe nature of Laplace fractal carpets.Fereydoon Family and Tamás Vicsek, editors, Dynamics of Fractal Surfaces, World Scientific(1991). A collection of reprints.Fereydoon Family, Y. C. Zhang, and Tamás Vicsek, “Invasion percolation in an external field:Dielectric breakdown in random media,” J. Phys. A. 19, L733–L737 (1986).Jens Feder, Fractals, Plenum Press (1988). This text discusses the applications as well as themathematics of fractals.Gary William Flake, The Computational Beauty of Nature, MIT Press (2000).J.-M. Garcia-Ruiz, E. Louis, P. Meakin, and L. M. Sander, editors, Growth Patterns in PhysicalSciences and Biology, NATO ASI Series B304, Plenum (1993).Peter Grassberger, “Critical percolation in high dimensions,” Phys. Rev. E 67, 036101-1–4 (2003).The author uses the Leath algorithm to estimate the value of p c .Thomas C. Halsey, “Diffusion limited aggregation: A model for pattern formation,” Physics Today53 (11), 36 (2000).J. M. Hammersley and D. C. Handscomb, Monte Carlo Methods, Methuen (1964). The chapteron percolation processes discusses a growth algorithm for percolation.H. J. Herrmann, “Geometrical cluster growth models and kinetic gelation,” Physics Reports 136,153–224 (1986).Robert C. Hilborn, Chaos and Nonlinear Dynamics, second edition, Oxford University Press(2000).Ofer Malcai, Daniel A. Lidar, Ofer Biham, and David Avnir, “Scaling range and cutoffs in empiricalfractals,” Phys. Rev. E, 56, 2817–2828 (1997). The authors show that experimentalreports of fractal behavior are typically based on a scaling range that spans only 0.5–2 decadesand discuss the possible implications of this limited scaling range.Benoit B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman (1983). An influentialand beautifully illustrated book on fractals.Imtiaz Majid, Daniel Ben-Avraham, Shlomo Havlin, and H. Eugene Stanley, “Exact-enumerationapproach to random walks on percolation clusters in two dimensions,” Phys. Rev. B 30, 1626(1984).