Chapter 13 - Davidson Physics

CHAPTER 14. FRACTALS AND KINETIC GROWTH MODELS 558Paul Meakin, Fractals, Scaling and Growth Far From Equilibrium, Cambridge University Press(1998). Also see P. Meakin, “The growth of rough surfaces and interfaces,” Physics Reports235, 189–289 (1993). The author has written many seminal articles on DLA and similarmodels.L. Niemeyer, L. Pietronero, and H. J. Wiesmann, “Fractal dimension of dielectric breakdown,”Phys. Rev. Lett. 52, 1033 (1984).H. O. Peitgen and P. H. Richter, The Beauty of Fractals, Springer-Verlag (1986).Luciano Pietronero and Erio Tosatti, editors, Fractals in Physics, North-Holland (1986). A collectionof research papers, many of which are accessible to the motivated reader.Raissa M. D’Souza, “Anomalies in simulations of nearest neighbor ballistic deposition,” Int. J.Mod. Phys. C 8 (4), 941–951 (1997). The author finds that ballistic deposition is a sensitivephysical test for correlations present in pseudorandom sequences.F. Reif, Fundamentals of Statistical and Thermal Physics, McGraw-Hill (1965). Einstein’s relationbetween the diffusion and mobility is discussed in Chapter 15.John C. Russ, Fractal Surfaces, Plenum Press (1994).Evelyn Sander, Leonard M. Sander, and Robert M. Ziff, “Fractals and Fractal Correlations,”Computers in Physics 8, 420–425 (1994). An introduction to fractal growth models and thecalculation of their properties.H. Eugene Stanley and Nicole Ostrowsky, editors, On Growth and Form, Martinus Nijhoff Publishers,Netherlands (1986). A collection of research papers at the same level as the 1984Family and Landau collection.Hideki Takayasu, Fractals in the Physical Sciences, John Wiley & Sons (1990).David D. Thornburg, Discovering Logo, Addison-Wesley (1983). The book is more accuratelydescribed by its subtitle, An Invitation to the Art and Pattern of Nature. The nature ofrecursive procedures and fractals are discussed using many simple examples.Donald L. Turcotte, Fractals and Chaos in Geology and Geophysics, Cambridge University Press(1992).Tamás Vicsek, Fractal Growth Phenomena, second edition, World Scientific Publishing (1992).This book contains an accessible introduction to diffusion limited and cluster-cluster aggregation.Bruce J. West, Fractal Physiology and Chaos in Medicine, World Scientific Publishing (1990).David Wilkinson and Jorge F. Willemsen, “Invasion percolation: A new form of percolation theory,”J. Phys. A 16, 3365–3376 (1983).Yu-Xia Zhang, Jian-Ping Sang, Xian-Wu Zou, and Zhun-Zhi Jin, “Random walk on percolationunder an external field,” Physica A 350, 163–172 (2005). The authors consider random walkswith a drift.