Fractal Concepts in Surface Growth

by
Albert-László Barabási, IBM T. J. Watson Research Center, Yorktown Heights, NY
H. Eugene Stanley, Boston University

Fractals and surfaces are two of the most widely-studied areas of modern physics. In fact, most surfaces in nature are fractals. In this book, Drs. Barabási and Stanley explain how fractals can be successfully used to describe and predict the morphology of surface growth. The authors begin by presenting basic growth models and the principles used to develop them. They next demonstrate how models can be used to answer specific questions about surface roughness. In the second half of the book, they discuss in detail two classes of phenomena: fluid flow in porous media and molecular beam epitaxy (MBE). In each case, the authors review the model and analytical approach, and present experimental results.

This books is the first attempt to unite the subjects of fractals and surfaces, and it will appeal to advanced undergraduate and graduate students in condensed matter physics and statistical mechanics. Because of the technological importance of BME, it will also be of interest to scientists, particularly materials scientists, working in industry and research.

Contents:

Part I: Introduction/Interfaces in Nature/Scaling Concepts/Fractal Concepts/ Part II: Nonequilibrium roughening/Random deposition and growth equations/ Linear theory/Kardar-Parisi-Zhang equation/Renormalization group approach/Discrete growth models/Part III: Interfaces in Random Media/Basic Phenomena/Models with quenched noise/Experiments/Part IV: Molecular Beam Epitaxy/Basic Phenomena of MBE/Linear theory of MBE/Nonlinear theory of MBE/Discrete models for MBE/MBE experiments/Submonolayer deposition/The roughening transition/Nonlocal growth models/Diffusion bias/Part V: Noise/Diffusive versus deposition noise/ Correlated noise/Rare events and the Zhang model/Part VI: Advanced Topics/ Multi-affine surfaces/Varients of the KPZ equation/Directed polymers/Part VII: Finale/Summary of the continuum growth equations/Outlook/Appendices/Numerical recipes/Dynamic renormalization group/Hamiltonian description

1995 c. 350 pp. Many line diagrams, some tables, many exercises

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