A comprehensive, 1998 account of the practical aspects and pitfalls of the applications of fractal modelling in the physical sciences.

The investigation of phenomena involving fractals has gone through a spectacular development in the last decade. Many physical, technological and biological processes have been shown to be related to and described by objects with non-integer dimensions. The physics of far-from-equilibrium growth phenomena represents one of the most important fields in which fractal geometry is widely applied. During the last couple of years considerable experimental, numerical and theoretical information has accumulated concerning such processes.This book, written by a well-known expert in the field, summarizes the basic concepts born in the studies of fractal growth and also presents some of the most important new results for more specialized readers. It also contains 15 beautiful color plates demonstrating the richness of the geometry of fractal patterns. Accordingly, it may serve as a textbook on the geometrical aspects of fractal growth and it treats this area in sufficient depth to make it useful as a reference book. No specific mathematical knowledge is required for reading this book which is intended to give a balanced account of the field.

This text describes the statistcal behavior of complex systems and shows how the fractional calculus can be used to model the behavior. The discussion emphasizes physical phenomena whose evolution is best described using the fractional calculus, such as systems with long-range spatial interactions or long-time memory. The book gives general strategies for understanding wave propagation through random media, the nonlinear response of complex materials, and the fluctuations of heat transport in heterogeneous materials.

The structure of a growth or an etch front on a surface is not only a subject of great interest from the practical point of view but also is of fundamental scientific interest. Very often surfaces are created under non-equilibrium conditions such that the morphology is not always smooth. In addition to a detailed description of the characteristics of random rough surfaces, Experimental Methods in the Physical Sciences, Volume 37, Characterization of Amorphous and Crystalline Rough Surface-Principles and Applications will focus on the basic principles of real and diffraction techniques for quantitative characterization of the rough surfaces. The book thus includes the latest development on the characterization and measurements of a wide variety of rough surfaces. The complementary nature of the real space and diffraction techniques is fully displayed. Key Features * An accessible description of quantitative characterization of random rough surfaces and growth/etch fronts * A detailed description of the principles, experimentation, and limitations of advanced real-space imaging techniques (such as atomic force microscopy) and diffraction techniques (such as light scattering, X-ray diffraction, and electron diffraction) * Characterization of a variety of rough surfaces (e.g., self-affine, mounded, anisotropic, and two-level surfaces) accompanied by quantitative examples to illustrate the essence of the principles * An insightful description of how rough surfaces are formed * Presentation of the most recent examples of the applications of rough surfaces in various areas

This book describes diffusion and transport in disordered media such as fractals and random resistor networks.

Thin film technology is used in many applications such as microelectronics, optics, hard and corrosion resistant coatings and micromechanics, and thin films form a uniquely versatile material base for the development of novel technologies within these industries. Thin film growth provides an important and up-to-date review of the theory and deposition techniques used in the formation of thin films.Part one focuses on the theory of thin film growth, with chapters covering nucleation and growth processes in thin films, phase-field modelling of thin film growth and surface roughness evolution. Part two covers some of the techniques used for thin film growth, including oblique angle deposition, reactive magnetron sputtering and epitaxial growth of graphene films on single crystal metal surfaces. This section also includes chapters on the properties of thin films, covering topics such as substrate plasticity and buckling of thin films, polarity control, nanostructure growth dynamics and network behaviour in thin films.With its distinguished editor and international team of contributors, Thin film growth is an essential reference for engineers in electronics, energy materials and mechanical engineering, as well as those with an academic research interest in the topic. - Provides an important and up-to-date review of the theory and deposition techniques used in the formation of thin films - Focusses on the theory and modelling of thin film growth, techniques and mechanisms used for thin film growth and properties of thin films - An essential reference for engineers in electronics, energy materials and mechanical engineering

This book focuses on the control of fractal behaviors in nonlinear dynamics systems, addressing both the principles and purposes of control. For fractals in different systems, it presents revealing studies on the theory and applications of control, reflecting a spectrum of different control methods used with engineering technology. As such, it will benefit researchers, engineers, and graduate students in fields of fractals, chaos, engineering, etc.