This book provides an interdisciplinary presentation of the current knowledge of pattern formation in complex system, with sufficiently many details, tools, and concrete examples to be useful for the graduate student or scientist entering this area of research.

Spatio-temporal patterns appear almost everywhere in nature, and their description and understanding still raise important and basic questions. However, if one looks back 20 or 30 years, definite progress has been made in the modeling of insta bilities, analysis of the dynamics in their vicinity, pattern formation and stability, quantitative experimental and numerical analysis of patterns, and so on. Universal behaviors of complex systems close to instabilities have been determined, leading to the wide interdisciplinarity of a field that is now referred to as nonlinear science or science of complexity, and in which initial concepts of dissipative structures or synergetics are deeply rooted. In pioneering domains related to hydrodynamics or chemical instabilities, the interactions between experimentalists and theoreticians, sometimes on a daily basis, have been a key to progress. Everyone in the field praises the role played by the interactions and permanent feedbacks between ex perimental, numerical, and analytical studies in the achievements obtained during these years. Many aspects of convective patterns in normal fluids, binary mixtures or liquid crystals are now understood and described in this framework. The generic pres ence of defects in extended systems is now well established and has induced new developments in the physics of laser with large Fresnel numbers. Last but not least, almost 40 years after his celebrated paper, Turing structures have finally been ob tained in real-life chemical reactors, triggering anew intense activity in the field of reaction-diffusion systems."

In materials, critical phenomena such as phase transitions, plastic deformation and fracture are intimately related to self-organization. Understanding the origin of spatio-temporal order in systems far from thermal equilibrium and the selection mechanisms of spatial structures and their symmetries is a major theme of present day research on the structure of continuous matter. Furthermore, the development of methods for producing spatially-ordered and self-assembled microstructure in solids by non-equilibrium methods opens the door to many technological applications. There is an increasing demand for a better understanding of new materials from a more fundamental point of view. In order to describe and understand the behavior of such materials, dynamical concepts related to non-equilibrium phenomena, irreversible thermodynamics, nonlinear dynamics, and bifurcation theory, are required. The generic presence of defects and their crucial influence on pattern formation and critical phenomena in extended systems is now well-established. Similar to observations in hydrodynamical, liquid crystal, and laser systems, defects in materials have a profound effect. We found it thus timely to develop a unified presentation of tools, concepts, and methods that are useful to material scientists and engineers. Although specialized treatments of various topics covered in this book are available, we feel that a comprehensive approach may give the reader a higher vantage point. Hence, emphasis is placed on combining the basic physical, mathematical and computational aspects with technological applications within the material's life-cycle, from processing, degradation to eventual failure. The book is divided into two parts that are organized as follows. The first volume of this book is devoted to the most basic concepts of the physics, mechanics and mathematical theory utilized in the analysis of non-equilibrium materials. The reader is exposed to a rigorous background on material deformation, defect theory transport processes, and the statistical mechanics and thermodynamics of phase transitions. Mathematical concepts of non-linear dynamics, such as bifurcation and instability theory, the dynamics of complex systems near pattern forming instabilities, the generic aspects of pattern formation, selection and stability are presented. Stochastic and numerical methods used in this field are also introduced. The methods and techniques developed in the first volume are applied in the second volume to specific problems in various advanced technologies. These applications include plastic and fracture instabilities, interfacial morphological instabilities in solidification, crystal growth, electro-deposition, surface instabilities in laser, plasma and chemical vapor processing, and material aging instabilities under irradiation and chemical corrosion attack.