Initially a subfield of solid state physics, the study of mesoscopic systems has evolved over the years into a vast field of research in its own right. Keeping track its rapid progress, this book provides a broad survey of the latest developments in the field. The focus is on statistics and dynamics of mesoscopic systems with special emphasis on topics like quantum chaos, localization, noise and fluctuations, mesoscopic optics and quantum transport in nanostructures. Written with nonspecialists in mind, this book will also be useful to graduate students wishing to familiarize themselves with this field of research.

Polymers are substances made of macromolecules formed by thousands of atoms organized in one (homopolymers) or more (copolymers) groups that repeat themselves to form linear or branched chains, or lattice structures. The concept of polymer traces back to the years 1920's and is one of the most significant ideas of last century. It has given great impulse to indus try but also to fundamental research, including life sciences. Macromolecules are made of sm all molecules known as monomers. The process that brings monomers into polymers is known as polymerization. A fundamental contri bution to the industrial production of polymers, particularly polypropylene and polyethylene, is due to the Nobel prize winners Giulio Natta and Karl Ziegler. The ideas of Ziegler and Natta date back to 1954, and the process has been improved continuously over the years, particularly concerning the design and shaping of the catalysts. Chapter 1 (due to A. Fasano ) is devoted to a review of some results concerning the modelling of the Ziegler- Natta polymerization. The specific ex am pie is the production of polypropilene. The process is extremely complex and all studies with relevant mathematical contents are fairly recent, and several problems are still open.

A rich variety of real-life physical problems which are still poorly understood are of a nonlinear nature. Examples include turbulence, granular flows, detonations and flame propagation, fracture dynamics, and a wealth of new biological and chemical phenomena which are being discovered. Particularly interesting among the manifestations of nonlinearity are coherent structures. This book contains reviews and contributions reporting on the state of the art regarding the role of coherent structures and patterns in nonlinear science.

The polymer industry raises a large number of relevant mathematical problems with respect to the quality of manufactured polymer parts. These include in particular questions about: - the production of the polymeric material from a monomer (based on the Ziegler-Natta catalytic process) - the crystallization kinetic of the polymer melt - the coupling of the crystallization process with the fluid dynamics of the manufacturing process such as extrusion, injection moulding of film blowing, etc.This book provides the first unified presentation of the mathematical modelling of polymerization, crystallization and extrusion of polymer melts, by means of advanced methods, presented in an accessible way for applied scientists and engineers. The present volume is the result of a long-term cooperation between different research teams in Europe within the ECMI Special Interest Group on "Polymers".

A rich variety of real-life physical problems which are still poorly understood are of a nonlinear nature. Examples include turbulence, granular flows, detonations and flame propagation, fracture dynamics, and a wealth of new biological and chemical phenomena which are being discovered. Particularly interesting among the manifestations of nonlinearity are coherent structures. This book contains reviews and contributions reporting on the state of the art regarding the role of coherent structures and patterns in nonlinear science.

Initially a subfield of solid state physics, the study of mesoscopic systems has evolved over the years into a vast field of research in its own right. Keeping track its rapid progress, this book provides a broad survey of the latest developments in the field. The focus is on statistics and dynamics of mesoscopic systems with special emphasis on topics like quantum chaos, localization, noise and fluctuations, mesoscopic optics and quantum transport in nanostructures. Written with nonspecialists in mind, this book will also be useful to graduate students wishing to familiarize themselves with this field of research.