Phase transitions in disordered systems and related dynamical phenomena are a topic of intrinsically high interest in theoretical and experimental physics. This book presents a unified view, adopting concepts from each of the disjoint fields of disordered systems and nonlinear dynamics. Special attention is paid to the glass transition, from both experimental and theoretical viewpoints, to modern concepts of pattern formation, and to the application of the concepts of dynamical systems for understanding equilibrium and nonequilibrium properties of fluids and solids. The content is accessible to graduate students, but will also be of benefit to specialists, since the presentation extends as far as the topics of ongoing research work.

This book deals with a series of topics on the cutting edge of nonlinear science, striking a balance between theory and experiment. It consists of two innovative introductory presentations on dynamical systems and fluid dynamics and six chapters on advanced research. A nontrivial interrelation between the different topics becomes apparent throughout the book as an indication of the underlying unity and genericity of nonlinear phenomena. There is a continuous emphasis on conceptual issues often introduced via concrete examples. A common feature is that most of the systems under study are extended, nonhomogeneous and far from equilibrium. The book also exhibits an interesting interplay between deterministic and stochastic approaches.

A new edition of this well-established monograph, this volume provides a comprehensive overview over the still fascinating field of chaos research. The authors include recent developments such as systems with restricted degrees of freedom but put also a strong emphasis on the mathematical foundations. Partly illustrated in color, this fourth edition features new sections from applied nonlinear science, like control of chaos, synchronisation of nonlinear systems, and turbulence, as well as recent theoretical concepts like strange nonchaotic attractors, on-off intermittency and spatio-temporal chaotic motion.

Fractals, Diffusion, and Relaxation in Disordered Complex Systems is a special guest-edited, two-part volume of Advances in Chemical Physics that continues to report recent advances with significant, up-to-date chapters by internationally recognized researchers.

This book is about the dynamics of coupled map lattices (CML) and of related spatially extended systems. It will be useful to post-graduate students and researchers seeking an overview of the state-of-the-art and of open problems in this area of nonlinear dynamics. The special feature of this book is that it describes the (mathematical) theory of CML and some related systems and their phenomenology, with some examples of CML modeling of concrete systems (from physics and biology). More precisely, the book deals with statistical properties of (weakly) coupled chaotic maps, geometric aspects of (chaotic) CML, monotonic spatially extended systems, and dynamical models of specific biological systems.

Understanding non-equilibrium properties of classical and quantum many-particle systems is one of the goals of contemporary statistical mechanics. Besides its own interest for the theoretical foundations of irreversible thermodynamics(e.g. of the Fourier's law of heat conduction), this topic is also relevant to develop innovative ideas for nanoscale thermal management with possible future applications to nanotechnologies and effective energetic resources. The first part of the volume (Chapters 1-6) describes the basic models, the phenomenology and the various theoretical approaches to understand heat transport in low-dimensional lattices (1D e 2D). The methods described will include equilibrium and nonequilibrium molecular dynamics simulations, hydrodynamic and kinetic approaches and the solution of stochastic models. The second part (Chapters 7-10) deals with applications to nano and microscale heat transfer, as for instance phononic transport in carbon-based nanomaterials, including the prominent case of nanotubes and graphene. Possible future developments on heat flow control and thermoelectric energy conversion will be outlined. This volume aims at being the first step for graduate students and researchers entering the field as well as a reference for the community of scientists that, from different backgrounds (theoretical physics, mathematics, material sciences and engineering), has grown in the recent years around those themes.

A valuable introduction for newcomers as well as an important reference and source of inspiration for established researchers, this book provides an up-to-date summary of central topics in the field of nonequilibrium statistical mechanics and dynamical systems theory. Understanding macroscopic properties of matter starting from microscopic chaos in the equations of motion of single atoms or molecules is a key problem in nonequilibrium statistical mechanics. Of particular interest both for theory and applications are transport processes such as diffusion, reaction, conduction and viscosity. Recent advances towards a deterministic theory of nonequilibrium statistical physics are summarized: Both Hamiltonian dynamical systems under nonequilibrium boundary conditions and non-Hamiltonian modelings of nonequilibrium steady states by using thermal reservoirs are considered. The surprising new results include transport coefficients that are fractal functions of control parameters, fundamental relations between transport coefficients and chaos quantities, and an understanding of nonequilibrium entropy production in terms of fractal measures and attractors. The theory is particularly useful for the description of many-particle systems with properties in-between conventional thermodynamics and nonlinear science, as they are frequently encountered on nanoscales.