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.

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.

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.

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.

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.

The usefulness of the book to the reader is exposure to many different classes of materials and relaxation phenomena. They are tied together by the universal relaxation and diffusion properties they share, and a consistent explanation of their origin. The readers can apply what they learn to solve their own problems and use it as a stepping-stone to make further advances in theoretical understanding of the origin of the universality.

The aim of the workshop was to bring together specialists in various fields where non-exponential relaxation is observed in order to compare models and experimental results and to examine the general physical principles governing this type of behaviour. Non-exponential relaxation is found in extremely diverse physical systems all of which can be classified as complex. The form of the relaxation is generally parametrized using logarithmic, algebraic or stretched exponential decay forms. The conceptually simplest mechanism for the non-exponential decay is a spectrum of relaxation rates due to non-interacting units each of which relaxes with a different intrinsic time constant. Clear experimental examples can be given where for instance the relaxation of a collection of isolated polymer molecules leads to an overall stretched exponential decay. Non-exponential relaxation is observed in all strongly interacting complex systems (structural glasses, spin glasses, etc ... ) where each elementary unit is in interaction with many other units.

In this book, a novel approach using equations with derivatives of fractional orders is applied to describe anomalous transport and relaxation in disordered semiconductors, dielectrics and quantum dot systems. A relationship between the self-similarity of transport, the Levy stable limiting distributions and the kinetic equations with fractional derivatives is established. It is shown that unlike the well-known Scher-Montroll and Arkhipov-Rudenko models, which are in a sense alternatives to the normal transport model, fractional differential equations provide a unified mathematical framework for describing normal and dispersive transport. The fractional differential formalism allows the equations of bipolar transport to be written down and transport in distributed dispersion systems to be described.

This book discusses the physics of the dynamics of ions in various ionically conducting materials, and applications including electrical energy generation and storage. The experimental techniques for measurements and characterization, molecular dynamics simulations, the theories of ion dynamics, and applications are all addressed by the authors, who are experts in their fields. The experimental techniques of measurement and characterization of dynamics of ions in glassy, crystalline, and liquid ionic conductors are introduced with the dual purpose of introducing the reader to the experimental activities of the field, and preparing the reader to understand the physical quantities derived from experiments. These experimental techniques include calorimetry, conductivity relaxation, nuclear magnetic resonance, light scattering, neutron scattering, and others. Methods of molecular dynamics simulations are introduced to teach the reader to utilize the technique for practical applications to specific problems. The results elucidate the dynamics of ions on some issues that are not accessible by experiments. The properties of ion dynamics in glassy, crystalline and liquid ionic conductors brought forth by experiments and simulations are shown to be universal, i.e. independent of physical and chemical structure of the ionic conductor as long as ion-ion interaction is the dominant factor. Moreover these universal properties of ion dynamics are shown to be isomorphic to other complex interacting systems including the large class of glass-forming materials with or without ionic conductivity.By covering the basic concepts, theories/models, experimental techniques and data, molecular dynamics simulations, and relating them together, Dynamics of Glassy, Crystalline and Liquid Ionic Conductors will be of great interest to many in basic and applied research areas from the broad and diverse communities of condensed matter physicists, chemists, materials scientists and engineers. The book also provides the fundamentals for an introduction to the field and it is written in such a way that can be used for teaching courses either at the undergraduate or graduate level in academic institutions.