An Introduction to Anomalous Diffusion and Relaxation

This book provides a contemporary treatment of the problems related to anomalous diffusion and anomalous relaxation. It collects and promotes unprecedented applications dealing with diffusion problems and surface effects, adsorption-desorption phenomena, memory effects, reaction-diffusion equations, and relaxation in constrained structures of classical and quantum processes. The topics covered by the book are of current interest and comprehensive range, including concepts in diffusion and stochastic physics, random walks, and elements of fractional calculus. They are accompanied by a detailed exposition of the mathematical techniques intended to serve the reader as a tool to handle modern boundary value problems. This self-contained text can be used as a reference source for graduates and researchers working in applied mathematics, physics of complex systems and fluids, condensed matter physics, statistical physics, chemistry, chemical and electrical engineering, biology, and many others.

Brings together the mathematical properties of fractional calculus and problems with real-life applications Examines the fundamental problems involving fractional diffusion equations in time as well as in the space variable Reference work for graduates & researchers in applied mathematics, complexity, statistical physics, chemical engineering

Autorentext
Luiz Roberto Evangelista is Professor of Physics in the Department of Physics, Universidade Estadual de Maringá (Paraná, Brazil), and Visiting Professor in the Polytechnic of Turin (Italy). He received his Ph.D. on theoretical physics (field theory and particle physics) from University of São Paulo, Brazil, in 1988. His research interests are in complex fluids, complex systems, and history of physics and include mathematical physics of liquid crystals, diffusion problems, adsorption-desorption phenomena, and modern boundary value problems with applications in liquid-crystalline systems and impedance spectroscopy. Ervin Kaminski Lenzi is Associate Professor in the Department of Physics, Universidade Estadual de Ponta Grossa (Paraná, Brazil). He received his Ph.D. on theoretical physics (statistical mechanics) from CBPF-Centro Brasileiro de Pesquisas Físicas (Rio de Janeiro, Brazil), in 2002. His research interests are in complex systems and stochastic processesand include anomalous diffusion processes, usual and fractional diffusion equations, and modern boundary value problems with applications in liquid-crystalline systems and impedance spectroscopy.

Inhalt
Preface.- Integral Transforms and Special Functions.- Concepts in Diffusion and Stochastic Processes.- Random Walks.- Elements of Fractional Calculus.- Fractional Anomalous Diffusion.- Adsorption Phenomena and Anomalous Behavior.- Reaction-Diffusion Problems.- Relaxation under Geometric Constraints I: Classical Processes.- Relaxation under Geometric Constraints II: Quantum Processes.- Index.