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基本説明
Includes major contributions, which extract and emphasize common principles and methods from dynamical systems theory, stochastic processes and disordered systems.
Full Description
This multi-author reference work provides a unique introduction to the currently emerging, highly interdisciplinary field of those transport processes that cannot be described by using standard methods of statistical mechanics. It comprehensively summarizes topics ranging from mathematical foundations of anomalous dynamics to the most recent experiments in this field. In so doing, this monograph extracts and emphasizes common principles and methods from many different disciplines while providing up-to-date coverage of this new field of research, considering such diverse applications as plasma physics, glassy material, cell science, and socio-economic aspects.
The book will be of interest to both theorists and experimentalists in nonlinear dynamics, statistical physics and stochastic processes. It also forms an ideal starting point for graduate students moving into this area. 18 chapters written by internationally recognized experts in this field provide in-depth introductions to fundamental aspects of anomalous transport.
Contents
In Memoriam: Radu Balescu
Part I FRACTIONAL CALCULUS AND STOCHASTIC THEORY
Threefold Introduction to Fractional Derivatives
(Rudolf Hilfer)
Random Processes with Infinite Moments
(Michael F. Shlesinger)
Continuous Time Random Walk, Mittag-Leffler Waiting Time and Fractional Diffusion: Mathematical Aspects
(Rudolf Gorenflo and Francesco Mainardi)
Introduction to the Theory of Lévy Flights
(Alexei V. Chechkin, Ralf Metzler, Joseph Klafter, and Vsevolod Yu. Gonchar)
Fractional Diffusion Models of Anomalous Transport
(Diego del-Castillo-Negrete)
Anomalous Kinetics Leads to Weak Ergodicity Breaking
(Eli Barkai)
Part II DYNAMICAL SYSTEMS AND DETERMINISTIC TRANSPORT
Deterministic (Anomalous) Transport
(Roberto Artuso and Giampaolo Cristadoro)
Anomalous Transport in Hamiltonian Systems
(Eduardo G. Altmann and Holger Kantz)
Anomalous Heat Conduction
(Stefano Lepri, Roberto Livi, and Antonio Politi)
Part III ANOMALOUS TRANSPORT IN DISORDERED SYSTEMS
Anomalous Relaxation in Complex Systems: From Stretched to Compressed Exponentials
(Jean-Philippe Bouchaud)
Anomalous Transport in Glass-Forming Liquids
(Walter Kob, Gustavo A. Appignanesi, J. Ariel Rodríguez Fris, and Ruben A. Montani)
Subdiffusion-Limited Reactions
(Santos Bravo Yuste, Katja Lindenberg, and Juan Jesús Ruiz-Lorenzo)
Anomalous Transport on Disordered Fractals
(Karl Heinz Hoffmann and Janett Prehl)
Part IV APPLICATIONS TO COMPLEX SYSTEMS AND EXPERIMENTAL RESULTS
Superstatistics: Theoretical Concepts and Physical
Applications
(Christian Beck)
Money Circulation Science -
Fractional Dynamics in Human
Mobility
(Dirk Brockmann)
Anomalous Molecular Displacement Laws in Porous Media and
Polymers Probed by Nuclear Magnetic Resonance Techniques
(Rainer Kimmich, Nail Fatkullin, Markus Kehr, and Yujie Li)
Anomalous Molecular Dynamics in Confined Spaces
(Rustem Valiullin and Jörg Kärger)
Paradigm Shift of the Molecular Dynamics Concept in the Cell Membrane: High-Speed Single-Molecule Tracking Revealed the Partitioning of the Cell Membrane
(A. Kusumi, Y. Umemura, N. Morone, and T. Fujiwara)
