Anomalous Transport: Foundations and ApplicationsRainer Klages, Günter Radons, Igor M. Sokolov 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
| 1 | |
Part I Fractional Calculus and Stochastic Theory | 13 |
Part II Dynamical Systems and Deterministic Transport | 241 |
Part III Anomalous Transport in Disordered Systems | 323 |
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Anomalous Transport: Foundations and Applications Rainer Klages,Günter Radons,Igor M. Sokolov Limited preview - 2008 |
Common terms and phrases
anomalous diffusion anomalous transport asymptotic behavior boundary Brownian cell Chem compartment correlation corresponding CTRW decay defined diffusion coefficient diffusion equation distribution domain dynamics ergodicity exponent exponential finite fluctuations flux Fourier fractal fractional calculus fractional derivative fractional diffusion equation fractional integrals function Gaussian gradient Hamiltonian Hamiltonian systems Hilfer jump Kärger Klafter Laplace Laplace transform lattice Lett Lévy distribution Lévy flights Lévy processes limit magnetic Mainardi master equation Math membrane skeleton Mittag-Leffler Mittag-Leffler function molecular molecules motion observed obtained parameter particle phase space Phys physical plasma membrane porous power-law probability density problem properties pulse Radu Balescu random walk regime relaxation rescaling scaling Section Sierpinski carpets simulations solution spatial statistical stochastic structure subdiffusive superdiffusive superstatistical survival probability temperature theory tion trajectories transform transmembrane proteins traps turbulence velocity zeolites