Umfang:
Online-Ressource (XXIII, 584 S.)
,
illustrations (some color), maps (some color)
Ausgabe:
Online-Ausg.
Ausgabe:
Online-Ausg.
ISBN:
9783527407224
Inhalt:
Anomalous Transport; Contents; Preface; List of Contributors; 1 In Memoriam: Radu Balescu; 1.1 Radu Balescu's Abstract for the Conference on Anomalous Transport in Bad Honnef; 1.2 The Scientific Career of Radu Balescu by Boris Weyssow; 1.3 My Memory of Radu Balescu by Angelo Vulpiani; 1.4 My Memory of Radu Balescu by Francesco Mainardi; 1.5 In Memoriam: Radu Balescu by Raul Sánchez; 1.6 Remembering Radu Balescu by Diego del-Castillo-Negrete; References; Part I Fractional Calculus and Stochastic Theory; Introduction to Part I; 2 Threefold Introduction to Fractional Derivatives
Inhalt:
2.1 Historical Introduction to Fractional Derivatives2.1.1 Leibniz; 2.1.2 Euler; 2.1.3 Paradoxa and Problems; 2.1.4 Liouville; 2.1.5 Fourier; 2.1.6 Grünwald; 2.1.7 Riemann; 2.2 Mathematical Introduction to Fractional Derivatives; 2.2.1 Fractional Integrals; 2.2.2 Fractional Derivatives; 2.2.3 Eigenfunctions; 2.3 Physical Introduction to Fractional Derivatives; 2.3.1 Basic Questions; 2.3.2 Fractional Space; 2.3.3 Fractional Time; 2.3.4 Identification of α from Models; Appendix A: Tables; Appendix B: Function Spaces; Appendix C: Distributions; References
Inhalt:
3 Random Processes with Infinite Moments3.1 St. Petersburg Paradox; 3.2 Holtsmark Distribution; 3.3 Activated Hopping; 3.4 Deterministic Examples of Long Tail Distributions; 3.5 RandomWalks and Master Equations; 3.6 RandomWalks and Upper Critical Dimensions; 3.7 Weierstrass Random Walk; 3.8 Fractal Time Random Walk; 3.9 Coupled Memory Random Walks: Diffusion or Telegraph Equation; 3.10 Random Walks: Coupled Memory Lévy Walks: Turbulent and Relativistic; References; 4 Continuous Time Random Walk, Mittag-Leffler Waiting Time and Fractional Diffusion: Mathematical Aspects; 4.1 Introduction
Inhalt:
4.2 An Outline of the Gnedenko-Kovalenko Theory of Thinning4.3 The Continuous Time Random Walk (CTRW); 4.4 Manipulations: Rescaling and Respeeding; 4.5 Power Laws and Asymptotic Universality of the Mittag-Leffler Waiting-Time Density; 4.6 Passage to the Diffusion Limit in Space; 4.7 The Time-Fractional Drift Process; 4.8 Conclusions; Appendix A: The Time-Fractional Derivatives; Appendix B: The Space-Fractional Derivatives; Appendix C: The Mittag-Leffler Function; References; 5 Introduction to the Theory of Lévy Flights; 5.1 Lévy Stable Distributions; 5.2 Underlying Random Walk Processes
Inhalt:
5.3 Space Fractional Fokker-Planck Equation5.4 Free Lévy Flights in the Semi-Infinite Domain; 5.4.1 First Passage Time and Leapover Properties; 5.4.2 Lévy Flights and the Method of Images; 5.5 Lévy Flights in External Fields; 5.5.1 Reminder: Stationary Solution of the Fokker-Planck Equation, α = 2; 5.5.2 Lévy Flights in an Harmonic Potential; 5.5.3 Lévy Flights in a Quartic Potential, 1 〈 2; 5.5.4 Lévy Flights in a More General Potential Well; 5.5.5 Kramers Problem for Lévy Flights; 5.6 Lévy Flights in Phase Space; 5.6.1 Langevin Description; 5.6.2 Velocity-Fractional Klein-Kramers Equation
Inhalt:
5.6.3 Space-Homogeneous Relaxation in Absence of External Field
Inhalt:
RAINER KLAGES, lecturer in applied mathematics at the Queen Mary University of London, studied physics and philosophy at the Technical University of Berlin. His research stations were Maryland/USA, Budapest, Brussels, and Dresden and his main research interests are nonlinear dynamics, complex systems, and nonequilibrium statistical mechanics. GÜNTER RADONS holds the Chair for theoretical physics, complex systems and nonlinear dynamics at the Institute of Physics, Chemnitz University of Technology. His main research interests are theoretical foundations of complex systems, data analysis and mo
Anmerkung:
Includes bibliographical references and index
Weitere Ausg.:
ISBN 9783527407224
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe Anomalous transport Weinheim : Wiley-VCH, 2008 ISBN 3527407227
Weitere Ausg.:
ISBN 9783527407224
Sprache:
Englisch
Fachgebiete:
Physik
Schlagwort(e):
Transportprozess
;
Electronic books
;
Aufsatzsammlung
DOI:
10.1002/9783527622979
Mehr zum Autor:
Klages, Rainer 1966-
Bookmarklink
