LEADER 05423nam 2200649 450 001 9910144118503321 005 20170809154535.0 010 $a1-281-94708-3 010 $a9786611947088 010 $a3-527-62297-7 010 $a3-527-62298-5 035 $a(CKB)1000000000555504 035 $a(EBL)481497 035 $a(OCoLC)264714632 035 $a(SSID)ssj0000103932 035 $a(PQKBManifestationID)11131006 035 $a(PQKBTitleCode)TC0000103932 035 $a(PQKBWorkID)10071642 035 $a(PQKB)10301352 035 $a(MiAaPQ)EBC481497 035 $a(EXLCZ)991000000000555504 100 $a20160819h20082008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aAnomalous transport $efoundations and applications /$fedited by Rainer Klages, Gu?nter Radons, and Igor M. Sokolov 210 1$aWeinheim, Germany :$cWILEY-VCH Verlag GmbH & Co. KGaA,$d2008. 210 4$dİ2008 215 $a1 online resource (610 p.) 300 $aDescription based upon print version of record. 311 $a3-527-40722-7 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $aAnomalous 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 Sa?nchez; 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 327 $a2.1 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 Gru?nwald; 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 ? from Models; Appendix A: Tables; Appendix B: Function Spaces; Appendix C: Distributions; References 327 $a3 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 Le?vy Walks: Turbulent and Relativistic; References; 4 Continuous Time Random Walk, Mittag-Leffler Waiting Time and Fractional Diffusion: Mathematical Aspects; 4.1 Introduction 327 $a4.2 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 Le?vy Flights; 5.1 Le?vy Stable Distributions; 5.2 Underlying Random Walk Processes 327 $a5.3 Space Fractional Fokker-Planck Equation5.4 Free Le?vy Flights in the Semi-Infinite Domain; 5.4.1 First Passage Time and Leapover Properties; 5.4.2 Le?vy Flights and the Method of Images; 5.5 Le?vy Flights in External Fields; 5.5.1 Reminder: Stationary Solution of the Fokker-Planck Equation, ? = 2; 5.5.2 Le?vy Flights in an Harmonic Potential; 5.5.3 Le?vy Flights in a Quartic Potential, 1 < 2; 5.5.4 Le?vy Flights in a More General Potential Well; 5.5.5 Kramers Problem for Le?vy Flights; 5.6 Le?vy Flights in Phase Space; 5.6.1 Langevin Description; 5.6.2 Velocity-Fractional Klein-Kramers Equation 327 $a5.6.3 Space-Homogeneous Relaxation in Absence of External Field 330 $aThis 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 606 $aPlasma turbulence 606 $aTransport theory 608 $aElectronic books. 615 0$aPlasma turbulence. 615 0$aTransport theory. 676 $a530.44 702 $aKlages$b Rainer 702 $aRadons$b G$g(Gu?nter), 702 $aSokolov$b Igor M.$f1958- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910144118503321 996 $aAnomalous transport$92170855 997 $aUNINA