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反常输运现象基础及其应用（Anomalous Transport Foundations and Applications）
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Anomalous Transport Foundations and Applications 目录： Table of contents : Anomalous Transport......Page 4 Contents......Page 8 Preface......Page 18 List of Contributors......Page 22 1 In Memoriam: Radu Balescu......Page 28 1.1 Radu Balescu’s Abstract for the Conference on Anomalous Transport in Bad Honnef......Page 29 1.2 The Scientific Career of Radu Balescu by Boris Weyssow......Page 30 1.3 My Memory of Radu Balescu by Angelo Vulpiani......Page 32 1.4 My Memory of Radu Balescu by Francesco Mainardi......Page 33 1.5 In Memoriam: Radu Balescu by Raul Sánchez......Page 35 1.6 Remembering Radu Balescu by Diego del-Castillo-Negrete......Page 37 References......Page 38 Part I Fractional Calculus and Stochastic Theory......Page 40 Introduction to Part I......Page 42 2.1.1 Leibniz......Page 44 2.1.3 Paradoxa and Problems......Page 45 2.1.4 Liouville......Page 47 2.1.7 Riemann......Page 48 2.2.1 Fractional Integrals......Page 49 2.2.2 Fractional Derivatives......Page 58 2.2.3 Eigenfunctions......Page 71 2.3.2 Fractional Space......Page 73 2.3.3 Fractional Time......Page 75 2.3.4 Identification of α from Models......Page 80 Appendix A: Tables......Page 86 Appendix B: Function Spaces......Page 88 Appendix C: Distributions......Page 92 References......Page 96 3.1 St. Petersburg Paradox......Page 102 3.2 Holtsmark Distribution......Page 103 3.3 Activated Hopping......Page 104 3.4 Deterministic Examples of Long Tail Distributions......Page 105 3.5 RandomWalks and Master Equations......Page 107 3.6 RandomWalks and Upper Critical Dimensions......Page 109 3.7 Weierstrass Random Walk......Page 110 3.8 Fractal Time Random Walk......Page 112 3.9 Coupled Memory Random Walks: Diffusion or Telegraph Equation......Page 113 3.10 Random Walks: Coupled Memory Lévy Walks: Turbulent and Relativistic......Page 116 References......Page 118 4.1 Introduction......Page 120 4.2 An Outline of the Gnedenko–Kovalenko Theory of Thinning......Page 122 4.3 The Continuous Time Random Walk (CTRW)......Page 125 4.4 Manipulations: Rescaling and Respeeding......Page 128 4.5 Power Laws and Asymptotic Universality of the Mittag-Leffler Waiting-Time Density......Page 130 4.6 Passage to the Diffusion Limit in Space......Page 131 4.7 The Time-Fractional Drift Process......Page 137 4.8 Conclusions......Page 140 Appendix A: The Time-Fractional Derivatives......Page 144 Appendix B: The Space-Fractional Derivatives......Page 146 Appendix C: The Mittag-Leffler Function......Page 150 References......Page 152 5 Introduction to the Theory of Lévy Flights......Page 156 5.1 Lévy Stable Distributions......Page 157 5.2 Underlying Random Walk Processes......Page 160 5.3 Space Fractional Fokker–Planck Equation......Page 162 5.4.1 First Passage Time and Leapover Properties......Page 164 5.4.2 Lévy Flights and the Method of Images......Page 167 5.5.2 Lévy Flights in an Harmonic Potential......Page 168 5.5.3 Lévy Flights in a Quartic Potential, 1 < 2......Page 169 5.5.4 Lévy Flights in a More General Potential Well......Page 171 5.5.5 Kramers Problem for Lévy Flights......Page 172 5.6.1 Langevin Description......Page 174 5.6.3 Space-Homogeneous Relaxation in Absence of External Field......Page 175 5.6.5 Relaxation of the Linear Oscillator [84]......Page 176 5.6.6 Relaxation in a Magnetized Plasma......Page 177 5.6.7 Damped Lévy Flights [89]......Page 179 5.7 Power-Law Truncated Lévy Flights......Page 180 5.8 Summary......Page 185 References......Page 186 6.1 Introduction......Page 190 6.2.1 Anomalous Transport of Tracers in Flows with Coherent Structures......Page 192 6.2.2 Continuous Time Random Walk Model and Fractional Diffusion......Page 197 6.3 Fractional Diffusion......Page 199 6.3.1 Fractional Derivatives......Page 200 6.3.2 Fractional Diffusion Equation: Green’s Function and Self-Similar Scaling......Page 204 6.3.3 Interplay of Regular and Fractional Diffusion......Page 206 6.3.4 Fractional Diffusion Equation for Truncated Lévy Processes......Page 208 6.3.5 Nonlocality and Uphill Transport......Page 212 6.3.6 Fractional Diffusion Models of Turbulent Transport......Page 217 6.4 Fractional Diffusion in Finite-Size Domains......Page 220 6.4.1 Finite-Size Domain Model......Page 221 6.4.2 Finite-Difference Numerical Integration Method......Page 222 6.4.3 Examples......Page 227 6.5 Summary and Conclusions......Page 235 References......Page 238 7.1 Introduction......Page 240 7.2 Normal Occupation Time Statistics......Page 242 7.2.1 Ergodicity for Bounded Normal Diffusion......Page 246 7.2.3 Occupation Times for Unbounded Normal Diffusion......Page 247 7.3 Anomalous Diffusion......Page 248 7.3.1 Derivation of Fractional Equation for Occupation Times......Page 249 7.3.2 Weak Ergodicity Breaking......Page 252 7.3.3 Example: Anomalous Diffusion in an Interval......Page 254 7.4 DeterministicWeak Ergodicity Breaking......Page 255 7.5 Discussion......Page 261 Appendix A......Page 264 References......Page 266 Part II Dynamical Systems and Deterministic Transport......Page 268 Introduction to Part II......Page 270 8.1 Introduction......Page 272 8.2 Transport and Thermodynamic Formalism......Page 273 8.3 The Periodic Orbits Approach......Page 276 8.4 One-Dimensional Transport: Kneading Determinant......Page 280 8.5 An Anomalous Example......Page 283 8.6 Probabilistic Approximations......Page 290 8.7 Conclusions......Page 292 References......Page 293 9.1 Introduction......Page 296 9.2 Continuous Time Random Walk Model......Page 297 9.3.1 Phase Space of Hamiltonian Systems......Page 299 9.3.2 Main Properties of Hamiltonian Chaos......Page 300 9.3.3 Connection to CTRW......Page 303 9.4.1 Incompressible Fluid Flows as Hamiltonian Systems......Page 305 9.4.2 Specific Model......Page 306 9.4.3 Transport Properties of Passive Tracers......Page 308 9.4.4 Effect of Noise Perturbation......Page 309 9.5 Discussion......Page 315 References......Page 316 10.1 Introduction......Page 320 10.2.1 Fourier and the Problem of Heat Transport in the Earth......Page 321 10.2.2 From the Old Kinetic Theory to Boltzmann......Page 322 10.2.3 The Harmonic Pathology and the Phonons......Page 324 10.2.4 The Fermi–Pasta–Ulam (FPU) Numerical Experiment......Page 325 10.3.1 Homogeneous Chain......Page 328 10.3.2 Disordered Chain......Page 331 10.4.1 Early Studies......Page 337 10.4.2 Green–Kubo Formalism......Page 338 10.4.4 The Strong-Chaos Regime......Page 339 10.4.5 Integrable Nonlinear Systems......Page 341 10.4.6 Universality......Page 342 10.4.7 Anomalous Diffusion......Page 344 References......Page 347 Part III Anomalous Transport in Disordered Systems......Page 350 Introduction to Part III......Page 352 11.1 Introduction......Page 354 11.2.1 Trapping-Induced Subdiffusion......Page 355 11.2.2 Two-Step Relaxation......Page 359 11.2.3 Superposition of Relaxation Times and Stretched Exponentials......Page 362 11.3.1 Superdiffusion and Lévy Flights......Page 365 11.3.2 Rearrangement-Induced Stress Fields in Elastic Media......Page 367 11.4 Conclusion......Page 370 References......Page 371 12.1 Introduction......Page 374 12.2 Model......Page 379 12.3 Results......Page 380 12.4 Summary......Page 391 References......Page 392 13.1 Introduction......Page 394 13.2 Subdiffusion Contexts and Modeling Approaches......Page 396 13.3 Target and Trapping Problem......Page 400 13.3.1 Target Problem......Page 401 13.3.2 Trapping Problem......Page 403 13.4.1 Annihilation and Coalescence Reactions......Page 405 13.4.2 Annihilation of Two Species, A + B → 0......Page 407 13.5 Reactions with Nonhomogeneous Distribution of Reactants......Page 408 13.5.1 Reaction–Subdiffusion Equations......Page 409 13.5.2 Reaction Fronts......Page 412 13.6 Reactants with Different (Sub)diffusion Exponents......Page 414 13.7 Finale......Page 419 References......Page 420 14.1 Motivation......Page 424 14.2 Anomalous Diffusion on Regular Sierpinski Carpets......Page 425 14.2.1 Regular Sierpinski Carpets......Page 426 14.2.2 Random Walks on Fractals......Page 428 14.2.3 Resistance Scaling Method......Page 430 14.2.4 Master Equation Approach......Page 432 14.2.5 Diffusion Simulation......Page 433 14.3 Anomalous Diffusion on Disordered Sierpinski Carpets......Page 434 14.3.1 Disordered Sierpinski Carpets......Page 435 14.3.2 Modeling Carpets and Calculating Diffusion Exponents......Page 436 14.3.3 Results and Discussion......Page 439 14.4 Fractional Differential Equation......Page 443 14.4.1 Sierpinski Gasket......Page 445 14.4.2 Koch Curve......Page 448 14.5 Summary......Page 451 References......Page 453 Part IV Applications to Complex Systems and Experimental Results......Page 456 Introduction to Part IV......Page 458 15.1 Introduction......Page 460 15.2 The Basic Idea......Page 461 15.3 Typical Distributions f(β)......Page 462 15.4 Asymptotic Behavior for Large Energies......Page 464 15.5 Anomalous Diffusion in Superstatistical Systems......Page 466 15.6 From Time Series to Superstatistics......Page 469 15.7 Overview of Applications......Page 472 15.8 Lagrangian Turbulence......Page 473 15.9 Defect Turbulence......Page 475 15.10 Statistics of Cosmic Rays......Page 477 15.11 Statistics of Train Delays......Page 480 15.12 Conclusion and Outlook......Page 482 References......Page 483 16 Money Circulation Science – Fractional Dynamics in Human Mobility......Page 486 16.2 Diffusive Dispersal and Reaction Kinetics......Page 487 16.2.2 A Word of Caution......Page 488 16.3 Long Distance Dispersal and Lévy Flights......Page 489 16.3.1 Lévy Flights......Page 490 16.4 Human Travel in the 21st Century......Page 491 16.5.1 The Lack of Scale in Money Movements......Page 493 16.6 Is That All?......Page 496 16.7 Scaling Analysis......Page 497 16.8 Scale Free Waiting Times......Page 498 16.9 Ambivalent Processes......Page 500 16.9.1 Scaling Relation......Page 501 16.9.2 The Limiting Function for Amibivalent Processes......Page 503 References......Page 509 17.1 General Introduction......Page 512 17.2 From Nano- to Milliseconds: Segment Diffusion in Polymer Melts......Page 514 17.2.1 Evaluation Theory for the Field-Cycling NMR Relaxometry Technique......Page 515 17.2.2 Results for Polymer Melts......Page 518 17.2.3 Discussion of the Results for Polymer Melts......Page 519 17.3.1 The Measuring Principles of Field-Gradient NMR Diffusometry......Page 522 17.3.2 Sub- and Superdiffusive Transport in Porous Glasses......Page 526 17.3.3 Discussion of the Results for Porous Glasses......Page 531 17.4.1 NMR Microscopy Diffusometry Techniques......Page 532 17.4.2 Diffusion of Solvents in Swollen Polymers......Page 536 17.4.3 Diffusion on Random-Site Percolation Clusters......Page 539 17.4.4 Discussion of the Results for Percolation Clusters......Page 541 17.5 General Discussion and Outlook......Page 542 References......Page 544 18.1 Introduction......Page 546 18.2.1 Zeolites......Page 547 18.2.2 Mesoporous Glass and Silica......Page 548 18.3.1 The Phenomenon and Measurement of Concentration......Page 549 18.3.2 Diffusion Measurement......Page 551 18.4.1 Single-File Diffusion......Page 553 18.4.2 Molecular Transport in Intersecting Channels......Page 554 18.5.1 Dynamics in Random Pore Spaces......Page 557 18.5.2 Molecular Dynamics in Channel Pores......Page 562 18.6 Conclusions......Page 566 References......Page 567 19.1 Introduction......Page 572 19.2 Thirty-Year Old Enigma about the Diffusion Rate of Membrane Molecules in the Plasma Membrane......Page 576 19.3 Macroscopic Diffusion Coefficients for Transmembrane Proteins are Suppressed by the Presence of the Membrane Skeleton......Page 578 19.4 Single-Molecule Tracking Revealed That Transmembrane Proteins Undergo Hop Diffusion......Page 579 19.5 Corralling Effects of the Membrane Skeleton for Transmembrane Proteins (the Membrane-Skeleton Fence Model)......Page 585 19.6 Phospholipids Also Undergo Hop Diffusion in the Plasma Membrane......Page 588 19.7 The Biological Significance of Oligomerization-Induced Trapping Based on the Membrane-Skeleton Fences and Pickets......Page 595 19.8 A Paradigm Shift of the Plasma Membrane Structure Concept is Necessary: From the Simple Two-dimensional Continuum Fluid Model to the Compartmentalized Fluid Model......Page 597 References......Page 599 Index......Page 602 |
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