The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics

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[1]  G. Mittag-Leffler,et al.  Sur la représentation analytique d’une branche uniforme d’une fonction monogène , 1901 .

[2]  L. Richardson,et al.  Atmospheric Diffusion Shown on a Distance-Neighbour Graph , 1926 .

[3]  C. Kenty.  On Radiation Diffusion and the Rapidity of Escape of Resonance Radiation from a Gas , 1932 .

[4]  S. Chandrasekhar.  Stochastic problems in Physics and Astronomy , 1943 .

[5]  P. Levy.  Processus stochastiques et mouvement brownien , 1948 .

[6]  S. Bochner.  Diffusion Equation and Stochastic Processes. , 1949, Proceedings of the National Academy of Sciences of the United States of America.

[7]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[8]  B. Gnedenko,et al.  Limit distributions for sums of shrunken random variables , 1954 .

[9]  A. Erdélyi,et al.  Tables of integral transforms , 1955 .

[10]  P. Levy.  Théorie de l'addition des variables aléatoires , 1955 .

[11]  E. M. Lifshitz,et al.  Electrodynamics of continuous media , 1961 .

[12]  R. Feynman,et al.  The Theory of a general quantum system interacting with a linear dissipative system , 1963 .

[13]  F. Spitzer.  Principles Of Random Walk , 1966 .

[14]  E. Montroll,et al.  Random Walks on Lattices. II , 1965 .

[15]  E. H. Lloyd,et al.  Long-Term Storage: An Experimental Study. , 1966 .

[16]  B. Mandelbrot.  Forecasts of Future Prices, Unbiased Markets, and "Martingale" Models , 1966 .

[17]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[18]  B. Mandelbrot.  The Variation of Some Other Speculative Prices , 1967 .

[19]  B. Mandelbrot.  How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension , 1967, Science.

[20]  P. A. P. Moran,et al.  An introduction to probability theory , 1968 .

[21]  B. Mandelbrot,et al.  Fractional Brownian Motions, Fractional Noises and Applications , 1968 .

[22]  Alexander Pollatsek,et al.  A theory of risk , 1970 .

[23]  Jerome Spanier,et al.  A general solution of the diffusion equation for semiinfinite geometries , 1972 .

[24]  H. Frauenfelder,et al.  Activation Energy Spectrum of a Biomolecule: Photodissociation of Carbonmonoxy Myoglobin at Low Temperatures , 1974 .

[25]  E. Montroll,et al.  Anomalous transit-time dispersion in amorphous solids , 1975 .

[26]  H Frauenfelder,et al.  Dynamics of ligand binding to myoglobin. , 1975, Biochemistry.

[27]  H. Scher,et al.  Time-dependent electrical transport in amorphous solids: As 2 Se 3 , 1977 .

[28]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[29]  G. Pfister,et al.  Dispersive (non-Gaussian) transient transport in disordered solids , 1978 .

[30]  Kurt Bernardo Wolf,et al.  Integral transforms in science and engineering , 1979 .

[31]  G. Matheron,et al.  Is transport in porous media always diffusive? A counterexample , 1980 .

[32]  P. V. von Hippel,et al.  Diffusion-driven mechanisms of protein translocation on nucleic acids. 1. Models and theory. , 1981, Biochemistry.

[33]  N. Kampen,et al.  Stochastic processes in physics and chemistry , 1981 .

[34]  Arak M. Mathai,et al.  The H-Function with Applications in Statistics and Other Disciplines. , 1981 .

[35]  Hari M. Srivastava,et al.  The H-functions of one and two variables, with applications , 1982 .

[36]  Bruce J. West,et al.  Fractal dimensionality of Lévy processes. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[37]  D. Sherrington.  Stochastic Processes in Physics and Chemistry , 1983 .

[38]  Y. Sinai.  The Limiting Behavior of a One-Dimensional Random Walk in a Random Medium , 1983 .

[39]  V. Balakrishnan,et al.  Anomalous diffusion in one dimension , 1985 .

[40]  K L Magleby,et al.  Quantitative description of three modes of activity of fast chloride channels from rat skeletal muscle. , 1986, The Journal of physiology.

[41]  W. Wyss.  The fractional diffusion equation , 1986 .

[42]  E. Sudicky.  A natural gradient experiment on solute transport in a sand aquifer: Spatial variability of hydraulic conductivity and its role in the dispersion process , 1986 .

[43]  I. Zschokke,et al.  Optical Spectroscopy of Glasses , 1986 .

[44]  M. Shlesinger,et al.  Stochastic pathway to anomalous diffusion. , 1987, Physical review. A, General physics.

[45]  Simmons,et al.  Discrete-time quantum mechanics. III. Spin systems. , 1987, Physical review. D, Particles and fields.

[46]  Peseckis.  Statistical dynamics of stable processes. , 1987, Physical review. A, General physics.

[47]  Frauenfelder,et al.  Glassy behavior of a protein. , 1989, Physical review letters.

[48]  A fractal scaling law for protein gating kinetics , 1989 .

[49]  T. Vicsek.  Fractal Growth Phenomena , 1989 .

[50]  Blumen,et al.  Enhanced diffusion in random velocity fields. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[51]  J. Bouchaud,et al.  Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications , 1990 .

[52]  M. Shlesinger,et al.  Lévy walk approach to anomalous diffusion , 1990 .

[53]  Hideki Takayasu,et al.  Fractals in the Physical Sciences , 1990 .

[54]  G. Weiss,et al.  A new class of long-tailed pausing time densities for the CTRW , 1990 .

[55]  Luciano Pietronero,et al.  FRACTALS IN PHYSICS , 1990 .

[56]  D. Jou,et al.  Rheological Modelling: Thermodynamical and Statistical Approaches , 1991 .

[57]  T. Nonnenmacher,et al.  Fractional integral operators and Fox functions in the theory of viscoelasticity , 1991 .

[58]  Yu. L. Klimontovich,et al.  Turbulent Motion. The Structure of Chaos , 1991 .

[59]  W. W. Wood,et al.  Large-Scale Natural Gradient Tracer Test in Sand and Gravel, , 1991 .

[60]  L. Gelhar,et al.  Field study of dispersion in a heterogeneous aquifer: 2. Spatial moments analysis , 1992 .

[61]  E. Eric Adams,et al.  Field study of dispersion in a heterogeneous aquifer , 1992 .

[62]  C. Welty,et al.  A Critical Review of Data on Field-Scale Dispersion in Aquifers , 1992 .

[63]  Thomas B. Stauffer,et al.  Database for the Second Macrodispersion Experiment (MADE-2). , 1993 .

[64]  O. Marichev,et al.  Fractional Integrals and Derivatives: Theory and Applications , 1993 .

[65]  J. Klafter,et al.  Scale-invariant motion in intermittent chaotic systems. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[66]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[67]  Joseph Klafter,et al.  Probability Distributions for Continuous-Time Random Walks with Long Tails , 1994 .

[68]  Fogedby.  Langevin equations for continuous time Lévy flights. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[69]  Anomalies without massless particles. , 1994, Physical review. D, Particles and fields.

[70]  Fogedby.  Lévy flights in random environments. , 1994, Physical review letters.

[71]  J. Klafter,et al.  Lévy statistics in a Hamiltonian system. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[72]  R. Metzler,et al.  Fractional model equation for anomalous diffusion , 1994 .

[73]  Correlation effects, generalized Brownian motion and anomalous diffusion , 1994 .

[74]  Joseph Klafter,et al.  Spectral random walk of a single molecule , 1994 .

[75]  E. Weibel,et al.  Fractals in Biology and Medicine , 1994 .

[76]  W. Glöckle,et al.  Fractional relaxation and the time-temperature superposition principle , 1994 .

[77]  Sum-over-histories representation for the causal Green function of free scalar field theory. , 1993, Physical review. D, Particles and fields.

[78]  Hilfer,et al.  Fractional master equations and fractal time random walks. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[79]  Zumofen,et al.  Absorbing boundary in one-dimensional anomalous transport. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[80]  Stapf,et al.  Proton and deuteron field-cycling NMR relaxometry of liquids in porous glasses: Evidence for Lévy-walk statistics. , 1995, Physical review letters.

[81]  P. M. Lee,et al.  Random Walks and Random Environments: Volume 1: Random Walks , 1995 .

[82]  Brian Berkowitz,et al.  On Characterization of Anomalous Dispersion in Porous and Fractured Media , 1995 .

[83]  R. Metzler,et al.  Relaxation in filled polymers: A fractional calculus approach , 1995 .

[84]  T F Nonnenmacher,et al.  A fractional calculus approach to self-similar protein dynamics. , 1995, Biophysical journal.

[85]  Zumofen,et al.  Laminar-localized-phase coexistence in dynamical systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[86]  M. Taqqu,et al.  Stable Non-Gaussian Random Processes : Stochastic Models with Infinite Variance , 1995 .

[87]  R. Metzler,et al.  Generalized viscoelastic models: their fractional equations with solutions , 1995 .

[88]  M. Shlesinger,et al.  REACTIONS CONTROLLED BY ENHANCED DIFFUSION : DETERMINISTIC AND STOCHASTIC APPROACHES , 1996 .

[89]  Stochastic processes with stable distributions in random environments. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[90]  竹中 茂夫.  G.Samorodnitsky,M.S.Taqqu:Stable non-Gaussian Random Processes--Stochastic Models with Infinite Variance , 1996 .

[91]  Michael C. Mackey,et al.  Universality classes for asymptotic behavior of relaxation processes in systems with dynamical disorder: Dynamical generalizations of stretched exponential , 1996 .

[92]  Parallel Transport in Gauge Theory on $M_4 \times Z_2$ Geometry , 1996, hep-th/9607069.

[93]  George Weiss,et al.  Random walks and random environments, volume 1: Random walks , 1996 .

[94]  P. A. Prince,et al.  Lévy flight search patterns of wandering albatrosses , 1996, Nature.

[95]  E. Fischer,et al.  NMR field gradient diffusometry of segment displacements in melts of entangled polymers , 1996 .

[96]  Shlesinger,et al.  Breakdown of Ovchinnikov-Zeldovich Segregation in the A+B-->0 Reaction under Lévy Mixing. , 1996, Physical review letters.

[97]  Compte,et al.  Stochastic foundations of fractional dynamics. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[98]  J. Bouchaud,et al.  Models of traps and glass phenomenology , 1996, cond-mat/9601012.

[99]  Maggs,et al.  Subdiffusion and Anomalous Local Viscoelasticity in Actin Networks. , 1996, Physical review letters.

[100]  Robert W. Seidel.  From Mars to Minerva: The Origins of Scientific Computing in the AEC Labs , 1996 .

[101]  Rosario N. Mantegna,et al.  Turbulence and financial markets , 1996, Nature.

[102]  T F Nonnenmacher,et al.  Anomalous diffusion of water in biological tissues. , 1996, Biophysical journal.

[103]  M. Shlesinger,et al.  Beyond Brownian motion , 1996 .

[104]  Igor M. Sokolov,et al.  PARADOXAL DIFFUSION IN CHEMICAL SPACE FOR NEAREST-NEIGHBOR WALKS OVER POLYMER CHAINS , 1997 .

[105]  Bruce J. West,et al.  FRACTIONAL DIFFUSION AND LEVY STABLE PROCESSES , 1997 .

[106]  Alexander I. Saichev,et al.  Fractional kinetic equations: solutions and applications. , 1997, Chaos.

[107]  C. Gerry,et al.  GENERATION AND PROPERTIES OF COLLECTIVE ATOMIC SCHRODINGER-CAT STATES , 1997 .

[108]  A. Compte,et al.  The generalized Cattaneo equation for the description of anomalous transport processes , 1997 .

[109]  Brian Berkowitz,et al.  ANOMALOUS TRANSPORT IN RANDOM FRACTURE NETWORKS , 1997 .

[110]  Ralf Metzler,et al.  Fractional diffusion: exact representations of spectral functions , 1997 .

[111]  Herbert Walther,et al.  Anomalous Dynamics of a Single Ion in an Optical Lattice , 1997 .

[112]  F. Mainardi,et al.  Fractals and fractional calculus in continuum mechanics , 1997 .

[113]  Ralf Metzler,et al.  FRACTIONAL DIFFUSION, WAITING-TIME DISTRIBUTIONS, AND CATTANEO-TYPE EQUATIONS , 1998 .

[114]  Igor M. Sokolov,et al.  ANOMALOUS TRANSPORT IN EXTERNAL FIELDS : CONTINUOUS TIME RANDOM WALKS AND FRACTIONAL DIFFUSION EQUATIONS EXTENDED , 1998 .

[115]  SHORT-TIME REGIME PROPAGATOR IN FRACTALS , 1998 .

[116]  I. Podlubny.  Fractional differential equations , 1998 .

[117]  Lisa Borland,et al.  Microscopic dynamics of the nonlinear Fokker-Planck equation: A phenomenological model , 1998 .

[118]  Hans C. Fogedby.  Lévy flights in quenched random force fields , 1998 .

[119]  Amblard et al. Reply , 1998 .

[120]  Erratum: Subdiffusion and Anomalous Local Viscoelasticity in Actin Networks [Phys. Rev. Lett. 77, 4470 (1996)] , 1998 .

[121]  GENERALIZED HUBER KINETICS FOR NONLINEAR RATE PROCESSES IN DISORDERED SYSTEMS : NONLINEAR ANALOGS OF STRETCHED EXPONENTIAL , 1998 .

[122]  P. A. Robinson,et al.  LEVY RANDOM WALKS IN FINITE SYSTEMS , 1998 .

[123]  H. Stanley,et al.  Optimizing the success of random searches , 1999, Nature.

[124]  George M. Zaslavsky,et al.  Chaotic Dynamics and the Origin of Statistical Laws , 1999 .

[125]  Budapešť,et al.  Anomalous diffusion in aperiodic environments , 1998, cond-mat/9809120.

[126]  R. Silbey,et al.  Distribution of single-molecule line widths , 1999 .

[127]  D. Kusnezov,et al.  Quantum Levy Processes and Fractional Kinetics , 1999, chao-dyn/9901002.

[128]  Ralf Metzler,et al.  Deriving fractional Fokker-Planck equations from a generalised master equation , 1999 .

[129]  Katarzyna Sznajd-Weron,et al.  Anomalous Diffusion From Basics to Applications , 1999 .

[130]  Bruce J. West,et al.  Fractional Calculus and the Evolution of Fractal Phenomena , 1999 .

[131]  Sune Jespersen,et al.  LEVY FLIGHTS IN EXTERNAL FORCE FIELDS : LANGEVIN AND FRACTIONAL FOKKER-PLANCK EQUATIONS AND THEIR SOLUTIONS , 1999 .

[132]  P. Lunkenheimer,et al.  Broadband dielectric spectroscopy on glass-forming propylene carbonate. , 1998, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[133]  A. Compte,et al.  Stochastic foundation of normal and anomalous Cattaneo-type transport , 1999 .

[134]  M. Tokuyama,et al.  Nonequilibrium statistical description of anomalous diffusion , 1999 .

[135]  J. Klafter,et al.  Anomalous Diffusion and Relaxation Close to Thermal Equilibrium: A Fractional Fokker-Planck Equation Approach , 1999 .

[136]  Rosario N. Mantegna,et al.  Book Review: An Introduction to Econophysics, Correlations, and Complexity in Finance, N. Rosario, H. Mantegna, and H. E. Stanley, Cambridge University Press, Cambridge, 2000. , 2000 .

[137]  Wolfgang P. Schleich,et al.  KEYHOLE LOOK AT LEVY FLIGHTS IN SUBRECOIL LASER COOLING , 1999 .

[138]  R. Gorenflo,et al.  Fractional calculus and continuous-time finance , 2000, cond-mat/0001120.

[139]  J. Klafter,et al.  Kramers' escape problem with anomalous kinetics: non-exponential decay of the survival probability , 2000 .

[140]  J. Klafter,et al.  From a Generalized Chapman−Kolmogorov Equation to the Fractional Klein−Kramers Equation† , 2000 .

[141]  UK,et al.  Structure and dynamics of liquid iron under Earth’s core conditions , 2000 .

[142]  J. Klafter,et al.  The random walk's guide to anomalous diffusion: a fractional dynamics approach , 2000 .

[143]  A. Caspi,et al.  Enhanced diffusion in active intracellular transport. , 2000, Physical review letters.

[144]  J. Kirchner,et al.  Fractal stream chemistry and its implications for contaminant transport in catchments , 2000, Nature.

[145]  George M. Zaslavsky,et al.  Quantum manifestation of Lévy-type flights in a chaotic system , 2000, nlin/0012028.

[146]  A. Compte,et al.  Generalized Diffusion−Advection Schemes and Dispersive Sedimentation: A Fractional Approach† , 2000 .

[147]  M. Gitterman,et al.  Mean first passage time for anomalous diffusion , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[148]  M. Vlad,et al.  Levy diffusion in a force field, huber relaxation kinetics, and nonequilibrium thermodynamics: H theorem for enhanced diffusion with Levy white noise , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[149]  R. Silbey,et al.  Fractional Kramers Equation , 2000 .

[150]  R. Hilfer.  Applications Of Fractional Calculus In Physics , 2000 .

[151]  Bouchaud,et al.  Multiple scaling regimes in simple aging models , 2000, Physical review letters.

[152]  Rangarajan,et al.  Anomalous diffusion and the first passage time problem , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[153]  S. Wearne,et al.  Fractional Reaction-Diffusion , 2000 .

[154]  Brian Berkowitz,et al.  Anomalous transport in laboratory‐scale, heterogeneous porous media , 2000 .

[155]  S. Havlin,et al.  Diffusion and Reactions in Fractals and Disordered Systems , 2000 .

[156]  J. Klafter,et al.  Subdiffusive transport close to thermal equilibrium: from the langevin equation to fractional diffusion , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[157]  Mingzhou Ding,et al.  FIRST PASSAGE TIME PROBLEM FOR BIASED CONTINUOUS-TIME RANDOM WALKS , 2000 .

[158]  Metzler,et al.  Generalized chapman-kolmogorov equation: A unifying approach to the description of anomalous transport in external fields , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[159]  Schofield,et al.  Three-dimensional direct imaging of structural relaxation near the colloidal glass transition , 2000, Science.

[160]  Ralf Metzler,et al.  Accelerating Brownian motion: A fractional dynamics approach to fast diffusion , 2000 .

[161]  J. Klafter,et al.  Strong anomaly in diffusion generated by iterated maps. , 2000, Physical review letters.

[162]  R. Gorenflo,et al.  Fractional calculus and continuous-time finance II: the waiting-time distribution , 2000, cond-mat/0006454.

[163]  Ralf Metzler,et al.  Boundary value problems for fractional diffusion equations , 2000 .

[164]  Levy distribution of single molecule line shape cumulants in glasses , 2000, Physical review letters.

[165]  Correction to “Anomalous transport in laboratory-scale, heterogeneous porous media” , 2000 .

[166]  Hari M. Srivastava,et al.  Operators of fractional integration and their applications , 2001, Appl. Math. Comput..

[167]  D. Chatenay,et al.  Kinetics and mechanism of DNA uptake into the cell nucleus , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[168]  R. Kimmich.  NMR: Tomography, Diffusometry, Relaxometry , 2001 .

[169]  E. Barkai.  CTRW pathways to the fractional diffusion equation , 2001, cond-mat/0108024.

[170]  E. Barkai,et al.  Fractional Fokker-Planck equation, solution, and application. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[171]  S. Redner.  A guide to first-passage processes , 2001 .

[172]  A. Caspi,et al.  A new dimension in retrograde flow: centripetal movement of engulfed particles. , 2001, Biophysical journal.

[173]  Jean-Philippe Bouchaud,et al.  Lévy Statistics and Laser Cooling: Introduction , 2001 .

[174]  A. Shushin.  Anomalous two-state model for anomalous diffusion. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[175]  R. Metzler.  Non-homogeneous random walks, generalised master equations, fractional Fokker-Planck equations, and the generalised Kramers-Moyal expansion , 2001 .

[176]  B. West,et al.  An ant in a gurge , 2001 .

[177]  Rina Schumer,et al.  Fractional Dispersion, Lévy Motion, and the MADE Tracer Tests , 2001 .

[178]  Yi-Sui Sun,et al.  Lévy flights in comet motion and related chaotic systems , 2001 .

[179]  W. Woyczynski,et al.  Growing fractal interfaces in the presence of self-similar hopping surface diffusion , 2001 .

[180]  D. Wirtz,et al.  Mechanics and multiple-particle tracking microheterogeneity of alpha-actinin-cross-linked actin filament networks. , 2001, Biophysical journal.

[181]  Fractional Klein-Kramers equation for superdiffusive transport: normal versus anomalous time evolution in a differential L{\'e}vy walk model , 2001, cond-mat/0107497.

[182]  Do strange kinetics imply unusual thermodynamics? , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[183]  Linear response in complex systems: CTRW and the fractional Fokker-Planck equations , 2001, cond-mat/0107632.

[184]  J. Klafter,et al.  The dynamical foundation of fractal stream chemistry: The origin of extremely long retention times , 2001, cond-mat/0202326.

[185]  Molecular switching with nonexponential relaxation patterns: a random walk approach. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[186]  Sergey V. Buldyrev,et al.  Properties of Lévy flights on an interval with absorbing boundaries , 2001 .

[187]  Jean-Philippe Bouchaud,et al.  Lévy Statistics and Laser Cooling , 2001 .

[188]  David A. Benson,et al.  Subordinated advection‐dispersion equation for contaminant transport , 2001 .

[189]  E. Lutz.  Fractional Langevin equation. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[190]  Robert Neuhauser,et al.  Blinking statistics in single semiconductor nanocrystal quantum dots , 2001 .

[191]  S B Yuste,et al.  Subdiffusion-limited A+A reactions. , 2001, Physical review letters.

[192]  Joseph Klafter,et al.  Anomalous motion of membranes under a localized external potential , 2001 .

[193]  Anomalous diffusion and phase relaxation. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[194]  Jinqiao Duan,et al.  Fractional Fokker-Planck Equation for Nonlinear Stochastic Differential Equations Driven by Non-Gaussian Levy Stable Noises , 1999, math/0409486.

[195]  Santos B. Yuste,et al.  Subdiffusion-limited A+A reactions. , 2001 .

[196]  Joseph F. Traub.  A Continuous Model of Computation , 2001, ArXiv.

[197]  E. Lutz,et al.  Fractional transport equations for Lévy stable processes. , 2001, Physical review letters.

[198]  T. Prosen,et al.  Anomalous diffusion and dynamical localization in polygonal billiards. , 2001, Physical review letters.

[199]  D. Caruana,et al.  The effect of hydrogen on the morphology of n-type silicon electrodes under electrochemical conditions , 2001 .

[200]  L. Zelenyi,et al.  "Strange" Fermi processes and power-law nonthermal tails from a self-consistent fractional kinetic equation. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[201]  Strange kinetics: conflict between density and trajectory description , 2001, cond-mat/0112205.

[202]  R. Hilfer,et al.  H-function representations for stretched exponential relaxation and non-Debye susceptibilities in glassy systems. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[203]  C. Tsallis,et al.  Anomalous diffusion: nonlinear fractional Fokker–Planck equation , 2002 .

[204]  D. Macdonald,et al.  Scale‐free dynamics in the movement patterns of jackals , 2002 .

[205]  Mano Singham,et al.  Philosophy Is Essential to the Intelligent Design Debate , 2002 .

[206]  Bruce J. West,et al.  Fractional Langevin model of memory in financial markets. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[207]  Alexander Puzenko,et al.  Damped oscillations in view of the fractional oscillator equation , 2002 .

[208]  Energy relaxation in Fermi–Pasta–Ulam arrays , 2001, cond-mat/0109361.

[209]  The diffusion-drift equation on comb-like structure , 2002 .

[210]  S. Wearne,et al.  Existence of Turing Instabilities in a Two-Species Fractional Reaction-Diffusion System , 2002, SIAM J. Appl. Math..

[211]  Sangyoub Lee,et al.  Fractional dynamics approach to diffusion-assisted reactions in disordered media , 2002 .

[212]  Ingve Simonsen,et al.  Optimal investment horizons , 2002 .

[213]  Seong-Min Yoon,et al.  DYNAMICAL BEHAVIOR OF CONTINUOUS TICK DATA IN FUTURES EXCHANGE MARKET , 2002, cond-mat/0212393.

[214]  M. Schulz,et al.  Lévy flights in a quenched jump length field: a 1-loop renormalization group approach , 2002 .

[215]  Erwin Frey,et al.  Tracer studies on f-actin fluctuations. , 2002, Physical review letters.

[216]  David A. Benson,et al.  Advection and dispersion in time and space , 2002 .

[217]  Anomalous dynamics of translocation. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[218]  Ralf Metzler,et al.  Diffusion on random-site percolation clusters: theory and NMR microscopy experiments with model objects. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[219]  Angelo Vulpiani,et al.  Superfast front propagation in reactive systems with non-Gaussian diffusion , 2002 .

[220]  Nonlinear electrophoresis of point‐like particles – is it possible? , 2002, Electrophoresis.

[221]  Breakdown of the Fluctuation-Dissipation Theorem for fast superdiffusion , 2002, cond-mat/0207718.

[222]  S. Jespersen,et al.  Anomalous diffusion and relaxation in macromolecular systems , 2002 .

[223]  Wulfram Gerstner,et al.  Spiking Neuron Models , 2002 .

[224]  Brian Berkowitz,et al.  Towards a unified framework for anomalous transport in heterogeneous media , 2002 .

[225]  L. Zelenyi,et al.  Nonequilibrium stationary states in the earth's magnetotail: Stochastic acceleration processes and nonthermal distribution functions , 2002 .

[226]  D Sornette,et al.  Diffusion of epicenters of earthquake aftershocks, Omori's law, and generalized continuous-time random walk models. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[227]  Chaos and transport properties of adatoms on solid surfaces , 2002 .

[228]  Inverse Statistics in Economics: The Gain-Loss Asymmetry , 2002 .

[229]  Fracton pairing mechanism for unconventional superconductors: Self-assembling organic polymers and copper-oxide compounds , 2002, cond-mat/0201504.

[230]  R. Segev,et al.  Long term behavior of lithographically prepared in vitro neuronal networks. , 2002, Physical review letters.

[231]  Anomalous diffusion, stable processes, and generalized functions. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[232]  Kim Christensen,et al.  A complexity view of rainfall. , 2002, Physical review letters.

[233]  Evidence for Lévy Random Walks in the Evolution of Comets from the Oort Cloud , 2002 .

[234]  Yuri Feldman,et al.  Non-Debye dielectric relaxation in complex materials , 2002 .

[235]  I. Sokolov,et al.  Superdiffusive Klein-Kramers equation: Normal and ano malous time evolution and Lévy walk moments , 2002 .

[236]  H. Habersack,et al.  On bed particle diffusion in gravel bed flows under weak bed load transport , 2002 .

[237]  Vicenç Méndez,et al.  Continuous-time random walks and traveling fronts. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[238]  S. C. Lim,et al.  Self-similar Gaussian processes for modeling anomalous diffusion. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[239]  Growth of Mo-oxide patterns by anomalous dynamic diffusion of cations , 2002 .

[240]  D. Montgomery,et al.  Partial entrainment of gravel bars during floods , 2002 .

[241]  Aleksei V. Chechkin,et al.  Stationary states of non-linear oscillators driven by Lévy noise , 2002 .

[242]  I M Sokolov,et al.  Retarding subdiffusion and accelerating superdiffusion governed by distributed-order fractional diffusion equations. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[243]  Enrico Scalas,et al.  Waiting-times and returns in high-frequency financial data: an empirical study , 2002, cond-mat/0203596.

[244]  M. Schulz.  Lévy flights in a quenched jump length field: a real space renormalization group approach , 2002 .

[245]  S. Stapf.  NMR investigations of correlations between longitudinal and transverse displacements in flow through random structured media , 2002 .

[246]  Angelo Vulpiani,et al.  Front propagation in reactive systems with anomalous diffusion , 2003 .

[247]  Quantum Kramers equation for energy diffusion and barrier crossing dynamics in the low-friction regime. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[248]  W. Schleich,et al.  Anomalous kinetics of heavy particles in light media , 2002 .

[249]  A. Caspi,et al.  Diffusion and directed motion in cellular transport. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[250]  Fractal dimension of the active zone for a p-doped poly(3,4-ethylenedioxythiophene) modified electrode towards a ferrocene probe , 2002 .

[251]  Vito Latora,et al.  Lévy scaling: the diffusion entropy analysis applied to DNA sequences. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[252]  P. W. Lamberti,et al.  Anomalous diffusion in the nonasymptotic regime. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[253]  H Eugene Stanley,et al.  Different scaling behaviors of commodity spot and future prices. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[254]  Igor Sokolov,et al.  Lévy flights in external force fields: from models to equations , 2002 .

[255]  R. Gorenflo,et al.  Fractional diffusion: probability distributions and random walk models , 2002 .

[256]  N. Laskin.  Fractional Schrödinger equation. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[257]  P. Lunkenheimer,et al.  Dielectric spectroscopy of glass-forming materials: α-relaxation and excess wing , 2002 .

[258]  Ya. L. Kobelev,et al.  Description of diffusion in fractal media on the basis of the Klimontovich kinetic equation in fractal space , 2002 .

[259]  I M Sokolov,et al.  Solutions of a class of non-Markovian Fokker-Planck equations. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[260]  P. Milly,et al.  Macroscale water fluxes 3. Effects of land processes on variability of monthly river discharge , 2002 .

[261]  Kharkov,et al.  Fractional kinetics for relaxation and superdiffusion in a magnetic field , 2002 .

[262]  Hans-Peter Scheffler,et al.  Stochastic solution of space-time fractional diffusion equations. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[263]  Ralf Metzler,et al.  From stretched exponential to inverse power-law: fractional dynamics, Cole-Cole relaxation processes, and beyond , 2002 .

[264]  A. Hansen,et al.  Relation between anomalous and normal diffusion in systems with memory. , 2002, Physical review letters.

[265]  R. Metzler,et al.  Space- and time-fractional diffusion and wave equations, fractional Fokker-Planck equations, and physical motivation , 2002 .

[266]  Hans-Peter Scheffler,et al.  Governing equations and solutions of anomalous random walk limits. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[267]  V. Uchaikin.  Multidimensional symmetric anomalous diffusion , 2002 .

[268]  Haw Yang,et al.  Probing single-molecule dynamics photon by photon , 2002 .

[269]  G. Zaslavsky.  Chaos, fractional kinetics, and anomalous transport , 2002 .

[270]  Y. Hidaka,et al.  Anomalous diffusion and Lévy distribution of particle velocity in soft-mode turbulence in electroconvection , 2002 .

[271]  R. Gorenflo,et al.  Discrete random walk models for space-time fractional diffusion , 2002, cond-mat/0702072.

[272]  Ralf Metzler,et al.  Physical pictures of transport in heterogeneous media: Advection‐dispersion, random‐walk, and fractional derivative formulations , 2002, cond-mat/0202327.

[273]  Shinji Saito,et al.  Molecular dynamics simulation of the ice nucleation and growth process leading to water freezing , 2002, Nature.

[274]  Subdiffusion and the cage effect studied near the colloidal glass transition , 2001, cond-mat/0111073.

[275]  Rudolf Hilfer,et al.  Experimental evidence for fractional time evolution in glass forming materials , 2002 .

[276]  Sonia Grego,et al.  The Motion of a Single Molecule, the λ-Receptor, in the Bacterial Outer Membrane , 2002 .

[277]  Rainer Kimmich,et al.  Strange kinetics, porous media, and NMR , 2002 .

[278]  M. Latif,et al.  A high resolution AGCM study of the El Niño impact on the North Atlantic/European sector , 2002 .

[279]  Zhenyu Zhang,et al.  Fidgety particles on surfaces: how do they jump, walk, group, and settle in virgin areas? , 2002 .

[280]  Malslashgorzata Klimek,et al.  Stationarity–conservation laws for fractional differential equations with variable coefficients , 2002 .

[281]  J. Ross,et al.  Systematic derivation of reaction-diffusion equations with distributed delays and relations to fractional reaction-diffusion equations and hyperbolic transport equations: application to the theory of Neolithic transition. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[282]  I. M. Sokolov,et al.  Fractional Fokker-Planck equation for ultraslow kinetics , 2003 .

[283]  J. Bisquert.  Fractional diffusion in the multiple-trapping regime and revision of the equivalence with the continuous-time random walk. , 2003, Physical review letters.

[284]  Mingzhou Ding,et al.  Processes with long-range correlations : theory and applications , 2003 .

[285]  J. Bao,et al.  Investigation on anomalous diffusion for nuclear fusion reactions , 2003 .

[286]  Lévy statistics and laser cooling—how rare events bring atoms to rest: F. Bardou, J. Bouchaud, A. Aspect, C. Cohen-Tannoudji; Cambridge University Press, Cambridge, 2001, 214pp, price £19.95 (paperback); £60.00 (hardback), ISBN 0-521-00422-5 (paperback), 0-521-80821-9 (hardback) , 2003 .

[287]  C. Tsallis,et al.  Crossover in diffusion equation: anomalous and normal behaviors. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[288]  André W. Visser,et al.  Random motility of plankton: diffusive and aggregative contributions , 2003 .

[289]  E. Marinari,et al.  Localization of denaturation bubbles in random DNA sequences , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[290]  The Fluctuation-Dissipation Theorem fails for fast superdiffusion , 2003, cond-mat/0304285.

[291]  F. Ren,et al.  Universality of stretched Gaussian asymptotic behaviour for the fractional Fokker–Planck equation in external force fields , 2003 .

[292]  E. Barkai.  Aging in subdiffusion generated by a deterministic dynamical system. , 2003, Physical review letters.

[293]  Mark Bates,et al.  Dynamics of DNA molecules in a membrane channel probed by active control techniques. , 2003, Biophysical journal.

[294]  R.M.C. de Almeida,et al.  Reaction–diffusion in high-k dielectrics on Si , 2003 .

[295]  E. Gaztañaga,et al.  Three-point temperature anisotropies in WMAP: Limits on CMB non-Gaussianities and nonlinearities , 2003 .

[296]  J. Klafter,et al.  When translocation dynamics becomes anomalous. , 2003, Biophysical journal.

[297]  Stable equilibrium based on Lévy statistics: Stochastic collision models approach. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[298]  Solar flare intermittency and the earth's temperature anomalies. , 2003, Physical review letters.

[299]  J. Jadżyn,et al.  Static and dynamic dielectric properties of strongly polar liquids in the vicinity of first order and weakly first order phase transitions. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[300]  Baowen Li,et al.  Anomalous heat conduction and anomalous diffusion in one-dimensional systems. , 2003, Physical review letters.

[301]  Yuan-Chung Cheng,et al.  Aging continuous time random walks , 2003 .

[302]  G. Aquino,et al.  Generalized master equation via aging continuous-time random walks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[303]  Ya. L. Kobelev,et al.  Anomalous diffusion with time-and coordinate-dependent memory , 2003 .

[304]  A. Stanislavsky.  Fractional dynamics from the ordinary Langevin equation. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[305]  H. R. Hicks,et al.  Numerical methods for the solution of partial difierential equations of fractional order , 2003 .

[306]  V E Lynch,et al.  Front dynamics in reaction-diffusion systems with Levy flights: a fractional diffusion approach. , 2002, Physical review letters.

[307]  N. Pottier.  Aging properties of an anomalously diffusing particule , 2002, cond-mat/0205307.

[308]  A. Tofighi,et al.  The intrinsic damping of the fractional oscillator , 2003 .

[309]  Andrea Carati,et al.  Lévy flights in the Landau-Teller model of molecular collisions. , 2003, Physical review letters.

[310]  V. Zaburdaev,et al.  Memory effects in stochastic transport , 2003 .

[311]  X. Xie,et al.  Protein Conformational Dynamics Probed by Single-Molecule Electron Transfer , 2003, Science.

[312]  Kazuhiko Seki,et al.  Fractional reaction-diffusion equation , 2003 .

[313]  H. Larralde,et al.  Lévy walk patterns in the foraging movements of spider monkeys (Ateles geoffroyi) , 2003, Behavioral Ecology and Sociobiology.

[314]  E Barkai,et al.  Lévy statistics for random single-molecule line shapes in a glass. , 2003, Physical review letters.

[315]  I. Sokolov,et al.  Competition between Lévy jumps and continuous drift , 2003 .

[316]  Ralf Metzler,et al.  Bifurcation, bimodality, and finite variance in confined Lévy flights. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[317]  W. L. Vargas,et al.  Fractional diffusion model for force distribution in static granular media. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[318]  Grégoire Altan-Bonnet,et al.  Bubble dynamics in double-stranded DNA. , 2003, Physical review letters.

[319]  Kwok Sau Fa,et al.  Anomalous diffusion: Fractional Fokker–Planck equation and its solutions , 2003 .

[320]  J. Klafter,et al.  Single stranded DNA translocation through a nanopore: a master equation approach. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[321]  Y. Pachepsky,et al.  Generalized Richards' equation to simulate water transport in unsaturated soils , 2003 .

[322]  Kwok Sau Fa,et al.  Linear Langevin equation with time-dependent drift and multiplicative noise term: exact study , 2003 .

[323]  V. Uchaikin.  Relaxation Processes and Fractional Differential Equations , 2003 .

[324]  Anatoly Lagutin,et al.  Anomalous diffusion equation: Application to cosmic ray transport , 2003 .

[325]  Lévy decoupled random walks , 2003 .

[326]  Growing surfaces with anomalous diffusion: results for the fractal Kardar-Parisi-Zhang equation. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[327]  A. Hanyga.  AN ANISOTROPIC COLE–COLE MODEL OF SEISMIC ATTENUATION , 2003 .

[328]  Compatibility of quantum states , 2002, quant-ph/0205033.

[329]  Y. Feldman,et al.  Relaxation peak broadening and polymer chain dynamics in aramid‐fiber‐reinforced nylon‐66 microcomposites , 2003 .

[330]  Non-Markovian stochastic Liouville equation and its Markovian representation. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[331]  J. Bao.  Transport in a flashing ratchet in the presence of anomalous diffusion , 2003 .

[332]  R. Friedrich,et al.  Statistics of Lagrangian velocities in turbulent flows. , 2003, Physical review letters.

[333]  V. Gonchar,et al.  Stable Lévy distributions of the density and potential fluctuations in the edge plasma of the U-3M torsatron , 2003 .

[334]  E. Lutz.  Anomalous diffusion and Tsallis statistics in an optical lattice , 2003 .

[335]  Giorgio Turchetti,et al.  Diffusion and memory effects for stochastic processes and fractional Langevin equations , 2003 .

[336]  G. Sardanashvily,et al.  LETTER TO THE EDITOR: The Liouville-Arnold-Nekhoroshev theorem for non-compact invariant manifolds , 2003 .

[337]  Fractional dynamics and nonlinear harmonic responses in dielectric relaxation of disordered liquids. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[338]  Rain, power laws, and advection. , 2002, Physical review letters.

[339]  K. Seki,et al.  Recombination kinetics in subdiffusive media , 2003 .

[340]  Anomalous diffusion and dielectric relaxation in an N-fold cosine potential. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[341]  ON FRACTIONAL RELAXATION , 2003 .

[342]  K. S. Fa,et al.  Power law diffusion coefficient and anomalous diffusion: analysis of solutions and first passage time. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[343]  S. Boldyrev,et al.  Lévy model for interstellar scintillations. , 2003, Physical review letters.

[344]  S. A. El-Wakil,et al.  The fractional Fokker–Planck equation on comb-like model , 2003 .

[345]  T. Geisel,et al.  Particle dispersion on rapidly folding random heteropolymers. , 2003, Physical review letters.

[346]  Dynamical heat channels. , 2003, Physical review letters.

[347]  J. R. Leith,et al.  Fractal scaling of fractional diffusion processes , 2003, Signal Process..

[348]  R. Nigmatullin,et al.  An anomalous diffusion model in an external force fields on fractals , 2003 .

[349]  L. Zelenyi,et al.  Ion transport and Lévy random walk across the magnetopause in the presence of magnetic turbulence , 2003 .

[350]  D Brockmann,et al.  Lévy flights in inhomogeneous media. , 2003, Physical review letters.

[351]  J. Klafter,et al.  Lévy-Driven Langevin Systems: Targeted Stochasticity , 2003 .

[352]  Giampaolo Cristadoro,et al.  Anomalous transport: a deterministic approach. , 2003, Physical review letters.

[353]  O. Bakunin.  Diffusion equations and turbulent transport , 2003 .

[354]  Aleksander Stanislavsky,et al.  Probability Interpretation of the Integral of Fractional Order , 2004 .

[355]  J. Klafter,et al.  Translocation of a single-stranded DNA through a conformationally changing nanopore. , 2003, Biophysical journal.

[356]  Inertial effects in anomalous dielectric relaxation of symmetrical top molecules. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[357]  F. So,et al.  A study of the subdiffusive fractional Fokker–Planck equation of bistable systems , 2004 .

[358]  R. Metzler,et al.  Nonspecific binding of the OR repressors CI and Cro of bacteriophage lambda. , 2004, Journal of theoretical biology.

[359]  Nested Fermi surfaces, optical peaks, and laser-induced structural transition in Al , 2004 .

[360]  J. Klafter,et al.  On the first passage of one-sided Lévy motions , 2004 .

[361]  Constructing a dodecagonal structure by projection in two stages , 2004 .

[362]  Aleksei V. Chechkin,et al.  Lévy Flights in a Steep Potential Well , 2003, cond-mat/0306601.

[363]  D. Reichman,et al.  Anomalous diffusion probes microstructure dynamics of entangled F-actin networks. , 2004, Physical review letters.

[364]  Mark M. Meerschaert,et al.  Limit theorems for continuous-time random walks with infinite mean waiting times , 2004, Journal of Applied Probability.

[365]  R. Metzler,et al.  In vivo non‐specific binding of λ CI and Cro repressors is significant , 2004 .

[366]  W. Coffey,et al.  Bimodal approximation for anomalous diffusion in a potential. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[367]  Comment on "Anomalous heat conduction and anomalous diffusion in one-dimensional systems". , 2004, Physical review letters.

[368]  P Grigolini,et al.  Random growth of interfaces as a subordinated process. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[369]  I. Tolic-Nørrelykke,et al.  Anomalous diffusion in living yeast cells. , 2004, Physical review letters.

[370]  S. Mukamel,et al.  Multipoint Fluorescence Quenching-Time Statistics for Single Molecules with Anomalous Diffusion , 2004 .

[371]  Classical intermittency and the quantum Anderson transition. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.