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  • 1
    Online-Ressource
    Online-Ressource
    An Introduction to Anomalous Diffusion and Relaxation (2023)
    Cham :Springer International Publishing :
    Details
    UID:
    almahu_9949420148002882
    Umfang: XX, 400 p. 68 illus., 2 illus. in color. , online resource.
    Ausgabe: 1st ed. 2023.
    ISBN: 9783031181504
    Serie: PoliTO Springer Series,
    Inhalt: This book provides a contemporary treatment of the problems related to anomalous diffusion and anomalous relaxation. It collects and promotes unprecedented applications dealing with diffusion problems and surface effects, adsorption-desorption phenomena, memory effects, reaction-diffusion equations, and relaxation in constrained structures of classical and quantum processes. The topics covered by the book are of current interest and comprehensive range, including concepts in diffusion and stochastic physics, random walks, and elements of fractional calculus. They are accompanied by a detailed exposition of the mathematical techniques intended to serve the reader as a tool to handle modern boundary value problems. This self-contained text can be used as a reference source for graduates and researchers working in applied mathematics, physics of complex systems and fluids, condensed matter physics, statistical physics, chemistry, chemical and electrical engineering, biology, and many others.
    Anmerkung: Preface -- Integral Transforms and Special Functions -- Concepts in Diffusion and Stochastic Processes -- Random Walks -- Elements of Fractional Calculus -- Fractional Anomalous Diffusion -- Adsorption Phenomena and Anomalous Behavior -- Reaction-Diffusion Problems -- Relaxation under Geometric Constraints I: Classical Processes -- Relaxation under Geometric Constraints II: Quantum Processes -- Index.
    In: Springer Nature eBook
    Weitere Ausg.: Printed edition: ISBN 9783031181498
    Weitere Ausg.: Printed edition: ISBN 9783031181511
    Weitere Ausg.: Printed edition: ISBN 9783031181528
    Sprache: Englisch
    DOI: 10.1007/978-3-031-18150-4
    URL: https://doi.org/10.1007/978-3-031-18150-4
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
    BibTip Andere fanden auch interessant ...
    Online-Ressource
    Open Access Wunsch
    HU Berlin
  • 2
    Online-Ressource
    Online-Ressource
    An Introduction to Anomalous Diffusion and Relaxation (2023)
    Cham : Springer
    Details
    UID:
    gbv_1830236601
    Umfang: 1 Online-Ressource (XX, 400 Seiten) , Illustrationen
    ISBN: 9783031181504
    Serie: PoliTO Springer Series
    Inhalt: Preface -- Integral Transforms and Special Functions -- Concepts in Diffusion and Stochastic Processes -- Random Walks -- Elements of Fractional Calculus -- Fractional Anomalous Diffusion -- Adsorption Phenomena and Anomalous Behavior -- Reaction-Diffusion Problems -- Relaxation under Geometric Constraints I: Classical Processes -- Relaxation under Geometric Constraints II: Quantum Processes -- Index.
    Inhalt: This book provides a contemporary treatment of the problems related to anomalous diffusion and anomalous relaxation. It collects and promotes unprecedented applications dealing with diffusion problems and surface effects, adsorption-desorption phenomena, memory effects, reaction-diffusion equations, and relaxation in constrained structures of classical and quantum processes. The topics covered by the book are of current interest and comprehensive range, including concepts in diffusion and stochastic physics, random walks, and elements of fractional calculus. They are accompanied by a detailed exposition of the mathematical techniques intended to serve the reader as a tool to handle modern boundary value problems. This self-contained text can be used as a reference source for graduates and researchers working in applied mathematics, physics of complex systems and fluids, condensed matter physics, statistical physics, chemistry, chemical and electrical engineering, biology, and many others.
    Weitere Ausg.: ISBN 9783031181498
    Weitere Ausg.: ISBN 9783031181511
    Weitere Ausg.: ISBN 9783031181528
    Weitere Ausg.: Erscheint auch als Druck-Ausgabe Evangelista, Luiz Roberto, 1958 - An introduction to anomalous diffusion and relaxation Cham : Springer, 2023 ISBN 9783031181498
    Weitere Ausg.: ISBN 9783031181511
    Weitere Ausg.: ISBN 9783031181528
    Sprache: Englisch
    Fachgebiete: Mathematik
    RVK:
    SK 820
    Schlagwort(e): Anomale Diffusion ; Relaxation
    DOI: 10.1007/978-3-031-18150-4
    URL: lizenzpflichtig
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
    BibTip Andere fanden auch interessant ...
    Online-Ressource
    Open Access Wunsch
    UB Potsdam
  • 3
    Online-Ressource
    Online-Ressource
    An introduction to anomalous diffusion and relaxation / (2023)
    Cham, Switzerland :Springer,
    Details
    UID:
    edoccha_9961000779302883
    Umfang: 1 online resource (411 pages)
    ISBN: 3-031-18150-6
    Serie: PoliTO Springer series
    Anmerkung: Intro -- Preface -- Contents -- About the Authors -- Symbols -- Sets -- Integral Transforms -- Special Functions of Fractional Calculus -- Fractional Operators -- 1 Integral Transforms and Special Functions -- 1.1 Integral Transforms -- 1.1.1 Fourier Transform -- 1.1.2 Laplace Transform -- 1.1.3 The Cauchy Integral Formula -- 1.2 Gamma and Related Functions -- 1.2.1 The Mellin Transform -- 1.3 Special Functions of Fractional Calculus -- 1.3.1 The Functions of the Mittag-Leffler Type -- 1.3.2 The Wright Function -- 1.3.3 The H-Function of Fox -- References -- 2 Concepts in Diffusion and Stochastic Processes -- 2.1 Molecular Diffusion -- 2.1.1 The Mean Square Displacement -- 2.2 Pioneering Studies on Diffusion Problems -- 2.3 Brownian Motion -- 2.3.1 The Works of Einstein, Smoluchowski, and Langevin -- 2.4 Generalized Langevin Equation -- 2.4.1 Derivation of a Diffusionlike Equation -- 2.5 Anomalous Diffusion: Basic Concepts -- 2.5.1 Superdiffusion -- 2.5.2 Lévy Flights -- 2.5.3 Subdiffusion -- References -- 3 Random Walks -- 3.1 Elementary Approach -- 3.1.1 Stochastic Variables -- 3.2 Random Walks: Nonlinear Fokker-Planck Equations -- 3.2.1 Nonlinear Random Walk -- 3.2.2 Generalized Random Walks -- 3.3 Continuous-Time Random Walk -- 3.3.1 Different Diffusive Regimes -- 3.3.2 Linear Reaction Dynamics -- 3.3.3 Coupled Jump-Length and Waiting-Time Distributions -- 3.3.4 Intermittent Continuous-Time Random Walk -- References -- 4 Elements of Fractional Calculus -- 4.1 Introduction -- 4.2 Early Definitions -- 4.3 The Riemann-Liouville Operators -- 4.4 The Grünwald-Letnikov Operators -- 4.5 The Caputo Operator -- 4.6 Some Space-Fractional Derivatives -- References -- 5 Fractional Anomalous Diffusion -- 5.1 A Space-Time Fractional Diffusion Equation -- 5.2 Generalized Space-Time Fractional Diffusion Equation -- 5.2.1 Composite Time Fractional Operator. , 5.2.2 Fractional Diffusion Equation: Singular Term -- 5.3 Tempered Fractional Diffusion Equation -- 5.4 Fractional Diffusion Equation in Heterogeneous Media -- 5.4.1 Free Case -- 5.4.2 External Force -- 5.5 Heterogeneous Media and Fractional Spatial Operator -- 5.6 Time Derivative Operators: A Comparison -- 5.6.1 Diffusion and Time Derivative Operators -- 5.6.2 Predicted Distributions: A Balance -- References -- 6 Adsorption Phenomena and Anomalous Behavior -- 6.1 Kinetic Equation: Normal and Fractional -- 6.1.1 Electrical Impedance in Liquid Crystals -- 6.2 Anomalous Diffusion in Complex Fluids -- 6.2.1 Diffusion and Surface Dynamics -- 6.2.2 Time-Dependent Solutions -- 6.3 Memory Kernels -- 6.3.1 Chemisorption and Physisorption Processes -- 6.3.2 Confined Systems: Periodically Varying Medium -- References -- 7 Reaction-Diffusion Problems -- 7.1 Diffusion and Kinetics -- 7.1.1 Reversible Linear Reaction -- 7.1.2 Irreversible Linear Reaction -- 7.2 Fractional Diffusion of Two Species -- 7.3 Subdiffusion and Linear Reaction -- 7.4 Hyperbolic Diffusion Equation with Reaction Terms -- 7.4.1 Diffusion-Reaction Processes -- References -- 8 Relaxation Under Geometric Constraints I: Classical Processes -- 8.1 Introduction -- 8.2 The Comb Model -- 8.3 Quenched and Annealed Disorder Mechanisms in Comb-Models -- 8.4 Generalized Fractal Structure of Backbones -- 8.5 Comb-Model and Reaction Diffusion -- 8.6 Diffusion and Reaction -- References -- 9 Relaxation Under Geometric Constraints II: Quantum Processes -- 9.1 Introduction -- 9.2 Constrained Quantum Motion in δ-Potential -- 9.3 Time Evolution and Asymptotic Behavior -- 9.4 Time-Dependent Schrödinger Equation in 3D -- 9.4.1 3D Constrained Quantum Model -- 9.4.2 Green's Function and Schrödinger Equation -- 9.4.3 Reduced Green's Functions and Fractional Derivatives. , 9.5 Time-Dependent Schrödinger Equation in Non-integer Dimensions -- 9.5.1 Marginal Probability Density Functions -- 9.5.2 Constrained Diffusion in Non-integer Dimensions -- References -- Index.
    Weitere Ausg.: Print version: Evangelista, Luiz Roberto An Introduction to Anomalous Diffusion and Relaxation Cham : Springer International Publishing AG,c2023 ISBN 9783031181498
    Sprache: Englisch
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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    Online-Ressource
    Charité
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