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Record Nr. |
UNINA9910639877403321 |
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Autore |
Evangelista L. R. |
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Titolo |
An introduction to anomalous diffusion and relaxation / / Luiz Roberto Evangelista, Ervin Kaminski Lenzi |
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Pubbl/distr/stampa |
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Cham, Switzerland : , : Springer, , [2023] |
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©2023 |
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ISBN |
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Descrizione fisica |
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1 online resource (411 pages) |
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Collana |
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Disciplina |
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Soggetti |
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Condensed matter |
Mathematical physics |
Statistical mechanics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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 |
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