Fractional dynamics : recent advances / Joseph Klafter, S. C. Lim, Ralf Metzler, editors.

Format:

Book

Contributor:

Klafter, J. (Joseph), editor.

Lim, S. C., editor.

Metzler, Ralf, editor.

Language:

English

Subjects (All):

Fractional calculus.

Dynamics.

Diffusion--Mathematical models.

Diffusion.

Physical Description:

1 online resource (530 p.)

Place of Publication:

Singapore : World Scientific, 2012.

Language Note:

English

Summary:

This volume provides the latest developments in the field of fractional dynamics, which covers fractional (anomalous) transport phenomena, fractional statistical mechanics, fractional quantum mechanics and fractional quantum field theory. The contributors are selected based on their active and important contributions to their respective topics. This volume is the first of its kind that covers such a comprehensive range of topics in fractional dynamics. It will point out to advanced undergraduate and graduate students, and young researchers the possible directions of research in this subject. I

Contents:

Preface; Contents; List of Contributors; Classical Systems; 1. Anomalous Diffusion and Fractional Transport Equations R. Metzler and J.-H. Jeon; 1. Introduction; 2. Continuous Time Random Walk and Fractional Diffusion; 2.1. Physical view of CTRW; 3. Fractional Fokker-Planck-Smoluchowski Equation; 3.1. Subdiffusive case; 3.2. Subordination scheme for the subdiffusive case; 3.3. Levy flights in external potentials; 3.4. Boundary value problems; 3.4.1. Subdiffusion; 3.4.2. Levy flights; 4. Randomness of Long Time Averages in Subdiffusive CTRW Processes; 5. Conclusions; Acknowledgments

References2. Stochastic Diffusion and Stable Noise-Induced Phenomena B. Dybiec and E. Gudowska-Nowak; 1. Introduction; 2. White Non-Gaussian Noises; 2.1. Escape from finite intervals; 2.2. Markovian non-Gaussian Kramers problem; 3. Bi-Fractional Kinetics; 3.1. Escape from finite intervals; 3.2. Non-Markovian Kramers problem; 4. Summary; Acknowledgments; References; 3. Characteristic Times of Anomalous Diffusion in a Potential W. T. Coffey, Y. P. Kalmykov and S. V. Titov; 1. Introduction; 2. Normal Diffusion; 3. Anomalous Diffusion

4. Fractional Diffusion of a Particle in a Double Well Potential5. Concluding Remarks; References; 4. Reactions in Subdiffusive Media and Associated Fractional Equations S. B. Yuste, E. Abad and K. Lindenberg; 1. Introduction; 2. Subdiffusion and Fractional Calculus; 3. Reactions Occurring at Spatially Fixed Locations; 3.1. Single-particle target problem; 3.2. Many-particle target problem; 3.3. Escape problems; 4. Reactions Occurring at Random Locations; 4.1. Mobile particles and traps; 4.2. Fractional diffusion-reaction equations; 4.3. Single-particle target problem with a reactivity field

4.4. Reaction-subdiffusion equations and morphogen gradient formation4.4.1. Constant reactivity; 4.4.2. Piecewise constant reactivity; 4.4.3. Exponentially decaying reactivity; 5. Final Remarks; Acknowledgments; References; 5. Natural and Modified Forms of Distributed-Order Fractional Diffusion Equations A. Chechkin, I. M. Sokolov and J. Klafter; 1. Introduction; 2. Two Forms of Time Fractional Diffusion Equations; 2.1. Riemann-Liouville form; 2.2. Caputo form; 3. Two Forms of Space Fractional Di.usion Equations; 3.1. Natural form; 3.2. Modified form

4. Natural Form of Distributed-Order Time Fractional Diffusion Equation4.1. Properties of the solution; 4.2. Generic case of double order equation: Decelerating subdiffusion; 4.3. Relation to CTRW; 4.4. Superslow diffusion; 4.4.1. Probability density function and mean square displacement; 4.4.2. Distributed-order fractional Fokker- Planck equation for superslow processes; 4.4.3. Relation to CTRW; 5. Modified Form of Distributed-Order Time Fractional Diffusion Equation; 5.1. Thermodynamical interpretation; 5.2. Generic case of double order equation: Accelerating subdiffusion

6. Natural Form of Distributed-Order Space Fractional Diffusion Equation

Notes:

Description based upon print version of record.

Includes bibliographical references at the end of each chapters and index.

Description based on print version record.

ISBN:

9789814340595

9814340596

OCLC:

858227993