Fractional Kinetics In Space Anomalous Transport Models

Author : Vladimir V Uchaikin
Publisher : World Scientific
ISBN 13 : 9813225440
Total Pages : 300 pages
Book Rating : 4.42/5 ( download)

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Download or read book Fractional Kinetics In Space: Anomalous Transport Models written by Vladimir V Uchaikin and published by World Scientific. This book was released on 2017-12-12 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is first of its kind describing a new direction in modeling processes taking place in interplanetary and interstellar space (magnetic fields, plasma, cosmic rays, etc.). This method is based on a special mathematical analysis — fractional calculus. The reader will find in this book clear physical explanation of the fractional approach and will become familiar with basic rules in this calculus and main results obtained in frame of this approach. In spite of its profound subject, the book is not overloaded by mathematical details. It contains many illustrations, rich citation and remains accessible to a wide circle of physicists.This book is addressed to graduate and postgraduate students, young and mature researchers specializing in applications of fractional calculus, astrophysics, solar-terrestrial science and physics of cosmic rays.

Author : V. V. Uchaikin
Publisher : World Scientific Publishing Company
ISBN 13 : 9789813225428
Total Pages : 300 pages
Book Rating : 4.24/5 ( download)

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Download or read book Fractional Kinetics in Space written by V. V. Uchaikin and published by World Scientific Publishing Company. This book was released on 2018 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is first of its kind describing a new direction in modeling processes taking place in interplanetary and interstellar space (magnetic fields, plasma, cosmic rays, etc.). This method is based on a special mathematical analysis fractional calculus. The reader will find in this book clear physical explanation of the fractional approach and will become familiar with basic rules in this calculus and main results obtained in frame of this approach. In spite of its profound subject, the book is not overloaded by mathematical details. It contains many illustrations, rich citation and remains accessible to a wide circle of physicists. This book is addressed to graduate and postgraduate students, young and mature researchers specializing in applications of fractional calculus, astrophysics, solar-terrestrial science and physics of cosmic rays.

Author : Vladimir Vasilʹevich Uchaĭkin
Publisher :
ISBN 13 : 9789813225435
Total Pages : 300 pages
Book Rating : 4.32/5 ( download)

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Download or read book Fractional Kinetics in Space written by Vladimir Vasilʹevich Uchaĭkin and published by . This book was released on 2017 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Vladimir Vasilʹevich Uchaĭkin
Publisher : World Scientific
ISBN 13 : 9814355429
Total Pages : 274 pages
Book Rating : 4.21/5 ( download)

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Download or read book Fractional Kinetics in Solids written by Vladimir Vasilʹevich Uchaĭkin and published by World Scientific. This book was released on 2013 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: The standard (Markovian) transport model based on the Boltzmann equation cannot describe some non-equilibrium processes called anomalous that take place in many disordered solids. Causes of anomality lie in non-uniformly scaled (fractal) spatial heterogeneities, in which particle trajectories take cluster form. Furthermore, particles can be located in some domains of small sizes (traps) for a long time. Estimations show that path length and waiting time distributions are often characterized by heavy tails of the power law type. This behavior allows the introduction of time and space derivatives of fractional orders. Distinction of path length distribution from exponential is interpreted as a consequence of media fractality, and analogous property of waiting time distribution as a presence of memory. In this book, a novel approach using equations with derivatives of fractional orders is applied to describe anomalous transport and relaxation in disordered semiconductors, dielectrics and quantum dot systems. A relationship between the self-similarity of transport, the Levy stable limiting distributions and the kinetic equations with fractional derivatives is established. It is shown that unlike the well-known Scher Montroll and Arkhipov Rudenko models, which are in a sense alternatives to the normal transport model, fractional differential equations provide a unified mathematical framework for describing normal and dispersive transport. The fractional differential formalism allows the equations of bipolar transport to be written down and transport in distributed dispersion systems to be described. The relationship between fractional transport equations and the generalized limit theorem reveals the probabilistic aspects of the phenomenon in which a dispersive to Gaussian transport transition occurs in a time-of-flight experiment as the applied voltage is decreased and/or the sample thickness increased. Recent experiments devoted to studies of transport in quantum dot arrays are discussed in the framework of dispersive transport models. The memory phenomena in systems under consideration are discussed in the analysis of fractional equations. It is shown that the approach based on the anomalous transport models and the fractional kinetic equations may be very useful in some problems that involve nano-sized systems. These are photon counting statistics of blinking single quantum dot fluorescence, relaxation of current in colloidal quantum dot arrays, and some others.

Author : G. M. Zaslavsky
Publisher :
ISBN 13 :
Total Pages : 120 pages
Book Rating : 4.07/5 ( download)

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Download or read book Chaos, Fractional Kinetics, and Anomalous Transport written by G. M. Zaslavsky and published by . This book was released on 2002 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Vasily E. Tarasov
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110571722
Total Pages : 327 pages
Book Rating : 4.21/5 ( download)

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Download or read book Applications in Physics written by Vasily E. Tarasov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-02-19 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This fifth volume collects authoritative chapters covering several applications of fractional calculus in physics, including electrodynamics, statistical physics and physical kinetics, and quantum theory.

Author : Anatoly Kochubei
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110571625
Total Pages : 489 pages
Book Rating : 4.22/5 ( download)

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Download or read book Basic Theory written by Anatoly Kochubei and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-02-19 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This first volume collects authoritative chapters covering the mathematical theory of fractional calculus, including fractional-order operators, integral transforms and equations, special functions, calculus of variations, and probabilistic and other aspects.

Author : Christos H. Skiadas
Publisher : Springer
ISBN 13 : 3030044831
Total Pages : 201 pages
Book Rating : 4.31/5 ( download)

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Download or read book Fractional Dynamics, Anomalous Transport and Plasma Science written by Christos H. Skiadas and published by Springer. This book was released on 2018-12-11 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects interrelated lectures on fractal dynamics, anomalous transport and various historical and modern aspects of plasma sciences and technology. The origins of plasma science in connection to electricity and electric charges and devices leading to arc plasma are explored in the first contribution by Jean-Marc Ginoux and Thomas Cuff. The second important historic connection with plasmas was magnetism and the magnetron. Victor J. Law and Denis P. Dowling, in the second contribution, review the history of the magnetron based on the development of thermionic diode valves and related devices. In the third chapter, Christos H Skiadas and Charilaos Skiadas present and apply diffusion theory and solution strategies to a number of stochastic processes of interest. Anomalous diffusion by the fractional Fokker-Planck equation and Lévy stable processes are studied by Johan Anderson and Sara Moradi in the fourth contribution. They consider the motion of charged particles in a 3-dimensional magnetic field in the presence of linear friction and of a stochastic electric field. Analysis of low-frequency instabilities in a low-temperature magnetized plasma is presented by Dan-Gheorghe Dimitriu, Maricel Agop in the fifth chapter. The authors refer to experimental results of the Innsbruck Q-machine and provide an analytical formulation of the related theory. In chapter six, Stefan Irimiciuc, Dan-Gheorghe Dimitriu, Maricel Agop propose a theoretical model to explain the dynamics of charged particles in a plasma discharge with a strong flux of electrons from one plasma structure to another. The theory and applications of fractional derivatives in many-particle disordered large systems are explored by Z.Z. Alisultanov, A.M. Agalarov, A.A. Potapov, G.B. Ragimkhanov. In chapter eight, Maricel Agop, Alina Gavrilut ̧ and Gabriel Crumpei explore the motion of physical systems that take place on continuous but non-differentiable curves (fractal curves). Finally in the last chapter S.L. Cherkas and V.L. Kalashnikov consider the perturbations of a plasma consisting of photons, baryons, and electrons in a linearly expanding (Milne-like) universe taking into account the metric tensor and vacuum perturbations.

Author : Georgij Moiseevič Zaslavskij
Publisher :
ISBN 13 :
Total Pages : 120 pages
Book Rating : 4.90/5 ( download)

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Download or read book Chaos, Fractional Kinetics, and Anomalous Transport written by Georgij Moiseevič Zaslavskij and published by . This book was released on 2002 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author :
Publisher :
ISBN 13 :
Total Pages : 121 pages
Book Rating : 4.96/5 ( download)

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Download or read book Chaos, Fractional Kinetics, and Anomalous Transport written by and published by . This book was released on 2002 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: