An Introduction to Anomalous Diffusion and Relaxation PDF Download
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Author: Luiz Roberto Evangelista
Publisher: Springer Nature
ISBN: 3031181506
Category : Science
Languages : en
Pages : 411
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Book Description
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.
Author: Luiz Roberto Evangelista
Publisher: Springer Nature
ISBN: 3031181506
Category : Science
Languages : en
Pages : 411
Get Book Here
Book Description
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.
Author: Andrzej Pekalski
Publisher: Springer
ISBN:
Category : Medical
Languages : en
Pages : 408
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Book Description
This collection of articles gives a nice overview of the fast growing field of diffusion and transport. The area of non-Browman statistical mechanics has many extensions into other fields like biology, ecology, geophysics etc. These tutorial lectures address e.g. Lévy flights and walks, diffusion on metal surfaces or in superconductors, classical diffusion, biased and anomalous diffusion, chemical reaction diffusion, aging in glassy systems, diffusion in soft matter and in nonsymmetric potentials, and also new problems like diffusive processes in econophysics and in biology.
Author: Andrzej Pekalski
Publisher: Springer
ISBN: 9783662142417
Category : Science
Languages : en
Pages : 382
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Book Description
This collection of articles gives a nice overview of the fast growing field of diffusion and transport. The area of non-Browman statistical mechanics has many extensions into other fields like biology, ecology, geophysics etc. These tutorial lectures address e.g. Lévy flights and walks, diffusion on metal surfaces or in superconductors, classical diffusion, biased and anomalous diffusion, chemical reaction diffusion, aging in glassy systems, diffusion in soft matter and in nonsymmetric potentials, and also new problems like diffusive processes in econophysics and in biology.
Author: K.L. Ngai
Publisher: Springer Science & Business Media
ISBN: 1441976493
Category : Science
Languages : en
Pages : 853
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Book Description
The usefulness of the book to the reader is exposure to many different classes of materials and relaxation phenomena. They are tied together by the universal relaxation and diffusion properties they share, and a consistent explanation of their origin. The readers can apply what they learn to solve their own problems and use it as a stepping-stone to make further advances in theoretical understanding of the origin of the universality.
Author: Rainer Klages
Publisher: John Wiley & Sons
ISBN: 9783527407224
Category : Science
Languages : en
Pages : 614
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Book Description
This multi-author reference work provides a unique introduction to the currently emerging, highly interdisciplinary field of those transport processes that cannot be described by using standard methods of statistical mechanics. It comprehensively summarizes topics ranging from mathematical foundations of anomalous dynamics to the most recent experiments in this field. In so doing, this monograph extracts and emphasizes common principles and methods from many different disciplines while providing up-to-date coverage of this new field of research, considering such diverse applications as plasma physics, glassy material, cell science, and socio-economic aspects. The book will be of interest to both theorists and experimentalists in nonlinear dynamics, statistical physics and stochastic processes. It also forms an ideal starting point for graduate students moving into this area. 18 chapters written by internationally recognized experts in this field provide in-depth introductions to fundamental aspects of anomalous transport.
Author: Luiz Roberto Evangelista
Publisher: Cambridge University Press
ISBN: 1107143551
Category : Mathematics
Languages : en
Pages : 361
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Book Description
Presents a unified treatment of anomalous diffusion problems using fractional calculus in a wide range of applications across scientific and technological disciplines.
Author: William Coffey
Publisher: World Scientific
ISBN: 9814355674
Category : Mathematics
Languages : en
Pages : 850
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Book Description
This volume is the third edition of the first-ever elementary book on the Langevin equation method for the solution of problems involving the translational and rotational Brownian motion of particles and spins in a potential highlighting modern applications in physics, chemistry, electrical engineering, and so on. In order to improve the presentation, to accommodate all the new developments, and to appeal to the specialized interests of the various communities involved, the book has been extensively rewritten and a very large amount of new material has been added. This has been done in order to present a comprehensive overview of the subject emphasizing via a synergetic approach that seemingly unrelated physical problems involving random noise may be described using virtually identical mathematical methods in the spirit of the founders of the subject, viz., Einstein, Langevin, Smoluchowski, Kramers, The book has been written in such a way that all the material should be accessible both to an advanced researcher and a beginning graduate student. It draws together, in a coherent fashion, a variety of results which have hitherto been available only in the form of scattered research papers and review articles.
Author: William T Coffey
Publisher: World Scientific
ISBN: 9813222018
Category : Science
Languages : en
Pages : 927
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Book Description
Our original objective in writing this book was to demonstrate how the concept of the equation of motion of a Brownian particle — the Langevin equation or Newtonian-like evolution equation of the random phase space variables describing the motion — first formulated by Langevin in 1908 — so making him inter alia the founder of the subject of stochastic differential equations, may be extended to solve the nonlinear problems arising from the Brownian motion in a potential. Such problems appear under various guises in many diverse applications in physics, chemistry, biology, electrical engineering, etc. However, they have been invariably treated (following the original approach of Einstein and Smoluchowski) via the Fokker-Planck equation for the evolution of the probability density function in phase space. Thus the more simple direct dynamical approach of Langevin which we use and extend here, has been virtually ignored as far as the Brownian motion in a potential is concerned. In addition two other considerations have driven us to write this new edition of The Langevin Equation. First, more than five years have elapsed since the publication of the third edition and following many suggestions and comments of our colleagues and other interested readers, it became increasingly evident to us that the book should be revised in order to give a better presentation of the contents. In particular, several chapters appearing in the third edition have been rewritten so as to provide a more direct appeal to the particular community involved and at the same time to emphasize via a synergetic approach how seemingly unrelated physical problems all involving random noise may be described using virtually identical mathematical methods. Secondly, in that period many new and exciting developments have occurred in the application of the Langevin equation to Brownian motion. Consequently, in order to accommodate all these, a very large amount of new material has been added so as to present a comprehensive overview of the subject.
Author: Trifce Sandev
Publisher: Springer Nature
ISBN: 3030296148
Category : Science
Languages : en
Pages : 357
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Book Description
Fractional equations and models play an essential part in the description of anomalous dynamics in complex systems. Recent developments in the modeling of various physical, chemical and biological systems have clearly shown that fractional calculus is not just an exotic mathematical theory, as it might have once seemed. The present book seeks to demonstrate this using various examples of equations and models with fractional and generalized operators. Intended for students and researchers in mathematics, physics, chemistry, biology and engineering, it systematically offers a wealth of useful tools for fractional calculus.
Author: Hans J. Haubold
Publisher: Springer Science & Business Media
ISBN: 3642033253
Category : Science
Languages : en
Pages : 190
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Book Description
This book represents Volume II of the Proceedings of the UN/ESA/NASA Workshop on the International Heliophysical Year 2007 and Basic Space Science, hosted by the National Astronomical Observatory of Japan, Tokyo, 18 - 22 June, 2007. It covers two programme topics explored in this and past workshops of this nature: (i) non-extensive statistical mechanics as applicable to astrophysics, addressing q-distribution, fractional reaction and diffusion, and the reaction coefficient, as well as the Mittag-Leffler function and (ii) the TRIPOD concept, developed for astronomical telescope facilities. The companion publication, Volume I of the proceedings of this workshop, is a special issue in the journal Earth, Moon, and Planets, Volume 104, Numbers 1-4, April 2009.
