An Introduction To Anomalous Diffusion And Relaxation
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An Introduction To Anomalous Diffusion And Relaxation
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Author : Luiz Roberto Evangelista
language : en
Publisher: Springer Nature
Release Date : 2023-01-01
An Introduction To Anomalous Diffusion And Relaxation written by Luiz Roberto Evangelista and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Science categories.
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.
Langevin Equation The With Applications To Stochastic Problems In Physics Chemistry And Electrical Engineering Fourth Edition
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Author : William T Coffey
language : en
Publisher: World Scientific
Release Date : 2017-03-22
Langevin Equation The With Applications To Stochastic Problems In Physics Chemistry And Electrical Engineering Fourth Edition written by William T Coffey and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-22 with Science categories.
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.
The Langevin Equation
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Author : William Coffey
language : en
Publisher: World Scientific
Release Date : 2012
The Langevin Equation written by William Coffey and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
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.
Fractional Equations And Models
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Author : Trifce Sandev
language : en
Publisher: Springer Nature
Release Date : 2019-11-23
Fractional Equations And Models written by Trifce Sandev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-23 with Science categories.
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.
Fractional Diffusion Equations And Anomalous Diffusion
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Author : Luiz Roberto Evangelista
language : en
Publisher: Cambridge University Press
Release Date : 2018-01-25
Fractional Diffusion Equations And Anomalous Diffusion written by Luiz Roberto Evangelista and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-25 with Mathematics categories.
Presents a unified treatment of anomalous diffusion problems using fractional calculus in a wide range of applications across scientific and technological disciplines.
Mathematical Methods In Medical And Biological Sciences
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Author : Harendra Singh
language : en
Publisher: Elsevier
Release Date : 2024-11-05
Mathematical Methods In Medical And Biological Sciences written by Harendra Singh and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-05 with Mathematics categories.
Mathematical Methods in Medical and Biological Sciences presents mathematical methods for computational models arising in the medical and biological sciences. The book presents several real-life medical and biological models, such as infectious and non-infectious diseases that can be modeled mathematically to accomplish profound research in virtual environments when the cost of laboratory expenses is relatively high. It focuses on mathematical techniques that provide global solutions for models arising in medical and biological sciences by considering their long-term benefits. In addition, the book provides leading-edge developments and insights for a range of applications, including epidemiological modeling of pandemic dynamics, viral infection developments, cancer developments, blood oxygen dynamics, HIV infection spread, reaction-diffusion models, polio infection spread, and chaos modeling with fractional order derivatives. - Presents the mathematical treatment of a wide range of real-life medical and biological models, including both infectious and non-infectious diseases - Provides in-depth analysis of the spread of Covid-19, polio, and HIV, including discussion of computational methods and applications - Includes computational modeling methods, along with their practical applications, providing the basis for further exploration and research in epidemiology and applied biomedical sciences
Proceedings Of The Third Un Esa Nasa Workshop On The International Heliophysical Year 2007 And Basic Space Science
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Author : Hans J. Haubold
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-01
Proceedings Of The Third Un Esa Nasa Workshop On The International Heliophysical Year 2007 And Basic Space Science written by Hans J. Haubold and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-01 with Science categories.
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.
Fractional Dynamics And Control
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Author : Dumitru Baleanu
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-19
Fractional Dynamics And Control written by Dumitru Baleanu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-19 with Technology & Engineering categories.
Fractional Dynamics and Control provides a comprehensive overview of recent advances in the areas of nonlinear dynamics, vibration and control with analytical, numerical, and experimental results. This book provides an overview of recent discoveries in fractional control, delves into fractional variational principles and differential equations, and applies advanced techniques in fractional calculus to solving complicated mathematical and physical problems.Finally, this book also discusses the role that fractional order modeling can play in complex systems for engineering and science.
Fractional Calculus And Waves In Linear Viscoelasticity An Introduction To Mathematical Models Second Edition
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Author : Francesco Mainardi
language : en
Publisher: World Scientific
Release Date : 2022-08-16
Fractional Calculus And Waves In Linear Viscoelasticity An Introduction To Mathematical Models Second Edition written by Francesco Mainardi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-16 with Mathematics categories.
Fractional Calculus and Waves in Linear Viscoelasticity (Second Edition) is a self-contained treatment of the mathematical theory of linear (uni-axial) viscoelasticity (constitutive equation and waves) with particular regard to models based on fractional calculus. It serves as a general introduction to the above-mentioned areas of mathematical modeling. The explanations in the book are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to delve further into the subject and explore the research literature. In particular the relevant role played by some special functions is pointed out along with their visualization through plots. Graphics are extensively used in the book and a large general bibliography is included at the end.This new edition keeps the structure of the first edition but each chapter has been revised and expanded, and new additions include a novel appendix on complete monotonic and Bernstein functions that are known to play a fundamental role in linear viscoelasticity.This book is suitable for engineers, graduate students and researchers interested in fractional calculus and continuum mechanics.
Langevin Equation The With Applications To Stochastic Problems In Physics Chemistry And Electrical Engineering 3rd Edition
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Author : Yuri P Kalmykov
language : en
Publisher: World Scientific
Release Date : 2012-07-31
Langevin Equation The With Applications To Stochastic Problems In Physics Chemistry And Electrical Engineering 3rd Edition written by Yuri P Kalmykov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-31 with Science categories.
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, etc. 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.