Fractional Dynamics In Comb Like Structures
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Fractional Dynamics In Comb Like Structures
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Author : Alexander Iomin
language : en
Publisher: World Scientific
Release Date : 2018-08-28
Fractional Dynamics In Comb Like Structures written by Alexander Iomin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-28 with Science categories.
Random walks often provide the underlying mesoscopic mechanism for transport phenomena in physics, chemistry and biology. In particular, anomalous transport in branched structures has attracted considerable attention. Combs are simple caricatures of various types of natural branched structures that belong to the category of loopless graphs. The comb model was introduced to understand anomalous transport in percolation clusters. Comb-like models have been widely adopted to describe kinetic processes in various experimental applications in medical physics and biophysics, chemistry of polymers, semiconductors, and many other interdisciplinary applications.The authors present a random walk description of the transport in specific comb geometries, ranging from simple random walks on comb structures, which provide a geometrical explanation of anomalous diffusion, to more complex types of random walks, such as non-Markovian continuous-time random walks. The simplicity of comb models allows to perform a rigorous analysis and to obtain exact analytical results for various types of random walks and reaction-transport processes.
Special Functions Of Fractional Calculus Applications To Diffusion And Random Search Processes
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Author : Trifce Sandev
language : en
Publisher: World Scientific
Release Date : 2022-10-07
Special Functions Of Fractional Calculus Applications To Diffusion And Random Search Processes written by Trifce Sandev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-07 with Mathematics categories.
This book aims to provide an overview of the special functions of fractional calculus and their applications in diffusion and random search processes. The book contains detailed calculations for various examples of anomalous diffusion, random search and stochastic resetting processes, which can be easily followed by the reader, who will be able to reproduce the obtained results. The book will be intended for advanced undergraduate and graduate students and researchers in physics, mathematics and other natural sciences due to the various examples which will be provided in the book.
Fractional Dynamics
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Author : Joseph Klafter
language : en
Publisher: World Scientific
Release Date : 2012
Fractional Dynamics written by Joseph Klafter 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 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. In addition to those who intend to work in this field and those already in the field, this volume will also be useful for researchers not directly involved in the field, but want to know the current status and trends of development in this subject. This latter group includes theoretical chemists, mathematical biologists and engineers.
Handbook Of Applications Of Chaos Theory
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Author : Christos H. Skiadas
language : en
Publisher: CRC Press
Release Date : 2017-12-19
Handbook Of Applications Of Chaos Theory written by Christos H. Skiadas and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-19 with Mathematics categories.
In addition to explaining and modeling unexplored phenomena in nature and society, chaos uses vital parts of nonlinear dynamical systems theory and established chaotic theory to open new frontiers and fields of study. Handbook of Applications of Chaos Theory covers the main parts of chaos theory along with various applications to diverse areas. Expert contributors from around the world show how chaos theory is used to model unexplored cases and stimulate new applications. Accessible to scientists, engineers, and practitioners in a variety of fields, the book discusses the intermittency route to chaos, evolutionary dynamics and deterministic chaos, and the transition to phase synchronization chaos. It presents important contributions on strange attractors, self-exciting and hidden attractors, stability theory, Lyapunov exponents, and chaotic analysis. It explores the state of the art of chaos in plasma physics, plasma harmonics, and overtone coupling. It also describes flows and turbulence, chaotic interference versus decoherence, and an application of microwave networks to the simulation of quantum graphs. The book proceeds to give a detailed presentation of the chaotic, rogue, and noisy optical dissipative solitons; parhelic-like circle and chaotic light scattering; and interesting forms of the hyperbolic prism, the Poincaré disc, and foams. It also covers numerous application areas, from the analysis of blood pressure data and clinical digital pathology to chaotic pattern recognition to economics to musical arts and research.
Complexity And Nonlinear Dynamics
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Author : Axel Bender
language : en
Publisher: SPIE-International Society for Optical Engineering
Release Date : 2007
Complexity And Nonlinear Dynamics written by Axel Bender and has been published by SPIE-International Society for Optical Engineering this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Science categories.
Proceedings of SPIE present the original research papers presented at SPIE conferences and other high-quality conferences in the broad-ranging fields of optics and photonics. These books provide prompt access to the latest innovations in research and technology in their respective fields. Proceedings of SPIE are among the most cited references in patent literature.
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.
Modeling And Analysis Of Modern Fluid Problems
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Author : Liancun Zheng
language : en
Publisher: Academic Press
Release Date : 2017-04-26
Modeling And Analysis Of Modern Fluid Problems written by Liancun Zheng and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-26 with Science categories.
Modeling and Analysis of Modern Fluids helps researchers solve physical problems observed in fluid dynamics and related fields, such as heat and mass transfer, boundary layer phenomena, and numerical heat transfer. These problems are characterized by nonlinearity and large system dimensionality, and 'exact' solutions are impossible to provide using the conventional mixture of theoretical and analytical analysis with purely numerical methods. To solve these complex problems, this work provides a toolkit of established and novel methods drawn from the literature across nonlinear approximation theory. It covers Padé approximation theory, embedded-parameters perturbation, Adomian decomposition, homotopy analysis, modified differential transformation, fractal theory, fractional calculus, fractional differential equations, as well as classical numerical techniques for solving nonlinear partial differential equations. In addition, 3D modeling and analysis are also covered in-depth. - Systematically describes powerful approximation methods to solve nonlinear equations in fluid problems - Includes novel developments in fractional order differential equations with fractal theory applied to fluids - Features new methods, including Homotypy Approximation, embedded-parameter perturbation, and 3D models and analysis
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.
Quantum Processes In Biology
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Author : José Antonio Fornés
language : en
Publisher: Springer Nature
Release Date : 2024-06-05
Quantum Processes In Biology written by José Antonio Fornés and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-05 with Science categories.
In recent years, extensive research on stochastic processes such as neuron networks, molecular motors, dynamics models, anomalous diffusion, and disordered media has led to the development of various methods for applying the Classical and Quantum Smoluchowski Equation to these phenomena. This book focuses on presenting the solution to the Fokker-Planck equation using the Crank-Nicholson formalism. This method is particularly effective for handling systems with numerous interactions, requiring vector and matrix-oriented approaches suitable for implementation in Matlab. Among the topics treated in the book are: Dynamics of protons in DNA, Photosynthesis and the quantum mechanochemical model, Entanglement, coherence and decoherence, Excitons in the Fenna-Mathews-Olson complex, and Energy exchange between cells. The author has made an incredible work in facilitating the understanding of these complex topics. This book includes a brief and clear explanation of the Quantum theory and also includes code to build useful software to use in research environments. This volume is particularly helpful for graduate students in physics and biology interested in understanding biological processes with the use of quantum physics tools.
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.