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High Accuracy Algorithm For The Differential Equations Governing Anomalous Diffusion: Algorithm And Models For Anomalous Diffusion

2019-01-22 Mathematics
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Release : 2019-01-22
Genre : Mathematics
Kind : eBook
Book Rating : 227/5 ( reviews)

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Book Synopsis High Accuracy Algorithm For The Differential Equations Governing Anomalous Diffusion: Algorithm And Models For Anomalous Diffusion by : Weihua Deng

Download or read book High Accuracy Algorithm For The Differential Equations Governing Anomalous Diffusion: Algorithm And Models For Anomalous Diffusion written by Weihua Deng. This book was released on 2019-01-22. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to extend the application field of 'anomalous diffusion', and describe the newly built models and the simulation techniques to the models.The book first introduces 'anomalous diffusion' from the statistical physics point of view, then discusses the models characterizing anomalous diffusion and its applications, including the Fokker-Planck equation, the Feymann-Kac equations describing the functional distribution of the anomalous trajectories of the particles, and also the microscopic model — Langevin type equation. The second main part focuses on providing the high accuracy schemes for these kinds of models, and the corresponding convergence and stability analysis.

Distribution of Statistical Observables for Anomalous and Nonergodic Diffusions

2022-04-11 Technology & Engineering
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Release : 2022-04-11
Genre : Technology & Engineering
Kind : eBook
Book Rating : 915/5 ( reviews)

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Book Synopsis Distribution of Statistical Observables for Anomalous and Nonergodic Diffusions by : Weihua Deng

Download or read book Distribution of Statistical Observables for Anomalous and Nonergodic Diffusions written by Weihua Deng. This book was released on 2022-04-11. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates statistical observables for anomalous and nonergodic dynamics, focusing on the dynamical behaviors of particles modelled by non-Brownian stochastic processes in the complex real-world environment. Statistical observables are widely used for anomalous and nonergodic stochastic systems, thus serving as a key to uncover their dynamics. This study explores the cutting edge of anomalous and nonergodic diffusion from the perspectives of mathematics, computer science, statistical and biological physics, and chemistry. With this interdisciplinary approach, multiple physical applications and mathematical issues are discussed, including stochastic and deterministic modelling, analyses of (stochastic) partial differential equations (PDEs), scientific computations and stochastic analyses, etc. Through regularity analysis, numerical scheme design and numerical experiments, the book also derives the governing equations for the probability density function of statistical observables, linking stochastic processes with PDEs. The book will appeal to both researchers of electrical engineering expert in the niche area of statistical observables and stochastic systems and scientists in a broad range of fields interested in anomalous diffusion, especially applied mathematicians and statistical physicists.

Fractional Diffusion Equations and Anomalous Diffusion

2018-01-25 Science
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Release : 2018-01-25
Genre : Science
Kind : eBook
Book Rating : 035/5 ( reviews)

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Book Synopsis Fractional Diffusion Equations and Anomalous Diffusion by : Luiz Roberto Evangelista

Download or read book Fractional Diffusion Equations and Anomalous Diffusion written by Luiz Roberto Evangelista. This book was released on 2018-01-25. Available in PDF, EPUB and Kindle. Book excerpt: Anomalous diffusion has been detected in a wide variety of scenarios, from fractal media, systems with memory, transport processes in porous media, to fluctuations of financial markets, tumour growth, and complex fluids. Providing a contemporary treatment of this process, this book examines the recent literature on anomalous diffusion and covers a rich class of problems in which surface effects are important, offering detailed mathematical tools of usual and fractional calculus for a wide audience of scientists and graduate students in physics, mathematics, chemistry and engineering. Including the basic mathematical tools needed to understand the rules for operating with the fractional derivatives and fractional differential equations, this self-contained text presents the possibility of using fractional diffusion equations with anomalous diffusion phenomena to propose powerful mathematical models for a large variety of fundamental and practical problems in a fast-growing field of research.

An Introduction to Anomalous Diffusion and Relaxation

2023-01-01 Science
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Release : 2023-01-01
Genre : Science
Kind : eBook
Book Rating : 506/5 ( reviews)

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Book Synopsis An Introduction to Anomalous Diffusion and Relaxation by : Luiz Roberto Evangelista

Download or read book An Introduction to Anomalous Diffusion and Relaxation written by Luiz Roberto Evangelista. This book was released on 2023-01-01. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Methods of Mathematical Modelling

2019-09-17 Technology & Engineering
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Release : 2019-09-17
Genre : Technology & Engineering
Kind : eBook
Book Rating : 481/5 ( reviews)

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Book Synopsis Methods of Mathematical Modelling by : Harendra Singh

Download or read book Methods of Mathematical Modelling written by Harendra Singh. This book was released on 2019-09-17. Available in PDF, EPUB and Kindle. Book excerpt: This book features original research articles on the topic of mathematical modelling and fractional differential equations. The contributions, written by leading researchers in the field, consist of chapters on classical and modern dynamical systems modelled by fractional differential equations in physics, engineering, signal processing, fluid mechanics, and bioengineering, manufacturing, systems engineering, and project management. The book offers theory and practical applications for the solutions of real-life problems and will be of interest to graduate level students, educators, researchers, and scientists interested in mathematical modelling and its diverse applications. Features Presents several recent developments in the theory and applications of fractional calculus Includes chapters on different analytical and numerical methods dedicated to several mathematical equations Develops methods for the mathematical models which are governed by fractional differential equations Provides methods for models in physics, engineering, signal processing, fluid mechanics, and bioengineering Discusses real-world problems, theory, and applications

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