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Functional Distribution Of Anomalous And Nonergodic Diffusion: From Stochastic Processes To Pdes

2022-06-20 Mathematics
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Release : 2022-06-20
Genre : Mathematics
Kind : eBook
Book Rating : 510/5 ( reviews)

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Book Synopsis Functional Distribution Of Anomalous And Nonergodic Diffusion: From Stochastic Processes To Pdes by : Weihua Deng

Download or read book Functional Distribution Of Anomalous And Nonergodic Diffusion: From Stochastic Processes To Pdes written by Weihua Deng. This book was released on 2022-06-20. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a pedagogical review of the functional distribution of anomalous and nonergodic diffusion and its numerical simulations, starting from the studied stochastic processes to the deterministic partial differential equations governing the probability density function of the functionals. Since the remarkable theory of Brownian motion was proposed by Einstein in 1905, it had a sustained and broad impact on diverse fields, such as physics, chemistry, biology, economics, and mathematics. The functionals of Brownian motion are later widely attractive for their extensive applications. It was Kac, who firstly realized the statistical properties of these functionals can be studied by using Feynman's path integrals.In recent decades, anomalous and nonergodic diffusions which are non-Brownian become topical issues, such as fractional Brownian motion, Lévy process, Lévy walk, among others. This volume examines the statistical properties of the non-Brownian functionals, derives the governing equations of their distributions, and shows some algorithms for solving these equations numerically.

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.

Distributions in the Physical and Engineering Sciences, Volume 3

2018-08-03 Mathematics
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Release : 2018-08-03
Genre : Mathematics
Kind : eBook
Book Rating : 865/5 ( reviews)

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Book Synopsis Distributions in the Physical and Engineering Sciences, Volume 3 by : Alexander I. Saichev

Download or read book Distributions in the Physical and Engineering Sciences, Volume 3 written by Alexander I. Saichev. This book was released on 2018-08-03. Available in PDF, EPUB and Kindle. Book excerpt: Continuing the authors’ multivolume project, this text considers the theory of distributions from an applied perspective, demonstrating how effective a combination of analytic and probabilistic methods can be for solving problems in the physical and engineering sciences. Volume 1 covered foundational topics such as distributional and fractional calculus, the integral transform, and wavelets, and Volume 2 explored linear and nonlinear dynamics in continuous media. With this volume, the scope is extended to the use of distributional tools in the theory of generalized stochastic processes and fields, and in anomalous fractional random dynamics. Chapters cover topics such as probability distributions; generalized stochastic processes, Brownian motion, and the white noise; stochastic differential equations and generalized random fields; Burgers turbulence and passive tracer transport in Burgers flows; and linear, nonlinear, and multiscale anomalous fractional dynamics in continuous media. The needs of the applied-sciences audience are addressed by a careful and rich selection of examples arising in real-life industrial and scientific labs and a thorough discussion of their physical significance. Numerous illustrations generate a better understanding of the core concepts discussed in the text, and a large number of exercises at the end of each chapter expand on these concepts. Distributions in the Physical and Engineering Sciences is intended to fill a gap in the typical undergraduate engineering/physical sciences curricula, and as such it will be a valuable resource for researchers and graduate students working in these areas. The only prerequisites are a three-four semester calculus sequence (including ordinary differential equations, Fourier series, complex variables, and linear algebra), and some probability theory, but basic definitions and facts are covered as needed. An appendix also provides background material concerning the Dirac-delta and other distributions.

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.

Modeling Anomalous Diffusion: From Statistics To Mathematics

2020-01-06 Mathematics
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Release : 2020-01-06
Genre : Mathematics
Kind : eBook
Book Rating : 011/5 ( reviews)

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Book Synopsis Modeling Anomalous Diffusion: From Statistics To Mathematics by : Weihua Deng

Download or read book Modeling Anomalous Diffusion: From Statistics To Mathematics written by Weihua Deng. This book was released on 2020-01-06. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on modeling the anomalous diffusion phenomena, being ubiquitous in the natural world. Both the microscopic models (stochastic processes) and macroscopic models (partial differential equations) have been built up. The relationships between the two kinds of models are clarified, and based on these models, some statistical observables are analyzed. From statistics to mathematics, the built models show their power with their associated applications.This book is important for students to develop basic skills to be able to succeed in their future research. In addition to introducing the related models or methods, it also provides the corresponding applications and simulation results, which will attract more readers ranging from mathematicians to physicists or chemists, to name a few.

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