Functional Distribution Of Anomalous And Nonergodic Diffusion From Stochastic Processes To Pdes PDF Download
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| Author | : Weihua Deng |
| Publisher | : World Scientific |
| Total Pages | : 258 |
| Release | : 2022-06-20 |
| Genre | : Mathematics |
| ISBN | : 9811250510 |
Download Functional Distribution Of Anomalous And Nonergodic Diffusion: From Stochastic Processes To Pdes Book in PDF, ePub and Kindle
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.
| Author | : Weihua Deng |
| Publisher | : CRC Press |
| Total Pages | : 211 |
| Release | : 2022-04-11 |
| Genre | : Technology & Engineering |
| ISBN | : 1000567915 |
Download Distribution of Statistical Observables for Anomalous and Nonergodic Diffusions Book in PDF, ePub and Kindle
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.
| Author | : Luiz Roberto Evangelista |
| Publisher | : Springer Nature |
| Total Pages | : 411 |
| Release | : 2023-01-01 |
| Genre | : Science |
| ISBN | : 3031181506 |
Download An Introduction to Anomalous Diffusion and Relaxation Book in PDF, ePub and Kindle
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 | : Weihua Deng |
| Publisher | : World Scientific |
| Total Pages | : 267 |
| Release | : 2020-01-06 |
| Genre | : Mathematics |
| ISBN | : 9811213011 |
Download Modeling Anomalous Diffusion: From Statistics To Mathematics Book in PDF, ePub and Kindle
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.
| Author | : Simo Särkkä |
| Publisher | : Cambridge University Press |
| Total Pages | : 327 |
| Release | : 2019-05-02 |
| Genre | : Business & Economics |
| ISBN | : 1316510085 |
Download Applied Stochastic Differential Equations Book in PDF, ePub and Kindle
With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
| Author | : Luiz Roberto Evangelista |
| Publisher | : Cambridge University Press |
| Total Pages | : 361 |
| Release | : 2018-01-25 |
| Genre | : Science |
| ISBN | : 1108663486 |
Download Fractional Diffusion Equations and Anomalous Diffusion Book in PDF, ePub and Kindle
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.
| Author | : Gandhimohan. M. Viswanathan |
| Publisher | : Cambridge University Press |
| Total Pages | : 179 |
| Release | : 2011-06-02 |
| Genre | : Science |
| ISBN | : 1139497553 |
Download The Physics of Foraging Book in PDF, ePub and Kindle
Do the movements of animals, including humans, follow patterns that can be described quantitatively by simple laws of motion? If so, then why? These questions have attracted the attention of scientists in many disciplines, and stimulated debates ranging from ecological matters to queries such as 'how can there be free will if one follows a law of motion?' This is the first book on this rapidly evolving subject, introducing random searches and foraging in a way that can be understood by readers without a previous background on the subject. It reviews theory as well as experiment, addresses open problems and perspectives, and discusses applications ranging from the colonization of Madagascar by Austronesians to the diffusion of genetically modified crops. The book will interest physicists working in the field of anomalous diffusion and movement ecology as well as ecologists already familiar with the concepts and methods of statistical physics.
| Author | : James Sethna |
| Publisher | : OUP Oxford |
| Total Pages | : 374 |
| Release | : 2006-04-07 |
| Genre | : Science |
| ISBN | : 0191566217 |
Download Statistical Mechanics Book in PDF, ePub and Kindle
In each generation, scientists must redefine their fields: abstracting, simplifying and distilling the previous standard topics to make room for new advances and methods. Sethna's book takes this step for statistical mechanics - a field rooted in physics and chemistry whose ideas and methods are now central to information theory, complexity, and modern biology. Aimed at advanced undergraduates and early graduate students in all of these fields, Sethna limits his main presentation to the topics that future mathematicians and biologists, as well as physicists and chemists, will find fascinating and central to their work. The amazing breadth of the field is reflected in the author's large supply of carefully crafted exercises, each an introduction to a whole field of study: everything from chaos through information theory to life at the end of the universe.
| Author | : Vicenç Méndez |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 321 |
| Release | : 2013-09-18 |
| Genre | : Science |
| ISBN | : 3642390102 |
Download Stochastic Foundations in Movement Ecology Book in PDF, ePub and Kindle
This book presents the fundamental theory for non-standard diffusion problems in movement ecology. Lévy processes and anomalous diffusion have shown to be both powerful and useful tools for qualitatively and quantitatively describing a wide variety of spatial population ecological phenomena and dynamics, such as invasion fronts and search strategies. Adopting a self-contained, textbook-style approach, the authors provide the elements of statistical physics and stochastic processes on which the modeling of movement ecology is based and systematically introduce the physical characterization of ecological processes at the microscopic, mesoscopic and macroscopic levels. The explicit definition of these levels and their interrelations is particularly suitable to coping with the broad spectrum of space and time scales involved in bio-ecological problems. Including numerous exercises (with solutions), this text is aimed at graduate students and newcomers in this field at the interface of theoretical ecology, mathematical biology and physics.
| Author | : Sunny Y. Auyang |
| Publisher | : Cambridge University Press |
| Total Pages | : 422 |
| Release | : 1998 |
| Genre | : Business & Economics |
| ISBN | : 9780521778268 |
Download Foundations of Complex-system Theories Book in PDF, ePub and Kindle
Analyzes approaches to the study of complexity in the physical, biological, and social sciences.
