Modeling Anomalous Diffusion: From Statistics To Mathematics PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Modeling Anomalous Diffusion: From Statistics To Mathematics PDF full book. Access full book title Modeling Anomalous Diffusion: From Statistics To Mathematics by Weihua Deng. Download full books in PDF and EPUB format.
Author: Weihua Deng Publisher: World Scientific ISBN: 9811213011 Category : Mathematics Languages : en Pages : 267
Book Description
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: Weihua Deng Publisher: World Scientific ISBN: 9811213011 Category : Mathematics Languages : en Pages : 267
Book Description
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: Weihua Deng Publisher: World Scientific Publishing Company ISBN: 9789811212994 Category : Mathematics Languages : en Pages : 268
Book Description
"One of the authors, Weihua Deng, has an interdisciplinary research background with a deep understanding on the related anomalous models from the viewpoint of mathematics and physics In this book, we not only introduce the widely investigated models but also discuss some new topics, for example, infinite densities, functionals, etc. This book will get more attention from undergraduates and some high-level students"--
Author: Weihua Deng Publisher: ISBN: 9789811213007 Category : Differential equations, Partial Languages : en Pages : 267
Book Description
"One of the authors, Weihua Deng, has an interdisciplinary research background with a deep understanding on the related anomalous models from the viewpoint of mathematics and physics In this book, we not only introduce the widely investigated models but also discuss some new topics, for example, infinite densities, functionals, etc. This book will get more attention from undergraduates and some high-level students"--
Author: Mark M. Meerschaert Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110560240 Category : Mathematics Languages : en Pages : 337
Book Description
Fractional calculus is a rapidly growing field of research, at the interface between probability, differential equations, and mathematical physics. It is used to model anomalous diffusion, in which a cloud of particles spreads in a different manner than traditional diffusion. This monograph develops the basic theory of fractional calculus and anomalous diffusion, from the point of view of probability. In this book, we will see how fractional calculus and anomalous diffusion can be understood at a deep and intuitive level, using ideas from probability. It covers basic limit theorems for random variables and random vectors with heavy tails. This includes regular variation, triangular arrays, infinitely divisible laws, random walks, and stochastic process convergence in the Skorokhod topology. The basic ideas of fractional calculus and anomalous diffusion are closely connected with heavy tail limit theorems. Heavy tails are applied in finance, insurance, physics, geophysics, cell biology, ecology, medicine, and computer engineering. The goal of this book is to prepare graduate students in probability for research in the area of fractional calculus, anomalous diffusion, and heavy tails. Many interesting problems in this area remain open. This book will guide the motivated reader to understand the essential background needed to read and unerstand current research papers, and to gain the insights and techniques needed to begin making their own contributions to this rapidly growing field.
Author: Qiang Du Publisher: SIAM ISBN: 1611975611 Category : Science Languages : en Pages : 181
Book Description
Studies of complexity, singularity, and anomaly using nonlocal continuum models are steadily gaining popularity. This monograph provides an introduction to basic analytical, computational, and modeling issues and to some of the latest developments in these areas. Nonlocal Modeling, Analysis, and Computation includes motivational examples of nonlocal models, basic building blocks of nonlocal vector calculus, elements of theory for well-posedness and nonlocal spaces, connections to and coupling with local models, convergence and compatibility of numerical approximations, and various applications, such as nonlocal dynamics of anomalous diffusion and nonlocal peridynamic models of elasticity and fracture mechanics. A particular focus is on nonlocal systems with a finite range of interaction to illustrate their connection to local partial differential equations and fractional PDEs. These models are designed to represent nonlocal interactions explicitly and to remain valid for complex systems involving possible singular solutions and they have the potential to be alternatives for as well as bridges to existing models. The author discusses ongoing studies of nonlocal models to encourage the discovery of new mathematical theory for nonlocal continuum models and offer new perspectives on traditional models, analytical techniques, and algorithms.
Author: John Crank Publisher: Oxford University Press ISBN: 9780198534112 Category : Mathematics Languages : en Pages : 428
Book Description
Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained.
Author: Weihua Deng Publisher: CRC Press ISBN: 1000567915 Category : Technology & Engineering Languages : en Pages : 211
Book Description
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: Cambridge University Press ISBN: 1107143551 Category : Mathematics Languages : en Pages : 361
Book Description
Presents a unified treatment of anomalous diffusion problems using fractional calculus in a wide range of applications across scientific and technological disciplines.
Author: Ivo Petráš Publisher: MDPI ISBN: 3039216082 Category : Mathematics Languages : en Pages : 114
Book Description
This book is focused on fractional order systems. Historically, fractional calculus has been recognized since the inception of regular calculus, with the first written reference dated in September 1695 in a letter from Leibniz to L’Hospital. Nowadays, fractional calculus has a wide area of applications in areas such as physics, chemistry, bioengineering, chaos theory, control systems engineering, and many others. In all those applications, we deal with fractional order systems in general. Moreover, fractional calculus plays an important role even in complex systems and therefore allows us to develop better descriptions of real-world phenomena. On that basis, fractional order systems are ubiquitous, as the whole real world around us is fractional. Due to this reason, it is urgent to consider almost all systems as fractional order systems. This Special Issue explores applications of such systems to control, synchronization, and various mathematical models, as for instance, MRI, long memory process, diffusion.
Author: Weihua Deng
Author: Weihua Deng
Author: Weihua Deng
Author: Weihua Deng
Author: Mark M. Meerschaert
Author: Ralf Metzler
Author: Qiang Du
Author: John Crank
Author: Weihua Deng
Author: Luiz Roberto Evangelista
Author: Ivo Petráš