Modeling Anomalous Diffusion From Statistics To Mathematics

Author : Weihua Deng,Ru Hou,Wanli Wang,Pengbo Xu
Publisher : World Scientific
Page : 267 pages
File Size : 54,9 Mb
Release : 2020-01-06
Category : Mathematics
ISBN : 9789811213014

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Modeling Anomalous Diffusion: From Statistics To Mathematics by Weihua Deng,Ru Hou,Wanli Wang,Pengbo Xu Pdf

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,Ru Hou,Wanli Wang,Pengbo Xu
Publisher : Unknown
Page : 267 pages
File Size : 52,9 Mb
Release : 2020
Category : Differential equations, Partial
ISBN : 9811213003

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Modeling Anomalous Diffusion by Weihua Deng,Ru Hou,Wanli Wang,Pengbo Xu Pdf

"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,Zhijiang Zhang
Publisher : World Scientific
Page : 295 pages
File Size : 48,7 Mb
Release : 2019-01-22
Category : Mathematics
ISBN : 9789813142220

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High Accuracy Algorithm For The Differential Equations Governing Anomalous Diffusion: Algorithm And Models For Anomalous Diffusion by Weihua Deng,Zhijiang Zhang Pdf

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.

Author : Weihua Deng,Xudong Wang,Daxin Nie,Xing Liu
Publisher : CRC Press
Page : 211 pages
File Size : 47,6 Mb
Release : 2022-04-11
Category : Technology & Engineering
ISBN : 9781000567915

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Distribution of Statistical Observables for Anomalous and Nonergodic Diffusions by Weihua Deng,Xudong Wang,Daxin Nie,Xing Liu Pdf

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 : Ralf Metzler,Carlos Mejía-Monasterio,Jürgen Vollmer
Publisher : Frontiers Media SA
Page : 221 pages
File Size : 49,9 Mb
Release : 2021-01-08
Category : Science
ISBN : 9782889663651

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Anomalous Transport: Applications, Mathematical Perspectives, and Big Data by Ralf Metzler,Carlos Mejía-Monasterio,Jürgen Vollmer Pdf

Author : Mark M. Meerschaert,Alla Sikorskii
Publisher : Walter de Gruyter GmbH & Co KG
Page : 337 pages
File Size : 46,6 Mb
Release : 2019-10-21
Category : Mathematics
ISBN : 9783110560244

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Stochastic Models for Fractional Calculus by Mark M. Meerschaert,Alla Sikorskii Pdf

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 : Luiz Roberto Evangelista,Ervin Kaminski Lenzi
Publisher : Cambridge University Press
Page : 361 pages
File Size : 46,6 Mb
Release : 2018-01-25
Category : Mathematics
ISBN : 9781107143555

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Fractional Diffusion Equations and Anomalous Diffusion by Luiz Roberto Evangelista,Ervin Kaminski Lenzi Pdf

Presents a unified treatment of anomalous diffusion problems using fractional calculus in a wide range of applications across scientific and technological disciplines.

Author : Kęstutis Kubilius,Yuliya Mishura,Kostiantyn Ralchenko
Publisher : Springer
Page : 390 pages
File Size : 55,5 Mb
Release : 2018-01-04
Category : Mathematics
ISBN : 9783319710303

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Parameter Estimation in Fractional Diffusion Models by Kęstutis Kubilius,Yuliya Mishura,Kostiantyn Ralchenko Pdf

This book is devoted to parameter estimation in diffusion models involving fractional Brownian motion and related processes. For many years now, standard Brownian motion has been (and still remains) a popular model of randomness used to investigate processes in the natural sciences, financial markets, and the economy. The substantial limitation in the use of stochastic diffusion models with Brownian motion is due to the fact that the motion has independent increments, and, therefore, the random noise it generates is “white,” i.e., uncorrelated. However, many processes in the natural sciences, computer networks and financial markets have long-term or short-term dependences, i.e., the correlations of random noise in these processes are non-zero, and slowly or rapidly decrease with time. In particular, models of financial markets demonstrate various kinds of memory and usually this memory is modeled by fractional Brownian diffusion. Therefore, the book constructs diffusion models with memory and provides simple and suitable parameter estimation methods in these models, making it a valuable resource for all researchers in this field. The book is addressed to specialists and researchers in the theory and statistics of stochastic processes, practitioners who apply statistical methods of parameter estimation, graduate and post-graduate students who study mathematical modeling and statistics.

Author : Vicenc Mendez,Daniel Campos,Frederic Bartumeus
Publisher : Unknown
Page : 330 pages
File Size : 48,9 Mb
Release : 2013-10-31
Category : Electronic
ISBN : 3642390110

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Stochastic Foundations in Movement Ecology by Vicenc Mendez,Daniel Campos,Frederic Bartumeus Pdf

Author : Ivo Petráš
Publisher : MDPI
Page : 114 pages
File Size : 54,6 Mb
Release : 2019-10-29
Category : Mathematics
ISBN : 9783039216086

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Fractional Order Systems by Ivo Petráš Pdf

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 : Edward C. Waymire
Publisher : Springer Science & Business Media
Page : 265 pages
File Size : 51,8 Mb
Release : 2010-06-14
Category : Mathematics
ISBN : 9780387293714

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Probability and Partial Differential Equations in Modern Applied Mathematics by Edward C. Waymire Pdf

"Probability and Partial Differential Equations in Modern Applied Mathematics" is devoted to the role of probabilistic methods in modern applied mathematics from the perspectives of both a tool for analysis and as a tool in modeling. There is a recognition in the applied mathematics research community that stochastic methods are playing an increasingly prominent role in the formulation and analysis of diverse problems of contemporary interest in the sciences and engineering. A probabilistic representation of solutions to partial differential equations that arise as deterministic models allows one to exploit the power of stochastic calculus and probabilistic limit theory in the analysis of deterministic problems, as well as to offer new perspectives on the phenomena for modeling purposes. There is also a growing appreciation of the role for the inclusion of stochastic effects in the modeling of complex systems. This has led to interesting new mathematical problems at the interface of probability, dynamical systems, numerical analysis, and partial differential equations. This volume will be useful to researchers and graduate students interested in probabilistic methods, dynamical systems approaches and numerical analysis for mathematical modeling in the sciences and engineering.

Author : Mark M. Meerschaert
Publisher : Elsevier
Page : 360 pages
File Size : 54,6 Mb
Release : 2007-06-18
Category : Mathematics
ISBN : 0123708575

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Mathematical Modeling by Mark M. Meerschaert Pdf

Mathematical Modeling, Third Edition is a general introduction to an increasingly crucial topic for today's mathematicians. Unlike textbooks focused on one kind of mathematical model, this book covers the broad spectrum of modeling problems, from optimization to dynamical systems to stochastic processes. Mathematical modeling is the link between mathematics and the rest of the world. Meerschaert shows how to refine a question, phrasing it in precise mathematical terms. Then he encourages students to reverse the process, translating the mathematical solution back into a comprehensible, useful answer to the original question. This textbook mirrors the process professionals must follow in solving complex problems. Each chapter in this book is followed by a set of challenging exercises. These exercises require significant effort on the part of the student, as well as a certain amount of creativity. Meerschaert did not invent the problems in this book--they are real problems, not designed to illustrate the use of any particular mathematical technique. Meerschaert's emphasis on principles and general techniques offers students the mathematical background they need to model problems in a wide range of disciplines. Increased support for instructors, including MATLAB material New sections on time series analysis and diffusion models Additional problems with international focus such as whale and dolphin populations, plus updated optimization problems

Author : Qiang Du
Publisher : SIAM
Page : 181 pages
File Size : 50,5 Mb
Release : 2019-03-20
Category : Science
ISBN : 9781611975611

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Nonlocal Modeling, Analysis, and Computation by Qiang Du Pdf

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 : Wen Chen,HongGuang Sun,Xicheng Li
Publisher : Springer Nature
Page : 381 pages
File Size : 50,8 Mb
Release : 2022-02-26
Category : Mathematics
ISBN : 9789811688027

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Fractional Derivative Modeling in Mechanics and Engineering by Wen Chen,HongGuang Sun,Xicheng Li Pdf

This textbook highlights the theory of fractional calculus and its wide applications in mechanics and engineering. It describes in details the research findings in using fractional calculus methods for modeling and numerical simulation of complex mechanical behavior. It covers the mathematical basis of fractional calculus, the relationship between fractal and fractional calculus, unconventional statistics and anomalous diffusion, typical applications of fractional calculus, and the numerical solution of the fractional differential equation. It also includes latest findings, such as variable order derivative, distributed order derivative and its applications. Different from other textbooks in this subject, the book avoids lengthy mathematical demonstrations, and presents the theories in close connection to the applications in an easily readable manner. This textbook is intended for students, researchers and professionals in applied physics, engineering mechanics, and applied mathematics. It is also of high reference value for those in environmental mechanics, geotechnical mechanics, biomechanics, and rheology.

Author : Anonim
Publisher : Academic Press
Page : 384 pages
File Size : 55,9 Mb
Release : 2013-01-28
Category : Technology & Engineering
ISBN : 9780123869968

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Mathematical Modeling by Anonim Pdf

The new edition of Mathematical Modeling, the survey text of choice for mathematical modeling courses, adds ample instructor support and online delivery for solutions manuals and software ancillaries. From genetic engineering to hurricane prediction, mathematical models guide much of the decision making in our society. If the assumptions and methods underlying the modeling are flawed, the outcome can be disastrously poor. With mathematical modeling growing rapidly in so many scientific and technical disciplines, Mathematical Modeling, Fourth Edition provides a rigorous treatment of the subject. The book explores a range of approaches including optimization models, dynamic models and probability models. Offers increased support for instructors, including MATLAB material as well as other on-line resources Features new sections on time series analysis and diffusion models Provides additional problems with international focus such as whale and dolphin populations, plus updated optimization problems