Modeling Anomalous Diffusion From Statistics To Mathematics
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Modeling Anomalous Diffusion From Statistics To Mathematics
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Author : Weihua Deng
language : en
Publisher: World Scientific
Release Date : 2020-01-06
Modeling Anomalous Diffusion From Statistics To Mathematics written by Weihua Deng and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-06 with Mathematics categories.
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.
Modeling Anomalous Diffusion
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Author : Weihua Deng
language : en
Publisher:
Release Date : 2020
Modeling Anomalous Diffusion written by Weihua Deng and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Differential equations, Partial categories.
"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"--
High Accuracy Algorithm For The Differential Equations Governing Anomalous Diffusion Algorithm And Models For Anomalous Diffusion
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Author : Weihua Deng
language : en
Publisher: World Scientific
Release Date : 2019-01-22
High Accuracy Algorithm For The Differential Equations Governing Anomalous Diffusion Algorithm And Models For Anomalous Diffusion written by Weihua Deng and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-22 with Mathematics categories.
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
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Author : Weihua Deng
language : en
Publisher: CRC Press
Release Date : 2022-04-11
Distribution Of Statistical Observables For Anomalous And Nonergodic Diffusions written by Weihua Deng and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-11 with Technology & Engineering categories.
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
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Author : Luiz Roberto Evangelista
language : en
Publisher: Cambridge University Press
Release Date : 2018-01-25
Fractional Diffusion Equations And Anomalous Diffusion written by Luiz Roberto Evangelista and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-25 with Mathematics categories.
Presents a unified treatment of anomalous diffusion problems using fractional calculus in a wide range of applications across scientific and technological disciplines.
Anomalous Transport Applications Mathematical Perspectives And Big Data
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Author : Ralf Metzler
language : en
Publisher: Frontiers Media SA
Release Date : 2021-01-08
Anomalous Transport Applications Mathematical Perspectives And Big Data written by Ralf Metzler and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-08 with Science categories.
Stochastic Models For Fractional Calculus
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Author : Mark M. Meerschaert
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-10-21
Stochastic Models For Fractional Calculus written by Mark M. Meerschaert and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-21 with Mathematics categories.
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.
Parameter Estimation In Fractional Diffusion Models
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Author : Kęstutis Kubilius
language : en
Publisher: Springer
Release Date : 2018-01-04
Parameter Estimation In Fractional Diffusion Models written by Kęstutis Kubilius and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-04 with Mathematics categories.
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.
Mathematical Modeling
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Author : Mark M. Meerschaert
language : en
Publisher: Elsevier
Release Date : 2007-06-18
Mathematical Modeling written by Mark M. Meerschaert and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-18 with Mathematics categories.
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
Mathematical Modeling
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Author : Mark Meerschaert
language : en
Publisher: Academic Press
Release Date : 2013-01-28
Mathematical Modeling written by Mark Meerschaert and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-28 with Mathematics categories.
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