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: World Scientific Publishing Company
Release Date : 2019-12-27
Modeling Anomalous Diffusion written by Weihua Deng and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-27 with Mathematics 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"--
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"--
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.
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.
Stochastic Models For Fractional Calculus
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Author : Mark M. Meerschaert
language : en
Publisher: Walter de Gruyter
Release Date : 2011-12-23
Stochastic Models For Fractional Calculus written by Mark M. Meerschaert and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-23 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.
Stochastic Foundations In Movement Ecology
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Author : Vicenç Méndez
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-18
Stochastic Foundations In Movement Ecology written by Vicenç Méndez and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-18 with Science categories.
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.
Mathematical And Statistical Methods For Actuarial Sciences And Finance
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Author : Marco Corazza
language : en
Publisher: Springer Nature
Release Date : 2024-08-01
Mathematical And Statistical Methods For Actuarial Sciences And Finance written by Marco Corazza and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-01 with Mathematics categories.
The book presents a collection of peer-reviewed short papers selected from those presented at the International Conference Mathematical and Statistical Methods for Actuarial Sciences and Finance – MAF2024. The year 2024 marks the twentieth anniversary of the first edition of this conference. The idea behind this book is that collaboration and cross-pollination between mathematicians and statisticians working in actuarial sciences and finance could enhance research in these fields. The effectiveness of this concept has been demonstrated by widespread participation across all editions, held at various locations including the University of Salerno, Italy (2004, 2006, 2010, 2014, and 2022); Ca' Foscari University of Venice, Italy (2008, 2012, and 2020); University Paris-Dauphine in Paris, France (2016); University Carlos III of Madrid, Madrid (2018); and University of Le Havre Normandie, Le Havre, France (2024). This effectiveness is also evident in the attention consistently shown by both the scientific community and professionals toward the volumes of peer-reviewed papers accompanying all past editions of MAF. The book is a valuable resource for academics, researchers, Ph.D. students, and professionals. Furthermore, it is also of interest to other readers with a quantitative background.
The Mathematics Of Diffusion
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Author : John Crank
language : en
Publisher: Oxford University Press
Release Date : 1979
The Mathematics Of Diffusion written by John Crank and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.
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.
Nonlocal Modeling Analysis And Computation
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Author : Qiang Du
language : en
Publisher: SIAM
Release Date : 2019-03-20
Nonlocal Modeling Analysis And Computation written by Qiang Du and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-20 with Science categories.
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.