Modeling Anomalous Diffusion
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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.
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 Diffusion
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Author : Andrzej Pekalski
language : en
Publisher: Springer
Release Date : 2014-03-12
Anomalous Diffusion written by Andrzej Pekalski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-12 with Science categories.
This collection of articles gives a nice overview of the fast growing field of diffusion and transport. The area of non-Browman statistical mechanics has many extensions into other fields like biology, ecology, geophysics etc. These tutorial lectures address e.g. Lévy flights and walks, diffusion on metal surfaces or in superconductors, classical diffusion, biased and anomalous diffusion, chemical reaction diffusion, aging in glassy systems, diffusion in soft matter and in nonsymmetric potentials, and also new problems like diffusive processes in econophysics and in biology.
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"--
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.
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.
Fractional Derivative Modeling In Mechanics And Engineering
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Author : Wen Chen
language : en
Publisher: Springer Nature
Release Date : 2022-02-26
Fractional Derivative Modeling In Mechanics And Engineering written by Wen Chen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-26 with Mathematics categories.
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.
Diffusion And Reactions In Fractals And Disordered Systems
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Author : Daniel ben-Avraham
language : en
Publisher: Cambridge University Press
Release Date : 2000-11-02
Diffusion And Reactions In Fractals And Disordered Systems written by Daniel ben-Avraham 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 2000-11-02 with Mathematics categories.
This book describes diffusion and transport in disordered media such as fractals and random resistor networks.
Fractional Order Modeling Of Nuclear Reactor From Subdiffusive Neutron Transport To Control Oriented Models
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Author : Vishwesh Vyawahare
language : en
Publisher: Springer
Release Date : 2018-02-03
Fractional Order Modeling Of Nuclear Reactor From Subdiffusive Neutron Transport To Control Oriented Models written by Vishwesh Vyawahare and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-03 with Technology & Engineering categories.
This book addresses the topic of fractional-order modeling of nuclear reactors. Approaching neutron transport in the reactor core as anomalous diffusion, specifically subdiffusion, it starts with the development of fractional-order neutron telegraph equations. Using a systematic approach, the book then examines the development and analysis of various fractional-order models representing nuclear reactor dynamics, ultimately leading to the fractional-order linear and nonlinear control-oriented models. The book utilizes the mathematical tool of fractional calculus, the calculus of derivatives and integrals with arbitrary non-integer orders (real or complex), which has recently been found to provide a more compact and realistic representation to the dynamics of diverse physical systems. Including extensive simulation results and discussing important issues related to the fractional-order modeling of nuclear reactors, the book offers a valuable resource for students and researchers working in the areas of fractional-order modeling and control and nuclear reactor modeling.
Modeling Calcium Signaling
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Author : Ritu Agarwal
language : en
Publisher: Springer Nature
Release Date : 2024-06-18
Modeling Calcium Signaling written by Ritu Agarwal and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-18 with Science categories.
This book focuses on the fundamental processes involved in calcium signaling through fractional mathematical modeling. The intended reader of the book is mathematically proficient students of cell biology, applied mathematics and mathematical biology who are interested in learning about modeling in cell biology. The book will inspire the graduate students and researchers to collaborate with experimentalists while studying the direction needed to explore the modeling literature. Organized into four chapters, the book introduces to fractional calculus and devoted to understanding the receptor activation by the ligand, that is Thrombin via fractional model incorporating the Caputo-Fabrizio fractional operator. It studies the calcium profile in red blood cells with the help of the advection-diffusion equation. The book further studies the process of buffering, aiding to the lowering of the calcium concentration in the cytosol, which rises due to calcium influx from extracellular space and intracellular storage. A mathematical model is studied to characterize the anomalous subdiffusion of cytosolic calcium.