Distribution of Statistical Observables for Anomalous and Nonergodic Diffusions
From Statistics to Mathematics
1st Edition
Published on 27. May 2024
Book
Paperback/Softback
227 pages
978-1-032-24523-2 (ISBN)
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.
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.
More details
Language
English
Place of publication
London
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
College/higher education
Professional and scholarly
Postgraduate, Professional, Undergraduate Advanced, and Undergraduate Core
Illustrations
3 s/w Zeichnungen, 20 s/w Tabellen, 3 s/w Abbildungen
20 Tables, black and white; 3 Line drawings, black and white; 3 Illustrations, black and white
Dimensions
Height: 229 mm
Width: 152 mm
Thickness: 13 mm
Weight
354 gr
ISBN-13
978-1-032-24523-2 (9781032245232)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Weihua Deng | Xudong Wang | Daxin Nie
Distribution of Statistical Observables for Anomalous and Nonergodic Diffusions
From Statistics to Mathematics
Book
04/2022
1st Edition
CRC Press
€121.30
Shipment within 10-20 days
Weihua Deng | Xudong Wang | Daxin Nie
Distribution of Statistical Observables for Anomalous and Nonergodic Diffusions
From Statistics to Mathematics
E-Book
04/2022
1st Edition
CRC Press
€63.49
Available for download
Weihua Deng | Xudong Wang | Daxin Nie
Distribution of Statistical Observables for Anomalous and Nonergodic Diffusions
From Statistics to Mathematics
E-Book
04/2022
1st Edition
CRC Press
€63.49
Available for download
Persons
Weihua Deng is a professor of mathematics and statistical physics at Lanzhou University, China. His research interests include scientific computation and numerical analysis, statistical physics and stochastic simulations, nonlinear dynamics and anomalous diffusion, nonlocal PDE and stochastic representation, artificial intelligence and big data.
Xudong Wang is a faculty member in the School of Science at Nanjing University of Science and Technology, China. His research focuses on stochastic processes, and stochastic modeling, as well as non-equilibrium statistical physics and his recent research interests include the theory and applications of normal and anomalous stochastic processes, and the stochastic models of intracellular transport.
Daxin Nie is a research assistant in the School of Mathematics and Statistics at Lanzhou University, China. His research interests are numerical analyses for all kinds of anomalous diffusion equations.
Xing Liu is a faculty member in the School of Mathematics and Economics at Hubei University of Education, China. He focuses on the research of the numerical methods and regularity of stochastic partial differential equation and his recent research interests include stochastic fractional diffusion equations and stochastic wave equation.
Xudong Wang is a faculty member in the School of Science at Nanjing University of Science and Technology, China. His research focuses on stochastic processes, and stochastic modeling, as well as non-equilibrium statistical physics and his recent research interests include the theory and applications of normal and anomalous stochastic processes, and the stochastic models of intracellular transport.
Daxin Nie is a research assistant in the School of Mathematics and Statistics at Lanzhou University, China. His research interests are numerical analyses for all kinds of anomalous diffusion equations.
Xing Liu is a faculty member in the School of Mathematics and Economics at Hubei University of Education, China. He focuses on the research of the numerical methods and regularity of stochastic partial differential equation and his recent research interests include stochastic fractional diffusion equations and stochastic wave equation.
Content
1. Statistical Observables 2. Numerical Methods for the Governing Equations of PDF of Statistical Observables 3. Numerical Methods for the Stochastic Governing Equations of PDF of Statistical Observables