Overview
- Most basic models of random structures are thoroughly investigated and illustrated, starting from their mathematical construction, their probabilistic properties, and their identification from data
- A comprehensive group of models and their links are available to the reader, helping him to develop his own research. The presentation is completed by exercises
- Applications of random models to the physics of random media will be helpful to researchers and engineers for their understanding and predictive use of well established and some new models of microstructures
Part of the book series: Interdisciplinary Applied Mathematics (IAM, volume 53)
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Table of contents (21 chapters)
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Front Matter
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Tools for Random Structures
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Front Matter
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Models of Random Structures
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Front Matter
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Keywords
About this book
This book covers methods of Mathematical Morphology to model and simulate random sets and functions (scalar and multivariate). The introduced models concern many physical situations in heterogeneous media, where a probabilistic approach is required, like fracture statistics of materials, scaling up of permeability in porous media, electron microscopy images (including multispectral images), rough surfaces, multi-component composites, biological tissues, textures for image coding and synthesis. The common feature of these random structures is their domain of definition in n dimensions, requiring more general models than standard Stochastic Processes.The main topics of the book cover an introduction to the theory of random sets, random space tessellations, Boolean random sets and functions, space-time random sets and functions (Dead Leaves, Sequential Alternate models, Reaction-Diffusion), prediction of effective properties of random media, and probabilistic fracture theories.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Morphological Models of Random Structures
Authors: Dominique Jeulin
Series Title: Interdisciplinary Applied Mathematics
DOI: https://doi.org/10.1007/978-3-030-75452-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-75451-8Published: 02 June 2021
Softcover ISBN: 978-3-030-75454-9Published: 03 June 2022
eBook ISBN: 978-3-030-75452-5Published: 01 June 2021
Series ISSN: 0939-6047
Series E-ISSN: 2196-9973
Edition Number: 1
Number of Pages: XXXII, 919
Number of Illustrations: 202 b/w illustrations, 89 illustrations in colour
Topics: Probability Theory and Stochastic Processes, Computational Science and Engineering, Geometry, Mathematical Modeling and Industrial Mathematics, Applications of Mathematics