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Stochastic Modeling of Microstructures

  • Kazimierz Sobczyk
  • David J. Kirkner

Table of contents

  1. Front Matter
    Pages i-ix
  2. Kazimierz Sobczyk, David J. Kirkner
    Pages 1-4
  3. Kazimierz Sobczyk, David J. Kirkner
    Pages 5-31
  4. Kazimierz Sobczyk, David J. Kirkner
    Pages 33-77
  5. Kazimierz Sobczyk, David J. Kirkner
    Pages 79-121
  6. Kazimierz Sobczyk, David J. Kirkner
    Pages 123-148
  7. Kazimierz Sobczyk, David J. Kirkner
    Pages 149-202
  8. Kazimierz Sobczyk, David J. Kirkner
    Pages 203-245
  9. Back Matter
    Pages 247-270

About this book

Introduction

A major challenge in applied mathematics and mechanics of materials is to describe various types of material microstructures. The details of the microstructure of most natural and engineered materials are usually obscure; uncertainty and randomness are the inherent features. This complexity due to material heterogeneity has not been A major challenge in applied mathematics and mechanics of materials is to describe various types of material microstructures. The details of the microstructure of most natural and engineered materials are usually obscure; uncertainty and randomness are the inherent features. This complexity due to material heterogeneity has not been adequately described by current classical models and theories. Stochastic Modeling of Microstructures presents a concise and unified presentation of the basic principles and tools for the modeling of real materials, natural and man-made, that possess complex, random heterogeneity. The book uses the language and methods of random field theory combined with the basic constructs of stochastic geometry and geometrical/spatial statistics in order to give the reader the knowledge necessary to model various types of material microstructures. The application of the theoretical constructs reviewed in the first three chapters to the analysis of empirical data via the tools of statistical inference is also discussed. The final chapters address practical aspects of specific modeling problems. Features- ú First comprehensive introduction to the comparatively new field of stochastic modeling of material microstructures ú Presentation of basic tools required from the diverse subjects of random field theory, stochastic geometry and spatial statistics ú Provides background concepts from probability theory and stochastic processes are provided ú Applications from various fields are discussed, including stochastic wave propagation and the mechanics of

Keywords

Microstructural Modeling Probability distribution Probability theory Random variable Stochastic Modeling Stochastic geometry Stochastic processes Transport Variance statistics stochastic process

Authors and affiliations

  • Kazimierz Sobczyk
    • 1
  • David J. Kirkner
    • 2
  1. 1.Institute of Fundamental Technological ResearchPolish Academy of SciencesWarsawPoland
  2. 2.Department of Civil Engineering and Geological SciencesUniversity of Notre DameNotre DameUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0121-2
  • Copyright Information Birkhäuser Boston 2001
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6622-8
  • Online ISBN 978-1-4612-0121-2
  • Series Print ISSN 2164-3679
  • Buy this book on publisher's site