Stochastic Modeling of Microstructures

1. Front Matter

   Pages i-ix

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2. Introduction

   • Kazimierz Sobczyk, David J. Kirkner

   Pages 1-4

3. Probability and Random Variables: A Short Résumé

   • Kazimierz Sobczyk, David J. Kirkner

   Pages 5-31

4. Continuous Random Fields

   • Kazimierz Sobczyk, David J. Kirkner

   Pages 33-77

5. Random Point Fields

   • Kazimierz Sobczyk, David J. Kirkner

   Pages 79-121

6. Statistical Inference

   • Kazimierz Sobczyk, David J. Kirkner

   Pages 123-148

7. Material Media Microstructure: Modeling Issues

   • Kazimierz Sobczyk, David J. Kirkner

   Pages 149-202

8. Physical Phenomena in Random Microstructures: Selected Applications

   • Kazimierz Sobczyk, David J. Kirkner

   Pages 203-245

9. Back Matter

   Pages 247-270

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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

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

"It is the objective of this book to provide the basic principles and results of the theory of random fields (both continuous and discrete) with special emphasis on methods that are important for the modeling of real random material microstructures…. The book may be viewed as a comprehensive introduction to the field of stochastic modeling of material microstructures and will be useful for researchers and professionals in material modeling, engineering and in applied mathematics in general." —Applications of Mathematics

• Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw, Poland

  Kazimierz Sobczyk

• Department of Civil Engineering and Geological Sciences, University of Notre Dame, Notre Dame, USA

  David J. Kirkner

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