Stochastic Modeling of Microstructures

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