Morphological Models of Random Structures
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Beschreibung
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.
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.
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
Autor*in
Dominique Jeulin
Themen in »Morphological Models of Random Structures«
mathematical morphology random closed sets random functions random media sequential models stochastic processes multi-scale random media numerical simulations materials sciences homogenization fracture statistics percolation