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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.
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CMDS-14, Paris, France, June 26–30, 2023
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The present book contains the proceedings of the 14th International Symposium on Continuum Models and Discrete Systems (CMDS14) held in Paris in June 2023. It contains 21 contributions that cover a broad range of topics in the wide field of mechanics and physics of heterogeneous media for discrete and continuous systems, from image analysis to models of random structures and to homogenization. The sessions in the CMDS conference series cover, in particular, the modeling of complex heterogeneous systems and metamaterials, structures and composites with extreme properties, deformable solids with microstructures, generalized continua, fracture and defect dynamics, fatigue, design of structured and architectured materials, micro and nanostructures, thermodynamics, transport theory and multiphysics coupling and methods ranging from homogenization theories to optimal design and machine-learning frameworks. Papers in the present volume are organized according to the following six main topics: probabilistic models, homogenization, solid mechanics, architectured materials, optics and metamaterials, machine learning methods.
CMDS-14, Paris, France, June 26–30, 2023
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