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This book presents the role of mesostructure on the properties of
composite materials. A complex percolation model is developed for
the material structure containing percolation clusters of phases
and interior boundaries. Modeling of technological cracks and the
percolation in the Sierpinski carpet are described. The interaction
of mesoscopic interior boundaries of the material, including the
fractal nature of interior boundaries, the oscillatory nature of it
interaction and also the stochastic model of the interior
boundaries' interaction, the genesis, structure, and properties are
discussed. One of part of the book introduces the percolation model
of the long-range effect which is based on the notion on the
multifractal clusters with transforming elements, and the theorem
on the field interaction of multifractals is described. In addition
small clusters, their characteristic properties and the criterion
of stability are presented.
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