Abstract
To solve the problems of physical material science, in particular, to study the structure of the material at the mesoscopic scale, to study the structure and properties of percolation clusters in the volume and on the surface of solids, the multifunctional percolation model has been developed. It is designed to study percolation clusters constructed by the Monte Carlo method using a wide range of algorithms, which allows using it for studying various phenomena and processes, including for studying of composites whose structural properties are predominantly formed with the help of connected regions. Depending on the purpose of the study, the role of percolation clusters in the model is played by various structural elements: internal boundaries, the accumulation of a different nature defects, a group of particles, phases of matter, cracks, and others. The basis of its computer implementation is an object-oriented approach, which makes it convenient to vary the objects of research, change their properties and conditions for carrying out computer experiments. The monograph introduces the idea of the Sierpinski carpet with a hybrid (finite–infinite) branching; the continuum percolation problem is considered, and the characteristics of the percolation transition on such a carpet are calculated.
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Herega, A. (2018). Complex Percolation Model of the Material Structure. In: The Selected Models of the Mesostructure of Composites. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-89704-2_2
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DOI: https://doi.org/10.1007/978-3-319-89704-2_2
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