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The Interaction of Mesoscopic Interior Boundaries of the Material

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The Selected Models of the Mesostructure of Composites

Part of the book series: SpringerBriefs in Physics ((SpringerBriefs in Physics))

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Abstract

In experimental and theoretical studies of internal boundaries and their role in the formation of properties of composite materials, much attention was paid to the influence of interphase and intergranular boundaries on the physicochemical and mechanical properties of matter. The brief review of the papers presented in this monograph allows us to delineate the range of problems and get an idea of phenomena in which internal boundaries are of decisive importance for explaining the properties of composites.In the third chapter of the monograph, a description of the analytical model of a multiscale network of matter interior boundaries is given. In this model, expressions for calculating the force fields of the Sierpinski prefractal and its modifications are derived. The model makes it possible to calculate the force fields of interior boundaries of an arbitrary shape as a superposition of the different prefractals’ fields. Relations for calculating such fields can be applied to the entire range of network sizes, in which there is self-similarity of interior boundaries. A computer stochastic model for the evolution of abstract systems with interacting subsystems is also proposed. It is used to study the properties of energy exchange processes between interior boundaries. It is assumed that the material structure is an open nonlinear dynamic system with interacting interior boundaries of three scale levels. The evolution of the energy state of the composites’ interior boundaries is described by a system of bilinear iterative equations. In the model, strange attractors arising in the phase space of interior boundaries’ energy are investigated. Attractors can be interpreted as stochastic self-oscillations supported in a dynamic system by an external source. They also can be interpreted as Lissajous figures of quasi-oscillatory processes. This opens the possibility of a visual determination of the nature and features of the different scale inhomogeneities’ interaction.

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  1. Department of Computer Systems, Odessa National Academy of Food Technologies, Odessa, Ukraine

    Alexander Herega

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Correspondence to Alexander Herega .

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Herega, A. (2018). The Interaction of Mesoscopic Interior Boundaries of the Material. In: The Selected Models of the Mesostructure of Composites. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-89704-2_4

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