The Selected Models of the Mesostructure of Composites (eBook)

Prof. Alexander Herega is head of the Department of Computer Systems and Full Professor of Department of Physics at Odessa National Academy of Food Technologies. He got the diploma at the Department of Theoretical Physics of I. Mechnikov Odessa State University, PhD and D Sc. degrees at Odessa National Academy of Food Technologies. He is a member of the American Physical Society (APS), American Chemical Society (ACS), and Ukrainian Physical Society. He belongs to the editorial board of the International Journal of Composite Materials, International Journal of Modern Physics and Application. He has more 100 publications and three text-books "Simulation and statistical modeling", "Constructive fractals in set theory", and "Course of physics". He teaches General Physics, Computer Science, Information Technologies and System Science. His areas of research are: Materials Science, Percolation Theory, Fractal Clusters, Dynamical Systems, Deterministic Chaos, Computer Simulation, and Modeling of Physical Phenomenon. 

Preface 6
Contents 8
Abstract 10
1 Introduction 11
References 13
2 Complex Percolation Model of the Material Structure 15
2.1 Percolation Clusters of Phases and Interior Boundaries 16
2.2 Modeling of Technological Cracks 21
2.3 Percolation in the Sierpinski Carpet 22
2.4 The Development of the Concept of the Immediate Neighborhood at Percolation Models 23
References 24
3 Percolation Model of the Long-Range Effect 26
3.1 The Anomalous Interaction in Semiconductors 27
3.2 Model of the Long-Range Effect. Clusters with Transforming Elements 28
3.3 Computer Implementation of the Model 30
3.4 Long-Range in Construction Composites 31
3.5 Conclusion 33
References 34
4 The Interaction of Mesoscopic Interior Boundaries of the Material 35
4.1 Interior Boundaries and Properties of Composite Materials 36
4.2 Fractal Nature of Interior Boundaries’ Networks. Force Field Model of Polyscale Network 40
4.3 The Oscillatory Interaction of Different Scales Structures. Stochastic Model of the Interior Boundaries’ Interaction 46
4.4 Conclusion 57
References 57
5 Small Clusters: Genesis, Structure, and Properties 60
5.1 Simulation of Coagulation in a Curvilinear Two-Phase Flow. Types of Clusters. ?-Criterion 61
5.2 Stability of Mesoscopic Clusters. The Theorem on the Field Interaction of Multifractals 67
References 72
6 Conclusion 74
Appendix A: Essay on Models 75
Appendix B: Some Parameters of Percolation Systems. Calculating Formulas 82
Appendix C: Dimensions: Genesis of Representations and Physical Applications 85
Appendix D: The Relative Order of the Heterogeneous Materials’ Structure 104