Computational Analysis of Structured Media presents a systematical approach to analytical formulae for the effective properties of deterministic and random composites. Schwarz's method and functional equations yield for use in symbolic-numeric computations relevant to the effective properties. The work is primarily concerned with constructive topics of boundary value problems, complex analysis, and their applications to composites. Symbolic-numerical computations are widely used to deduce new formulae interesting for applied mathematicians and engineers. The main line of presentation is the investigation of two-phase 2D composites with non-overlapping inclusions randomly embedded in matrices.
- Computational methodology for main classes of problems in structured media
- Theory of Representative Volume Element
- Combines exact results, Monte-Carlo simulations and Resummation techniques under one umbrella
- Contains new analytical formulae obtained in the last ten years and it combines different asymptotic methods with the corresponding computer implementations
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1. Introduction 2. Complex potentials and R-linear problem 3. Constructive Homogenization 4. From basic sums to effective conductivity and RVE 5. Introduction to the method of Self-Similar Approximants 6. Conductivity of Regular Composite. Square Lattice 7. Conductivity of Regular Composite. Hexagonal Array 8. Effective Conductivity of 3D Regular Composites 9. Random 2D Composites 10. Elastic problem 11. Table of the main analytical formulae
Simon Gluzman is presently an Independent Researcher (Toronto, Canada) and formerly a Research Associate at PSU in Applied Mathematics. He is interested in Re-summation methods in theory of random and regular composites and the method of self-similar and rational approximants.
Vladimir Mityushev is the head of the modeling and simulation laboratory at the department of computer science and computational methods at the Pedagogical University of Kraków, Poland, a leader of the research group www.materialica.plus. He is interested in mathematical modeling and computer simulations, Industrial mathematics and boundary value problems and their applications.
Wojciech Nawalaniec is an Associate Professor in applied mathematics at Pedagogical University of Cracow, Kraków. He is interested in Computational methods, such as symbolic computation, mathematical modeling and algorithms.