Computational Analysis Of Structured Media

Paperback | October 1, 2017

bySimon Gluzman, Vladimir Mityushev, Wojciech Nawalaniec

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Computational analysis of Structured Media presents a generalized convergent method of Schwarz and functional equations yield for use in symbolic-numeric computations relevant to the effective evaluation of 2D composite properties. The work is primarily concerned with constructive topics of boundary value problems, complex analysis and their applications to composites and porous media. Symbolic-numerical computations are widely used to deduce new formulae interesting for mathematiciains and engineers. The main line of presentation is the investigation of two-phase composites with non-overlapping inclusions randomly embedded in matrices. A direct approach is applied to estimate the effective properties of random 2D composites. First, deterministic boundary value problems are solved for all locations of inclusions, i.e., for all events of the considered probabilistic space C by the generalized method of Schwarz. Second, the effective properties are calculated in analytical form and averaged over C. This is related to the classic method based on the average probabilistic values involving the $n$-point correlation functions. However, the authors avoid computation of the correlation functions and compute their weighted moments of high orders by an indirect method which does not address to the correlation functions. The effective properties are exactly expressed through these moments. It is proved that the generalized method of Schwarz converges for an arbitrary multiply connected doubly periodic domain and for an arbitrary contrast parameter. Similar techniques are applicable to porous media. The proposed method yields effective algorithm in symbolic-numeric form. Uniform computational methodology for main classes of 2d transport problems in structured media Combines exact results, Monte-Carlo simulations and resummation techniques under one umbrella Contains new results obtained in the last five years and it combines different asymptotic methods with the corresponding computer implementations

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Computational analysis of Structured Media presents a generalized convergent method of Schwarz and functional equations yield for use in symbolic-numeric computations relevant to the effective evaluation of 2D composite properties. The work is primarily concerned with constructive topics of boundary value problems, complex analysis and...

Simon Gluzman is presently an Independent Researcher (Toronto, Canada) and formerly a Research Associate at PSU in Applied Mathematics. He is interested in Resummation methods in theory of random and regular composites and the method of self-similar approximants and rational approximants.Vladimir Mityushev is the head of modelling and ...
Format:PaperbackDimensions:330 pages, 8.75 × 6.35 × 0.68 inPublished:October 1, 2017Publisher:Academic PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0128110465

ISBN - 13:9780128110461

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Table of Contents

1. Theory of 2D composite 2. Introduction to the method of self-similar approximants 3. Square lattice array of superconducting cylinders 4. Hexagonal array of superconducting cylinders 5. Random 2D composite 6. Macroscopic properties of porous media 7. Special topics in theory of composites 8. Implications for 3D composite