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BL
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| Record Number
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872388
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| Title & Author
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Computational Analysis of Structured Media
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| Publication Statement
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Academic Pr, 2017.
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| Series Statement
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Mathematical Analysis and its Applications
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| Page. NO
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1 online resource
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| ISBN
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0128110473
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: 9780128110478
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0128110465
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9780128110461
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| Contents
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Front Cover -- Computational Analysis of Structured Media -- Copyright -- Dedication -- Contents -- Acknowledgment -- Preface -- Reference -- Chapter 1: Introduction -- Reference -- Chapter 2: Complex Potentials and R-linear problem -- 1. Complex potentials -- 2. R-linear problem -- 3. Metod of functional equations -- Reference -- Chapter 3: Constructive homogenization -- 1. Introduction -- 2. Deterministic and stochastic approaches -- 3. Series expansions for the local fields and effective tensors. Traditional approach
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4. Schwarzâ#x80;#x99;s method5. Remark on asymptotic methods -- Reference -- Chapter 4: From Basic Sums to effective conductivity and RVE) -- 1. Basic Sums -- 2. Identical circular inclusions. -- 3. Representative volume element -- 4. Method of Rayleigh -- Reference -- Chapter 5: Introduction to the method of self-similar approximants -- 1. Brief introduction to extrapolation -- 2. Algebraic renormalization and self-similar bootstrap -- 3. Extrapolation problem and self-similar approximants -- 4. Corrected Padà ̈approximants for indeterminate problem
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5. Calculation of critical exponents6. Interpolation with self-similar root approximants -- Reference -- Chapter 6: Conductivity of regular composite. Square lattice -- 1. Introduction -- 2. Critical point, square array -- 3. Critical Index s -- 4. Crossover formula for all concentrations -- 5. Expansion near the threshold -- 6. Additive ansatz. Critical amplitude and formula for all concentrations -- 7. Interpolation with high-concentration Padà ̈approximants -- 8. Comment on contrast parameter -- Reference
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Chapter 7: Conductivity of regular composite. Hexagonal array 1. Effective conductivity and critical properties of a hexagonal array of superconducting cylinders -- 2. Series for hexagonal array of superconducting cylinders -- 3. Critical Point -- 4. Critical index and amplitude -- 5. Critical amplitude and formula for all concentrations -- 6. Interpolation with high-concentration Padà ̈approximants -- 7. Discussion of the ansatz -- 8. Square and hexagonal united -- 9. Dependence on contrast parameter -- Reference
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Chapter 8: Effective Conductivity of 3D regular composites 1. Modified Dirichlet problem. Finite number of balls -- 2. 3D periodic problems -- 3. Triply periodic functions -- 4. Functional equations on periodic functions -- 5. Analytical formulae for the effective conductivity. Discussion and overview of the known results. -- 6. Non-conducting inclusions embedded in an conducting matrix. FCC lattice -- 7. Non-conducting inclusions embedded in an conducting matrix. SC and BCC lattices -- Reference -- Chapter 9: Random 2D composites
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| Abstract
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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.
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| Subject
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Composite materials-- Mathematical models.
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| Subject
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Composite materials-- Mathematical models.
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| Subject
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TECHNOLOGY ENGINEERING-- Engineering (General)
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| Subject
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TECHNOLOGY ENGINEERING-- Reference.
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| Dewey Classification
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620.1/18
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| LC Classification
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TA418.9.C6
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