Computational Analysis of Structured Media

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....

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Academic Pr 2017.
Colección:Mathematical Analysis and its Applications
Temas:
Composite materials > Mathematical models.
Composites > Mod�eles math�ematiques.
TECHNOLOGY & ENGINEERING > Engineering (General)
TECHNOLOGY & ENGINEERING > Reference.
Composite materials > Mathematical models
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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
  • 4. Schwarz�a#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 Pad�A� approximants for indeterminate problem
  • 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 Pad�A� approximants
  • 8. Comment on contrast parameter
  • Reference
  • 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 Pad�A� approximants
  • 7. Discussion of the ansatz
  • 8. Square and hexagonal united
  • 9. Dependence on contrast parameter
  • Reference
  • 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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