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Computational Analysis of Structured Media

  • 1st Edition - September 11, 2017
  • Latest edition
  • Authors: Simon Gluzman, Vladimir Mityushev, Wojciech Nawalaniec
  • Language: English

Computational Analysis of Structured Media presents a systematical approach to analytical formulae for the effective properties of deterministic and random composites. Schwarz’s… Read more

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Description

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.

Key features

  • 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

Readership

Applied mathematicians at graduate level and above and mathematically advanced engineers interested in macroscopic property analysis in deterministic and random composites for scientific or industrial ends.

Table of contents

1. Introduction2. Complex potentials and R-linear problem3. Constructive Homogenization4. From basic sums to effective conductivity and RVE5. Introduction to the method of Self-Similar Approximants6. Conductivity of Regular Composite. Square Lattice7. Conductivity of Regular Composite. Hexagonal Array8. Effective Conductivity of 3D Regular Composites9. Random 2D Composites10. Elastic problem11. Table of the main analytical formulae

Review quotes

"In conclusion, the treatise is very interesting and well written. The computational analysis of composites is given by using the classical analytic formulae in the complex domain. The analysis may be readily extended to special geometry, motion, material and alike of structured media. The treatise can be used even as a “basic reference” for teaching a graduate course, and it is highly recommended to researchers in applied mathematics and computational mechanics."—Zentralblatt MATH

Product details

  • Edition: 1
  • Latest edition
  • Published: September 11, 2017
  • Language: English

About the authors

SG

Simon Gluzman

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.
Affiliations and expertise
Independent Researcher, Toronto, Canada

VM

Vladimir Mityushev

Vladimir Mityushev is the Professor of Cracow University of Technology, 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. .
Affiliations and expertise
Institute of Mathematics, Faculty of Computer Science and Telecommunications, Cracow University of Technology, Kraków, Poland

WN

Wojciech Nawalaniec

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.
Affiliations and expertise
Associate Professor, Applied Mathematics, Pedagogical University of Cracow, Krakow, Poland

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