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Analytic materials.

Graeme W Milton1

  • 1Department of Mathematics , University of Utah , Salt Lake City, UT 84112-0090, USA.

Proceedings. Mathematical, Physical, and Engineering Sciences
|December 14, 2016
PubMed
Summary
This summary is machine-generated.

This study develops the theory of inhomogeneous analytic materials, classifying them into complete and incomplete types based on integer parameters. It also reviews methods for identifying these materials in two-dimensional systems and discusses metamaterials for practical applications.

Keywords:
analytic materialsexact solutionsinhomogeneous materialslinear partial differential equationsmetamaterialswave equations

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Area of Science:

  • Physics
  • Materials Science
  • Electromagnetism

Background:

  • Inhomogeneous materials present challenges in theoretical modeling.
  • Analytic functions offer a framework for describing material properties.

Purpose of the Study:

  • To develop a comprehensive theory for inhomogeneous analytic materials.
  • To classify these materials and explore their identification methods.
  • To review relevant exact results and applications in metamaterials.

Main Methods:

  • Developing a theoretical framework for analytic materials.
  • Classifying materials based on integer parameters (p).
  • Utilizing properties of divergence-free and curl-free fields in 2D systems.

Main Results:

  • Identification of three types of analytic materials: complete and incomplete of rank p.
  • A method for identifying analytic materials in 2D using field properties.
  • Review of existing results and the role of metamaterials.

Conclusions:

  • The theory provides a robust classification for analytic materials.
  • The methods facilitate the identification and potential realization of these materials.
  • Metamaterials offer a pathway to engineer desired material coefficients.