Waves in composites and metamaterials

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Welcome to this learning project about Waves in composites and metamaterials!

Contents 1 Learning Project Summary 2 Content summary 3 Goals 4 Contents 4.1 Lessons 4.2 Readings and other resources

[edit] Learning Project Summary

• Project code:
• Suggested Prerequisites:
  • Partial differential equations
  • Introduction to Elasticity
  • Electromagnetism
• Time investment: 6 months
• Portal:Engineering and Technology
• School:Engineering, Mathematics
• Department:Mechanical Engineering, Electrical Engineering
• Stream: Applied mathematics
• Level: Graduate

[edit] Content summary

This course is an introduction to metamaterials and composites and how they interact with electromagnetic and elastic waves.

Update June 17, 2009: The content is organized based on the lecture notes of Prof. Graeme W. Milton (University of Utah). Professor Milton has asked that his contribution be acknowledged in the notes or the lecture notes removed from Wikiversity.

The first author of these Wikiversity notes has, in addition to transcribing the lectures given in class, added significantly to the content of the course by expanding on portions that were glossed over in class. The idea for creating the notes was that of the author of the Wikiversity notes. The notes have subsequently been corrected and modified by several other anonymous authors.

[edit] Goals

This learning project aims to give the student the basic tools needed to start working on metamaterials and waves in composites.

[edit] Contents

[edit] Lessons

• Lecture 1: Rainbows
• Lecture 2: Airy theory
• Lecture 3: Maxwell equations in media
• Lecture 4: Fresnel equations
• Lecture 5: Perfect lenses and negative density materials
• Lecture 6: Anisotropic mass and generalization
• Lecture 7: Elastodynamics and electrodynamics
• Lecture 8: Acoustic metamaterials and negative moduli
• Lecture 9: Fading memory and waves in layered media
• Lecture 10: Airy solution and WKB solution
• Lecture 11: TE waves in multilayered media
• Lecture 12: Continuum limit and propagator matrix
• Lecture 13: Waves in layered media and point sources
• Lecture 14: Point sources and EM vector potentials
• Lecture 15: Mie theory and Bloch theorem
• Lecture 16: Bloch waves and the quasistatic limit
• Lecture 17: Bloch waves in elastodynamics and bubbly fluids
• Lecture 18: Duality relations and phase interchange identity in laminates
• Lecture 19: Backus formula for laminates and rank-1 laminates
• Lecture 20: Hierarchical laminates and Hilbert space formalism
• Lecture 21: Effective tensors using Hilbert space formalism
• Lecture 22: Transformation-based cloaking in electromagnetism
• Lecture 23: Transformation-based cloaking in mechanics
• Lecture 24: Willis equations for elastodynamics

[edit] Readings and other resources

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