Metamaterials are artificially structured media with unique and exotic properties not observed in natural materials. These include, for example electromagnetic materials with permittivity and permeability both designed to achieve novel effects, such as a negative refractive index, and elastic materials configured to give a negative or anisotropic effective mass density at a given frequency. They are typically constructed from high contrast materials, and the macroscopic fields needed to describe their effective behaviors are not simple averages of the local fields. They frequently gain their properties from microscopic resonances. The potential applications of such materials are growing and include lenses that have subwavelength focussing, and electromagnetic and acoustic cloaks that hide objects and leave incoming waves unscattered. Metamaterials also include materials for which the equations governing their continuum electromagnetic or elastodynamic macroscopic behavior are unlike any found in nature. This workshop brings together three groups of people: physicists and engineers working on metamaterials and their applications; mathematicians who are studying homogenization in high contrast materials and who are providing a greater understanding of the mathematics of metamaterials; and numerical analysts interested in the solving the microscopic and macroscopic equations governing the behavior of metamaterials. Many challenges remain, such as seeking a better understanding of what novel behaviors and applications metamaterials can achieve in practice; exploring what is theoretically possible by homogenization theory; and finding efficient and accurate numerical algorithms for solving the partial differential equations to accelerate progress in the field.
Susanne Brenner
(Louisiana State University)
Maria-Carme Calderer
(University of Minnesota, Twin Cities)
Tatsuo Itoh
(University of California, Los Angeles (UCLA))
Robert Kohn, Co-chair
(New York University)
Jichun Li, Co-chair
(University of Nevada, Las Vegas)
Graeme Milton, Co-chair
(University of Utah)
Chi-Wang Shu
(Brown University)
Richard Ziolkowski
(University of Arizona)
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