Journal
PHYSICAL REVIEW APPLIED
Volume 14, Issue 5, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevApplied.14.054068
Keywords
-
Categories
Funding
- National Science Foundation [DMS-1814854]
- Air Force Office of Scientific Research [FA9550-17-1-0093]
- Korean Advanced Institute of Science and Technology (KAIST) mathematical research station (KMRS)
Ask authors/readers for more resources
Almost four decades ago, Bergman and Milton independently showed that the isotropic effective electric permittivity of a two-phase composite material with a given volume fraction is constrained to lie within lens-shaped regions in the complex plane that are bounded by two circular arcs. An implication of particular significance is a set of limits to the maximum and minimum absorption of an isotropic composite material at a given frequency. Here, after giving a short summary of the underlying theory, we show that the bound corresponding to one of the circular arcs is at least almost optimal by introducing a certain class of hierarchical laminates. In regard to the second arc, we show that a tighter bound can be derived using variational methods. This tighter bound is optimal as it corresponds to assemblages of doubly coated spheres, which can be easily approximated by more realistic microstructures. We briefly discuss the implications for related problems, including bounds on the complex polarizability.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available