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For practical applications of variational bounds to the eeective properties of composite materials, the information available is often not that required by the formulas for the optimal bounds. It is therefore important to determine what can be said rigorously about various unknown material properties when some other properties are known. The key quantities… (More)

- D J Eyre, G W Milton
- 2007

A numerical scheme is presented to compute the response of a composite material to an applied eld. The scheme is based on an iteration that uses a Fourier transform based projection method to compute the response of a reference material to the applied eld, and a contraction mapping to relate the response of the reference material to the response of the… (More)

- Marc Briane, Graeme W. Milton
- SIAM Journal of Applied Mathematics
- 2010

In an electromagnetic cloak based on a transformation approach, reduced sets of material properties are generally favored due to their easier implementation in reality, although a seemingly inevitable drawback of undesired scattering exists in such cloaks. Here, the authors suggest the use of high-order transformations to create smooth moduli at the outer… (More)

- Graeme W. Milton
- 2008

Metamaterials are constructed such that, for a narrow range of frequencies, the momentum density depends on the local displacement gradient, and the stress depends on the local velocity. In these models the momentum density generally depends not only on the strain, but also on the local rotation, and the stress is generally not symmetric. A variant is… (More)

Eshelby showed that if an inclusion is of elliptic or ellipsoidal shape then for any uniform elastic loading the field inside the inclusion is uniform. He then conjectured that the converse is true, i.e. that if the field inside an inclusion is uniform for all uniform loadings, then the inclusion is of elliptic or ellipsoidal shape. We call this the weak… (More)

Solutions for the fields in a coated cylinder where the core radius is bigger than the shell radius are seemingly unphysical, but can be given a physical meaning if one transforms to an equivalent problem by unfolding the geometry. In particular the unfolded material can act as an impedance matched hyperlens, and as the loss in the lens goes to zero finite… (More)

We analyze the performance of a planar lens based on realistic negative index material in a generalized geometry. We demonstrate that the conventional su-perlens design (where the lens is centered between the object and the image) is not optimal from the resolution point-of-view, develop an analytical expression for the resolution limit of a generalized… (More)

The response of the " perfect lens " , consisting of a slab of lossless material of thickness d with ε s = µ s = −1 at one frequency ω 0 is investigated. It is shown that as time progresses the lens becomes increasingly opaque to any physical TM line dipole source located a distance d 0 < d/2 from the lens and which has been turned on at time t = 0. Here a… (More)

- G W Milton, D J Eyre, J V Mantese
- 2007

Dispersion inequalities are presented to check for the self-consistency of experimentally obtained complex moduli, such as the complex dielectric constant, magnetic permeability, and complex bulk and shear moduli of viscoelastic materials. Unlike the Kramers-Kronig dispersion relations, they only require measurements over a nite frequency range. They can… (More)