Learn More
Scaling limits of critical percolation models show major differences between low and high dimensional models. The article discusses the formulation of the continuum limit for the former case. A mathematical framework is proposed for the direct description of the limiting continuum theory. The resulting structure is expected to exhibit strict conformal(More)
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)
We analyze the two-dimensional potential around a coated cylinder placed in a nonuniform field. In two special cases the system behaves as if the core of the cylinder were enlarged and the shell absent. These are when the shell dielectric constant is the negative of either the core dielectric constant or the matrix dielectric constant. When the shell(More)
Spherical cloaking using nonlinear transformations for improved segmentation into concentric isotropic coatings. Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this(More)
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)
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)
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)