Anomalous localized resonance using a folded geometry in three dimensions

If a body of dielectric material is coated by a plasmonic structure of negative dielectric material with nonzero loss parameter, then cloaking by anomalous localized resonance (CALR) may occur as the loss parameter tends to zero. It was proved in other papers by authors that if the coated structure is circular (2D) and dielectric constant of the shell is a negative constant (with loss parameter), then CALR occurs, and if the coated structure is spherical (3D), then CALR does not occur. The aim of this paper is to show that the CALR takes place if the spherical coated structure has a specially designed anisotropic dielectric tensor. The anisotropic dielectric tensor is designed by unfolding a folded geometry

Spectral theory of a Neumann-Poincar\'e-type operator and analysis of anomalous localized resonance II

If a body of dielectric material is coated by a plasmonic structure of negative dielectric constant with nonzero loss parameter, then cloaking by anomalous localized resonance (CALR) may occur as the loss parameter tends to zero. The aim of this paper is to investigate this phenomenon in two and three dimensions when the coated structure is radial, and the core, shell and matrix are isotropic materials. In two dimensions, we show that if the real part of the permittivity of the shell is -1 (under the assumption that the permittivity of the background is 1), then CALR takes place. If it is different from -1, then CALR does not occur. In three dimensions, we show that CALR does not occur. The analysis of this paper reveals that occurrence of CALR is determined by the eigenvalue distribution of the Neumann-Poincar\'e-type operator associated with the structure

Progress on the Strong Eshelby's Conjecture and Extremal Structures for the Elastic Moment Tensor

We make progress towards proving the strong Eshelby's conjecture in three dimensions. We prove that if for a single nonzero uniform loading the strain inside inclusion is constant and further the eigenvalues of this strain are either all the same or all distinct, then the inclusion must be of ellipsoidal shape. As a consequence, we show that for two linearly independent loadings the strains inside the inclusions are uniform, then the inclusion must be of ellipsoidal shape. We then use this result to address a problem of determining the shape of an inclusion when the elastic moment tensor (elastic polarizability tensor) is extremal. We show that the shape of inclusions, for which the lower Hashin-Shtrikman bound either on the bulk part or on the shear part of the elastic moment tensor is attained, is an ellipse in two dimensions and an ellipsoid in three dimensions

Présentation atypique d’une granulomatose avec polyangeite: à propos d’une observation pédiatrique

La granulomatose avec polyangéite (GPA) est une vascularite nécrosante systémique, caractérisée par une inflammation granulomateuse, une nécrose tissulaire et une vascularite touchant les vaisseaux de moyen et, surtout, de petit calibre, elle touche rarement l'enfant

The essential spectrum of the Neumann–Poincaré operator on a domain with corners

Exploiting the homogeneous structure of a wedge in the complex plane, we compute the spectrum of the anti-linear Ahlfors-Beurling transform acting on the associated Bergman space. Consequently, the similarity equivalence between the Ahlfors--Beurling transform and the Neumann-Poincare operator provides the spectrum of the latter integral operator on a wedge. A localization technique and conformal mapping lead to the first complete description of the essential spectrum of the Neumann-Poincare operator on a planar domain with corners, with respect to the energy norm of the associated harmonic field

A Capabilities View of Accessibility in Policy and Practice in Jordan and Peru

We explore the recent evolution of accessibility-related policy in Jordan and Peru, and specifically consider issues around assistive technology access for people with severe vision impairments. We find differences in capacity development and institutions in the two countries over time and how it impacts the ways in which recent policy consultations have taken place, and propose a capabilities framework as a means to examine and contextualize these differences. Narratives of assistive technology use by people in both countries emphasize ways in which the capabilities approach is also a valuable tool in understanding aspirations and how social interactions evolve with access to assistive technology. We argue that the findings from Peru and Jordan, given the diversity of policy environments, infrastructure, and socio-economic attitudes towards people with disabilities, give us an important lens towards understanding the evolution of disability rights and policies in various low and middle-income countries around the world

Spectral theory of a Neumann-Poincare-type operator and analysis of cloaking due to anomalous localized resonance

The aim of this paper is to give a mathematical justification of cloaking due to anomalous localized resonance (CALR). We consider the dielectric problem with a source term in a structure with a layer of plasmonic material. Using layer potentials and symmetrization techniques, we give a necessary and sufficient condition on the fixed source term for electromagnetic power dissipation to blow up as the loss parameter of the plasmonic material goes to zero. This condition is written in terms of the Newtonian potential of the source term. In the case of concentric disks, we make the condition even more explicit. Using the condition, we are able to show that for any source supported outside a critical radius CALR does not take place, and for sources located inside the critical radius satisfying certain conditions CALR does take place as the loss parameter goes to zero.Comment: 24 page

Modeling active electrolocation in weakly electric fish

In this paper, we provide a mathematical model for the electrolocation in weakly electric fishes. We first investigate the forward complex conductivity problem and derive the approximate boundary conditions on the skin of the fish. Then we provide a dipole approximation for small targets away from the fish. Based on this approximation, we obtain a non-iterative location search algorithm using multi-frequency measurements. We present numerical experiments to illustrate the performance and the stability of the proposed multi-frequency location search algorithm. Finally, in the case of disk- and ellipse-shaped targets, we provide a method to reconstruct separately the conductivity, the permittivity, and the size of the targets from multi-frequency measurements.Comment: 37 pages, 11 figure

Computational science and re-discovery: open-source implementations of ellipsoidal harmonics for problems in potential theory

We present two open-source (BSD) implementations of ellipsoidal harmonic expansions for solving problems of potential theory using separation of variables. Ellipsoidal harmonics are used surprisingly infrequently, considering their substantial value for problems ranging in scale from molecules to the entire solar system. In this article, we suggest two possible reasons for the paucity relative to spherical harmonics. The first is essentially historical---ellipsoidal harmonics developed during the late 19th century and early 20th, when it was found that only the lowest-order harmonics are expressible in closed form. Each higher-order term requires the solution of an eigenvalue problem, and tedious manual computation seems to have discouraged applications and theoretical studies. The second explanation is practical: even with modern computers and accurate eigenvalue algorithms, expansions in ellipsoidal harmonics are significantly more challenging to compute than those in Cartesian or spherical coordinates. The present implementations reduce the "barrier to entry" by providing an easy and free way for the community to begin using ellipsoidal harmonics in actual research. We demonstrate our implementation using the specific and physiologically crucial problem of how charged proteins interact with their environment, and ask: what other analytical tools await re-discovery in an era of inexpensive computation?Comment: 25 pages, 3 figure

Enhanced statistical stability in coherent interferometric imaging

http://iopscience.iop.org/0266-5611/International audienc