Full-wave simulations of electromagnetic cloaking structures

Based on a coordinate transformation approach, Pendry {\it et al.} have reported electromagnetically anisotropic and inhomogeneous shells that, in theory, completely shield an interior structure of arbitrary size from electromagnetic fields without perturbing the external fields. We report full-wave simulations of the cylindrical version of this cloaking structure using ideal and nonideal (but physically realizable) electromagnetic parameters in an effort to understand the challenges of realizing such a structure in practice. The simulations indicate that the performance of the electromagnetic cloaking structure is not especially sensitive to modest permittivity and permeability variations. This is in contrast to other applications of engineered electromagnetic materials, such as subwavelength focusing using negative refractive index materials. The cloaking performance degrades smoothly with increasing loss, and effective low-reflection shielding can be achieved with a cylindrical shell composed of an eight (homogeneous) layer approximation of the ideal continuous medium

Groupoid normalizers of tensor products

We consider an inclusion B [subset of or equal to] M of finite von Neumann algebras satisfying B′∩M [subset of or equal to] B. A partial isometry vset membership, variantM is called a groupoid normalizer if vBv*,v*Bv[subset of or equal to] B. Given two such inclusions B<sub>i</sub> [subset of or equal to] M<sub>i</sub>, i=1,2, we find approximations to the groupoid normalizers of [formula] in [formula], from which we deduce that the von Neumann algebra generated by the groupoid normalizers of the tensor product is equal to the tensor product of the von Neumann algebras generated by the groupoid normalizers. Examples are given to show that this can fail without the hypothesis [formula], i=1,2. We also prove a parallel result where the groupoid normalizers are replaced by the intertwiners, those partial isometries vset membership, variantM satisfying vBv*[subset of or equal to] B and v*v,vv*[set membership, variant] B

Constraints on non-thermal Dark Matter from Planck lensing extraction

Distortions of CMB temperature and polarization anisotropy maps caused by gravitational lensing, observable with high angular resolution and sensitivity, can be used to constrain the sterile neutrino mass, offering several advantages against the analysis based on the combination of CMB, LSS and Ly\alpha forest power spectra. As the gravitational lensing effect depends on the matter distribution, no assumption on light-to-mass bias is required. In addition, unlike the galaxy clustering and Ly\alpha forest power spectra, the projected gravitational potential power spectrum probes a larger range of angular scales, the non-linear corrections being required only at very small scales. Taking into account the changes in the time-temperature relation of the primordial plasma and the modification of the neutrino thermal potential, we compute the projected gravitational potential power spectrum and its correlation with the temperature in the presence of DM sterile neutrino. We show that the cosmological parameters are generally not biased when DM sterile neutrino is included. From this analysis we found a lower limit on DM sterile neutrino mass m_s >2.08 keV at 95% CL, consistent with the lower mass limit obtained from the combined analysis of CMB, SDSS 3D power spectrum and SDSS Ly\alpha forest power spectrum ($m_{\nu_s}>1.7$ keV). We conclude that although the information that can be obtained from lensing extraction is rather limited due to the high level of the lensing noise of Planck experiment, weak lensing of CMB offers a valuable alternative to constrain the dark matter sterile neutrino mass.Comment: 15 pages, 6 figure

Unbiased bases (Hadamards) for 6-level systems: Four ways from Fourier

In quantum mechanics some properties are maximally incompatible, such as the position and momentum of a particle or the vertical and horizontal projections of a 2-level spin. Given any definite state of one property the other property is completely random, or unbiased. For N-level systems, the 6-level ones are the smallest for which a tomographically efficient set of N+1 mutually unbiased bases (MUBs) has not been found. To facilitate the search, we numerically extend the classification of unbiased bases, or Hadamards, by incrementally adjusting relative phases in a standard basis. We consider the non-unitarity caused by small adjustments with a second order Taylor expansion, and choose incremental steps within the 4-dimensional nullspace of the curvature. In this way we prescribe a numerical integration of a 4-parameter set of Hadamards of order 6.Comment: 5 pages, 2 figure

Equivalence-based Security for Querying Encrypted Databases: Theory and Application to Privacy Policy Audits

Motivated by the problem of simultaneously preserving confidentiality and usability of data outsourced to third-party clouds, we present two different database encryption schemes that largely hide data but reveal enough information to support a wide-range of relational queries. We provide a security definition for database encryption that captures confidentiality based on a notion of equivalence of databases from the adversary's perspective. As a specific application, we adapt an existing algorithm for finding violations of privacy policies to run on logs encrypted under our schemes and observe low to moderate overheads.Comment: CCS 2015 paper technical report, in progres

Phase Conjugation and Negative Refraction Using Nonlinear Active Metamaterials

We present experimental demonstration of phase conjugation using nonlinear metamaterial elements. Active split-ring resonators loaded with varactor diodes are demonstrated theoretically to act as phase-conjugating or time-reversing discrete elements when parametrically pumped and illuminated with appropriate frequencies. The metamaterial elements were fabricated and shown experimentally to produce a time reversed signal. Measurements confirm that a discrete array of phase-conjugating elements act as a negatively-refracting time reversal RF lens only 0.12$\lambda$ thick