Plasmonic Cloaking of Cylinders: Finite Length, Oblique Illumination and Cross-Polarization Coupling

Metamaterial cloaking has been proposed and studied in recent years following several interesting approaches. One of them, the scattering-cancellation technique, or plasmonic cloaking, exploits the plasmonic effects of suitably designed thin homogeneous metamaterial covers to drastically suppress the scattering of moderately sized objects within specific frequency ranges of interest. Besides its inherent simplicity, this technique also holds the promise of isotropic response and weak polarization dependence. Its theory has been applied extensively to symmetrical geometries and canonical 3D shapes, but its application to elongated objects has not been explored with the same level of detail. We derive here closed-form theoretical formulas for infinite cylinders under arbitrary wave incidence, and validate their performance with full-wave numerical simulations, also considering the effects of finite lengths and truncation effects in cylindrical objects. In particular, we find that a single isotropic (idealized) cloaking layer may successfully suppress the dominant scattering coefficients of moderately thin elongated objects, even for finite lengths comparable with the incident wavelength, providing a weak dependence on the incidence angle. These results may pave the way for application of plasmonic cloaking in a variety of practical scenarios of interest.Comment: 17 pages, 11 figures, 2 table

Efficient Prediction Designs for Random Fields

For estimation and predictions of random fields it is increasingly acknowledged that the kriging variance may be a poor representative of true uncertainty. Experimental designs based on more elaborate criteria that are appropriate for empirical kriging are then often non-space-filling and very costly to determine. In this paper, we investigate the possibility of using a compound criterion inspired by an equivalence theorem type relation to build designs quasi-optimal for the empirical kriging variance, when space-filling designs become unsuitable. Two algorithms are proposed, one relying on stochastic optimization to explicitly identify the Pareto front, while the second uses the surrogate criteria as local heuristic to chose the points at which the (costly) true Empirical Kriging variance is effectively computed. We illustrate the performance of the algorithms presented on both a simple simulated example and a real oceanographic dataset

Clifford group dipoles and the enactment of Weyl/Coxeter group W(E8) by entangling gates

Peres/Mermin arguments about no-hidden variables in quantum mechanics are used for displaying a pair (R, S) of entangling Clifford quantum gates, acting on two qubits. From them, a natural unitary representation of Coxeter/Weyl groups W(D5) and W(F4) emerges, which is also reflected into the splitting of the n-qubit Clifford group Cn into dipoles C$\pm$n . The union of the three-qubit real Clifford group C+ 3 and the Toffoli gate ensures a orthogonal representation of the Weyl/Coxeter group W(E8), and of its relatives. Other concepts involved are complex reflection groups, BN pairs, unitary group designs and entangled states of the GHZ family.Comment: version revised according the recommendations of a refere

A "poor man's" approach to topology optimization of natural convection problems

Topology optimization of natural convection problems is computationally expensive, due to the large number of degrees of freedom (DOFs) in the model and its two-way coupled nature. Herein, a method is presented to reduce the computational effort by use of a reduced-order model governed by simplified physics. The proposed method models the fluid flow using a potential flow model, which introduces an additional fluid property. This material property currently requires tuning of the model by comparison to numerical Navier-Stokes based solutions. Topology optimization based on the reduced-order model is shown to provide qualitatively similar designs, as those obtained using a full Navier-Stokes based model. The number of DOFs is reduced by 50% in two dimensions and the computational complexity is evaluated to be approximately 12.5% of the full model. We further compare to optimized designs obtained utilizing Newton's convection law.Comment: Preprint version. Please refer to final version in Structural Multidisciplinary Optimization https://doi.org/10.1007/s00158-019-02215-

Intersection numbers for subspace designs

Intersection numbers for subspace designs are introduced and $q$-analogs of the Mendelsohn and K\"ohler equations are given. As an application, we are able to determine the intersection structure of a putative $q$-analog of the Fano plane for any prime power $q$. It is shown that its existence implies the existence of a $2$-$(7,3,q^4)_q$ subspace design. Furthermore, several simplified or alternative proofs concerning intersection numbers of ordinary block designs are discussed