Arbitrary beam control using passive lossless metasurfaces enabled by orthogonally-polarized custom surface waves

For passive, lossless impenetrable metasurfaces, a design technique for arbitrary beam control of receiving, guiding, and launching is presented. Arbitrary control is enabled by a custom surface wave in an orthogonal polarization such that its addition to the incident (input) and the desired scattered (output) fields is supported by a reactive surface impedance everywhere on the reflecting surface. Such a custom surface wave (SW) takes the form of an evanescent wave propagating along the surface with a spatially varying envelope. A growing SW appears when an illuminating beam is received. The SW amplitude stays constant when power is guided along the surface. The amplitude diminishes as a propagating wave (PW) is launched from the surface as a leaky wave. The resulting reactive tensor impedance profile may be realized as an array of anisotropic metallic resonators printed on a grounded dielectric substrate. Illustrative design examples of a Gaussian beam translator-reflector, a probe-fed beam launcher, and a near-field focusing lens are provided

Self-dual Hopfions

We construct static and time-dependent exact soliton solutions with non-trivial Hopf topological charge for a field theory in 3+1 dimensions with the target space being the two dimensional sphere S**2. The model considered is a reduction of the so-called extended Skyrme-Faddeev theory by the removal of the quadratic term in derivatives of the fields. The solutions are constructed using an ansatz based on the conformal and target space symmetries. The solutions are said self-dual because they solve first order differential equations which together with some conditions on the coupling constants, imply the second order equations of motion. The solutions belong to a sub-sector of the theory with an infinite number of local conserved currents. The equation for the profile function of the ansatz corresponds to the Bogomolny equation for the sine-Gordon model.Comment: plain latex, no figures, 23 page

A highly miniaturized electron and ion energy spectrometer prototype for the rapid analysis of space plasmas.

MEMS (Micro Electro-Mechanical Systems) plasma analyzers are a promising possibility for future space missions but conventional instrument designs are not necessarily well suited to micro-fabrication. Here, a candidate design for a MEMS-based instrument has been prototyped using electron-discharge machining. The device features 10 electrostatic analyzers that, with a single voltage applied to it, allow five different energies of electron and five different energies of positive ion to be simultaneously sampled. It has been simulated using SIMION and the electron response characteristics tested in an instrument calibration chamber. Small deviations found in the electrode spacing of the as-built prototype were found to have some effect on the electron response characteristics but do not significantly impede its performance

Variation-norm and fluctuation estimates for ergodic bilinear averages

For any dynamical system, we show that higher variation-norms for the sequence of ergodic bilinear averages of two functions satisfy a large range of bilinear Lp estimates. It follows that, with probability one, the number of fluctuations along this sequence may grow at most polynomially with respect to (the growth of) the underlying scale. These results strengthen previous works of Lacey and Bourgain where almost surely convergence of the sequence was proved (which is equivalent to the qualitative statement that the number of fluctuations is finite at each scale). Via transference, the proof reduces to establishing new bilinear Lp bounds for variation-norms of truncated bilinear operators on R, and the main ingredient of the proof of these bounds is a variation-norm extension of maximal Bessel inequalities of Lacey and Demeter--Tao--Thiele.Comment: 37 pages, new version fixed some references not displaying correctl

Quantum Gauss Jordan Elimination

In this paper we construct the Quantum Gau\ss Jordan Elimination (QGJE) Algorithm and estimate the complexity time of computation of Reduced Row Echelon Form (RREF) of an $N\times N$ matrix using QGJE procedure. The main theorem asserts that QGJE has computation time of order $2^{N/2}$

Trade and financial development

The differences in financial development between advanced and developing countries are pronounced. It has been observed, both theoretically and empirically, that these differences in countries'financial systems are a source of comparative advantage and trade. This paper points out that to the extent a country's financial development is endogenous, it will in turn be influenced by trade. The paper builds a model in which a country's financial development is an equilibrium outcome of the economy's productive structure: in countries with large financially intensive sectors financial systems are more developed. When a wealthy and a poor country open to trade, the financially dependent sectors grow in the wealthy country, and so does the financial system. By contrast, as the financially intensive sectors shrink in the poor country, demand for external finance decreases and the domestic financial system deteriorates. This paper describes the authors'test model using data on financial development for a sample of 77 countries. The authors find that the main predictions of the model are borne out in the data: trade openness is associatedwith faster financial development in wealthier countries, and with slower financial development in poorer ones.Payment Systems&Infrastructure,Economic Theory&Research,Environmental Economics&Policies,Fiscal&Monetary Policy,Labor Policies,Economic Theory&Research,Environmental Economics&Policies,TF054105-DONOR FUNDED OPERATION ADMINISTRATION FEE INCOME AND EXPENSE ACCOUNT,Macroeconomic Management,Inequality