Design optimisation of ring elements for broadband reflectarray antennas

Plane wave scattering from a flat surface consisting of two periodic arrays of ring elements printed on a grounded dielectric sheet is investigated. It is shown that the reflection phase variation as a function of ring diameter is controlled by the difference in the centre resonant frequency of the two arrays. Simulated and measured results at X-band demonstrate that this parameter can be used to reduce the gradient and improve the linearity of the reflection phase versus ring size slope. These are necessary conditions for the re-radiating elements to maximise the bandwidth of a microstrip reflectarray antenna. The scattering properties of a conventional dual resonant multilayer structure and an array of concentric rings printed on a metal backed dielectric substrate are compared and the trade-off in performance is discussed.

Non-locality of two ultracold trapped atoms

We undertake a detailed analysis of the non-local properties of the fundamental problem of two trapped, distinguishable neutral atoms that interact with a short-range potential characterized by an s-wave scattering length. We show that this interaction generates continuous variable (CV) entanglement between the external degrees of freedom of the atoms and consider its behaviour as a function of both, the distance between the traps and the magnitude of the inter-particle scattering length. We first quantify the entanglement in the ground state of the system at zero temperature and then, adopting a phase-space approach, test the violation of the Clauser-Horn-Shimony-Holt inequality at zero and non-zero temperature and under the effects of general dissipative local environments.

Forward modelling to determine the observational signatures of white-light imaging and interplanetary scintillation for the propagation of an interplanetary shock in the ecliptic plane

Recent coordinated observations of interplanetary scintillation (IPS) from the EISCAT, MERLIN, and STELab, and stereoscopic white-light imaging from the two heliospheric imagers (HIs) onboard the twin STEREO spacecraft are significant to continuously track the propagation and evolution of solar eruptions throughout interplanetary space. In order to obtain a better understanding of the observational signatures in these two remote-sensing techniques, the magnetohydrodynamics of the macro-scale interplanetary disturbance and the radio-wave scattering of the micro-scale electron-density fluctuation are coupled and investigated using a newly constructed multi-scale numerical model. This model is then applied to a case of an interplanetary shock propagation within the ecliptic plane. The shock could be nearly invisible to an HI, once entering the Thomson-scattering sphere of the HI. The asymmetry in the optical images between the western and eastern HIs suggests the shock propagation off the Sun–Earth line. Meanwhile, an IPS signal, strongly dependent on the local electron density, is insensitive to the density cavity far downstream of the shock front. When this cavity (or the shock nose) is cut through by an IPS ray-path, a single speed component at the flank (or the nose) of the shock can be recorded; when an IPS ray-path penetrates the sheath between the shock nose and this cavity, two speed components at the sheath and flank can be detected. Moreover, once a shock front touches an IPS ray-path, the derived position and speed at the irregularity source of this IPS signal, together with an assumption of a radial and constant propagation of the shock, can be used to estimate the later appearance of the shock front in the elongation of the HI field of view. The results of synthetic measurements from forward modelling are helpful in inferring the in-situ properties of coronal mass ejection from real observational data via an inverse approach.

On the solvability of second kind integral equations on the real line

This paper considers general second kind integral equations of the form(in operator form φ − kφ = ψ), where the functions k and ψ are assumed known, with ψ ∈ Y, the space of bounded continuous functions on R, and k such that the mapping s → k(s, · ), from R to L1(R), is bounded and continuous. The function φ ∈ Y is the solution to be determined. Conditions on a set W ⊂ BC(R, L1(R)) are obtained such that a generalised Fredholm alternative holds: If W satisfies these conditions and I − k is injective for all k ∈ W then I − k is also surjective for all k ∈ W and, moreover, the inverse operators (I − k) − 1 on Y are uniformly bounded for k ∈ W. The approximation of the kernel in the integral equation by a sequence (kn) converging in a weak sense to k is also considered and results on stability and convergence are obtained. These general theorems are used to establish results for two special classes of kernels: k(s, t) = κ(s − t)z(t) and k(s, t) = κ(s − t)λ(s − t, t), where κ ∈ L1(R), z ∈ L∞(R), and λ ∈ BC((R\{0}) × R). Kernels of both classes arise in problems of time harmonic wave scattering by unbounded surfaces. The general integral equation results are here applied to prove the existence of a solution for a boundary integral equation formulation of scattering by an infinite rough surface and to consider the stability and convergence of approximation of the rough surface problem by a sequence of diffraction grating problems of increasingly large period.

The impedance boundary value problem for the Helmholtz equation in a half-plane

We prove unique existence of solution for the impedance (or third) boundary value problem for the Helmholtz equation in a half-plane with arbitrary L∞ boundary data. This problem is of interest as a model of outdoor sound propagation over inhomogeneous flat terrain and as a model of rough surface scattering. To formulate the problem and prove uniqueness of solution we introduce a novel radiation condition, a generalization of that used in plane wave scattering by one-dimensional diffraction gratings. To prove existence of solution and a limiting absorption principle we first reformulate the problem as an equivalent second kind boundary integral equation to which we apply a form of Fredholm alternative, utilizing recent results on the solvability of integral equations on the real line in [5].

Análise espectral de reflectarrays com substratos de duas camadas dielétricas anisotrópicas uniaxiais

Recently, an amazing development has been observed in telecommunication systems. Two good examples of this development are observed in mobile communication and aerospace systems. This impressive development is related to the increasing need for receiving and transmitting communication signals. Particularly, this development has required the study of new antennas and filters. This work presents a fullwave analysis of reflectarrays. The considered structures are composed by arrays of rectangular conducting patches printed on multilayer dieletric substrates, that are mounted on a ground plane. The analysis is developed in the spectral domain, using an equivalent transmission line method in combination with Galerkin method. Results for the reflection coefficient of these structures are presented and compared to those available in the literature. A good agreement was observed. Particularly, the developed analysis uses the transmission lines theory in combination with the incident potentials and the field continuity equations, at the structures interfaces, for obtaining the scattered field components expressions as function of the patch surface currents and of the incident field. Galerkin method is used to determine the unknown coefficients in the boundary value problem. Curves for the reflection coefficient of several reflectarray geometries are presented as function of frequency and of the structural parameters

Análise espectral de reflectarrays com substrato de duas camadas dielétricas anisotrópicas uniaxiais

Recently, an amazing development has been observed in telecommunication systems. Two good examples of this development are observed in mobile communication and aerospace systems. This impressive development is related to the increasing need for receiving and transmitting communication signals. Particularly, this development has required the study of new antennas and filters. This work presents a fullwave analysis of reflectarrays. The considered structures are composed by arrays of rectangular conducting patches printed on multilayer dieletric substrates, that are mounted on a ground plane. The analysis is developed in the spectral domain, using an equivalent transmission line method in combination with Galerkin method. Results for the reflection coefficient of these structures are presented and compared to those available in the literature. A good agreement was observed. Particularly, the developed analysis uses the transmission lines theory in combination with the incident potentials and the field continuity equations, at the structures interfaces, for obtaining the scattered field components expressions as function of the patch surface currents and of the incident field. Galerkin method is used to determine the unknown coefficients in the boundary value problem. Curves for the reflection coefficient of several reflectarray geometries are presented as function of frequency and of the structural parameters

Solitons in tunnel-coupled repulsive and attractive condensates

We study solitons in the condensate trapped in a double-well potential with far-separated wells, when the s-wave scattering length has different signs in the two parts of the condensate. By employing the coupled-mode approximation it is shown that there are unusual stable bright solitons in the condensate, with the larger share of atoms being gathered in the repulsive part. Such unusual solitons derive their stability from the quantum tunneling and correspond to the strong coupling between the parts of the condensate. The ground state of the system, however, corresponds to weak coupling between the condensate parts, with the larger share of atoms being gathered in the attractive part of the condensate.

Structure of large two-neutron halos in light exotic nuclei

The structure of three-body halo nuclei formed by two neutrons and a core (nnc) is studied using zero-range interactions. The halo wave function can be completely parameterized only by the s-wave scattering lengths and two-neutron separation energy. The sizes and the neutron-neutron correlation function of Li-11 and Be-14 are calculated and compared to experimental data. A general classification scheme for three-body halos with two identical particles is discussed as well as the critical conditions to allow excited Efimov states.

Nonlinear Schrodinger equation for a superfluid Fermi gas in the BCS-BEC crossover

We introduce a quasianalytic nonlinear Schrodinger equation with beyond mean-field corrections to describe the dynamics of a zero-temperature dilute superfluid Fermi gas in the crossover from the weak-coupling Bardeen-Cooper-Schrieffer (BCS) regime, where k(F)parallel to a parallel to << 1 with a the s-wave scattering length and k(F) the Fermi momentum, through the unitarity limit k(F)a ->+/-infinity to the Bose-Einstein condensation (BEC) regime where k(F)a > 0. The energy of our model is parametrized using the known asymptotic behavior in the BCS, BEC, and the unitarity limits and is in excellent agreement with accurate Green's-function Monte Carlo calculations. The model generates good results for frequencies of collective breathing oscillations of a trapped Fermi superfluid.

Nonlinear Schrodinger equation for a superfluid Bose gas from weak coupling to unitarity: Study of vortices

We introduce a nonlinear Schrodinger equation to describe the dynamics of a superfluid Bose gas in the crossover from the weak-coupling regime, where an(1/3)<<1 with a the interatomic s-wave scattering length and n the bosonic density, to the unitarity limit, where a ->+infinity. We call this equation the unitarity Schrodinger equation (USE). The zero-temperature bulk equation of state of this USE is parametrized by the Lee-Yang-Huang low-density expansion and Jastrow calculations at unitarity. With the help of the USE we study the profiles of quantized vortices and vortex-core radius in a uniform Bose gas. We also consider quantized vortices in a Bose gas under cylindrically symmetric harmonic confinement and study their profile and chemical potential using the USE and compare the results with those obtained from the Gross-Pitaevskii-type equations valid in the weak-coupling limit. Finally, the USE is applied to calculate the breathing modes of the confined Bose gas as a function of the scattering length.

Geophysical and Hydrological Evaluation of Two Bog Complexes in a Northern Peatland: Implications for the Distribution of Biogenic Gases at the Basin Scale

Ground penetrating radar (GPR) was used to determine peat basin geometry and the spatial distribution of free-phase biogenic gasses in two separate units of a northern peatland (Central and Southern Unit of Caribou Bog, Maine). The Central Unit is characterized by a deep basin structure (15 m maximum depth) and a raised (eccentric) bog topographic profile (up to 2 m topographic variation). Here numerous regions of electromagnetic (EM) wave scattering are considered diagnostic of the presence of extensive free-phase biogenic gas. In contrast, the Southern Unit is shallower (8 m maximum depth) and has a slightly convex upwards bog profile (less than 1 m topographic variation), and areas of EM wave scattering are notably absent. The biogenic gas zones interpreted from GPR in the Central Unit are associated with: (1) wooded heath vegetation at the surface, (2) open pools at the surface, (3) high water table elevations near the center of the basin, and (4) a region of overpressure (at approximately 5 m depth) immediately below the zone of free-phase gas accumulation. The latter suggests (1) a transient pressure head associated with low hydraulic conductivity resulting from the biogenic gasses themselves or confining layers in the peat that restrict both gas release and groundwater flow and/or (2) overpressure in the peat column as a result of the gas buildup itself. In contrast, the Southern Unit, where zones of EM scattering are absent, is characterized by: (1) predominantly shrub vegetation, (2) a lack of open pools, (3) only minor variations (less than 1 m) in water table elevation throughout the entire unit; and (4) generally upward groundwater flow throughout the basin. The results illustrate the nonuniformity of free-phase biogenic gas distribution at the peat basin scale and provide insights into the processes and controls associated with CH4 and CO2 accumulation in peatlands.

Three-dimensional solitons in coupled atomic-molecular Bose-Einstein condensates

We present a theoretical analysis of three-dimensional (3D) matter-wave solitons and their stability properties in coupled atomic and molecular Bose-Einstein condensates (BECs). The soliton solutions to the mean-field equations are obtained in an approximate analytical form by means of a variational approach. We investigate soliton stability within the parameter space described by the atom-molecule conversion coupling, the atom-atom s-wave scattering, and the bare formation energy of the molecular species. In terms of ordinary optics, this is analogous to the process of sub- or second-harmonic generation in a quadratic nonlinear medium modified by a cubic nonlinearity, together with a phase mismatch term between the fields. While the possibility of formation of multidimensional spatiotemporal solitons in pure quadratic media has been theoretically demonstrated previously, here we extend this prediction to matter-wave interactions in BEC systems where higher-order nonlinear processes due to interparticle collisions are unavoidable and may not be neglected. The stability of the solitons predicted for repulsive atom-atom interactions is investigated by direct numerical simulations of the equations of motion in a full 3D lattice. Our analysis also leads to a possible technique for demonstrating the ground state of the Schrodinger-Newton and related equations that describe Bose-Einstein condensates with nonlocal interparticle forces.

First-principles quantum simulations of dissociation of molecular condensates: Atom correlations in momentum space

We investigate the quantum many-body dynamics of dissociation of a Bose-Einstein condensate of molecular dimers into pairs of constituent bosonic atoms and analyze the resulting atom-atom correlations. The quantum fields of both the molecules and atoms are simulated from first principles in three dimensions using the positive-P representation method. This allows us to provide an exact treatment of the molecular field depletion and s-wave scattering interactions between the particles, as well as to extend the analysis to nonuniform systems. In the simplest uniform case, we find that the major source of atom-atom decorrelation is atom-atom recombination which produces molecules outside the initially occupied condensate mode. The unwanted molecules are formed from dissociated atom pairs with nonopposite momenta. The net effect of this process-which becomes increasingly significant for dissociation durations corresponding to more than about 40% conversion-is to reduce the atom-atom correlations. In addition, for nonuniform systems we find that mode mixing due to inhomogeneity can result in further degradation of the correlation signal. We characterize the correlation strength via the degree of squeezing of particle number-difference fluctuations in a certain momentum-space volume and show that the correlation strength can be increased if the signals are binned into larger counting volumes.

A simple electromagnetic model for understanding the operation of a MIMO system

Recent years have witnessed intense research in multiple input multiple output (MIMO) wireless communications systems, which use multiple element antennas (MEA) for signal transmission and reception. In this paper, we have described a novel electromagnetic model to investigate the effect of mutual coupling, inter-element spacing and array geometry on the capacity of MIMO systems. Simulation results have been presented illustrating the application of the proposed model. The presented model concept stems from a hollow waveguide analogue. Using this model other aspects such as richness of scattering environment (spacing and clustering), the effect of hard versus soft scatterers and pin hole effect can be investigated.