On mathematical and physical principles of transformations of the coherent radar backscatter matrix

The congruential rule advanced by Graves for polarization basis transformation of the radar backscatter matrix is now often misinterpreted as an example of consimilarity transformation. However, consimilarity transformations imply a physically unrealistic antilinear time-reversal operation. This is just one of the approaches found in literature to the description of transformations where the role of conjugation has been misunderstood. In this paper, the different approaches are examined in particular in respect to the role of conjugation. In order to justify and correctly derive the congruential rule for polarization basis transformation and properly place the role of conjugation, the origin of the problem is traced back to the derivation of the antenna height from the transmitted field. In fact, careful consideration of the role played by the Green’s dyadic operator relating the antenna height to the transmitted field shows that, under general unitary basis transformation, it is not justified to assume a scalar relationship between them. Invariance of the voltage equation shows that antenna states and wave states must in fact lie in dual spaces, a distinction not captured in conventional Jones vector formalism. Introducing spinor formalism, and with the use of an alternate spin frame for the transmitted field a mathematically consistent implementation of the directional wave formalism is obtained. Examples are given comparing the wider generality of the congruential rule in both active and passive transformations with the consimilarity rule.

On the nonminimal vector coupling in the Duffin-Kemmer-Petiau theory and the confinement of massive bosons by a linear potential

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Scattering of positronium by H, He, Ne, and Ar

The low-energy scattering of the ortho-positronium (Ps) by H, He, Ne, and Ar atoms has been investigated in the coupled-channel framework by using a recently proposed time-reversal symmetric non-local electron-exchange model potential with a single parameter C. For H and He, we use a three-Ps-state coupled-channel model and, for Ar and Ne, we use a static-exchange model. The sensitivity of the results is studied with respect to the parameter C. Present low-energy cross-sections for He, Ne and Ar are in good agreement with experiment. (C) 2000 Elsevier B.V. B.V. All rights reserved.

Resonances in positronium-rubidium and positronium-cesium scattering

Scattering of ortho positronium (Ps) by cesium and rubidium atoms has been investigated employing a three-Ps-state coupled-channel model with Ps(1s,2s,2p) states using a time-reversal-symmetric regularized electron-exchange model potential. We find a narrow S-wave singlet resonance at 5.057 eV of width 0.003 eV in the Ps-Rb system and at 5.067 eV of width 0.003 eV in the Ps-Cs system. Singlet P-wave resonances in both systems are found at 5.3 eV of width 0.4 eV. Singlet D-wave structures are found at 5.4 eV in both systems. The pronounced P- and D-wave resonances in these systems lead to easily detectable local minima in the low-energy elastic cross sections. We also report results for elastic and Ps-excitation cross sections for Pa scattering by Rb and Cs. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Positronium atom scattering by H-2 in a coupled-channel framework

The scattering of ortho-positronium (Ps) by H-2 has been investigated using a three-Ps-state (Ps(1s,2s, 2p)H-2(X (1)Sigma(g)(+))) coupled-channel model and using the Born approximation for higher excitations and ionization of Ps and B (1)Sigma(u)(+) and b (3)Sigma(u)(+) excitations of H-2. We employ a recently proposed time-reversal-symmetric non-local electron-exchange model potential. We present a calculational scheme for solving the body-frame fixed-nuclei coupled-channel scattering equations for Ps-H-2, which simplifies the numerical solution technique considerably. Ps ionization is found to have the leading contribution to target-elastic and all target-inelastic processes. The total cross sections at low and medium energies are in good agreement with experiment.

Differential and partial cross sections of elastic and inelastic positronium-helium-atom scattering

Scattering of positronium (Ps) by a helium atom has been investigated in a three-Ps-state coupled-channel model including Ps(1s,2s,2p) states using a recently proposed time-reversal-symmetric regularized electron-exchange model potential. Specifically, we report results of differential cross sections for elastic scattering and target-elastic Ps excitations. We also present results for total and different partial cross sections and compare them with experiment and other calculations.

S-, P- and D-wave resonances in positronium-sodium and positronium-potassium scattering

Scattering of positronium (Ps) by sodium and potassium atoms has been investigated employing a three-Ps-state coupled-channel model with Ps(ls,2s,2p) states using a time-reversal-symmetric regularized electron-exchange model potential fitted to reproduce accurate theoretical results for PsNa and PsK binding energies. We find a narrow S-wave singlet resonance at 4.58 eV of width 0.002 eV in the Ps-Na system and at 4.77 eV of width 0.003 eV in the Ps-K system. Singlet P-wave resonances in both systems are found at 5.07 eV of width 0.3 eV. Singlet D-wave structures are found at 5.3 eV in both systems. We also report results for elastic and Ps-excitation cross sections for Ps scattering by Na and K.

Generalized point interactions in one-dimensional quantum mechanics

There is a four-parameter family of point interactions in one-dimensional quantum mechanics. They represent all possible self-adjoint extensions of the kinetic energy operator. If time-reversal invariance is imposed, the number of parameters is reduced to three. One of these point interactions is the familiar delta function potential but the other generalized ones do not seem to be widely known. We present a pedestrian approach to this subject and comment on a recent controversy in the literature concerning the so-called delta' interaction. We emphasize that there is little resemblance between the delta' interaction and what its name suggests.

Sobre interações escalares e vetoriais na teoria de Duffin-Kemmer-Petiau

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Quantization of unstable linear scalar fields in static spacetimes

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Differential cross sections for elastic and inelastic positronium-hydrogen-atom scattering

A time reversal symmetric regularized electron exchange model was used to elastic scattering, target elastic Ps excitations and target inelastic excitation of hydrogen in a five state coupled model. A singlet Ps-H-S-wave resonance at 4.01 eV of width 0.15 eV and a P-wave resonance at 5.08 eV of width 0.004 eV were obtained using this model. The effect on the convergence of the coupled-channel scheme due to the inclusion of the excited Ps and H states was also analyzed.

Construção exata de sólitons de Hopf

Pós-graduação em Física - IFT

Constrained least square pre-distortion scheme for multiuser ultra-wideband

The study proposes a constrained least square (CLS) pre-distortion scheme for multiple-input single-output (MISO) multiple access ultra-wideband (UWB) systems. In such a scheme, a simple objective function is defined, which can be efficiently solved by a gradient-based algorithm. For the performance evaluation, scenarios CM1 and CM3 of the IEEE 802.15.3a channel model are considered. Results show that the CLS algorithm has a fast convergence and a good trade-off between intersymbol interference (ISI) and multiple access interference (MAI) reduction and signal-to-noise ratio (SNR) preservation, performing better than time-reversal (TR) pre-distortion.

Comparison of multiple-input single-output single-user ultra-wideband systems with pre-distortion

This paper presents a performance analysis of a baseband multiple-input single-output ultra-wideband system over scenarios CM1 and CM3 of the IEEE 802.15.3a channel model, incorporating four different schemes of pre-distortion: time reversal, zero-forcing pre-equaliser, constrained least squares pre-equaliser, and minimum mean square error pre-equaliser. For the third case, a simple solution based on the steepest-descent (gradient) algorithm is adopted and compared with theoretical results. The channel estimations at the transmitter are assumed to be truncated and noisy. Results show that the constrained least squares algorithm has a good trade-off between intersymbol interference reduction and signal-to-noise ratio preservation, providing a performance comparable to the minimum mean square error method but with lower computational complexity. Copyright (C) 2011 John Wiley & Sons, Ltd.

Behaviour and applications of elastic waves in structures and metamaterials

The present thesis focuses on elastic waves behaviour in ordinary structures as well as in acousto-elastic metamaterials via numerical and experimental applications. After a brief introduction on the behaviour of elastic guided waves in the framework of non-destructive evaluation (NDE) and structural health monitoring (SHM) and on the study of elastic waves propagation in acousto-elastic metamaterials, dispersion curves for thin-walled beams and arbitrary cross-section waveguides are extracted via Semi-Analytical Finite Element (SAFE) methods. Thus, a novel strategy tackling signal dispersion to locate defects in irregular waveguides is proposed and numerically validated. Finally, a time-reversal and laser-vibrometry based procedure for impact location is numerically and experimentally tested. In the second part, an introduction and a brief review of the basic definitions necessary to describe acousto-elastic metamaterials is provided. A numerical approach to extract dispersion properties in such structures is highlighted. Afterwards, solid-solid and solid-fluid phononic systems are discussed via numerical applications. In particular, band structures and transmission power spectra are predicted for 1P-2D, 2P-2D and 2P-3D phononic systems. In addition, attenuation bands in the ultrasonic as well as in the sonic frequency regimes are experimentally investigated. In the experimental validation, PZTs in a pitch-catch configuration and laser vibrometric measurements are performed on a PVC phononic plate in the ultrasonic frequency range and sound insulation index is computed for a 2P-3D phononic barrier in the sonic frequency range. In both cases the numerical-experimental results comparison confirms the existence of the numerical predicted band-gaps. Finally, the feasibility of an innovative passive isolation strategy based on giant elastic metamaterials is numerically proved to be practical for civil structures. In particular, attenuation of seismic waves is demonstrated via finite elements analyses. Further, a parametric study shows that depending on the soil properties, such an earthquake-proof barrier could lead to significant reduction of the superstructure displacement.