Aliasing and oblique dual pair designs for consistent sampling

In this paper we study some aspects of oblique duality between finite sequences of vectors \cF and \cG lying in finite dimensional subspaces \cW and \cV, respectively. We compute the possible eigenvalue lists of the frame operators of oblique duals to \cF lying in \cV; we then compute the spectral and geometrical structure of minimizers of convex potentials among oblique duals for \cF under some restrictions. We obtain a complete quantitative analysis of the impact that the relative geometry between the subspaces \cV and \cW has in oblique duality. We apply this analysis to compute those rigid rotations $U$ for \cW such that the canonical oblique dual of U\cdot \cF minimize every convex potential; we also introduce a notion of aliasing for oblique dual pairs and compute those rigid rotations $U$ for \cW such that the canonical oblique dual pair associated to U\cdot \cF minimize the aliasing. We point out that these two last problems are intrinsic to the theory of oblique duality.Comment: 23 page

Constraints on the NMSSM from the oblique parameters

Electroweak precision measurements, encoded in the oblique parameters, give strong constraints on physics beyond the Standard Model. The oblique parameters S, T, U (V, W, X) are calculated in the next-to-minimal supersymmetric model (NMSSM). We outline the calculation of the oblique parameters in terms of one-loop gauge-boson selfenergies and find sensitive restrictions for the NMSSM parameter space.Comment: 11 pages, 7 figures, 1 tabl

Oblique Matching Pursuit

A method for selecting a suitable subspace for discriminating signal components through an oblique projection is proposed. The selection criterion is based on the consistency principle introduced by M. Unser and A. Aldroubi and extended by Y. Elder. An effective implementation of this principle for the purpose of subspace selection is achieved by updating of the dual vectors yielding the corresponding oblique projector.Comment: Last version- as it will appear in IEEE SPL. IEEE Signal Processing Letters (in press

Experiments on single oblique laminar-instability waves in a boundary layer: Introduction, growth, and transition

The laminar-turbulent transition in an incompressible flat-plate boundary layer was studied experimentally by using a spanwise array of computer-controlled surface heating elements to generate small disturbances. Oblique Tollmien-Schlichting waves were successfully introduced, and their downstream development into the intermittent region was studied using flush-mounted hot-film wall-shear sensors and dye flow visualization. Comparative studies of the development of single oblique waves were made for various wave angles, frequencies, and amplitudes. As these single oblique waves grew and began to break down, higher harmonics and subharmonics appeared in the wall shear. The amplitude of the subharmonic component decreased rapidly with increasing oblique-wave angle, so that a 10 degrees oblique wave had a subharmonic amplitude an order of magnitude below that for a two-dimensional (2-D) wave. Thus, the nonlinear mechanism that produces the subharmonic is affected by the symmetry of the primary wave. Intermittency measurements, carried out farther downstream, show that a 2-D wave is most effective in moving the transition point upstream, for a given power input

An investigation of aeroelastic phenomena associated with an oblique winged aircraft

Oblique wing aeroelasticity studies are reviewed. The static aeroelastic stability characteristics of oblique wing aircraft, lateral trim requirements for 1-g flight, and the dynamic aeroelastic stability behavior of oblique winged aircraft, primarily flutter, are among the topics studied. The similarities and differences between oblique winged aircraft and conventional, bilaterally symmetric, swept wing aircraft are emphasized

Resonant Interactions Between Protons and Oblique Alfv\'en/Ion-Cyclotron Waves

Resonant interactions between ions and Alfv\'en/ion-cyclotron (A/IC) waves may play an important role in the heating and acceleration of the fast solar wind. Although such interactions have been studied extensively for "parallel" waves, whose wave vectors ${\bf k}$ are aligned with the background magnetic field ${\bf B}_0$, much less is known about interactions between ions and oblique A/IC waves, for which the angle $\theta$ between ${\bf k}$ and ${\bf B}_0$ is nonzero. In this paper, we present new numerical results on resonant cyclotron interactions between protons and oblique A/IC waves in collisionless low-beta plasmas such as the solar corona. We find that if some mechanism generates oblique high-frequency A/IC waves, then these waves initially modify the proton distribution function in such a way that it becomes unstable to parallel waves. Parallel waves are then amplified to the point that they dominate the wave energy at the large parallel wave numbers at which the waves resonate with the particles. Pitch-angle scattering by these waves then causes the plasma to evolve towards a state in which the proton distribution is constant along a particular set of nested "scattering surfaces" in velocity space, whose shapes have been calculated previously. As the distribution function approaches this state, the imaginary part of the frequency of parallel A/IC waves drops continuously towards zero, but oblique waves continue to undergo cyclotron damping while simultaneously causing protons to diffuse across these kinetic shells to higher energies. We conclude that oblique A/IC waves can be more effective at heating protons than parallel A/IC waves, because for oblique waves the plasma does not relax towards a state in which proton damping of oblique A/IC waves ceases

Klein tunneling through an oblique barrier in graphene ribbons

We study a transmission coefficient of graphene nanoribbons with a top gate which acts as an oblique barrier. Using a Green function method based on the Dirac-like equation, scattering among transverse modes due to the oblique barrier is taken into account numerically. In contrast to the 2-dimensional graphene sheet, we find that the pattern of transmission in graphene ribbons depends strongly on the electronic structure in the region of the barrier. Consequently, irregular structures in the transmission coefficient are predicted while perfect transmission is still calculated in the case of metallic graphene independently of angle and length of the oblique barrier

Electroweak Effective Operators and Higgs Physics

We derive bounds from oblique parameters on the dimension-6 operators of an effective field theory of electroweak gauge bosons and the Higgs doublet. The loop- induced contributions to the S, T, and U oblique parameters are sensitive to these contributions and we pay particular attention to the role of renormalization when computing loop corrections in the effective theory. Limits on the coefficients of the effective theory from loop contributions to oblique parameters yield complementary information to direct Higgs production measurements.Comment: 33 pages, 6 figures; additional scalar operator included and references adde