Compensation for higher order mode coupling between inclined coupling slots and radiating slots in planar slotted waveguide arrays

Summary form only given. Geometric simplicity, efficiency and polarization purity make slot antenna arrays ideal solutions for many radar, communications and navigation applications, especially when high power, light weight and limited scan volume are priorities. Resonant arrays of longitudinal slots have a slot spacing of one-half guide wavelength at the design frequency, so that the slots are located at the standing wave peaks. Planar arrays are implemented using a number of rectangular waveguides (branch line guides), arranged side-by-side, while waveguides main lines located behind and at right angles to the branch lines excite the radiating waveguides via centered-inclined coupling slots. Planar slotted waveguide arrays radiate broadside beams and all radiators are designed to be in phase.

Application of higher-order spectra for automated grading of diabetic maculopathy

Diabetic macular edema (DME) is one of the most common causes of visual loss among diabetes mellitus patients. Early detection and successive treatment may improve the visual acuity. DME is mainly graded into non-clinically significant macular edema (NCSME) and clinically significant macular edema according to the location of hard exudates in the macula region. DME can be identified by manual examination of fundus images. It is laborious and resource intensive. Hence, in this work, automated grading of DME is proposed using higher-order spectra (HOS) of Radon transform projections of the fundus images. We have used third-order cumulants and bispectrum magnitude, in this work, as features, and compared their performance. They can capture subtle changes in the fundus image. Spectral regression discriminant analysis (SRDA) reduces feature dimension, and minimum redundancy maximum relevance method is used to rank the significant SRDA components. Ranked features are fed to various supervised classifiers, viz. Naive Bayes, AdaBoost and support vector machine, to discriminate No DME, NCSME and clinically significant macular edema classes. The performance of our system is evaluated using the publicly available MESSIDOR dataset (300 images) and also verified with a local dataset (300 images). Our results show that HOS cumulants and bispectrum magnitude obtained an average accuracy of 95.56 and 94.39 % for MESSIDOR dataset and 95.93 and 93.33 % for local dataset, respectively.

Nonlinear analysis for the pre- and post-yield behaviour of a hybrid structure by a higher-order element with the refined plastic hinge approach

Efficient and accurate geometric and material nonlinear analysis of the structures under ultimate loads is a backbone to the success of integrated analysis and design, performance-based design approach and progressive collapse analysis. This paper presents the advanced computational technique of a higher-order element formulation with the refined plastic hinge approach which can evaluate the concrete and steel-concrete structure prone to the nonlinear material effects (i.e. gradual yielding, full plasticity, strain-hardening effect when subjected to the interaction between axial and bending actions, and load redistribution) as well as the nonlinear geometric effects (i.e. second-order P-d effect and P-D effect, its associate strength and stiffness degradation). Further, this paper also presents the cross-section analysis useful to formulate the refined plastic hinge approach.

Shock propagation in gas dynamics: explicit form of higher order compatibility conditions

With the use of tensor analysis and the method of singular surfaces, an infinite system of equations can be derived to study the propagation of curved shocks of arbitrary strength in gas dynamics. The first three of these have been explicitly given here. This system is further reduced to one involving scalars only. The choice of dependent variables in the infinite system is quite important, it leads to coefficients free from singularities for all values of the shock strength.

Higher-Order Nonlinearity In Accretion Disks: Quasi-Periodic Oscillations Of Black Hole And Neutron Star Sources And Their Spin

We propose a unified model to explain Quasi-Periodic Oscillation (QPO), particularly of high frequency, observed from black hole and neutron star systems globally. We consider accreting systems to be damped harmonic oscillators exhibiting epicyclic oscillations with higher-order nonlinear resonance to explain QPO. The resonance is expected to be driven by the disturbance from the compact object at its spin frequency. The model explains various properties parallelly for both types of the compact object. It describes QPOs successfully for ten different compact sources. Based on this, we predict the spin frequency of the neutron star Sco X-1 and specific angular momentum of black holes GRO J1655–40, XTE J1550–564, H1743–322, and GRS 1915+105.

Unsteady laminar compressible stagnation-point boundary-layer flow over a three-dimensional body: Higher order effects

The unsteady laminar compressible three-dimensional stagnation-point boundary-layer flow with variable properties has been studied when the velocity of the incident stream, mass transfer and wall temperature vary arbitrarily with time. The second-order unsteady boundary-layer equations for all the effects have been derived by using the method of matched asymptotic expansions. Both nodal and saddle point flows as well as cold and hot wall cases have been considered. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. Computations have been carried out for an accelerating stream, a decelerating stream and a fluctuating stream. The results indicate that the unsteady free stream velocity distributions, the nature of the stagnation point, the mass transfer, the wall temperature and the variation of the density-viscosity product across the boundary significantly affect the skin friction and heat transfer. The variation of the wall temperature with time strongly affects the heat transfer whereas its effect is comparatively less on skin friction. Suction increases the skin friction and heat transfer but injection does the opposite. The skin friction in the x direction due to the combined effects of first- and second-order boundary layers is less than the skin-friction in the x direction due to the first-order boundary layers for all the parameters. The overall skin friction in the z direction and heat transfer are more or less than the first-order boundary layers depending upon the values of the various parameters.

Non-Abelian monopoles break color. II. Field theory and quantum mechanics

Many grand unified theories (GUT's) predict non-Abelian monopoles which are sources of non-Abelian (and Abelian) magnetic flux. In the preceding paper, we discussed in detail the topological obstructions to the global implementation of the action of the "unbroken symmetry group" H on a classical test particle in the field of such a monopole. In this paper, the existence of similar topological obstructions to the definition of H action on the fields in such a monopole sector, as well as on the states of a quantum-mechanical test particle in the presence of such fields, are shown in detail. Some subgroups of H which can be globally realized as groups of automorphisms are identified. We also discuss the application of our analysis to the SU(5) GUT and show in particular that the non-Abelian monopoles of that theory break color and electroweak symmetries.

The Spin-Statistics Relation and Noncommutative Quantum Field Theory

The efforts of combining quantum theory with general relativity have been great and marked by several successes. One field where progress has lately been made is the study of noncommutative quantum field theories that arise as a low energy limit in certain string theories. The idea of noncommutativity comes naturally when combining these two extremes and has profound implications on results widely accepted in traditional, commutative, theories. In this work I review the status of one of the most important connections in physics, the spin-statistics relation. The relation is deeply ingrained in our reality in that it gives us the structure for the periodic table and is of crucial importance for the stability of all matter. The dramatic effects of noncommutativity of space-time coordinates, mainly the loss of Lorentz invariance, call the spin-statistics relation into question. The spin-statistics theorem is first presented in its traditional setting, giving a clarifying proof starting from minimal requirements. Next the notion of noncommutativity is introduced and its implications studied. The discussion is essentially based on twisted Poincaré symmetry, the space-time symmetry of noncommutative quantum field theory. The controversial issue of microcausality in noncommutative quantum field theory is settled by showing for the first time that the light wedge microcausality condition is compatible with the twisted Poincaré symmetry. The spin-statistics relation is considered both from the point of view of braided statistics, and in the traditional Lagrangian formulation of Pauli, with the conclusion that Pauli's age-old theorem stands even this test so dramatic for the whole structure of space-time.

Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.

Induced higher-order aberrations after laser in situ keratomileusis (LASIK) performed with wavefront-guided IntraLase femtosecond laser in moderate to high astigmatism

Background Wavefront-guided Laser-assisted in situ keratomileusis (LASIK) is a widespread and effective surgical treatment for myopia and astigmatic correction but whether it induces higher-order aberrations remains controversial. The study was designed to evaluate the changes in higher-order aberrations after wavefront-guided ablation with IntraLase femtosecond laser in moderate to high astigmatism. Methods Twenty-three eyes of 15 patients with moderate to high astigmatism (mean cylinder, −3.22 ± 0.59 dioptres) aged between 19 and 35 years (mean age, 25.6 ± 4.9 years) were included in this prospective study. Subjects with cylinder ≥ 1.5 and ≤2.75 D were classified as moderate astigmatism while high astigmatism was ≥3.00 D. All patients underwent a femtosecond laser–enabled (150-kHz IntraLase iFS; Abbott Medical Optics Inc) wavefront-guided ablation. Uncorrected (UDVA), corrected (CDVA) distance visual acuity in logMAR, keratometry, central corneal thickness (CCT) and higher-order aberrations (HOAs) over a 6 mm pupil, were assessed before and 6 months, postoperatively. The relationship between postoperative change in HOA and preoperative mean spherical equivalent refraction, mean astigmatism, and postoperative CCT were tested. Results At the last follow-up, the mean UDVA was increased (P < 0.0001) but CDVA remained unchanged (P = 0.48) and no eyes lost ≥2 lines of CDVA. Mean spherical equivalent refraction was reduced (P < 0.0001) and was within ±0.50 D range in 61 % of eyes. The average corneal curvature was flatter by 4 D and CCT was reduced by 83 μm (P < 0.0001, for all), postoperatively. Coma aberrations remained unchanged (P = 0.07) while the change in trefoil (P = 0.047) postoperatively, was not clinically significant. The 4th order HOAs (spherical aberration and secondary astigmatism) and the HOA root mean square (RMS) increased from −0.18 ± 0.07 μm, 0.04 ± 0.03 μm and 0.47 ± 0.11 μm, preoperatively, to 0.33 ± 0.19 μm (P = 0.004), 0.21 ± 0.09 μm (P < 0.0001) and 0.77 ± 0.27 μm (P < 0.0001), six months postoperatively. The change in spherical aberration after the procedure increased with an increase in the degree of preoperative myopia. Conclusions Wavefront-guided IntraLASIK offers a safe and effective option for vision and visual function improvement in astigmatism. Although, reduction of HOA is possible in a few eyes, spherical-like aberrations are increased in majority of the treated eyes.

Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.

Noncommutative Quantum Field Theory : Problem of Time and Some Applications

In this thesis the current status and some open problems of noncommutative quantum field theory are reviewed. The introduction aims to put these theories in their proper context as a part of the larger program to model the properties of quantized space-time. Throughout the thesis, special focus is put on the role of noncommutative time and how its nonlocal nature presents us with problems. Applications in scalar field theories as well as in gauge field theories are presented. The infinite nonlocality of space-time introduced by the noncommutative coordinate operators leads to interesting structure and new physics. High energy and low energy scales are mixed, causality and unitarity are threatened and in gauge theory the tools for model building are drastically reduced. As a case study in noncommutative gauge theory, the Dirac quantization condition of magnetic monopoles is examined with the conclusion that, at least in perturbation theory, it cannot be fulfilled in noncommutative space.

Higher twist and higher order contributions to the pion electromagnetic form factor

The O(m(pi)4/(m(u) + (d))2Q2) and O(alpha(S)2) corrections to the leading term of the perturbative QCD calculation of the pion electromagnetic form factor are examined numerically. Both sets of terms provide significant corrections for values of Q2 between 1 and 15 GeV2/c2.

FIR system identification based on subspaces of a higher order cumulant matrix

A new linear algebraic approach for identification of a nonminimum phase FIR system of known order using only higher order (>2) cumulants of the output process is proposed. It is first shown that a matrix formed from a set of cumulants of arbitrary order can be expressed as a product of structured matrices. The subspaces of this matrix are then used to obtain the parameters of the FIR system using a set of linear equations. Theoretical analysis and numerical simulation studies are presented to characterize the performance of the proposed methods.