Parabolic Modulation Research Articles

Relative Equivariant Motives and Modules

AbstractWe introduce and study various categories of (equivariant) motives of (versal) flag varieties. We relate these categories with certain categories of parabolic (Demazure) modules. We show that the motivic decomposition type of a versal flag variety depends on the direct sum decomposition type of the parabolic module. To do this we use localization techniques of Kostant and Kumar in the context of generalized oriented cohomology as well as the Rost nilpotence principle for algebraic cobordism and its generic version. As an application, we obtain new proofs and examples of indecomposable Chow motives of versal flag varieties.

Spatiotemporal vector and scalar solitons of the coupled nonlinear Schrödinger equation with spatially modulated cubic–quintic–septimal nonlinearities

The spatially modulated cubic–quintic–septimal nonlinearities and transverse modulation are introduced to study the impact on a (3 + 1)-dimensional N-coupled nonlinear Schrodinger equation. As an example, we derive two-component spatiotemporal localized mode solutions including vector multipole and vortex solitons and scalar soliton. The values of the modulation depth q and the topological charge k adjust the construction of vector and scalar solitons. If their values are both chosen as 0, scalar soliton is exhibited; if the value of the modulation depth q becomes 0 and 1, vector multipole and vortex solitons can be displayed, respectively. In two kinds of cubic–quintic–septimal nonlinear media with the transverse parabolic modulation and without transverse modulation, characteristics of vector multipole and vortex solitons and scalar soliton are discussed.

Consideration of the Impact of the Environmental Conditions when Designing Heat-Receiving Systems of the Solar Cylindrical Parabolic Modules

The aerohydrodynamic and heat exchange characteristics in the cylindrical heat receiver of a solar cylindrical parabolic concentrating module are investigated. The mathematical model is based on the Navier- Stokes equation system for a laminar flow in a channel. The model is implemented using the control volume method. The created computer algorithm allows carrying out parametric studies and revealing the most rational geometric, dynamic, and power parameters of the process. The proposed model describes the general physical outlines of the heat exchange in a cylindrical heat receiver which allows estimating the influence of the environment—wind velocity, ambient temperature, etc.—on it.

Parabolic-Modulated Sliding-Mode Voltage Control of a Buck Converter

Conventional hysteresis-modulation-based sliding-mode (SM) controller exhibits a varying switching frequency. Existing SM controllers for achieving constant-switching-frequency operation often have complicated structures and/or are less straightforward to design to meet different steady state, transient, and loading requirements. In this paper, a new direct SM voltage controller based on parabolic modulation (PM) is proposed and applied to a buck converter. The objective is to achieve constant-switching-frequency operation of a switching converter with simple control structure and good operating performance. Both theoretical study and experimental work on a buck converter show that the proposed PM-based SM control can achieve 1) constant switching frequency in the continuous-conduction mode (CCM) and quasi-constant switching frequency in the discontinuous-conduction mode (DCM) of operation, 2) inherent input-disturbances rejection and superior reference tracking performance, and 3) seamless mode transition between CCM and DCM.

Construction method and optical characterization of parabolic solar modules for concentration systems

A process to build modular solar reflectors by using plane mirrors and a sandwich structure has been developed. We applied this process to manufacture parabolic modules that can be assembled in a parabolic dish of 5m in diameter with the focus at 2.5m. This paper discusses the evaluation of the light collection performances of a single parabolic module. The reflectance of the mirror material was characterized by means of a UV–Vis spectrophotometer, in the 250–1200nm wavelength range, and of a pyrheliometer, with respect to a direct solar spectrum. The illumination profile of a module mounted on a sun-tracking system was tested by power density measurements in and out of the focal plane, and spots were compared with a theoretical one. In order to evaluate the high-flux solar energy arriving at the focus of a module, a flat-plate calorimeter was built. The study was carried out by measuring the energy absorbed by the water flow and the external losses due to convection. Based on an energy balance, the intercept factor and the overall optical efficiency of the collector were estimated.

Electro-optic time lens with an extended time aperture

We propose what we believe to be a new approach to correct the residual aberrations of time lenses implemented through electro-optic sinusoidal phase modulation. The method is based on a single modulator driven with various harmonic channels coming from the same clock signal. Proper weighting of the amplitude and phase of the channels allows us to achieve nearly perfect parabolic phase modulation over a fraction of the clock period. We show numerically that our proposal only requires three harmonics of the clock frequency to achieve truly parabolic modulation over a time window that extends across 70% of the period. We illustrate the benefits of this aberration-free scheme in a pulse compression scenario and compare its performance with previous conventional Fourier optimization techniques. Our study offers simple guidelines to achieve indeed quadratic phase modulation in situations where electro-optic phase modulation in lithium niobate is required, such as integrated frequency comb technology or high-speed optical pulse shaping.

Comparison of Parabolic and Gaussian Lateral Cosine Modulations in Ultrasound Imaging, Displacement Vector Measurement, and Elasticity Measurement

Previously, we proposed to set ultrasound (US) beam-forming parameters in order to realize the required point spread function (PSF) on the basis of optimization theory. In this report, for high quality-lateral cosine modulation (LCM) US imaging and measurements of accurate displacement vector and elasticity (i.e., strain tensor, shear modulus), after briefly reviewing our trials that broke away from the use of the Fraunhofer approximation to determine the apodization function, images and measurements obtained for an agar phantom are shown. In this study, the previously reported lateral parabolic modulation (PAM) and lateral Gaussian envelope cosine modulation (LGECM) are carried out. Comparisons of the spatial resolutions of the US images obtained and the measurement accuracies of the displacement vectors and elasticity measurements obtained using our previously developed multidimensional autocorrelation and Doppler methods (i.e., MAM and MDM) are also made. The development of next-generation US imaging systems has already begun.

Standard bases for affine parabolic modules and nonsymmetric Macdonald polynomials

We establish a connection between (degenerate) nonsymmetric Macdonald polynomials and standard bases and dual standard bases of maximal parabolic modules of affine Hecke algebras. Along the way we prove a (weak) polynomiality result for coefficients of symmetric and nonsymmetric Macdonald polynomials.

Charge polarization effects and hole spectra characteristics in AlxGa1−xN/GaN superlattices

We study the effects of charge polarization on the extended physical properties of superlattices, such as transmission coefficients and valence band structure. We consider both linear and parabolic modulation of the band edge. Based on the theory of finite periodic systems, analytic expressions and high precision calculations of the relevant physical quantities for n-cell systems are obtained. Well-known features of these systems are identified. Besides the well-known energy band structure, we have also the field band structure, with interesting characteristics. Wider field gaps at stronger internal electric fields and higher density of field bands for larger layer widths are some of these characteristics. Well defined level density asymmetries identify the minibands induced by charge polarization or the so-called quantum confining Stark effect. We present the n-cell transmission amplitudes, transmission coefficients and miniband structures for different values of the relevant parameters.

On the Hermitian-Einstein Tensor of a Complex Homogenous Vector Bundle

AbstractWe prove that any holomorphic, homogenous vector bundle admits a homogenous minimal metric—a metric for which the Hermitian-Einstein tensor is diagonal in a suitable sense. The concept of minimality depends on the choice of the Jordan-Holder filtration of the corresponding parabolic module. We show that the set of all admissible Hermitian-Einstein tensors of certain class of minimal metrics is a convex subset of the euclidean space. As an application, we obtain an algebraic criterion for semistability of homogenous holomorphic vector bundles.