Higher-order Components Research Articles

FEM models and Fourier decomposition of three thick septa

The CEBAF recirculating linear accelerator uses 26 septa: 8 thin, 17 thick and one Lamberston. We report here on detailed FEM models of one thick current-sheet septum, the Lambertson, and a new thick-septum concept which contains features of both. The last has higher-order field components within a factor of two of the current-sheet septum and much lower current density in the conductor were it used as a “drop-in” replacement in CEBAF. There are accelerator layouts in which the new concept is superior to the current sheet septum in both harmonic content and current density.

Practical open-concentric spherical microphone array design

The problem of higher order sound field capture is considered. First-order microphone arrays, such as tetrahedral A-format designs, are commonplace, while interest remains in the increased spatial resolution delivered by higher order arrays. Such arrays typically consist of pressure microphones mounted on a solid spherical baffle, with which higher-order spatial components are estimated algorithmically. This produces a design trade-off, with small arrays being preferred for spatial aliasing performance and large arrays being preferred for reduced amplification of microphone capsule noise at low frequencies. A practical open sphere design is proposed that contains microphones mounted at multiple radii to fulfill both criteria. Coupled with the use of cardioid microphones, such an array captures higher order soundfields over a wider audio bandwidth than baffled spherical designs of fixed radius.

Influence of magnetization pattern in three-phase permanent magnet synchronous machines

This paper investigates the influence of different magnetization patterns in the performance of three-phase permanent magnet synchronous motors (PMSMs). Three magnetization patterns widely used in surface-mounted PMSMs are radial magnetization, parallel magnetization and Halbach magnetization. In this paper, these magnetization patterns are applied to 9-slot/10-pole and 12-slot/10-pole surface-mounted PMSMs. The electromagnetic characteristics and performance of the motors such as air gap flux density distributions, phase back-emf, cogging torque, unbalance magnetic force and output torque are intensively evaluated in 2D finite element method. Important findings indicate that PMSMs with ideal Halbach magnetization exhibit almost zero cogging torque and sinusoidal phase back-emf waveform. Parallel magnetization and radial magnetization yield more trapezoidal phase back-emf waveform which results in higher torque ripples. One way to minimize the torque ripples is by reducing the higher-order harmonic components in the phase back-emf waveform which can be achieved with the best value of magnet pole arc. Additionally, a potential cost saving can be realized since the motor has smaller magnet volume as being demonstrated in the case of 9-slot/10-pole, three-phase surface-mounted PMSM in this paper.

The Revolution Revolution: Magnetic Morphology Driven Spin-down∗

Abstract Observations of young open clusters (OCs) show a bimodal distribution of rotation periods that has been difficult to explain with existing stellar spin-down models. Detailed magnetohydrodynamic (MHD) stellar wind simulations have demonstrated that surface magnetic field morphology has a strong influence on wind-driven angular momentum loss. Observations suggest that faster rotating stars store a larger fraction of their magnetic flux in higher-order multipolar components of the magnetic field. In this work, we present an entirely predictive new model for stellar spin-down that accounts for the stellar surface magnetic field configuration. We show how a magnetic complexity that evolves from complex toward simple configurations as a star spins down can explain the salient features of stellar rotation evolution, including the bimodal distribution of both slow and fast rotators seen in young OCs.

A Coarse-to-Fine Autofocus Approach for Very High-Resolution Airborne Stripmap SAR Imagery

An autofocus operation is an indispensable procedure to obtain well-focused images for synthetic-aperture radar (SAR) systems without precise navigation devices. Three challenges have been faced in the very high-resolution (VHR) airborne SAR autofocus due to the long cumulative time: the varying along-track velocity, the residual range cell migration (RCM), and the range-dependent phase errors with higher order components. When it comes to the stripmap mode, the autofocus becomes more complicated, since the scenario with a few strong scatterers is more likely to be encountered with a moving beam. Combining the merits of parametric and nonparametric autofocus algorithms, a robust motion error estimation method is proposed in this paper. First, we perform a stripmap multiaperture mapdrift autofocus operation to extract the along-track velocity and the most range-invariant errors, removing the residual RCM at a subaperture scale. Second, one referential center block is selected to retrieve the residual range-invariant error, which can eliminate the residual RCM globally in the range dimension. With a global high-quality input, the residual range-variant phase errors can be retrieved precisely utilizing a center-to-edge local maximum-likelihood weighted phase gradient autofocus kernel at last. Experiments on real VHR airborne stripmap SAR data are performed to demonstrate the robustness of the proposed method.

Characterizing the Effects of MR Image Quality Metrics on Intrinsic Connectivity Brain Networks: A Multivariate Approach.

Motion-induced artifact detection has become a fixture in the assessment of functional magnetic resonance imaging (fMRI) quality control. However, the effects of other MR image quality (IQ) metrics on intrinsic connectivity brain networks are largely unexplored. Accordingly, we report herein the initial assessment of the effects of a comprehensive list of IQ metrics on resting state networks using a multivariate analysis of covariance (MANCOVA) approach based on high-order spatial independent component analysis (ICA). Three categories of MR IQ metrics were considered: (1) metrics for artifacts including the AFNI outlier ratio and quality index, framewise displacement, and ghost to signal ratio, (2) metrics for the temporal quality of MRI data including the temporal framewise change in global BOLD signals (DVARS), global correlation of time-series, and temporal signal to noise ratio, (3) metrics for the structural quality of MRI data including the entropy focus criterion, foreground-background energy ratio, full-width half maximum smoothness, and static signal to noise ratio. After FDR-correction for multiple comparisons, results showed significant effects of the static and temporal signal to noise ratios on the spatial map intensities of the basal ganglia, default-mode and cerebellar networks. AFNI outlier ratio, framewise displacement and DVARS exhibited significant effects on the BOLD power spectra of sensorimotor networks. The global correlation of time-series displayed wide-spread modulation of the spectral power in most networks. Further investigations of the effect of IQ metrics on the characteristics of intrinsic connectivity brain networks allow more accurate interpretation of the fMRI results.

Tunable high-order single-sideband signal generator with optical carrier suppression using dual-parallel Mach–Zehnder modulator

A tunable high-order single-sideband signal generator with optical carrier suppression (SSB-OCS generator) is proposed, which is based on frequency multiplication operation using dual-parallel Mach–Zehnder modulator (DPMZM) and Mach–Zehnder interferometer (MZI). By changing all the modulators at maximum or minimum transmission point simultaneously, the amplitude of input radio frequency (RF) signals and the phase difference between input RF signals, two high-order even or odd signals with opposite amplitude of one sideband, are generated by upper DPMZM and lower DPMZM, respectively. Then, two optical signals are coupled to reserve one sideband, and the coupled SSB-OCS signal is injected into an MZI to suppress high-order intermodulation components. The simulated results show that the first-, second-, and third-order SSB-OCS signals can be achieved, and the suppression ratio is over 30 dB, which agrees well with the theoretical prediction. This scheme is featured by the capability to generate tunable high-order SSB-OCS signal with high suppression ratio, and the operation is simple and flexible. Finally, an experiment was carried out to demonstrate the feasibility of the proposed scheme, and a first- and second-order SSB-OCS signal were obtained, respectively, and the suppression ratio is over 24 dB.

An experimental decomposition of nonlinear forces on a surface-piercing column: Stokes-type expansions of the force harmonics

Wave loading on marine structures is the major external force to be considered in the design of such structures. The accurate prediction of the nonlinear high-order components of the wave loading has been an unresolved challenging problem. In this paper, the nonlinear harmonic components of hydrodynamic forces on a bottom-mounted vertical cylinder are investigated experimentally. A large number of experiments were conducted in the Danish Hydraulic Institute shallow water wave basin on the cylinder, both on a flat bed and a sloping bed, as part of a European collaborative research project. High-quality data sets for focused wave groups have been collected for a wide range of wave conditions. The high-order harmonic force components are separated by applying the ‘phase-inversion’ method to the measured force time histories for a crest focused wave group and the same wave group inverted. This separation method is found to work well even for locally violent nearly-breaking waves formed from bidirectional wave pairs. It is also found that the $n$th-harmonic force scales with the $n$th power of the envelope of both the linear undisturbed free-surface elevation and the linear force component in both time variation and amplitude. This allows estimation of the higher-order harmonic shapes and time histories from knowledge of the linear component alone. The experiments also show that the harmonic structure of the wave loading on the cylinder is virtually unaltered by the introduction of a sloping bed, depending only on the local wave properties at the cylinder. Furthermore, our new experimental results reveal that for certain wave cases the linear loading is actually less than 40 % of the total wave loading and the high-order harmonics contribute more than 60 % of the loading. The significance of this striking new result is that it reveals the importance of high-order nonlinear wave loading on offshore structures and means that such loading should be considered in their design.

Cassini radar observation of Punga Mare and environs: Bathymetry and composition

In January 2015 (fly-by T108), the Cassini radar observed Punga Mare, Titan's northernmost and third-largest sea, in altimetry mode during closest approach. The ground track intercepted a section of the mare and a system of channels and flooded areas connecting Punga to Kraken Mare. We use a processing technique, successfully adopted for Ligeia Mare and Ontario Lacus, for detecting echoes from the sea floor and constraining the depth and composition of these liquid bodies. We find that, along the radar transect, Punga Mare has a maximum measured depth of 110 m. The relative reduction in backscatter of the seafloor, as a function of increasing depth, suggests a liquid loss tangent of 3±1×10−5. While this value is within the formal uncertainty of the loss tangent derived for Ligeia Mare, the best-fit solution is lower and is consistent with a nearly pure binary methane-nitrogen liquid with little to no ethane or higher order components. The indication of very low amounts of ethane toward the pole suggests that atmospheric processes are controlling the surface liquid composition of Titan's seas.

Double-Layer Capacitance at Ionic Liquid–Boron-Doped Diamond Electrode Interfaces Studied by Fourier Transformed Alternating Current Voltammetry

This article reports the electrochemical double layer behavior at the interfaces of ionic liquids (ILs) and a boron-doped diamond (BDD) electrode as measured by large-amplitude Fourier transformed alternating current (AC) voltammetry (FT-ACV). Data are collected over a ≥2 V potential range and fitted to a simple resistor–capacitor circuit model. The absence of significant higher-order AC harmonic components implies nearly ideal capacitive behavior in the potential ranges examined. Capacitance values for two protic ILs and three aprotic ILs range from 3 to 8 μF cm–2 and generally increase (1–2 μF cm–2 V–1) as the potential is swept from negative to positive values. Capacitance–potential data display little dependence on the composition of the IL. The generally featureless, linear dependence of capacitance on potential over a wide potential range is similar to that reported for BDD electrodes in aqueous electrolyte media, suggesting that the BDD electrode is largely insensitive to the nature of the electrolyte media. The present study concludes that FT-ACV affords an efficient approach to probe the IL–electrode interface, with minimal capacitive hysteresis based on the potential scanning direction.

Artifacts in time-resolved Kelvin probe force microscopy.

Kelvin probe force microscopy (KPFM) has been used for the characterization of metals, insulators, and semiconducting materials on the nanometer scale. Especially in semiconductors, the charge dynamics are of high interest. Recently, several techniques for time-resolved measurements with time resolution down to picoseconds have been developed, many times using a modulated excitation signal, e.g., light modulation or bias modulation that induces changes in the charge carrier distribution. For fast modulation frequencies, the KPFM controller measures an average surface potential, which contains information about the involved charge carrier dynamics. Here, we show that such measurements are prone to artifacts due to frequency mixing, by performing numerical dynamics simulations of the cantilever oscillation in KPFM subjected to a bias-modulated signal. For square bias pulses, the resulting time-dependent electrostatic forces are very complex and result in intricate mixing of frequencies that may, in some cases, have a component at the detection frequency, leading to falsified KPFM measurements. Additionally, we performed fast Fourier transform (FFT) analyses that match the results of the numerical dynamics simulations. Small differences are observed that can be attributed to transients and higher-order Fourier components, as a consequence of the intricate nature of the cantilever driving forces. These results are corroborated by experimental measurements on a model system. In the experimental case, additional artifacts are observed due to constructive or destructive interference of the bias modulation with the cantilever oscillation. Also, in the case of light modulation, we demonstrate artifacts due to unwanted illumination of the photodetector of the beam deflection detection system. Finally, guidelines for avoiding such artifacts are given.

Metasurface Enabled Wide-Angle Fourier Lens.

Fourier optics, the principle of using Fourier transformation to understand the functionalities of optical elements, lies at the heart of modern optics, and it has been widely applied to optical information processing, imaging, holography, etc. While a simple thin lens is capable of resolving Fourier components of an arbitrary optical wavefront, its operation is limited to near normal light incidence, i.e., the paraxial approximation, which puts a severe constraint on the resolvable Fourier domain. As a result, high-order Fourier components are lost, resulting in extinction of high-resolution information of an image. Other high numerical aperture Fourier lenses usually suffer from the bulky size and costly designs. Here, a dielectric metasurface consisting of high-aspect-ratio silicon waveguide array is demonstrated experimentally, which is capable of performing 1D Fourier transform for a large incident angle range and a broad operating bandwidth. Thus, the device significantly expands the operational Fourier space, benefitting from the large numerical aperture and negligible angular dispersion at large incident angles. The Fourier metasurface will not only facilitate efficient manipulation of spatial spectrum of free-space optical wavefront, but also be readily integrated into micro-optical platforms due to its compact size.

Modifiability in Emotional Understanding Among Children With Learning Disabilities

Children with specific learning disabilities (SLD) exhibit specific difficulties in high-order components of emotional understanding that involve language (e.g., recognition of complex emotions from situations), or defining emotions and providing examples. The objectives of the current study were to study (a) modifiability of emotional understanding using a short-term mediation program aimed at enhancing emotional understanding among children with SLD as compared with typically developing (TD) children, (b) the correlation of language ability with emotional understanding. A sample of 64 boys with SLD and 33 TD boys (9–11 years old) were administered emotional understanding measures, and tests of language processing. The children were given the Language of Emotions Mediation Program and retested on the emotional understanding measures. Children with SLD revealed initial lower level of emotional understanding than TD children but higher pre- to postmediation improvement. The correlation between emotional understanding measures and verbal ability decreased from pre- to postmediation only in children with SLD. These findings indicate less cohesiveness between the two domains because of the mediation program.

Relativistic turbulence with strong synchrotron and synchrotron self-Compton cooling

Many relativistic plasma environments in high-energy astrophysics, including pulsar wind nebulae, hot accretion flows onto black holes, relativistic jets in active galactic nuclei and gamma-ray bursts, and giant radio lobes, are naturally turbulent. The plasma in these environments is often so hot that synchrotron and inverse-Compton (IC) radiative cooling becomes important. In this paper we investigate the general thermodynamic and radiative properties (and hence the observational appearance) of an optically thin relativistically hot plasma stirred by driven magnetohydrodynamic (MHD) turbulence and cooled by radiation. We find that if the system reaches a statistical equilibrium where turbulent heating is balanced by radiative cooling, the effective electron temperature tends to attain a universal value $\theta = kT_e/m_e c^2 \sim 1/\sqrt{\tau_T}$, where $\tau_T=n_e\sigma_T L \ll 1$ is the system's Thomson optical depth, essentially independent of the strength of turbulent driving or magnetic field. This is because both MHD turbulent dissipation and synchrotron cooling are proportional to the magnetic energy density. We also find that synchrotron self-Compton (SSC) cooling and perhaps a few higher-order IC components are automatically comparable to synchrotron in this regime. The overall broadband radiation spectrum then consists of several distinct components (synchrotron, SSC, etc.), well separated in photon energy (by a factor $\sim \tau_T^{-1}$) and roughly equal in power. The number of IC peaks is checked by Klein-Nishina effects and depends logarithmically on $\tau_T$ and the magnetic field. We also examine the limitations due to synchrotron self-absorption, explore applications to Crab PWN and blazar jets, and discuss links to radiative magnetic reconnection.

Detection of increase in corneal irregularity due to pterygium using Fourier series harmonic analyses with multiple diameters.

To determine steep increase of corneal irregularity induced by advancement of pterygium. A total of 456 eyes from 456 consecutive patients with primary pterygia were examined for corneal topography and advancement of pterygium with respect to the corneal diameter. Corneal irregularity induced by the pterygium advancement was evaluated by Fourier harmonic analyses of the topographic data that were modified for a series of analysis diameters from 1mm to 6mm. Incidences of steep increases in the asymmetry or higher-order irregularity components (inflection points) were determined by using segmented regression analysis for each analysis diameter. The pterygium advancement ranged from 2% to 57%, with a mean of 22.0%. Both components showed steep increases from the inflection points. The inflection points in the higher-order irregularity component altered with the analysis diameter (14.0%-30.6%), while there was no alternation in the asymmetry components (35.5%-36.8%). For the former component, the values at the inflection points were obtained in a range of 0.16 to 0.25 D. The Fourier harmonic analyses for a series of analysis diameters revealed that the higher-order irregularity component increased with the pterygium advancement. The analysis results confirmed the precedence of corneal irregularity due to pterygium advancement.

Spodumene, α-LiAlSi2O6 – A new natural SRS-active crystal with three χ(3)-promoting vibrational modes

α-LiAlSi2O6, known as mineral spodumene, is introduced as a novel SRS-active crystal with monoclinic symmetry C2/c. Under picosecond laser excitation Raman-induced steady-state χ(3)-nonlinear generation in the visible and near-IR is observed in the crystals. All recorded Stokes and anti-Stokes high-order lasing components are identified and correspond to three SRS-promoting phonon modes with ωSRS1 ≈ 709 cm−1, ωSRS2 ≈ 357 cm−1 and ωSRS3 ≈ 1074 cm−1. On the basis of the results of a spontaneous Raman scattering study they were assigned to vibrations of the tetrahedral [SiO4] groups of the silicate chains and lattice modes of Li-O or Al-O of the crystal structure. A brief review in tabular form of so far known SRS-active natural crystals (minerals) is given as well.

Strategies for achieving intense single-cycle pulses with in-line post-compression setups.

Intense few- and single-cycle pulses are powerful tools in different fields of science Today, third- and higher-order terms in the remnant spectral phase of the pulses remain a major obstacle for obtaining high-quality few- and single-cycle pulses from in-line post-compression setups. In this Letter, we show how input pulse shaping can successfully be applied to standard post-compression setups to minimize the occurrence of high-order phase components during nonlinear propagation and to directly obtain pulses with durations down to 3fs. Furthermore, by combining this pulse shaping of the input pulse with new-generation broadband chirped mirrors and material addition for remnant third-order phase correction, pulses down to 2.2fs duration have been measured.

Measurement of pre-bunched beam’s longitudinal form factor based on radiation from a tunable-gap undulator

The form factor, representing the statistical characteristics of a bunch's longitudinal distribution, is one of the most essential properties of a pre-bunched electron beam and is used for many types of frontier accelerator applications. We demonstrated the measurement of a pre-bunched beam's longitudinal form factor component based on coherent radiation from a widely tunable-gap undulator. The radiation energy from bunches with different longitudinal properties was measured as a function of undulator gap. The root-mean-square length of a 60 pC ultrashort quasi-Gaussian bunch generated by linac and chicane compression ranged from 75 fs to 240 fs, as obtained by fitting the radiation energy curve. Furthermore, the form factor component of the bunch train based on nonlinear longitudinal space charge oscillation was measured, and a higher-order harmonic component was observed with the proposed method than with the widely used coherent transition radiation method. The proposed method may satisfy the requirements of sub-fs bunch length measurement with proper undulator design.

Magnetic field topology and chemical spot distributions of the Ap star HD 119419

Context.Analysis of high-resolution spectropolarimetric time-series observations of early-type magnetic stars is currently the most advanced method of obtaining detailed information on their surface magnetic field topologies and horizontal spot distributions.Aims.In this study we analyse a new set of high-quality full Stokes vector observations of the magnetic Ap star HD 119419 – a member of the 14 Myr old Lower Cen-Cru association – for the purpose of studying the surface field topology and mapping the chemical abundance spots.Methods.We made use of the circular and linear polarisation data collected for HD 119419 with the HARPSpol instrument at the ESO 3.6-m telescope. These observations were analysed with a multi-line magnetic diagnostic technique and modelled in detail with a Magnetic Doppler imaging (MDI) code.Results.We present a new set of high-precision mean longitudinal magnetic field measurements and derive a revised stellar rotational period by comparing our measurements with the literature data. We also redetermine the basic stellar atmospheric parameters. Our four Stokes parameter magnetic inversions reveal a moderately complex surface field topology with a mean field strength of 18 kG and a maximum local strength of 24 kG. A poloidal dipolar component dominates the magnetic energy spectrum of the surface field in HD 119419. However, significant contributions of the higher-order spherical harmonic components are also present. We show that the dipole plus quadrupole part of the reconstructed field geometry is incapable of reproducing the observed amplitudes and shapes of the StokesQandUprofiles. The chemical abundance distributions of Fe, Cr, Ti, and Nd, derived self-consistently with the magnetic field geometry, are characterised by large abundance gradients and a lack of clear correlation with the magnetic field structure.Conclusions.This full Stokes vector analysis of HD 119419 extends the modern hot-star magnetic mapping investigations to an open cluster Ap star with a well-determined age. Further, MDI studies of cluster members will allow us to study the field topologies and chemical abundance spots as a function of stellar age.

High-Order Moment Recursive State Estimation of Markov Jump Linear Systems

A high-order moment recursive state estimator is designed to achieve the minimum mean square error estimation of a Markov jump linear system (MJLS) whose state distribution obeys a generalized Gaussian distribution (GGD). The operation properties of the cumulant generating function are explored to transform the stochastic MJLS into a high-order component form. Based on the transformed high-order moment deterministic system, a Kalman filter is applied to estimate the high-order moment information of the state variable, such as the skewness and kurtosis of the GGD. This method allows for the estimation of the Gaussian distribution, such as the two special cases, mean and variance. A comparison with the existing results of the mean error estimation demonstrates the higher estimation accuracy for the simulation. The application of the proposed method to economic and power systems demonstrates its effectiveness and advantages.