Symmetric Components Research Articles

Dual subaperture stitching for large flat mirror testing.

The Ritchey-Common test is a widely used method for testing flat mirrors with a larger reference spherical mirror. However, with the increase in the size of the flat mirror, the fabrication of the spherical mirror becomes more time consuming and expensive. In this study, we developed a novel technique to test a large flat mirror with a smaller reference sphere using a dual subaperture stitching (DSS) method. One part of the DSS technique is a modified Ritchey-Common test, which uses a reference sphere smaller than the flat mirror. The other part involves scanning along the centerline of the flat mirror. The former can be used to determine the surface form error (SFE), except for rotationally symmetric components, such as power and spherical aberrations, which can be measured by the latter. To perform the stitching process using a smaller reference sphere, the flat mirror was repeatedly rotated by a fixed angular step. One of the advantages of the rotation of the flat mirror is that it can be used to identify the errors resulting from the reference sphere, which do not vary during the rotation of the flat mirror. We verified the DSS method using a 152 mm diameter optical flat mirror and determined the root-mean-square (rms) measurement error to be only 0.2 nm, which was comparable to the error of the full-aperture interferometric measurement. In addition, we tested a 1.2 m diameter flat mirror with a reference sphere with an aperture of 0.8 m and measured its SFE to be 11.9±0.5nm rms.

Multi-stable quantum droplets in optical lattices

We address the nonlinear dynamics of binary Bose-Einstein condensates with mutually symmetric spinor components trapped in an optical lattice. The interaction between the repulsive Lee–Huang–Yang nonlinearity and the intercomponent attraction as well as Bragg scattering of an optical lattice results in formation of multi-peaked quantum droplets. Even- and odd-symmetric droplets can bifurcate from Bloch modes of the corresponding periodic systems. Linear stability analysis corroborated by direct evolution simulations reveals that even-symmetric droplets with different norms and different number of peaks can evolve stably at the same chemical potential, i.e., multi-stable droplets are possible in the present scheme. Besides the droplets in the semi-infinite gap, the properties of droplets in the first finite bandgap are also discussed. Both even- and odd-symmetric droplets are stable in almost their whole existence domains. We reveal that optical lattice plays an important role for the stabilization of droplets, in sharp contrast to the nonlinear system without a lattice modulation. We, thus, furnish a paradigmatic example of multi-stable quantum droplets held in optical lattices.

A simulation-based mechanistic study of turbulent wind blowing over opposing water waves

Abstract

Influence of an Additional Indexing Rotary Axis on Wire Electrical Discharge Machining Performance for the Automated Manufacture of Fir Tree Slots

Abstract The demand for higher efficiency in aircraft propulsion engines leads to materials with increasing thermomechanical strengths and new designs inducing filigree geometries of blisks and disks. Because of new designs which induce tighter tolerances, the high mechanical process forces in conventional cutting processes like broaching cause inacceptable geometrical deviations and high tooling costs. Due to the electro-thermal material removal mechanism, electrical discharge machining (EDM) ensures a force free and thus precise machining. The manufacture of fir tree slots in nickel-based alloys by wire EDM has been investigated in the last few years and the process was verified as an alternative technology for broaching. To get a better competitive position, the productivity can be prospectively increased by using an additional indexing rotary axis which ensures a precise and automated production of rotationally symmetric components and reduce production times, e.g., for the manufacture of fir tree slots on a disk. Nevertheless, the application of these axes cause changed flushing conditions and can also affect the electrical contacting as well. Both influence the process performance and demand a technology development or adjustment of standard machining technologies. The influence of these changed machining conditions has not been investigated scientifically to date. In this paper, the surface integrity and process performance of fir tree slots machined by wire EDM on the machine table are compared with the manufacture by using an additional indexing rotary axis.

Antisymmetric cross-correlation of line-intensity maps as a probe of reionization

We present a new estimator for the cross-correlation signal between line intensity maps to probe the Epoch of Reionization. The proposed estimator is the hitherto neglected antisymmetric component of the cross-correlation, under the exchange of line-of-sight positions. We consider the cross-correlation between HI and CO fluctuations, and forecast the improvement in precision on reionization parameters when the antisymmetric contribution is accounted for. As a way to break the degeneracy between astrophysics and cosmology in the intensity mapping power spectrum, we study the ratio between the antisymmetric and symmetric components. While our results depend on the highly uncertain astrophysical modelling, we show that in most standard scenarios including the antisymmetric contribution as a complementary probe can lead to a significant gain in information.

Enhancement of microwave detection sensitivity in un-biased perpendicular magnetic tunnel junctions using voltage controlled magnetic anisotropy

We perform a numerical study of microwave detection using an unbiased magnetic tunnel junction with a perpendicularly magnetized free layer by utilizing the phenomena of Voltage Control Magnetic Anisotropy (VCMA). We show that the field angle for achieving maximum sensitivity is significantly affected by the presence of the VCMA effect. The combination of VCMA effect and spin-transfer torque (STT) enhances the maximum sensitivity by >30% compared to the case of pure STT. We explain this behavior using the symmetric voltage component that arises solely due to the VCMA effect in the spin-torque ferromagnetic resonance spectra. We also show the presence of meta-stable states at the low field for which the sensitivity in the presence of the VCMA effect is enhanced by ~70%. For the chosen device parameters, we predict a maximum sensitivity value of 1400 mV/mW, which is comparable to commercial semiconductor-based unbiased Schottky detectors.

Distinct Growth Rates of the Two ENSO Types

AbstractEl Niño‐Southern Oscillation (ENSO) events can be grouped into two types based on their sea surface temperature anomaly spatial patterns, that is, eastern Pacific (EP) and central Pacific (CP) types. In this study, we propose a new method to empirically diagnose linear growth rates of the EP and CP ENSO types due to a limitation of applying the traditional Bjerknes stability index method simply to these two types. We spatially project the peak‐time symmetric component of the mixed‐layer oceanic heat budget terms onto the ENSO‐related sea surface temperature anomaly patterns to estimate the ENSO grow rate. After validating the method by comparing it with the Bjerknes stability index, we show that the growth rate is positive for the CP ENSO type and weakly negative for the EP ENSO type, contributed by different feedback terms. The Coupled Model Intercomparison Project Phase 5‐based multimodel ensemble mean shows similar characteristics as the reanalysis for the EP ENSO type rather than the CP ENSO type.

Frictional drag between superconducting LaAlO3/SrTiO3 nanowires

We report frictional drag measurements between two superconducting LaAlO3/SrTiO3 nanowires. In these experiments, current passing through one nanowire induces a voltage across a nearby electrically isolated nanowire. The frictional drag signal contains both symmetric and anti-symmetric components. The anti-symmetric component arises from the rectification of quantum shot noise in the drive nanowire by the broken symmetry in the drag nanowire. The symmetric component in the drag resistance is ascribed to rectification of thermal noise in the drive nanowire during superconducting-normal transition. The suppression of the symmetric component is observed when a normal nanowire is used as either a drag or drive nanowire with the other nanowire superconducting. The absence of symmetric drag resistance between a normal drag nanowire and a superconducting drive nanowire suggests a higher electron-hole asymmetry in the superconducting LaAlO3/SrTiO3 nanowire arising from the 1D nature of superconductivity at LaAlO3/SrTiO3 interface.

Anisotropic magnetoresistance in spin\u2013orbit semimetal {hbox {SrIrO}}_{3}

{hbox {SrIrO}}_{3}, the three-dimensional member of the Ruddlesden–Popper iridates, is a paramagnetic semimetal characterised by a the delicate interplay between spin–orbit coupling and Coulomb repulsion. In this work, we study the anisotropic magnetoresistance (AMR) of {hbox {SrIrO}}_{3} thin films, which is closely linked to spin–orbit coupling and probes correlations between electronic transport, magnetic order and orbital states. We show that the low-temperature negative magnetoresistance is anisotropic with respect to the magnetic field orientation, and its angular dependence reveals the appearance of a fourfold symmetric component above a critical magnetic field. We show that this AMR component is of magnetocrystalline origin, and attribute the observed transition to a field-induced magnetic state in {hbox {SrIrO}}_{3}.

Estimation for a Class of Semiparametric Pareto Mixture Densities

We study the estimation of a class of semiparametric mixture models, where the models have a symmetric nonparametric component and a parametric component of Pareto distribution with unknown parameters. We establish an estimation procedure by minimizing a criterion function after dealing with the jump point. We study the large sample properties of the proposed estimator, and prove consistency and asymptotic normality of the parameter estimation. For the nonparametric component, bias and variance are derived, and a rule-of-thumb bandwidth selection method is given. Simulation studies demonstrate good performance of the proposed methodology.

Density deconvolution for generalized skew-symmetric distributions

The density deconvolution problem is considered for random variables assumed to belong to the generalized skew-symmetric (GSS) family of distributions. The approach is semiparametric in that the symmetric component of the GSS distribution is assumed known, and the skewing function capturing deviation from the symmetric component is estimated using a deconvolution kernel approach. This requires the specification of a bandwidth parameter. The mean integrated square error (MISE) of the GSS deconvolution estimator is derived, and two bandwidth estimation methods based on approximating the MISE are also proposed. A generalized method of moments approach is also developed for estimation of the underlying GSS location and scale parameters. Simulation study results are presented including a comparing the GSS approach to the nonparametric deconvolution estimator. For most simulation settings considered, the GSS estimator is seen to have performance superior to the nonparametric estimator.

Characteristics of component matrices chosen for toric lens powers in symmetric dioptric power space

Real distinct principal powers and corresponding perpendicular meridians of a lens or surface combine as factors of a 2×2 power matrix for calculation. A scalar matrix that represents the nearest sphere power component, may be extracted from this. Non-spherical or astigmatic matrix power component(s) remain. The purpose of this paper is to analyse the contribution that astigmatic components in two planes make to the lens power. These basic power members of the set of matrix basic components provide the preferred meridians as they combine linearly to complete the power matrix of a lens or surface. Essentially invertible independent matrices make for symmetric basic components. The maximum number of mutually orthogonal matrices in a vector space of finite dimension form a basis for that space. Properties of basic matrices are latent in the use of optometric power vectors. This paper attempts to make the case for the explicit mention of orthogonal bases of matrices in order to support calculations of power.

Structures of wing-tip vortices at low Reynolds numbers and their modelling

The structures of wing-tip vortices at a low Reynolds number () are studied by direct numerical simulation. After confirming the basic features of the wing-tip vortices, the distributions of axial vorticity and velocity are investigated in detail. The vorticity distribution consists of a dominant symmetric component, quadrupole components responsible for elliptical deformation of the vortex core and the other small components. The symmetric component of vorticity is in reasonable agreement with the Moore-Saffman model (Moore & Saffman 1973 Proc. R. Soc. Lond. 333, 491) for the three types of wing planform considered: the rectangular, elliptic and delta wings. The agreement between numerical results and the Moore-Saffman model is not good for the symmetric component of axial velocity since the boundary layer component is small owing to the incomplete roll-up of the vortex sheet shed from the boundary layer. However, the vortex component of the axial velocity is correctly predicted by the Moore-Saffman model. The elliptical deformation of the vortex core is characterized by the aspect ratio and the direction of the major axis. It is found that the elliptical deformation is not uniform in the streamwise direction, which implies that the wing-tip vortices cannot be always modelled by a two-dimensional vortex pair. The evolution of the elliptical deformation along the streamwise direction is shown to be described by two-dimensional vortex dynamics under the boundary-layer approximation. The equations of motion of an elliptic vortex patch in a straining field predicts correctly the rate of change of the direction, but fails to predict that of the aspect ratio, for which the equation derived for axisymmetrization of vortices gives a good prediction.

Global ITG eigenmodes: From ballooning angle and radial shift to Reynolds stress and nonlinear saturation

We present global linear and nonlinear simulations of ion temperature gradient instabilities based on a fluid formulation, with an adapted version of the JOREK code. These simulations are performed in realistic global tokamak equilibria based on the solution of the Grad–Shafranov equation. Benchmarking of linear growth rates was successfully completed with respect to previously published data. We find two distinct types of eigenstructures, depending on the magnetic shear. For high shear, when the coupling of poloidal harmonics is strong, ballooning-type eigenmodes are formed, which are up-down asymmetric with a finite ballooning angle, θ0. The poloidal harmonics which form the global eigenmode are found to demonstrate a radial shift, being centered well outside of their corresponding rational surface. Stronger diamagnetic effects increase both θ0 and proportionately shift the m harmonics to larger radii (by as much as two rational surfaces). In the low shear regime, the unstable eigenmodes become narrowly localized between neighboring pairs of rational surfaces, and exhibit no up-down asymmetry. Our simulations also show the generation of finite Reynolds stress due to nonlocal/global profile effects. This stress possesses both poloidally symmetric (n=m=0) and asymmetric (finite-m) components. Turbulent saturation in nonlinear simulations is demonstrated for both shear regimes.

Effect of Winding Connections on Thrust and Current Asymmetry of Linear Induction Machines Considering End Effect

Linear induction motors (LIMs), applied in the field of electromagnetic emission, due to end effect, show the characteristics of thrust rapid decline, and current asymmetry increasing in the process of high-speed movement. This article studies the effect of stator winding connections on thrust and current asymmetry of six-phase shifted 30° LIM considering the static and the longitudinal end effect. The study compares three connections by finite-element analysis, namely, open-end, star, and triangular connections. The theory of symmetric component method is introduced to analyze the asymmetric characteristics caused by the end effect. The output thrust and current asymmetries of the motor under three connection modes are compared in detail. The simulation results show that there is no difference among the three connection modes when only considering static end effect, but once considering dynamic end effect, the output current symmetry of star connection is better than that of the open and triangular connection. Also, Adopting variable slip frequency control method can not only improve output thrust of motor, but also improve current symmetry, especially at high speed obviously, when compared with constant slip frequency control method. The research will be helpful to motor thrust optimization control and winding design in the future.

Reinforcement learning for robotic assembly of fuel cell turbocharger parts with tight tolerances

The efficiency of a fuel cell is not only dependent on the stack, but also to a large extent on the turbocharger, which is responsible for providing the required airflow. Since the individual components, especially those of the rotor, are subject to high demands on manufacturing accuracy, it is crucial to ensure a precise and robust assembly. In order to achieve a scalable assembly process, this paper presents a method for a robot-based assembly of the rotationally symmetric components of the rotor. The assembly task has been reduced to the two essential problems: search and insertion. On this basis, a system was developed, which is able to learn the joining process independently and compensate for positioning inaccuracies with the help of reinforcement learning in combination with a position-controlled robot. The applied reinforcement learning strategy is based on the measurement data of a 6-axis force/torque sensor, with which the current contact state can be evaluated and a decision for the next step can be made. The experimental verification shows that an automation of the assembly process is possible with the proposed strategy. The robot is able to perform the search operation successfully, whereas limitations to the achievable accuracies of the insertion process could be found.

Observation of two sound modes in a binary superfluid gas

We study the propagation of sound waves in a binary superfluid gas with two symmetric components. The binary superfluid is constituted using a Bose-Einstein condensate of $^{23}$Na in an equal mixture of two hyperfine ground states. Sound waves are excited in the condensate by applying a local spin-dependent perturbation with a focused laser beam. We identify two distinct sound modes, referred to as density sound and spin sound, where the densities of the two spin components oscillate in phase and out of phase, respectively. The observed sound propagation is explained well by the two-fluid hydrodynamics of the binary superfluid. The ratio of the two sound velocities is precisely measured with no need for absolute density calibration, and we find it in quantitatively good agreement with known interaction properties of the binary system.

Uniformity of thickness of metal sheets by patchwork blanks: potential of adhesive bonding

The sheet metal forming operations generally involve the production of parts characterized by a non-uniform thickness distribution. However, in some cases, a product characterized by a distribution of thicknesses that is as uniform as possible may be desirable. This result can be obtained by using multiphase processes or by subtraction or addition of material from the blank. In this work, which deals with the method for adding material, an innovative methodology has been proposed as an alternative to the welding process. Specifically, the methodology is based on the bonding of a patch (before the deformation process), on the base plate with a constant thickness, in the area that most suffers from the thinning caused by the forming process. In this way, it was possible to influence the deformation of the patchwork blank and its thicknesses distribution. Through finite element analysis, it was possible to study the formability of a patchwork blank by varying the thickness and size of the patch, in order to produce an axially symmetric component by stretching through a hemispherical punch. Preliminary experimental tests demonstrated the reliability of the bonding and the potential of this method to uniform the final thickness of the sheet.

Advanced reproducing kernel meshfree modeling of cracked curved shells for mixed-mode stress resultant intensity factors

A meshfree approach for analyzing the fracture mechanics parameters in cracked curved shells is presented. The reproducing kernel (RK) meshfree method and mapping technique are employed to approximate cracked curvilinear surfaces and field variables. In order to model the crack segment, the meshfree discretization techniques are used. The stabilized conforming nodal integration (SCNI) and sub-domain stabilized conforming integration (SSCI) techniques are adopted to accurately integrate the stiffness matrix. The contour integral is chosen to evaluate the fracture mechanics parameters and discretized using the RKs and SSCI. The J-integral value is separated into symmetric and asymmetric components using the decomposition method to extract the mode-I and -II stress resultant intensity factors (SRIFs). The numerical results reveal that the accurate J-integral value and mixed-mode SRIFs of cracked curved shells can be effectively evaluated using the proposed formulation and discretization. The simplified fatigue crack propagation is also presented.

Numerical and Experimental Investigation of Aluminum/CFRP Hybrid Tubes with Rubber-like Interlayer

In the automotive, aerospace, printing, and sports industries, the development of hybrid CFRP-metal components is becoming increasingly important and used. The coupling of metal with CFRP, in axial symmetric components, results in reduced production costs and an increase in mechanical properties such as bending, torsional stiffness, mass reduction, and critical speed, when compared to the single material-built ones. The challenge for engineers is to design hybrid co-cured tubes with external metal layers, which avoid possible detachments and delaminations due to the mismatching coefficients of thermal expansion of the two materials. In this work, residual thermal stresses and strain have been studied with numerical models based on Finite Element Method (FEM) and compared with experimental tests. The FEM model allowed for the investigation of the influence of length, diameters, thickness and interface layer material on residual thermal stress peaks near the free edges zone. To reduce the risk of premature failure,the interleaving of a rubber-like layer is proposed and experimentally validated.