Elliptical Eccentricity Research Articles

Improved sliding mode tracking control for spacecraft electromagnetic separation supporting on-orbit assembly

This paper addresses the electromagnetic separation problem for mass-unknown spacecraft in elliptical orbits that play a significant role in on-orbit assembly and other future space missions. First, the relative motion dynamics model between the platform (target spacecraft) and module (chaser spacecraft) is presented with the lumped disturbance resulting from external disturbances, elliptical eccentricity and unknown mass, and a compliant reference trajectory is designed by applying the idea of trigonometric-function. Then, an improved sliding mode controller is developed to ensure that the tracking errors of relative motion can converge to near the equilibrium point. In order to avoid adverse impacts, the elliptical eccentricity and unknown mass are fully considered by using the developed control approach, and the global asymptotic stability of the closed-loop system is analyzed by strict theoretical proof. Combined with spacecraft electromagnetic docking technology, the electromagnetic separation scheme can make on-orbit assembly easy to achieve with certain advantages, e.g., it doesn’t consume propellant and thus doesn’t cause plume contamination, and has reversible, continuous and non-contact characteristics. Finally, numerical simulations are performed to illustrate the effectiveness and feasibility of the developed control approach.

Nonlinear Dynamic Numerical Analysis of Solid-liquid Separation Rolling Bearing-Rotor System Finite Element Discrete Modeling

Based on a rolling bearing-single disc rotor, centrifugal force is generated due to the influence of unbalanced factors such as rotor eccentric excitation, bearing restraint stiffness, and rotating stator clearance, which leads to the imbalance of the rotor system, resulting in the problem of friction between the rotor and the stator. This paper establishes a dynamic model of a single-disk rotor supported by rolling bearings, and the fourth-order Runge-Kutta numerical integration method is used to solve it. Bifurcation behavior and nonlinear dynamic response at a rotational speed. The results show that the nonlinear dynamic characteristics of the system are significantly different due to changes in elliptic eccentricity, rotational speed, and bearing constraint stiffness; when the rotational speed increases, the system gradually appears bifurcation, quasi-periodic motion, and instability increases. Therefore, reasonable selection of the working speed of the rotor and the gap between the stator and the rotor can reduce the non-periodic vibration caused by the unbalanced force and improve the stability of the system operation.

Active Disturbance Rejection Control for Delayed Electromagnetic Docking of Spacecraft in Elliptical Orbits

In this article, an active disturbance rejection control (ADRC) scheme is proposed for the electromagnetic docking of spacecraft in the presence of time-varying delay, fault signals, external disturbances, and elliptical eccentricity. By introducing an auxiliary variable, an intermediate observer (IO) is presented to estimate the relative motion information and the total disturbance resulting from fault signals, unknown mass, external disturbances, and elliptical eccentricity. Then, an ADRC scheme is developed to guarantee that the relative position, relative velocity, and the estimation errors of relative motion information and the total disturbance can all converge into the neighborhood of the equilibrium. With the proposed control scheme, the time-delay factor is fully considered in the controller design to avoid adverse effect, and the uniform ultimate boundedness stability of the entire closed-loop system is analyzed with a rigorous theoretical proof. In comparison to conventional ADRC and other state-of-the-art schemes, the proposed ADRC scheme has several advantages, e.g., high accuracy, strong robustness, and requires no prior knowledge of the fault, time-varying delay and states information due to IO-based relative motion information and total disturbance estimations. Finally, numerical simulations are performed to show the effectiveness of the proposed control scheme.

Visual indentation apparatus and finite element modelling as a method to characterize 3D mechanical properties of facial skin in vivo

Knowledge of the mechanical properties of human skin has essential applications in cosmetic, dermatology and surgical fields. In this study, a hybrid experimental–numerical method was developed to characterize the human skin mechanical properties in vivo. An indentation experiment was physically conducted and simulated by finite element (FE) analysis. In the physical experiment, an indenter made of transparent glass was adopted so that the elliptical eccentricity in the contact area between skin and indenter could be monitored in real-time. In FE simulation, the dermis and subcutaneous tissue were modeled as anisotropic hyperelastic material and isotropic elastic material, respectively. By fitting the FE results to the experimental data, the three-dimensional (3D) mechanical properties of skin, including the dermis and subcutaneous tissue were determined. Furthermore, to demonstrate the ineffectiveness of the hybrid experimental–numerical method, a sensitivity analysis was conducted. In this sensitivity analysis, it is shown that the different mechanical parameters have a different contribution to the final FE result. Finally, the effect of subcutaneous tissue for in vivo skin indentation measurement was also evaluated.

Aperture elongation of the femoral tunnel on the lateral cortex in anatomical double-bundle anterior cruciate ligament reconstruction using the outside-in technique.

In anatomical anterior cruciate ligament reconstruction surgery using the outside-in technique, the aperture of the femoral lateral cortex may become elliptical.Retrospective cross-sectional studyTo evaluate the extent of elliptical eccentricity in lateral apertures relative to aperture positioning and clinical failure rate in anatomical anterior cruciate ligament double-bundle reconstruction using outside-in technique.In 75 patients, the aperture elongation factor was defined as the ratio of the major axis of the elliptical aperture to the drill size. Using the lateral epicondyle as a reference point, the lateral femur was divided into sections by distance and angle, and the minimum area was evaluated to assess the relationship between the elongation factor and aperture position of the lateral cortex for each bundle. The incidence and associated clinical performance regarding cortical button migration were also investigated.Aperture elongation factors were 120.2 ± 13.3% and 120.0 ± 16.3% on the anteromedial (AM) and posterolateral (PL) sides, respectively. Femoral tunnel elongation was smallest when the entry point axis were both between 30 to 60° and distance was between 10 to 20 mm and 0 to 10 mm on the AM and PL sides, respectively. During the postoperative follow-up period, intra-tunnel migration was confirmed in 4 of 75 cases (5.3%). Fixation failure neither affected clinical scores nor knee laxity.Areas of minimum elongation for each bundle on both AM and PL sides were found anteroproximally to the lateral epicondyle and positioned near each other. Elongation did not directly affect the clinical outcome.Level of evidence grade: prognostic level III

Observer-based control for spacecraft electromagnetic docking

Electromagnetic docking could enable autonomous spacecraft docking with no need for propellant consumption and without plume contamination. This paper addresses the robust electromagnetic docking problem for spacecraft in the presence of external disturbances, fault signals, unknown mass, elliptical eccentricity, measurement errors and input constraints. In this scenario, an intermediate observer is developed to estimate the relative motion information and the lumped disturbance resulting from these uncertainties. Based on this, an anti-disturbance controller is proposed, where the compensation of the lumped disturbance is considered. It is proved via Lyapunov analysis that the intermediate observer-based controller can achieve the objective of spacecraft electromagnetic docking with input constraints and in the presence of uncertainties. Finally, the observer-based controller is illustrated, in simulation, to demonstrate the effectiveness and improved performance compared with a disturbance observer-based controller.

Spoof surface plasmon polariton‐fed circularly polarized leaky‐wave antenna with suppressed side‐lobe levels

A wide-angle scanning circularly polarized (CP) leaky-wave antenna (LWA) with suppressed side-lobe levels (SLLs) is proposed, which can be a good candidate for future radar and wireless communication systems. The LWA consists of 12 cross slotted elliptical patch elements, which are fed by a microstrip spoof surface plasmon polariton (SSPP) line. Two fundamental modes of the patch array with two orthogonal polarizations can be excited by the electromagnetic coupling between the array and the SSPP line. By optimizing the elliptical eccentricity e and etching cross slots on the elliptical patch array, a 90° phase difference is introduced, and then, the CP radiation is realized. A tapered aperture field distribution is also realized by adjusting coupling intensities between the patch elements and the SSPP line, which is beneficial to reduce the SLLs. The electrical size of the LWA is 1.29λ0 × 6.02λ0 × 0.08λ0, where λ0 is air wavelength at 12.9 GHz (broadside direction). Both the simulated and measured results indicate that the CP operating band is 12.0 to 15.0 GHz. The proposed CP LWA scans continuously from −14° to 38°. In the whole operating band, the axial ratios are less than 3 dB, and the SLLs are less than −20 dB as well.

Constrained fuel-free control for spacecraft electromagnetic docking in elliptical orbits

This paper addresses the control problem of spacecraft electromagnetic docking in the presence of external disturbances, fault signals, elliptical eccentricity, and input magnitude and rate constraints (MRCs). More specifically, the dynamic model of translational motion in an elliptical orbit is derived first; by analyzing the influence of external disturbances, fault signals and elliptical eccentricity, a lumped disturbance is reconstructed to facilitate the controller design. Then, a state feedback control strategy based on disturbance observer, i.e. a disturbance observer-based controller (DOBC), is proposed, where the compensation of the lumped disturbance is considered. This controller thus has the nature of fault tolerance and robustness, and it requires no mass information on chaser or target spacecraft, no information on external disturbances, fault signals or even orbital elements except for semi-major axis. By choosing new state variables using the information on relative motion and estimation errors, an augmented plant is established. Using Lyapunov stability analysis, which shows that all states are uniformly ultimately bounded, sufficient conditions for the existence of the disturbance observer and controller subject to input MRCs are given based on linear matrix inequalities (LMIs). Numerical simulations are performed to demonstrate the validity and performance of the proposed strategy.

SOAR observations of the high-viscosity accretion disc of the dwarf nova V4140 Sagitarii in quiescence and in outburst

We report the analysis of 22 B-band light curves of the dwarf nova V4140 Sgr obtained with SOI/SOAR during two nights along the decline of a superoutburst in 2006 Sep 12-24 and in quiescence over 50 days following the superoutburst. Three-dimensional eclipse mapping of the outburst light curves indicates that the accretion disc is elliptical (eccentricity e=0.13) and that superhump maximum occurs when the mass donor star is aligned with the bulge of the elliptical disc. The accretion disc is geometrically thin both in outburst and in quiescence; it fills the primary Roche lobe in outburst and shrinks to about half this size in quiescence. The stability of the eclipse shape, width and depth along quiescence and the derived disc surface brightness distribution indicate that the quiescent accretion disc is in a high-viscosity, steady-state. Flickering mapping of the quiescent data reveal that the low-frequency flickering arises from an azimuthally-extended stream-disc impact region at disc rim and from the innermost disc region, whereas the high-frequency flickering originates in the accretion disc. Assuming the disc-related flickering to be caused by fluctuations in the energy dissipation rate induced by magneto-hydrodynamic turbulence (Gertseema & Achterberg 1992), we find that the quiescent disc viscosity parameter is large (alpha ~ 0.2-0.4) at all radii. The high-viscosity quiescent disc and the inferred low disc temperatures in superoutburst are inconsistent with expectations of the disc-instability model, and lead to the conclusion that the outbursts of V4140 Sgr are powered by mass transfer bursts from its donor star.

Effect of Chirality on Dispersion Characteristics of Uniaxial Anisotropic Chiral Elliptical Waveguide

AbstractIn this paper, the dispersion characteristic of elliptical waveguide consisting of uniaxial anisotropic chiral medium is investigated. The eigenvalue equation for the waveguide that is to be studied is deduced by solving the Mathieu and modified Mathieu functions. The cutoff frequencies for several lower order even modes have been calculated and their dispersion characteristics are correspondingly plotted. The effects of elliptical eccentricity and chirality on the mode cutoff frequencies and mode transmission are examined numerically.

Modal analysis and dispersion curves of an elliptical W-type single mode fiber

In this paper, the propagation of electromagnetic waves in W-type elliptical dielectric optical fiber having various cladding layers is presented. The presented fiber has concentric core and cladding which have elliptical cross section and the refractive index of one of the inner cladding (the cladding between first clad and last clad) maximum. Using elliptic cylindrical coordinates, boundary conditions are derived and longitudinal field components for the even and odd modes are obtained. The characteristic equation for the fiber to be studied is determined by solving the Mathieu (q > 0) and the modified Mathieu functions (q < 0). In order to study the fundamental mode, the modal index m is put as m = 1. Finally, the cutoff frequencies for several lower order modes have been calculated and their dispersion characteristics are plotted. The effects of elliptical eccentricity e on the mode cutoff frequencies and mode transmissions are also addressed. The analysis shows that one can control the propagation property of optical fiber by increasing the number of inner claddings. These claddings provide additional degree of freedom to control the modes.

A general solution for Stokes flow and its application to the problem of a rigid plate translating in a fluid

A general solution for 3D Stokes flow is given which is different from, and more compact than the existing ones and more compact than them in that it involves only two scalar harmonic functions. The general solution deduced is combined with the potential theory method to study the Stokes flow induced by a rigid plate of arbitrary shape translating along the direction normal to it in an unbounded fluid. The boundary integral equation governing this problem is derived. When the plate is elliptic, exact analytical results are obtained not only for the drag force but also for the velocity distributions. These results include and complete the ones available for a circular plate. Numerical examples are provided to illustrate the main results for circular and elliptic plates. In particular, the elliptic eccentricity of a plate is shown to exhibit significant influences.

Computing Eigen value equation and modal dispersion characteristics of an elliptical Bragg waveguide

Using the method of separation of variables in the elliptical coordinate system, a recursive formula for the electromagnetic fields in a new type of Bragg waveguide having elliptical core cross section with multilayered cladding is derived. The eigen equation is written in the form of Mathieu and the modified Mathieu functions and a dispersion relation is obtained for various modes supported by the proposed Bragg waveguide. The cutoff frequencies for several lower order even-odd modes have been calculated and their propagation characteristics are plotted. The results show that the dispersion curves are discontinuous and modes can exist only in particular wavelength bands. The effects of elliptical eccentricity on the mode cutoff values and mode transmission are addressed. Finally, the modal birefringence in the said waveguide is also estimated.

Limitations of single kernel near-infrared hyperspectral imaging of soft wheat for milling quality

Soft wheat milling quality assessment typically begins in the later stages of wheat breeding programmes and continues after cultivar release in commercial milling and processing operations. Near-infrared (NIR) hyperspectral (HS) image analysis, a technique that is gaining interest in food and pharmaceutical inspection research, was explored as an alternative procedure for milling quality evaluation. Three quality properties were studied, flour yield (the weight fraction of flour to whole grain), softness equivalent (a gauge of how easily flour is released from the kernel during break), and sucrose solvent retention capacity (SRC, related to arabinoxylans, which influence water absorption during dough mixing) because of their high degree of heritability and influence on soft wheat quality. NIR HS reflectance images (1000–1700 nm) of non-touching kernels were collected on more than 120 pure cultivars or advanced lines of soft red and white wheat. Five morphological properties (area, elliptical eccentricity and major and minor axis lengths, and ellipsoidal volume) and three spectral properties (principal component scores 1–3) were exhaustively examined in multiple linear regression models for each quality property and in nonparametric classification into low, medium, and high groups using texture properties (contrast, correlation, energy, and homogeneity) calculated from grey-level co-occurrence matrices of principal component scores images. Results indicated that softness equivalent exhibited the highest correlation with HS properties, while sucrose SRC had the lowest correlation. The combination of morphological and spectral properties produced better models than either property group alone. However, because of the inherent chemical and physical complexities of wheat, HS imaging will not be sufficient so as to replace actual pilot milling procedures.

Analytical Study of Pair Production Rate from Vacuum in an Elliptic Polarized Field by a Two-Level Transition Technique

Electron-positron pair production rate created from vacuum in the presence of an elliptically polarized laser field is investigated. By applying the technique of two level transition amplitude, a routine for obtaining pair production rate is presented, and approximate analytical expressions are given both for the low frequency strong field regime and the high frequency weak field regime. We found that for an elliptically polarized field, the electron-positron pair production rate decrease when the elliptic eccentricity increase in the high frequency weak field regime, however, in the low frequency strong field regime, there is almost the same electron-positron pair production rate as in the constant electric field case.

A detailed statistical representation of the local structure of optical vortices in random wavefields

The statistical properties near phase singularities in a complex wavefield are here studied by means of the conditional distributions of the real and imaginary Gaussian components, given a common zero crossing point. The exact distribution is expressed as a Slepian model, where a regression term provides the main structure, with parameters given by the gradients of the Gaussian components at the singularity, and Gaussian non-stationary residuals that provide local variability. This technique differs from the linearization (Taylor expansion) technique commonly used. The empirically and theoretically verified elliptic eccentricity of the intensity contours in the vortex core is a property of the regression term, but with different normalization compared to the classical theory. The residual term models the statistical variability around these ellipses. The radii of the circular contours of the current magnitude are similarly modified by the new regression expansion and also here the random deviations are modeled by the residual field.

Three dimensional wave scattering by arrays of elliptical and circular cylinders

Recently, Chatjigeorgiou and Mavrakos (2009, 2010a) provided an analytic solution for the three dimensional wave scattering by arrays of elliptical cylinders. The present paper extends the contents of the existing study to tackle the problem of the hydrodynamic interactions between elliptical and circular cylinders. The main task is to derive an analytic solution for the total velocity potential for an arbitrary body of the array and accordingly, to express the hydrodynamic pressure, the exciting forces and the wave elevation in compact analytic closed-forms. The solution method is rather complicated as it considers the circular cylinders as different geometries and not special cases of elliptical cylinders with zero elliptic eccentricity. Nevertheless, the adopted procedure enhances the mathematical reconstruction of the physical subject as it requires the derivation and the employment of addition theorems that transform expressions from elliptic to polar coordinate systems in all four possible combinations.

Study on Scattering of Left-Handed Materials Elliptical Cylinder

Left-handed Materials (LHM) is a kind of structural materials of artificial cycle which permittivity ε and permeability μ are both negative. This article mainly studied the electromagnetic scattering characteristics of LHM by using the method of rigorous modal matching, and discussed the variation of corresponding elliptical eccentricity, its loss and negatively permittivity on the effect of radar cross section by numerical calculation .

Optimal design of hollow elliptical waveguide for THz radiation

Based on propagation equations of and metal-coated elliptical waveguide, we derived the characteristic equations of the waveguides. And the relationship between effective refractive index and ellipticity for two-layer media waveguide. Also obtained the relationships between attenuation coefficient and metal conductivity, elliptical eccentricity and ellipse semi-major axis for the latter waveguide. We got the corresponding ellipse eccentricities of different frequency in the THz band. The results showed that the elliptical waveguide was more suitable than the circular waveguide for transmitting THz wave. Our results were helpful in optimal designing of elliptical waveguide.

Simulated elliptical bioprosthetic valve deformation: Implications for asymmetric transcatheter valve deployment

The asymmetric, elliptical shape of a transcatheter aortic valve (TAV), after implantation into a calcified aortic root, has been clinically observed. However, the impact of elliptical TAV configuration on TAV leaflet stress and strain distribution and valve regurgitation is largely unknown. In this study, we developed computational models of elliptical TAVs based on a thin pericardial bioprosthetic valve model recently developed. Finite element and computational fluid dynamics simulations were performed to investigate TAV leaflet structural deformation and central backflow leakage, and compared with those of a nominal symmetric TAV. From the results, we found that for a distorted TAV with an elliptical eccentricity of 0.68, the peak stress increased significantly by 143% compared with the nominal circular TAV. When the eccentricity of an elliptical TAV was larger than 0.5, a central backflow leakage was likely to occur. Also, deployment of a TAV with a major calcified region perpendicular to leaflet coaptation line was likely to cause a larger valve leakage. In conclusion, the computational models of elliptical TAVs developed in this study could improve our understanding of the biomechanics involved in a TAV with an elliptical configuration and facilitate optimal design of next-generation TAV devices.