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The steady discharge of a high-voltage corona is analyzed as a singular perturbation problem. The small parameter is the ratio of the length of the ionization region to the total gap length. By this method, current versus voltage characteristics can be calculated analytically.
We describe here a new phenomenon characterized by unusual patterns of ion drifts inside ion density depletion regions observed by the AE-E satellite in the low-latitude F region. In about 30 depletions, vertical ion drift relative to the background was upward on the western sides, downward on the eastern sides, and zero near the middle where the density depletion was greatest. These drift characteristics are distinct from those observed in plasma bubble depletions. The structures reported here were observed on circular orbits below 300 km altitude and had density depletions of up to 2 orders of magnitude or more below the ambient ion density. The upward and downward drift excursions were up to 200 m/s relative to the background. Almost all these structures were observed over oceans or near coasts and largely between +/- 10 deg and +/- 30 deg clip latitude. The structures were observed mostly as isolated, single depletion regions with the majority of them about 250 km wide in the east-west direction. They occurred during quiet magnetic conditions with near-equal occurrence frequencies in the premidnight and postmidnight periods. The characteristic density and drift signatures indicate westward propagating disturbances in which the bottomside F layer is first lifted and then returned back to its original position, leaving the ionosphere undisturbed after the disturbance passes by. The estimated speed of these disturbances is of the order of 200 m/s. These unique solitary plasma disturbances, which we designate as singular plasma disturbances, are associated with a propagating source of E x B drift, not driven by neutral perturbations at the altitude of observation.
The unsteady aerodynamics of a two-dimensional wing at sonic speed are studied by using so-called classical sonic theories (linear), approached from supersonic flow (M=1+0) or subsonic flow (M=1-0). In the former approach, the exact expressions of lift and lift distribution are obtained in terms of Fresnel integrals, while in the latter approach an integral equation must be solved, the kernel function of which is obtained from the subsonic Possio's equation and has a root singularity. The discrete analysis is adopted on the basis of the semicircle method (SCM) and the weighting function for subsonic-flow-Gauss-quadrature, as well as modified characteristics obtained from both approaches agree quite well with each other. The results obtained by the present computations are compared with those of DLM-C (subsonic 2D code) developed by ANDO et al, and are found to give a reasonable outer boundary for subsonic unsteady aerodynamics.
An analytical investigation of the mechanics and failure modes of delamination initiated from a service-induced surface flaw in angle-ply fiber reinforced composites is presented. The analysis employs a hybrid-stress finite element method including a crack-tip singular element with its field variables expressed by Muskhelishvili's complex stress functions. Solutions are obtained for delaminated composites with various laminate parameters. The results elucidate unique and important characteristics of delamination crack-tip response and interlaminar stress transfer mechanisms. Of particular interest are the mixed-mode stress intensity factors associated with the delamination crack. The influence of ply orientation on KI and KII and their effects on subsequent crack extension are discussed.
The most robust estimators minimizing Wahba's loss function are Davenport's q method and the Singular Value Decomposition (SVD) method. The q method is faster than the SVD method with three or more measurements. The other algorithms are less robust since they solve the characteristic polynomial equation to find the maximum eigenvalue of Davenport's K matrix. They are only preferable when speed or processor power is an important consideration. Of these, Fast Optimal Attitude Matrix (FOAM) is the most robust and faster than the q method. Robustness is only an issue for measurements with widely differing accuracies, so the fastest algorithms, Quaternion ESTimator (QUEST), EStimator of the Optimal Quaternion (ESOQ), and ESOQ2, are well suited to star sensor applications.
A study of the mechanics and failure modes of delamination initiated from a surface flaw in angle-ply fiber-reinforced composites is presented. The analysis employs a hybrid-stress finite-element method including a crack-tip singular element with its field variables expressed by Muskhelishvili's complex stress functions. Solutions are obtained for the delaminated composites with various laminate parameters. The results elucidate unique and important characteristics of delamination crack-tip response and interlaminar stress transfer mechanisms. Of particular interest are the mixed-mode stress-intensity factors associated with the delamination crack. The influence of ply orientation on KI and KII and their effects on subsequent crack extension are discussed.
The methodology and a rigorous solution formulation are presented for stress intensity factors (SIF's, k) and total strain energy release rates (SERR, G(sub T)) of a multicracked plate, that has fully interacting cracks and is subjected to a far-field arbitrary stress state. The fundamental perturbation problem is derived, and the steps needed to formulate the system of singular integral equations whose solution gives rise to the evaluation of the SIF's are identified. Parametric studies are conducted for two, three, and four crack problems. The sensitivity and characteristics of the model is demonstrated.
Despite obvious similarities in their electronic and crystallographic structures, it remains unclear whether the interactions that shape the normal and superconducting (SC) state properties of high-T c cuprates and infinite-layer nickelates (ILNs) have the same origin. This question has been brought into sharper focus with recent studies on ILNs of improved crystallinity that reveal a SC dome of comparable extent and similar transport properties above T c as the hole-doped cuprates. The evolution of these properties in the magnetic-field-induced normal state, however, has yet to be determined. Here, we examine the magnetotransport properties of new-generation Nd 1−x Sr x NiO 2 films in the T → 0 limit across the phase diagram in fields up to 54 T. This extensive study reveals that the limiting low-T form of the normal-state resistivity in ILNs exhibits non-Fermi-liquid behaviour over an extended doping range inside the SC dome, rather than at a singular quantum critical point. While there are clear differences in the charge dynamics of ILNs and cuprates, most notably in the magnetoresistance, our findings reveal that both systems exhibit anomalous metallicity characteristic of a quantum critical phase.
Accomplishments in vortex flap research are summarized. A singular feature of the vortex flap is that, throughout the range of angle of attack range, the flow type remains qualitatively unchanged. Accordingly, no large or sudden change in the aerodynamic characteristics, as happens when forcibly maintained attached flow suddenly reverts to separation, will occur with the vortex flap. Typical wind tunnel test data are presented which show the drag reduction potential of the vortex flap concept applied to a supersonic cruise airplane configuration. The new technology offers a means of aerodynamically augmenting roll-control effectiveness on slender wings at higher angles of attack by manipulating the vortex flow generated from leading edge separation. The proposed manipulator takes the form of a flap hinged at or close to the leading edge, normally retracted flush with the wing upper surface to conform to the airfoil shape.
Gravitational forces are of cardinal importance in the dynamics of spacecraft; magnetic attractions sometime play a significant role also, as was the case with the Long Duration Exposure Facility, and as is now true for the first segment of Space Station Freedom. Both satellites depend on gravitational moment and a device known as a magnetic damper to stabilize their orientation. Magnetic fields are mathematically similar to gravitational fields in one important respect: each can be regarded as a gradient of a potential function that, in turn, can be described as an infinite series of spherical harmonics. Consequently, the two fields can be computed, in part, with quantities that need only be evaluated once, resulting in a savings of time when both fields are needed. The objective of this material is to present magnetic field and gravitational force expressions, and point out the terms that belong to both this is accomplished in Section 1 and 2. Section 3 contains the deductive reasoning with which one obtains the expressions of interest. Finally, examples in Section 4 show these equations can be used to reproduce others that arise in connection with special cases such as the magnetic field produced by a tilted dipole, and gravitational force exerted by an oblate spheroid. The mathematics are discussed in the context of terrestrial fields; however, by substituting appropriate constants, the results can be made applicable to fields belonging to other celestial bodies. The expressions presented here share the characteristics of algorithms set forth for computing gravitational force. In particular, computation is performed speedily by means of recursion formulae, and the expressions do not suffer from the shortcoming of a singularity when evaluated at points that lie on the polar axis.
Abstract Background Docosahexaenoic acid (DHA) and calcidiol could be enriched in chicken for improving public nutrition and health. It remains unclear if supranutritional levels of DHA and calcidiol impair growth performance or metabolism of broiler chickens. This study was to determine singular and combined effects of high levels of supplemental DHA-rich microalgal biomass or oil and calcidiol on growth performance, concentrations of triglycerides, cholesterol, and nonesterfied fatty acids in plasma, liver, breast, and thigh, and biophysical properties of tibia. Methods In Exp. 1, 144 day-old Cornish chicks were divided into 4 groups (6 cages/treatment, 6 birds/cage), and were fed a corn-soybean meal basal diet (BD), BD + 10,000 IU calcidiol/kg (BD + Cal), BD + 1% DHA-rich Aurantiochytrium (1.2 g DHA/kg; BD + DHA), and BD + Cal + DHA for 6 weeks. In Exp. 2, 180 day-old chicks were divided into 5 groups, and were fed: BD, BD + DHA (0.33% to 0.66% oil, 1.5 to 3.0 g DHA/kg), BD + DHA + EPA (1.9% to 3.8% eicosapentaenoic acid-rich Nannochloropsis sp. CO18, 0.3 to 0.6 g EPA/kg), BD + DHA + calcidiol (6000 to 12,000 IU/kg diet), and BD + DHA + EPA + Cal for 6 weeks. Results Birds fed BD + Cal diet in Exp. 1 and BD + DHA + EPA diet in Exp. 2 had higher ( P < 0.05) body weight gain (10%–11%) and gain:feed ratio (7%), and lower ( P < 0.05) total cholesterol and triglyceride concentrations in plasma (18%–54%), liver (8%–26%), breast (19%–26%), and thigh (10%–19%), respectively, over the controls. The two diets also improved ( P < 0.05) tibial breaking strength (8%–24%), total bone volume (2%–13%), and (or) bone mineral density (3%–19%) of chickens. Conclusion Supranutrition of dietary calcidiol and DHA alone or together did not produce adverse effects, but led to moderate improvements of growth performance, lipid profiles of plasma and muscle, and bone properties of broiler chickens.
Detailed measurements of longitudinal mean velocity, turbulence intensity, space correlations, and spectra made in the wake of two rectangular scaled models in simulated atmospheric boundary-layer winds are presented. The model buildings were 1:50 scale models of two trailers. Results of a flow visualization study of the wake geometry are analyzed with some singular point theorems. Two hypothetical flow patterns of the detailed wake geometry are proposed. Some preliminary studies of the vortex wake, effects of the model size, model aspect ratios, and boundary layer characteristics on the decay rate and extent of the wake are also presented and discussed.
The aerodynamic characteristics of potential flow past an axisymmetric slender body and a thin airfoil are calculated using a uniform perturbation analysis method. The method is based on the superposition of potentials of point singularities distributed inside the body. The strength distribution satisfies a linear integral equation by enforcing the flow tangency condition on the surface of the body. The complete uniform asymptotic expansion of its solution is obtained with respect to the slenderness ratio by modifying and adapting an existing technique. Results calculated by the perturbation analysis method are compared with the existing surface singularity panel method and some available analytical solutions for a number of cases under identical conditions. From these comparisons, it is found that the perturbation analysis method can provide quite accurate results for bodies with small slenderness ratio. The present method is much simpler and requires less memory and computation time than existing surface singularity panel methods of comparable accuracy.
We present a machine learning-based magnetohydrodynamic (MHD) classifier and regressor that utilizes real or complex-valued 3D magnetic sensor array data to determine neoclassical tearing mode (NTM) onset times in tokamaks with millisecond accuracy. The input dataset consists of poloidal profiles of complex Fourier amplitudes with an n = 1 toroidal mode number from 144 human-labeled ITER Baseline Scenario discharges in the DIII-D tokamak, spanning both tearing-dominated and sawtooth-dominated regimes. Since m, n = 2,1 NTMs frequently emerge alongside sawteeth at the same frequency in this scenario, the focus is on isolating the m = 1 and m = 2 components of the n = 1 MHD mode near the tearing onset. To improve model regularization and prediction stability, singular value decomposition was applied to balance the sawtooth and tearing datasets. The enriched datasets facilitated training neural networks that learn the key distinguishing features of sawtooth and tearing modes in the poloidal profiles of their magnetic amplitude and phase. When the modes occur independently, the networks achieve perfect classification due to the modes’ distinct characteristics and low measurement noise. In the more experimentally relevant case where both modes coexist, the networks maintain exceptional performance across key metrics. Tests on synthetic data with known ground truth demonstrate the superior accuracy of the neural network trained on complex-valued input compared to models using real amplitude, phase, or pseudo-complex data, achieving both a mean time delay and standard deviation below 1 ms. Notably, standard linear regression methods fitting the dominant singular modes to the data closely match the neural network’s performance. Applying these methods across a broad range of H-mode scenarios will enable future studies to systematically identify dominant NTM triggers as scenario-specific variables, paving the way for more effective tearing mode avoidance strategies in future fusion reactor designs.
Unsteady heat transfer characterization on the combustion surfaces of Rotational Detonation Engines (RDE) is not well understood. It is generally thought that the complex nature of the unsteady, reacting, compressible fluid flow inside the combustion anulus of the RDE causes the convective heat transfer coefficient to be significantly higher than it is in other applications. Empirical models that have been used to analyze this strictly apply to steady flows where dimensionless groups can be employed. The reacting flow fields that are characteristic of RDEs are inherently compressible, three dimensional, unsteady, and turbulent, having properties that change by orders of magnitude throughout the flow field. They will therefore contain multiple length scales and time scales operating everywhere in the flow during all times. Because of this it is not likely that the RDE flow fields will lend themselves to explanation using simple dimensionless parameters. The dimensionless groups have meaning only in situations where length scales and time scales are singular and well defined. In spite of this it may be possible to get a relatively good idea of what the convection heat transfer coefficient is. In this work a numerical study is performed where the inside wall surface temperature distribution in the RDE outer body is systematically changed over a given range that would be characteristic of the start-up flows inside an RDE. For each case, temperature distributions inside the outer containment wall of the RDE was calculated and compared with experimental data. The closet match can then be used to directly calculate the convection heat transfer coefficient on the inside surface of the RDE.
A model is suggested to study the viscid-inviscid interaction associated with steady incompressible flow past wedges of arbitrary angles. It is shown from this analysis that the determination of the nearly constant pressure (base pressure) prevailing within the near wake is really the heart of the problem and this pressure can only be determined from these interactive considerations. The basic free streamline flow field is established through two discrete parameters which should adequately describe the inviscid flow around the body and the wake. The viscous flow processes such as boundary-layer buildup along the wedge surface, jet mixing, recompression, and reattachment which occurs along the region attached to the inviscid flow in the sense of the boundary-layer concept, serve to determine the aforementioned parameters needed for the establishment of the inviscid flow. It is found that the point of reattachment behaves as a saddle point singularity for the system of equations describing the viscous recompression process. Detailed results such as the base pressure, pressure distributions on the wedge surface, and the wake geometry as well as the influence of the characteristic Reynolds number are obtained. Discussion of these results and their comparison with the experimental data are reported.
The paper deals with the development of a design method for a servo component in the frequency domain using singular values and its application to a reusable rocket engine. A general methodology used to design a class of linear multivariable controllers for intelligent control systems is presented. Focus is placed on performance and robustness characteristics, and an estimator design performed in the framework of the Kalman-filter formalism with emphasis on using a sensor set different from the commanded values is discussed. It is noted that loop transfer recovery modifies the nominal plant noise intensities in order to obtain the desired degree of robustness to uncertainty reflected at the plant input. Simulation results demonstrating the performance of the linear design on a nonlinear engine model over all power levels during mainstage operation are discussed.
The present investigation shows that a finite element scheme with a weighted least squares variational principle is applicable to the problem of transonic flow around a harmonically oscillating airfoil. For the flat plate case, numerical results compare favorably with the exact solution. The obtained numerical results for the transonic problem, for which an exact solution is not known, have the characteristics of known experimental results. It is demonstrated that the performance of the employed numerical method is independent of equation type (elliptic or hyperbolic) and frequency. The weighted least squares principle allows the appropriate modeling of singularities, which such a modeling of singularities is not possible with normal least squares.