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Numerical procedures for the calculation of the stresses in monocoques III : calculation of the bending moments in fuselage frames

This report deals with the calculation of the bending moments in and the distortions of fuselage rings upon which known concentrated and distributed loads are acting. In the procedure suggested, the ring is divided into a number of beams each having a constant radius of curvature. The forces and moments caused in the end sections of the beams by individual unit displacements of the end sections are listed in a table designated as the operations table in conformity with Southwell's nomenclature. The operations table and the external loads are equivalent to a set of linear equations. For their solution the following three procedures are presented: 1) Southwell's method of systematic relaxations. This is a step-by-step approximation procedure guided by the physical interpretation of the changes in the values of the unknown. 2) The growing unit procedure in which the individual beams are combined successively into beams of increasing length until finally the entire ring becomes a single beam. In each step of the procedure a set of not more than three simultaneous linear equations is solved. 3) Solution of the entire set of simultaneous equations by the methods of the matrix calculus. In order to demonstrate the manner in which the calculations may be carried out, the following numerical examples are worked out: 1) Curved beam with both its end sections rigidly fixed. The load is a concentrated force. 2) Egg-shape ring with symmetric concentrated loads. 3) Circular ring with antisymmetric concentrated loads and shear flow (torsion of the fuselage). 4) Same with V-braces incorporated in the ring. 5) Egg-shape ring with antisymmetric concentrated loads and shear flow (torsion of the fuselage). 6) Same with V-braces incorporated in the ring. The results of these calculations are checked, whenever possible, by calculations carried out according to known methods of analysis. The agreement is found to be good. The amount of work necessary for the solution of ring problems by the methods described in the present report is practically independent of the degree of redundancy of the structure. For this reason the methods are recommended for use particularly in problems of rings having one or more internal bracing elements.

LOADS - FUSELAGES↗

The narrow rings of Jupiter, Saturn and Uranus

The origin of the newly discovered narrow ring systems around Jupiter, Saturn and Uranus is considered. It is pointed out that both the Uranian and Jovian ring systems have mean orbital radii of 1.8 planetary radii and lie within the Roche zones of their respective planets, and it is suggested that the Jovian ring is the product of the disintegration of a satellite that entered the Roche zone, and that large numbers of small particles are now in horseshoe orbits about the Lagrangian equilibrium points of the remnant chunks. Analysis of the path of a ring particle in a horseshoe orbit is shown to result in ring structures in agreement with those observed for the circular rings of Jupiter and the highly eccentric ring of Uranus. The stability of these ring systems is then considered, and it is suggested that the F ring of Saturn, which lies outside the Roche zone, represents primordial matter not yet accreted by small satellites just inside the Mimas first-order resonances.

Dermott, S. F.↗

Stability of structural rings under uniformly distributed radial loads

Energy method analysis establishes parameters governing stability of circular rings acted upon by constant, uniformly distributed loads. Energy method is used so that nonlinear behavior of structure before buckling can be accounted for. Method affords conceptually superior basis for analyzing the axisymmetric deviation mode.

Williams, H. E.↗

Precession of inclined rings

It is proposed that node alignment across an inclined ring is maintained by the self-gravity of the ring, which cancels the tendency for differential node precession due to the planet's multiple moments. The analysis is confined to circular rings, which is a self-consistent approximation because the interactions among circular and inclined ringlets do not generate secular perturbations of eccentricity.

Borderies, N.↗

Observational studies of Saturn's rings

Several noteworthy phenomena in Saturn's rings were investigated which have until now received an inadequate amount of attention. Among these are the periodic variation of the spokes in the B ring and eccentric features throughout the rings. One of the major discoveries by Voyager was the existence of eccentric features within the predominantly circular rings of Saturn. Several of these nonaxisymmetric features are narrow elliptical rings which share many characteristics with the rings of Uranus. In recent work, two narrow ringlets were added to the list of eccentric features in the rings of Saturn. Voyager imaging and occultation data are now in hand, as well as image-processing software which allows accurate absolute positional measurements to be made in Voyager imaging data. Work is in progress to re-examine this region of Saturn's rings and to study the possibility of a dynamical interaction between the outer B ring edge, the Huygens ringlet and the nearby Mimas 2:1 resonance. An understanding of the kinematics and dynamics of this region promises to yield important clues to a matter of great interest in both theoretical and observation ring studies.

Porco, Carolyn C.↗

The morphology of and locations of star formation in impact induced ring galaxies

Observed ring galaxies appear to fall into two major types. The first tends to consist of isolated galaxies which display a smooth, apparently circular ring and a central nucleus. These have been variously classified as R(S) by de Vaucouleurs (1959) and as type O by Few and Madore (1986). The second class of ring galaxy nearly always has a close companion of comparable size (no less than about one tenth that of the ring galaxy). In these objects the ring is knotty in appearance, is usually elliptical, even when deprojected on the sky, and is often open on one side, having a 'horse shoe' or 'banana' shape. The nucleus does not usually appear at the center of the ring and is sometimes apparently absent, giving rise to an 'empty ring' galaxy. deVaucouleurs et al. (1976) designated this second type as RING, while Few and Madore (1986) have classified similar galaxies as P type. These galaxies have elevated far IR emission, bright HII regions, and blue spectral colors. The different environments of the two types or ring galaxy, together with their overall morphological and spectral differences suggest that the R(S)/O type are most probably the result of an instability that occurs in isolated galaxies, whereas the RING/P type appears to be the result of a recent collision between two roughly equal mass objects, at least one of which is a disk galaxy. Theys and Spiegel (1976) studied a sample of this latter type and identified three subclasses: RE: galaxies with crisp, empty rings; RN: galaxies like those of RE but with off-center nuclei; RK: galaxies having single dominant knots or condensations in the rings. A presentation of a preliminary understanding of the connections between these different observed forms in terms of parameters which are intrinsic to the galaxy system, such as time since collision and impact parameter, and in terms of our line of sight view is the purpose of this paper. Here we report results we have obtained from three dimensional computer simulations of collisions between equal mass galaxies, one of which is a rotating, disk galaxy containing both gas and stars and the other is an elliptical containing stars only. We have used a combined n-body/SPH program (see Balsara, 1990) to model fully self consistent models in which the halo mass is 2.5 times that of the disk and gas comprises ten percent of the disk mass.

Lamb, Susan A.↗

Line fluorescence from the ring around supernova 1987A

Observations in lambda 5007 which reveal an ellipse of line emission around SN 1987A are reviewed. A simple expression for the rate at which the kinematically accessible paraboloid sweeps over the length of a thin uniform circular ring is derived, and a simple integral expression for the light curve F(t) of a fluorescent line in terms of epsilon(t), the local line emissivity, is presented. Many simple examples of the relationship between epsilon(t) and F(t) are graphed, and the results are used to deduce the characteristics of the local emissivity functions which produce the best fit to the observed semiforbidden N III 1750 and N V 1240 light curves. The N III and N V light curves are inverted to find the functions epsilon(t) which give best fits to the observations.

Dwek, Eli↗

The nature of circular maria based on gravity studies.

Current thinking on the evolution of major lunar morphological features, i.e., large lunar circular basins, and on the nature and origin of surface structures observed in the fill deposits is summarized. The great lunar circular basins must result from high-velocity impact of large bodies with the moon. A hydrostatic mechanism is outlined, and a working hypothesis is presented for the evolution of lunar circular basins subsequent to their origin by impact. In the main appeal is made to Doppler gravity data to support the hypothesis, although photographic and altimetric information is also used. It is considered that all large ringed circular basins follow a common evolutionary path of superisostatic volcanic flooding followed by partial and variable isostatic adjustment. The difference between basins is the amount of flooding, which in turn may be related to the center of figure-center of mass offset of the moon.

Phillips, R. J.↗

A granular flow model for dense planetary rings

In the present study of the viscosity of a differentially rotating particle disk, in the limiting case where the particles are densely packed and their collective behavior resembles that of a liquid, the pressure tensor is derived from both the equations of hydrodynamics and a simple kinetic model of collisions due to Haff (1983). Density waves and narrow circular rings are unstable if the liquid approximation applies, and the consequent nonlinear perturbations may generate 'splashing' of the ring material in the vertical direction. These results are pertinent to the origin of the ellipticities of ringlets, the nonaxisymmetric features near the outer edge of the Saturn B ring, and unexplained residuals in kinematic models of the Saturn and Uranus rings.

Borderies, N.↗

Collaborative Research: Polymer Macrocycles: A novel topology to control dynamics of rubbery materials

Understanding the dynamics of polymers of different topologies is an important field of study and one of the most important unanswered questions in this field is "how do circular polymers move," particularly in the melt state. New information suggests that molecular topology, specifically circular rings, impacts the response of materials in nanometer- scale confinement. The work performed here tackles these subjects through a collaboration in which specialists in polymer synthesis, polymer rheology and scattering methods, and in the physics of nanoconfinement work together to investigate the thermophysical behavior of circular macromolecules. The project goals are to use a novel synthesis method of "green" oxidative polymerization to produce high purity macrocycles and to investigate their linear viscoelastic behavior in order to fully characterize the dynamics of circular macromolecules to sizes that correspond to linear molecule entanglement densities higher than previously obtainable with synthetic polymers. Chemical chain end characterization and critical edge fractionation coupled with direct visualization of the prepared polymers through the use of polymer amplification methods are proposed in order to quantify the numbers of circular and linear molecules in each sample. The study of the linear viscoelastic response of blends of linear and circular molecules is also to be undertaken in the project. Nonlinear viscoelastic measurements, including extensional viscosity, are to be made. Strong differences in behavior between linear chains and circular ones also provides an important opportunity for new technology to break the "magic triangle" for tires: it is believed that improving one of the three key attributes - traction, wear, rolling resistance - necessarily sacrifices at least one of the others. Rubber made from cyclic polymers has the potential to break out of this triangle by reducing the so-called Payne effect in reinforced rubbers because circular macromolecules are less sensitive to nanoconfinement than their linear counterparts. The work has as one objective to characterize the impact of nanoconfinement on the behavior of large circular macromolecules. In addition, the dynamics of carbon black filled circular macromolecules are to be studied to test the hypothesis that the resulting rubbery materials will exhibit a reduced Payne effect.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Mascons - Progress toward a unique solution for mass distribution.

Through a series of analyses with high-altitude Lunar Orbiter and low-altitude Apollo 15 Doppler gravity data, it is shown that the Serenity mascon is a thin body whose horizontal dimensions are well determined and show a strong correlation with circular wrinkle ridge structure. Analysis to date has not uniquely determined the depth of the anomalous mass. However, geological evidence strongly suggests that the mass excess is near the surface, because (1) the surface solution has a geometry highly suggestive of the partial filling of a ringed circular basin, and (2) the boundaries of the anomalous mass separate regions of shallow and deep mare flooding.

Phillips, R. J.↗

Properties of the SN 1987A circumstellar ring and the distance to the Large Magellanic Cloud

The distance to SN 1987A was determined by comparing the angular size of its circumstellar ring, measured from an HST image obtained in a narrow forbidden O III 5007 A filter, with its absolute size derived from an analysis of the light curves of narrow UV lines measured with the IUE. The analysis confirms that the observed elliptical structure is a circular ring seen at a mean inclination of i = 42.8 + or - 2.6 deg and provides a determination of its absolute diameter of (1.27 + or - 0.07) x 10 to the 18th cm. Its ratio to the angular diameter of 1.66 + or - 0.03 arcsec gives an accurate determination of the distance to SN 1987A, i.e., d(1987A) = 51.2 + or - 3.1 kpc.

Panagia, N.↗

Characterize the Rings in Protoplanetary Disks Formed by an Eccentric Instability [Slides]

Typical long-term time evolution of gas surface density in a disk undergoing eccentric mode instability (EMI). In a disk with no initial substructures or external perturbers, EMI generates a growing one arm spiral (top right). After EMI saturates, the disk continues to evolve with a long-lived coherent eccentric pattern. If the disk has strong wave damping, the disk is then left with circular rings. Synthesized dust continuum images of some EMI simulations from this IC project show some characteristics similar to the actual PPD images.

79 ASTRONOMY AND ASTROPHYSICS↗

Photometry, Centroid and Point-spread Function Measurements in the LSST Camera Focal Plane Using Artificial Stars

Abstract The Vera C. Rubin Observatory’s LSST Camera (LSSTCam) pixel response has been characterized using laboratory measurements with a grid of artificial stars. We quantify the contributions to photometry, centroid, point-spread function size, and shape measurement errors due to small anomalies in the LSSTCam CCDs. The main sources of those anomalies are quantum efficiency variations and pixel area variations induced by the amplifier segmentation boundaries and “tree-rings”—circular variations in silicon doping concentration. This laboratory study using artificial stars projected on the sensors shows overall small effects. The residual effects on point-spread function (PSF) size and shape are below 0.1%, meeting the ten-year LSST survey science requirements. However, the CCD mid-line presents distortions that can have a moderate impact on PSF measurements. This feature can be avoided by masking the affected regions. Effects of tree-rings are observed on centroids and PSFs of the artificial stars and the nature of the effect is confirmed by a study of the flat-field response. Nevertheless, further studies of the full-focal plane with stellar data should more completely probe variations and might reveal new features, e.g., wavelength-dependent effects. The results of this study can be used as a guide for the on-sky operation of LSSTCam.

79 ASTRONOMY AND ASTROPHYSICS↗

Spatially-resolved Spectroscopy of the IC443 Pulsar Wind Nebula and Environs

Deep Chandra ACIS observations of the region around the putative pulsar, CXOU J061705.3+222117, in the supernova remnant IC443 reveal, for the first time, a ring-like morphology surrounding the pulsar and a jet-like structure oriented roughly north-south across the ring and through the pulsar location. The observations further confirm that (1) the spectrum and flux of the central object are consistent with a rotation-powered pulsar interpretation, (2) the non-thermal surrounding nebula is likely powered by the pulsar wind, and (3) the thermal-dominated spectrum at greater distances is consistent with emission from the supernova remnant. The cometary shape of the nebula, suggesting motion towards the southwest (or, equivalently, flow of ambient medium to the northeast), appears to be subsonic; there is no evidence for a strong bow shock, and the circular ring is not distorted by motion through the ambient medium.

Swartz, D. A.↗

Self-organized patterns at the plasma–liquid anode interface in a helium glow discharge: temporal development and mechanisms

Self-organization at the plasma–liquid anode interface is a commonly observed phenomenon for atmospheric pressure glow plasmas, resulting in patterns with distinctive shapes such as circular ring, star-shaped, and gear-like structures, depending primarily on the discharge current and solution conductivity. Recent studies have shown that the electrode gap distance, solute used for liquid anode solution, and gas composition can also significantly impact pattern formation. Nonetheless, an overarching model or explanation of the key underlying mechanisms consistent with all experimentally observed trends is not yet reported. We propose a key underlying mechanism enabling pattern formation motivated by a detailed parametric study of pattern formation complemented by the temporal development of patterns and consistent with all observed trends. Pattern formation was observed to be on a time scale of 100 μs, similar to the time scales of gas heating and evaporation. It was found that a minimum water evaporation rate of (3.5 ± 0.5) × 10 –6 kg s –1 and reduced electric field in the positive column of 16.6 ± 0.4 Td is required for pattern formation in the investigated cases irrespective of solution conductivity and gas composition for NaCl solutions. Nonetheless, the presence of cations for which the corresponding metal atom has a low ionization energy was identified as a necessary condition for pattern formation. Furthermore, the reported results suggest that the presence of a small amount of metal atoms in the gas phase with low ionization energy enhances the overall ionization rate in the near anode region which triggers pattern formation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Influence of liquid conductance on the temporal evolution of self-organization patterns in atmospheric pressure DC glow discharges

Abstract Self-Organized Patterns (SOPs) at plasma-liquid interface in atmospheric pressure plasma discharges refer to the formation of intricate and puzzling structures due to the interplay of electrodynamic and hydrodynamic processes. Studies conducted to date have shown that this phenomenon results in the formation of distinctive patterns such as circular ring, star, gear, dots, spikes, etc., and primarily depends on working gas, electrolyte type, gap distance, current, conductivity, etc. However, an adequate understanding of how these patterns change from one type to another is still not available. This study aims to elucidate the influence of initial liquid conductance ( σ i ) on the temporal evolution of SOPs in liquid-anode discharges. The discharge was generated in a pin-to-liquid anode configuration at a constant helium (He) flow rate of 500 sccm and DC applied voltage of 6 kV at a gap distance of 12 mm. Through the gradual increment of σ i from 1.8 μ S to 4820 μ S, we observe that the trend in the evolution of SOPS takes place as solid discs, spikes, dots, rings, double rings, and stars. The continuous formation of reactive species onto the liquid anode in all conductive solutions results in a decrease in pH, an increase in bulk liquid temperature, and an increase in total dissolved solutes, and these have been confirmed through experimental measurements. Observations using optical emission spectroscopy show that the electrons at the plasma-liquid interface participate in the reduction of cations followed by their excitation & ionization due to which electron density as well as emissions from excited species (mainly hydroxyl radicals & excited nitrogen) decrease with time. Our investigation provides experimental evidence on the presence of cations at the plasma-liquid interface required for SOP formation.

Physics↗

Assembly of the MOLLER Toroidal Magnets at Jefferson Lab

The MOLLER experiment at the Thomas Jefferson National Accelerator Facility (JLab) aims to precisely measure the weak interaction between electrons. This experiment leverages the 12 GeV electron beam and will run for three years. A crucial component of MOLLER is a system of five uniquely shaped water-cooled toroidal magnets. These magnets, possessing seven-fold symmetry, are designed to focus particles by separating electrons scattered off hydrogen in a liquid hydrogen target. The five magnets separate electrons scattered off electrons (Møller scattering) and protons (elastic e-p scattering) within target into approximately circular rings at the detector. Here, this paper presents the assembly process for these five toroidal magnets, detailing critical steps including epoxy application, pin insertion, soldering and brazing, coil assembly, and alignment, all performed to meet stringent magnet specifications. Additionally, it discusses challenges encountered during construction and highlights lessons learned, offering insights for future magnet development projects.

Lamont, Joseph [Thomas Jefferson National Accelera↗