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All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Theoretical shell-model signatures in heavy-ion, coherent pion production

A comprehensive summary of a many-body, microscopic, particle-hole formalism is presented that describes coherent, subthreshold, pion production in peripheral, heavy-ion collisions. The formalism uses a new separable model transition interaction that produces Delta-hole states in either the projectile or target nucleus. Shell-model states described by harmonic oscillator functions are used in the calculation of Delta formation and decay and Lorentz-contraction effects of the nucleus not at rest are included. An analytical expression to lowest multipole order for the differential cross section is examined. The sensitivity of the theoretical results to the shell-model states is determined with preliminary shape results compared with data. The effects of higher multipoles are examined with attention paid to the second-order multipole value.

Maung, Khin M.↗
NASA NTRS1974

A dust-shell model of the infrared object HD 45677

A dust-shell model of the infrared star HD-45677 was constructed by means of a generalization of the mathematical techniques of Huang. The model shows that an isotropically scattering, uniform-density spherical circumstellar dust shell is able to account for the observed emergent energy distribution. The extinction properties of the grains required depend on the energy distribution incident on the inner boundary of the shell such that gray grains are needed if the stellar temperature is about 13,000 K and a reciprocal wavelength extinction law is indicated for a star of 20,000 K. This model for HD 45677 is compared with that of Dyck and Milkey, who propose free-free emission from a circumstellar gas shell to account for the observed infrared excess.

Apruzese, J. P.↗
NASA NTRS2007

Shell Models of RMHD Turbulence and the Heating of Solar Coronal Loops

A simplified nonlinear numerical model for the development of incompressible magnetohydrodynamics in the presence of a strong magnetic field B|| and stratification, nicknamed 'Shell-Atm,' is presented. In planes orthogonal to the mean field, the nonlinear incompressible dynamics is replaced by two-dimensional shell models for the complex variables u and b, allowing one to reach large Reynolds numbers while at the same time carrying out sufficiently long integrations to obtain good statistics at moderate computational cost. The shell models of different planes are coupled by Alfve'n waves propagating along B||. The model may be applied to open or closed magnetic field configurations where the axial field dominates and the plasma pressure is low; here we apply it to the specific case of a magnetic loop of the solar corona heated by means of turbulence driven by photospheric motions, and we use statistics for its analysis. The Alfven waves interact nonlinearly and form turbulent spectra in the directions perpendicular and, through propagation, also parallel to the mean field. A heating function is obtained and shown to be intermittent; the average heating is consistent with values required for sustaining a hot corona and is proportional to the aspect ratio of the loop to the -1.5 power, and haracteristic properties of heating events are distributed as power laws. Crosscorrelations show a delay of dissipation compared with energy content.

corona↗
NASA NTRS1971

Vibration characteristics of Z-ring-stiffened 60 deg conical shell models of a planetary entry spacecraft

An experimental investigation of the vibration characteristics of a 60 deg conical shell model of a planetary entry vehicle is described and the results presented. Model configurations include the shell with or without one or two Z-ring stiffeners and with or without a simulated payload. Tests were conducted with the model clamped at the small diameter and with the model suspended at the simulated payload. Additionally, calculated results obtained from application of several analytical procedures reported in the literature are presented together with comparisons between experimental and calculated frequencies and meridional mode shapes. Generally, very good frequency agreement between experimental and calculated results was obtained for all model configurations. For small values of circumferential mode number, however, the frequency agreement decreased as the number of ring stiffeners increased. Overall agreement between experimental and calculated mode shapes was generally good. The calculated modes usually showed much larger curvatures in the vicinity of the rings than were observed in the experimentally measured mode shapes. Dual resonances associated with modal preference were noted for the shell without Z-ring stiffeners, whereas the addition of stiffeners produced resonances for which the model responded in two or more modes over different sections of the shell length.

Naumann, E. C.↗
NASA NTRS1994

Discrete-Layer Piezoelectric Plate and Shell Models for Active Tip-Clearance Control

The objectives of this work were to develop computational tools for the analysis of active-sensory composite structures with added or embedded piezoelectric layers. The targeted application for this class of smart composite laminates and the analytical development is the accomplishment of active tip-clearance control in turbomachinery components. Two distinct theories and analytical models were developed and explored under this contract: (1) a discrete-layer plate theory and corresponding computational models, and (2) a three dimensional general discrete-layer element generated in curvilinear coordinates for modeling laminated composite piezoelectric shells. Both models were developed from the complete electromechanical constitutive relations of piezoelectric materials, and incorporate both displacements and potentials as state variables. This report describes the development and results of these models. The discrete-layer theories imply that the displacement field and electrostatic potential through-the-thickness of the laminate are described over an individual layer rather than as a smeared function over the thickness of the entire plate or shell thickness. This is especially crucial for composites with embedded piezoelectric layers, as the actuating and sensing elements within these layers are poorly represented by effective or smeared properties. Linear Lagrange interpolation polynomials were used to describe the through-thickness laminate behavior. Both analytic and finite element approximations were used in the plane or surface of the structure. In this context, theoretical developments are presented for the discrete-layer plate theory, the discrete-layer shell theory, and the formulation of an exact solution for simply-supported piezoelectric plates. Finally, evaluations and results from a number of separate examples are presented for the static and dynamic analysis of the plate geometry. Comparisons between the different approaches are provided when possible, and initial conclusions regarding the accuracy and limitations of these models are given.

Heyliger, P. R.↗
NASA NTRS1985

Onion-shell model for cosmic ray electrons and radio synchrotron emission in supernova remnants

The spectrum of cosmic ray electrons, accelerated in the shock front of a supernova remnant (SNR), is calculated in the test-particle approximation using an onion-shell model. Particle diffusion within the evolving remnant is explicity taken into account. The particle spectrum becomes steeper with increasing radius as well as SNR age. Simple models of the magnetic field distribution allow a prediction of the intensity and spectrum of radio synchrotron emission and their radial variation. The agreement with existing observations is satisfactory in several SNR's but fails in other cases. Radiative cooling may be an important effect, especially in SNR's exploding in a dense interstellar medium.

Beck, R.↗
NASA NTRS1977

The moon's permanent magnetic field - A cratered-shell model

The possibility is considered that the properties of the larger-scale lunar magnetic field may depend in a rather straightforward manner on the geometrical properties of the distribution of larger craters. The relevant effects of cratering are analyzed in the framework of a model of a spherically symmetric shell magnetized to some specific intensity by a concentric dipolar magnetic field. The remanent dipole moment of the model is determined by calculating the dipole moment of the material removed to form craters and them computing the remanent dipole moment for three mutually orthogonal orientations of the magnetizing dipole. The resulting absolute values for the remanent dipole moment are found to be comparable to the upper limit of 10 to the -19th power G-cu cm estimated from Apollo subsatellite measurements. It is concluded that for a crust with an empirically reasonable mean magnetization, the craters can account for a dipole moment as great as that indicated by the estimated upper limit.

Weiss, H.↗
NASA NTRS1988

Hierarchic plate and shell models based on p-extension

This paper is concerned with formulations of finite element models for beams, arches, plates and shells based on the principle of virtual work. The focus is on computer implementation of hierarchic sequences of finite element models suitable for numerical solution of a large variety of practical problems which may concurrently contain thin and thick plates and shells, stiffeners, and regions where three dimensional representation is required. The approximate solutions corresponding to the hierarchic sequence of models converge to the exact solution of the fully three dimensional model. The stopping criterion is based on (1) estimation of the relative error in energy norm; (2) equilibrium tests; and (3) observation of the convergence of quantities of interest.

Szabo, Barna A.↗
NASA NTRS1989

Hierarchic plate and shell models based on p-extension

Formulation of hierarchic sequences of finite element models for beams, arches, plates and shells based on the principle of virtual work is described. The exact solutions corresponding to models in the hierarchic sequence converge to the exact solution of the fully three-dimensional problem of linear elasticity. The stopping criterion is that the functionals of interest must be substantially independent of the choice of the model. This process is closely related to p-extensions. Aspects of implementation are discussed in connection with axisymmetric shells and an example is presented. An application of superconvergent extraction methods for the computation of stress resultants is demonstrated.

Szabo, B. A.↗
NASA NTRS1988

Hierarchic plate and shell models based on p-extension

Formulations of finite element models for beams, arches, plates and shells based on the principle of virtual work was studied. The focus is on computer implementation of hierarchic sequences of finite element models suitable for numerical solution of a large variety of practical problems which may concurrently contain thin and thick plates and shells, stiffeners, and regions where three dimensional representation is required. The approximate solutions corresponding to the hierarchic sequence of models converge to the exact solution of the fully three dimensional model. The stopping criterion is based on: (1) estimation of the relative error in energy norm; (2) equilibrium tests, and (3) observation of the convergence of quantities of interest.

Szabo, Barna A.↗
NASA NTRS1997

Variability in shell models of GRBs

Many cosmological models of gamma-ray bursts (GRBs) assume that a single relativistic shell carries kinetic energy away from the source and later converts it into gamma rays, perhaps by interactions with the interstellar medium or by internal shocks within the shell. Although such models are able to reproduce general trends in GRB time histories, it is difficult to reproduce the high degree of variability often seen in GRBs. The authors investigate methods of achieving this variability using a simplified external shock model. Since the model emphasizes geometric and statistical considerations, rather than the detailed physics of the shell, it is applicable to any theory that relies on relativistic shells. They find that the variability in GRBs gives strong clues to the efficiency with which the shell converts its kinetic energy into gamma rays.

Sumner, M. C.↗
NASA NTRS2016

CME Flux Rope and Shock Identifications and Locations: Comparison of White Light Data, Graduated Cylindrical Shell Model, and MHD Simulations

Coronal mass ejections (CMEs) are major transient phenomena in the solar corona that are observed with ground-based and spacecraft-based coronagraphs in white light or with in situ measurements by spacecraft. CMEs transport mass and momentum and often drive shocks. In order to derive the CME and shock trajectories with high precision, we apply the graduated cylindrical shell (GCS) model to fit a flux rope to the CME directed toward STEREO A after about 19:00 UT on 29 November 2013 and check the quality of the heliocentric distance-time evaluations by carrying out a three-dimensional magnetohydrodynamic (MHD) simulation of the same CME with the Block Adaptive Tree Solar-Wind Roe Upwind Scheme (BATS-R-US) code. Heliocentric distances of the CME and shock leading edges are determined from the simulated white light images and magnetic field strength data. We find very good agreement between the predicted and observed heliocentric distances, showing that the GCS model and the BATS-R-US simulation approach work very well and are consistent. In order to assess the validity of CME and shock identification criteria in coronagraph images, we also compute synthetic white light images of the CME and shock. We find that the outer edge of a cloud-like illuminated area in the observed and predicted images in fact coincides with the leading edge of the CME flux rope and that the outer edge of a faint illuminated band in front of the CME leading edge coincides with the CME-driven shock front.

Schmidt, J. M.↗
NASA NTRS2004

Toward Effective Shell Modeling of Wrinkled Thin-Film Membranes Exhibiting Stress Concentrations

Geometrically nonlinear shell finite element analysis has recently been applied to solar-sail membrane problems in order to model the out-of-plane deformations due to structural wrinkling. Whereas certain problems lend themselves to achieving converged nonlinear solutions that compare favorably with experimental observations, solutions to tensioned membranes exhibiting high stress concentrations have been difficult to obtain even with the best nonlinear finite element codes and advanced shell element technology. In this paper, two numerical studies are presented that pave the way to improving the modeling of this class of nonlinear problems. The studies address the issues of mesh refinement and stress-concentration alleviation, and the effects of these modeling strategies on the ability to attain converged nonlinear deformations due to wrinkling. The numerical studies demonstrate that excessive mesh refinement in the regions of stress concentration may be disadvantageous to achieving wrinkled equilibrium states, causing the nonlinear solution to lock in the membrane response mode, while totally discarding the very low-energy bending response that is necessary to cause wrinkling deformation patterns. An element-level, strain-energy density criterion is suggested for facilitating automated, adaptive mesh refinements specifically aimed at the modeling of thin-film membranes undergoing wrinkling deformations.

Tessler, Alexander↗
NASA NTRS1973

A cylindrical shell model of the NASA-MPE barium ion cloud experiment.

A computer model is developed using infinitely long concentric cylindrical shells to represent the neutral atoms, ions and electrons in the barium cloud. The neutral shells are given a distribution of positions and velocities whose parameters are chosen to be consistent with the dynamics of the release. From this distribution, the ion and electron shells are generated at random using the observed time constant for photoionization. The ion and electron shells thus formed are followed using self-consistent equations of motion. Various averages which could be compared with observation of the actual cloud are calculated at regular time intervals. An unexpected result is the predicted very early return of the magnetic field within the cloud to its ambient value.

Grauer, A. D.↗
NASA NTRS1992

Axisymmetric spherical shell models of mantle convection with variable properties and free and rigid lids

Axisymmetric spherical shell numerical simulations of mantle convection were carried out to investigate the influence of two end-member surface stress conditions: stress-free and rigid. These correspond approximately to a subducting or a rigid lithosphere and can be seen as end-member models of the surface of Venus. Our model assumed an effective Rayleigh number of 3 x 10 exp 6, similar to that for earth, and included uniform internal heating and depth-dependent thermal expansivity and thermal conductivity. The simulations utilized a Newtonian viscosity which was constant or varied with depth and/or temperature. We show how the temperature, speed, and vorticity fields change qualitatively and quantitatively with surface temperature, surface stress condition, internal heating and viscosity distribution. We find that a rigid lid and viscosity which increases with depth both promote steady large-scale circulation with smaller-scale circulation in the upper mantle.

Leitch, A. M.↗
NASA NTRS1986

Delta excitations and shell-model information in heavy-ion, charge-exchange reactions

We calculate total cross sections for coherent pion production using localized plane-wave approximations for the shell-structure of valence nucleons that are excited to delta particles in the intermediate state in the (12C, 12B) and (12C, 12N) charge-exchange, heavy-ion reactions. We find comparable agreement to projectile downshift data for 12C(12C, 12B)12N. Then we improve the formalism by replacing the localized plane wave bound states with harmonic oscillator states which are imbedded in a multipole expansion approach and calculate pion differential cross sections to test for the sensitivity of the spectra to the single-particle mass parameter.

NASA Program Space Medicine↗