Correlation of magnetic moment variation in axisymmetric and multipolar magnetic mirrors.
Charged particle behavior in axisymmetric and multipolar magnetic mirrors, correlating magnetic moment variation and computing motion equations
Roth, J. R.↗
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Displacement of rays in a turbulent medium.
Rays associated Fokker-Planck relation for isotropic turbulence diffusion equation, discussing logarithmic refractive index, moments and path length
Liu, C. H.↗
Constitutive relations associated with the Mott-Smith distribution function
It is shown that the distribution function assumed by Mott-Smith determines a unique relation between heat flux, stress, and fluid velocity given by q = (3/2) tau u - i.e., it provides a constitutive relation for heat flux, and it also determines a simple expression for the ratio of third-order central moments. These expressions allow the equation of transfer for (C sub x) squared to be cast in a form that yields a nonlinear constitutive relation for stress. The results obtained from the Mott-Smith ansatz are compared with the theory of Baganoff and Nathenson (1970) and results from a numerical solution of the Boltzmann equation for shock-wave structure obtained by Hicks et al. (1972).
Nathenson, M.↗
A theory for predicting composite laminate warpage resulting from fabrication
Linear laminate theory is used with the moment-curvature relationship to derive equations for predicting end deflections due to warpage without solving the coupled fourth-order partial differential equations of the plate. Composite micro- and macrohyphenmechanics are used with laminate theory to assess the contribution of factors such as ply misorientation, fiber migration, and fiber and/or void volume ratio nonuniformity on the laminate warpage. Using these equations, it was found that a 1 deg error in the orientation angle of one ply was sufficient to produce warpage end deflection equal to two laminate thicknesses in a 10 inch by 10 inch laminate made from 8 ply Mod-I/epoxy. Using a sensitivity analysis on the governing parameters, it was found that a 3 deg fiber migration or a void volume ratio of three percent in some plies is sufficient to produce laminate warpage corner deflection equal to several laminate thicknesses. Tabular and graphical data are presented which can be used to identify possible errors contributing to laminate warpage and/or to obtain an a priori assessment when unavoidable errors during fabrication are anticipated.
Chamis, C. C.↗
A theory for predicting composite laminate warpage resulting from fabrication
Linear laminate theory is used in conjunction with the moment-curvature relationship to derive equations for predicting end deflections due to warpage without solving the coupled fourth-order partial differential equations of the plate. Using these equations, it is found that a 1 deg error in the orientation angle of one ply is sufficient to produce warpage end deflection equal to two laminate thicknesses in a 10 inch by 10 inch laminate made from 8-ply Mod-I/epoxy. From a sensitivity analysis on the governing parameters, it is found that a 3 deg fiber migration or a void volume ratio of three percent in some plies is sufficient to produce laminate warpage corner deflection equal to several laminate thicknesses. Tabular and graphical data are presented which can be used to identify possible errors contributing to laminate warpage and/or to obtain an a priori assessment when unavoidable errors during fabrication are anticipated.
Chamis, C. C.↗
Unsteady flow model for circulation-control airfoils
An analysis and a numerical lifting surface method are developed for predicting the unsteady airloads on two-dimensional circulation control airfoils in incompressible flow. The analysis and the computer program are validated by correlating the computed unsteady airloads with test data and also with other theoretical solutions. Additionally, a mathematical model for predicting the bending-torsion flutter of a two-dimensional airfoil (a reference section of a wing or rotor blade) and a computer program using an iterative scheme are developed. The flutter program has a provision for using the CC airfoil airloads program or the Theodorsen hard flap solution to compute the unsteady lift and moment used in the flutter equations. The adopted mathematical model and the iterative scheme are used to perform a flutter analysis of a typical CC rotor blade reference section. The program seems to work well within the basic assumption of the incompressible flow.
Rao, B. M.↗
Anisotropic velocity distributions in M87 - Is a supermassive black hole necessary
A collisionless distribution of stars with an anisotropic velocity distribution is considered as a model for the cores of spherical galaxies. The first moment of the corresponding Boltzmann equation is integrated to give the resulting density and velocity dispersion profiles. These distributions plus a central point source of light give a good fit to the data from recent observations of M87 without requiring a supermassive central object. This model requires one less fitting parameter than published models incorporating a central black hole. The same model with no point source of light also provides a good fit to the normal E1 galaxy NGC 3379. The success of this model in describing the cores of both M87 and NGC 3379 suggests that a supermassive black hole is not necessary in either.
Duncan, M. J.↗
Bow-tie antennas on a dielectric half-space - Theory and experiment
A new formulation is discussed for the rigous calculation of the radiation pattern of a bow-tie antenna of finite length and infinitesimal thickness, placed on a lossless dielectric substrate. The analysis is based on a representation of the current density on the metal surface of the antenna as a sum of an imposed (quasistatic) term and a set of current modes with unknown amplitudes. Free-space fields that are expressed in terms of continuous spectra of symmetrized plane waves are matched to the current modes using the method of moments. The resulting set of equations are solved for the unknown current amplitudes. The calculations show that for increasing bow length the antenna impedance spirals rapidly to a value predicted by transmission line theory. The theory also shows that the E-plane pattern of a two-wavelength, 60-deg bow-tie antenna is dominated by low-loss current modes propagating at the dielectric wavenumber. As the bow tie narrows, the loss of the modes increases, and the dominant wavenumber tends to the quasi-static value. Pattern measurements made at 94 GHz are shown to agree well with theoretical predictions. Measurements for a long-wire antenna, a linear array of bow-tie elements, and a log-periodic antenna are also presented.
Compton, Richard C.↗
Computational vortex dynamics in two and three dimensions
A discussion of some solutions and outstanding problems of dissipationless and nearly dissipationless flows in two and three dimensions is presented. In particular, two-dimensional steady-state solutions, linear stability and nonlinear evolutions including axisymmetrization of isolated vortex regions and merger or condensation of like-signed vorticity regions, are reviewed. These results are obtained from pseudo-spectral codes, contour dynamical (CD) codes and a new Hamiltonian moment-model of the Euler equations
Melander, Mogens V.↗
The weight distribution and randomness of linear codes
Finding the weight distributions of block codes is a problem of theoretical and practical interest. Yet the weight distributions of most block codes are still unknown except for a few classes of block codes. Here, by using the inclusion and exclusion principle, an explicit formula is derived which enumerates the complete weight distribution of an (n,k,d) linear code using a partially known weight distribution. This expression is analogous to the Pless power-moment identities - a system of equations relating the weight distribution of a linear code to the weight distribution of its dual code. Also, an approximate formula for the weight distribution of most linear (n,k,d) codes is derived. It is shown that for a given linear (n,k,d) code over GF(q), the ratio of the number of codewords of weight u to the number of words of weight u approaches the constant Q = q(-)(n-k) as u becomes large. A relationship between the randomness of a linear block code and the minimum distance of its dual code is given, and it is shown that most linear block codes with rigid algebraic and combinatorial structure also display certain random properties which make them similar to random codes with no structure at all.
Cheung, K.-M.↗
Synchrotron radiation from Neptune - Neptune's magnetic field and electron population
On the basis of radio measurements of Neptune at 20 cm, one can infer the presence of about 0.4 mJy synchrotron radiation. By assuming a dipole-like magnetic field, with the energetic electrons confined to the magnetic equator, Neptune's magnetic dipole moment is estimated. Its electron population should be between that in Uranus' and Jupiter's magnetospheres. If the electrons are injected by the solar wind, local acceleration processes in the magnetosphere are required to energize the particles, because adiabatic diffusion alone is not sufficient.
De Pater, Imke↗
Scattering from dielectric structures above impedance surfaces and resistive sheets
Interest in understanding of electromagnetic interaction with rough surfaces has prompted the study of scattering from typical dielectric humps over impedance surfaces. It is shown that the Green's function of the problem for a resistive sheet resembles that of the impedance surface. Hence both problems are considered here. A numerical solution for the scattered field of a two-dimensional dielectric object, possibly inhomogeneous, with arbitrary cross section above the impedance surface or resistive sheet is sought. First the Green's function of the problem is derived based on the exact image theory. This form of the Green's function is amenable to numerical computation. Then the induced polarization currents are calculated by casting the integral equations into a matrix equation via the method of moments. Numerical problems in calculation of the Green's function when both source and observation points are close to the surface are discussed. Comparison of numerical results with a perturbation solution shows excellent agreement between the two methods.
Sarabandi, Kamal↗
N-body realizations of compound galaxies
A prescription for constructing N-body models of galaxies consisting of more than one component is described. Spatial density profiles are realized exactly, but the phase space distribution is approximated using moments of the collisionless Boltzmann equation. While this approach is not fully rigorous, empirical tests suggest that it is adequate for studies of, e.g., interacting galaxies and the forced response of galaxies to imposed perturbations such as bars.
Hernquist, Lars↗
Electromagnetic Scattering From a Rectangular Cavity Recessed in a 3-D Conducting Surface
The problem of electromagnetic (EM) scattering from an aperture backed by a rectangular cavity recessed in a three-dimensional conducting body is analyzed using the coupled field integral equation approach. Using the free-space Green's function, EM fields scattered outside the cavity are determined in terms of (1) an equivalent electric surface current density flowing on the three-dimensional conducting surface of the object including the cavity aperture and (2) an equivalent magnetic surface current density flowing over the aperture only. The EM fields inside the cavity are determined using the waveguide modal expansion functions. Making the total tangential electric and magnetic fields across the aperture continuous and subjecting the total tangential electric field on the outer conducting three-dimensional surface of the object to zero, a set of coupled integral equations is obtained. The equivalent electric and magnetic surface currents are then obtained by solving the coupled integral equation using the Method of Moments. The numerical results on scattering from rectangular cavities embedded in various three-dimensional objects are compared with the results obtained by other numerical techniques.
Deshpande, M. D.↗
Energy Stable Flux Formulas For The Discontinuous Galerkin Discretization Of First Order Nonlinear Conservation Laws
We consider the discontinuous Galerkin (DG) finite element discretization of first order systems of conservation laws derivable as moments of the kinetic Boltzmann equation. This includes well known conservation law systems such as the Euler For the class of first order nonlinear conservation laws equipped with an entropy extension, an energy analysis of the DG method for the Cauchy initial value problem is developed. Using this DG energy analysis, several new variants of existing numerical flux functions are derived and shown to be energy stable.
Barth, Timothy↗
Using EIGER for Antenna Design and Analysis
EIGER (Electromagnetic Interactions GenERalized) is a frequency-domain electromagnetics software package that is built upon a flexible framework, designed using object-oriented techniques. The analysis methods used include moment method solutions of integral equations, finite element solutions of partial differential equations, and combinations thereof. The framework design permits new analysis techniques (boundary conditions, Green#s functions, etc.) to be added to the software suite with a sensible effort. The code has been designed to execute (in serial or parallel) on a wide variety of platforms from Intel-based PCs and Unix-based workstations. Recently, new potential integration scheme s that avoid singularity extraction techniques have been added for integral equation analysis. These new integration schemes are required for facilitating the use of higher-order elements and basis functions. Higher-order elements are better able to model geometrical curvature using fewer elements than when using linear elements. Higher-order basis functions are beneficial for simulating structures with rapidly varying fields or currents. Results presented here will demonstrate curren t and future capabilities of EIGER with respect to analysis of installed antenna system performance in support of NASA#s mission of exploration. Examples include antenna coupling within an enclosed environment and antenna analysis on electrically large manned space vehicles.
Champagne, Nathan J.↗
Direct Solve of Electrically Large Integral Equations for Problem Sizes to 1M Unknowns
Matrix methods for solving integral equations via direct solve LU factorization are presently limited to weeks to months of very expensive supercomputer time for problems sizes of several hundred thousand unknowns. This report presents matrix LU factor solutions for electromagnetic scattering problems for problem sizes to one million unknowns with thousands of right hand sides that run in mere days on PC level hardware. This EM solution is accomplished by utilizing the numerical low rank nature of spatially blocked unknowns using the Adaptive Cross Approximation for compressing the rank deficient blocks of the system Z matrix, the L and U factors, the right hand side forcing function and the final current solution. This compressed matrix solution is applied to a frequency domain EM solution of Maxwell's equations using standard Method of Moments approach. Compressed matrix storage and operations count leads to orders of magnitude reduction in memory and run time.
Shaeffer, John↗
Strain Gage Loads Calibration Testing with Airbag Support for the Gulfstream III SubsoniC Research Aircraft Testbed (SCRAT)
This paper describes the design and conduct of the strain gage load calibration ground test of the SubsoniC Research Aircraft Testbed, Gulfstream III aircraft, and the subsequent data analysis and its results. The goal of this effort was to create and validate multi-gage load equations for shear force, bending moment, and torque for two wing measurement stations. For some of the testing the aircraft was supported by three air bags in order to isolate the wing structure from extraneous load inputs through the main landing gear. Thirty-two strain gage bridges were installed on the left wing. Hydraulic loads were applied to the wing lower surface through a total of 16 load zones. Some dead weight load cases were applied to the upper wing surface using shot bags. Maximum applied loads reached 54,000 pounds.
trailing edge flap↗