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Computational reflection is a well-known and powerful way to speed up the proof process in an interactive theorem prover. This presentation introduces the concept using PVS, and showcases 2 of the strategies using the method.
Several non-reflecting computational boundary conditions that meet certain criteria and have potential applications to duct acoustics are evaluated for their effectiveness. The same interior solution scheme, grid, and order of approximation are used to evaluate each condition. Sparse matrix solution techniques are applied to solve the matrix equation resulting from the discretization. Modal series solutions for the sound attenuation in an infinite duct are used to evaluate the accuracy of each non-reflecting boundary conditions. The evaluations are performed for sound propagation in a softwall duct, for several sources, sound frequencies, and duct lengths. It is shown that a recently developed nonlocal boundary condition leads to sound attenuation predictions considerably more accurate for short ducts. This leads to a substantial reduction in the number of grid points when compared to other non-reflecting conditions.
We examine an absorbing buffer layer technique for use as a non-reflecting boundary condition in the numerical simulation of flows. One such formulation was by Ta'asan and Nark for the linearized Euler equations. They modified the flow inside the buffer zone to artificially make it supersonic in the layer. We examine how this approach can be extended to the nonlinear Euler equations. We consider both a conservative and a non-conservative form modifying the governing equations in the buffer layer. We compare this with the case that the governing equations in the layer are the same as in the interior domain. We test the effectiveness of these buffer layers by a simulation of an excited axisymmetric jet based on a nonlinear compressible Navier-Stokes equations.
Computer-generated reflection holograms hold substantial promise as a means of carrying out complex machining, marking, scribing, welding, soldering, heat treating, and similar processing operations simultaneously and without moving the work piece or laser beam. In the study described, a photographically reduced transparency of a 64 x 64 element Lohmann hologram was used to make a mask which, in turn, was used (with conventional photoresist techniques) to produce a holographic reflector. Images from a commercial CO2 laser (150W TEM(00)) and the holographic reflector are illustrated and discussed.
An equation is derived to compute the amount of diffuse light reflected by a particulate surface, such as on Mars or an asteroid. The method traces the paths of rays within an ensemble of randomly shaped grains and finds the eventual probability of emission. The amount of diffuse, unpolarized emitted light is obtained in terms of the real index of refraction, the imaginary index, and the average diameter of particles making up the surface. The equation is used to compute the empirical rule for obtaining the planetary albedo from the slope of its polarization curve. Accuracy of the equation, estimated at + or - 4%, seems justified because of quantitative agreement with experimental measures of the empirical rule. It is also shown that the equation can be applied to bubble-enclosing surfaces such as volcanic foams. Results for the indices of the moon, Mars, Io, and Europa are obtained and compared with other data.
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A previous dichroic plate analysis has assumed that an ideal uniform plane wave illuminates the dichroic plate at a single angle of incidence. In fact, a horn radiates energy at the dichroic plate and illuminates it at many different angles. To model the horn and dichroic plate system, the horn pattern is represented as a group of plane waves traveling in different directions. The details of this analysis are presented this article. The calculated and measured reflected radiation patterns show good agreement. The noise temperature predicted from the horn pattern model is shown to be more accurate than that from a simple plane-wave model.
Characteristics of tropospheric desert aerosols are derived by comparing nadir spectral reflectivities computed from the radiative transfer models with reflectivities measured from Landsat. Over the ocean, reflectivities are compared, but over land the comparison is carried out by determining the ratios of the nadir reflectivity of the surface-atmosphere system over heavy aerosol concentration to the reflectivity of the underlying surface. This remote sensing technique is found to be a sensitive approach for measuring n sub 2, the imaginary part of the refractive index. The desert aerosols under study, in the Iran and Pakistan area, are essentially pure scatterers, inasmuch as an n sub 2 value of 0.001 + or - 0.001 was determined for each of the four Landsat spectral bands, that is, for a spectral interval from 0.5 to 1.1 microns.
The direct problem is to compute reflection coefficients for an assumed electron-density profile, using a full-wave solution. The inverse problem is treated numerically, using derivatives of the reflection matrix with respect to model parameters. A technique for the rapid computation of the derivatives is described. An algorithm for determining resolution in the profile is discussed.
During 1971 and 1972 research was conducted on two fallow fields in the proposed Oahe Irrigation Project to investigate the relationship between the tonal variations observed on aerial photographs and the principal soil limitations of the area. A grid sampling procedure was used to collected detailed field data during the 1972 growing season. The field data was compared to imagery collected on May 14, 1971 at 3050 meters altitude. The imagery and field data were initially evaluated by a visual analysis. Correlation and regression analysis revealed a highly significant correlation and regression analysis revealed a highly significant correlation between the digitized color infrared film data and soil properties such as organic matter content, color, depth to carbonates, bulk density and reflectivity. Computer classification of the multiemulsion film data resulted in maps delineating the areas containing claypan and erosion limitations. Reflectance data from the red spectral band provided the best results.
The computed-tomography imaging spectrometer (CTIS) is a device which captures the spatial and spectral content of a rapidly evolving same in a single image frame. The most recent CTIS design is optically all reflective and uses as its dispersive device a stated the-art reflective computer generated hologram (CGH). This project focuses on the instrument's transition from laboratory to field. This design will enable the CTIS to withstand a harsh desert environment. The system is modeled in optical design software using a tolerance analysis. The tolerances guide the design of the athermal mount and component parts. The parts are assembled into a working mount shell where the performance of the mounts is tested for thermal integrity. An interferometric analysis of the reflective CGH is also performed.
A general computer graphics based model is presented for computer generation of objects of arbitrary shape and for calculating Bidirectional Reflectance Factor (BRF) and scattering from them, in the optical region. The computer generation uses a modified Lindemayer system (L system) approach. For rendering on a computer screen, the object is divided into polygons, and innovative computer graphics techniques are used to display the object and to calculate the scattering and reflectance from the object. The use of the technique is illustrated with scattering from canopies of simulated corn plants and from a snow covered mountain. The scattering is quantified using measures like BRF and albedo and by rendering the objects with brightness of each of the two facets of a polygon proportional to the amount of light scattered from the object in the viewer's direction.
Stepper motors are widely used on most spacecraft mechanisms requiring repeatable and reliable performance. The unique detent torque characteristics of these type of motors makes them behave differently when subjected to low duty cycle excitations where the applied driving pulses are only energized for a fraction of the pulse duration. This phenomenon is even more pronounced in discrete permanent magnet stepper motors used in the space industry. While the inherent high detent properties of discrete permanent magnets provide desirable unpowered holding performance characteristics, it results in unique behavior especially in low duty cycles. Notably, the running torque reduces quickly to the unpowered holding torque when the duty cycle is reduced. The space industry's accepted methodology of calculating the Motorization Ratio (or Torque Margin) is more applicable to systems where the power is continuously applied to the motor coils like brushless DC motors where the cogging torques are low enough not to affect the linear performance of the motors as a function of applied current. This paper summarizes the theoretical and experimental studies performed on a number of space qualified motors under different pulse rates and duty cycles. It is the intention of this paper to introduce a new approach to calculate the Motorization Ratios for discrete permanent magnet steppers under all full and partial duty cycle regimes. The recommended approach defines two distinct relationships to calculate the Motorization Ratio for 100 percent duty cycle and partial duty cycle, when the motor detent (unpowered holding torque) is the main contributor to holding position. These two computations reflect accurately the stepper motor physical behavior as a function of the command phase (ON versus OFF times of the pulses), pointing out how the torque contributors combine. Important points highlighted under this study are the torque margin computations, in particular for well characterized mechanisms. The rationale at CDR level versus TRR/TRB level will be discussed, aiming at avoiding too much conservatism for units that have extensive test and in flight heritage. A critical topic is related to the magnetic losses and how to sort out such phenomena as a function of the motor type being used. For instance, detent torque is a major contributor that has no reason to evolve during life and is not an uncontrolled torque loss.
Diffraction properties of lossy periodic gratings with the metal base were investigated by solving Maxwell's equations numerically using the differential method. Two periodic surfaces were employed in the simulation: triangle structure and tilting triangle structure. Based on the numerical solution and in conjunction with the algorithm of Adams-Moulton, we computed reflection coefficients of plane waves with different wavelengths and different incident angles. The dielectric properties were also explored using various dielectric constants. The results show that the reflection coefficients of both TE and TM waves are quite sensitive to the incident angles of the plane waves when the metal sheet exists, which is in good agreement with the experimental data.
A human's ability to perform physical tasks is limited, not only by his intelligence, but by his physical strength. If, in an appropriate environment, a machine's mechanical power is closely integrated with a human arm's mechanical power under the control of the human intellect, the resulting system will be superior to a loosely integrated combination of a human and a fully automated robot. Therefore, we must develop a fundamental solution to the problem of 'extending' human mechanical power. The work presented here defines 'extenders' as a class of robot manipulators worn by humans to increase human mechanical strength, while the wearer's intellect remains the central control system for manipulating the extender. The human, in physical contact with the extender, exchanges power and information signals with the extender. The aim is to determine the fundamental building blocks of an intelligent controller, a controller which allows interaction between humans and a broad class of computer-controlled machines via simultaneous exchange of both power and information signals. The prevalent trend in automation has been to physically separate the human from the machine so the human must always send information signals via an intermediary device (e.g., joystick, pushbutton, light switch). Extenders, however are perfect examples of self-powered machines that are built and controlled for the optimal exchange of power and information signals with humans. The human wearing the extender is in physical contact with the machine, so power transfer is unavoidable and information signals from the human help to control the machine. Commands are transferred to the extender via the contact forces and the EMG signals between the wearer and the extender. The extender augments human motor ability without accepting any explicit commands: it accepts the EMG signals and the contact force between the person's arm and the extender, and the extender 'translates' them into a desired position. In this unique configuration, mechanical power transfer between the human and the extender occurs because the human is pushing against the extender. The extender transfers to the human's hand, in feedback fashion, a scaled-down version of the actual external load which the extender is manipulating. This natural feedback force on the human's hand allows him to 'feel' a modified version of the external forces on the extender. The information signals from the human (e.g., EMG signals) to the computer reflect human cognitive ability, and the power transfer between the human and the machine (e.g., physical interaction) reflects human physical ability. Thus the information transfer to the machine augments cognitive ability, and the power transfer augments motor ability. These two actions are coupled through the human cognitive/motor dynamic behavior. The goal is to derive the control rules for a class of computer-controlled machines that augment human physical and cognitive abilities in certain manipulative tasks.
The paper describes the technique of planetary electron reflection magnetometry (PERM), a method for measuring the magnitude, direction, and scale size of magnetic fields near the surface of the moon and other planetary bodies with weak and small-scale-size surface fields. It is noted that the PERM technique is based on the ability of magnetic fields to reflect charged particles. A qualitative account of the implementation of the technique is presented along with some results obtained by the Apollo 15 and 16 Particles and Fields subsatellites. The quantitative aspects of PERM are treated by examining solutions to the equation of motion of a charged particle in a magnetic field, computing reflection coefficients on the basis of trajectory calculations, and determining the direction of the lunar surface magnetic field. The sensitivity of the PERM technique is calculated, and effects of lunar electric fields and spacecraft potentials on the measurements are described. Extension of the technique to Mars and Venus is discussed.
Significant findings during this report period are: (1) The feasibility of using techniques for obtaining and using atmospheric parameter to transform ERTS data into absolute target reflectance was demonstrated. (2) Ground-truth instrumentation must have a dynamic range of 100,000 for obtaining the full set of atmospheric parameters encountered in the field. (3) Atmospheric transmittance for January through May 1973 varied from 13 to 18 percent in the ERTS bands. (4) Energy scattered to the spacecraft from the atmosphere for the March overflight was equivalent to that produced by a target having a reflectance of 11% in band 4, 5% in band 5, 3% in band 6, and 1% in band 7. (5) This atmospheric radiance varies as a function of sun zenith angle (scatter angle) and is predicted to change by 30% for sun angles at the latitude of the Michigan test site. (6) If not removed from spacecraft measurements before computing reflectance of surface targets, this radiance is a major source of error.
In this paper, we examine the effectiveness of absorbing layers as non-reflecting computational boundaries for the Euler equations. The absorbing-layer equations are simply obtained by splitting the governing equations in the coordinate directions and introducing absorption coefficients in each split equation. This methodology is similar to that used by Berenger for the numerical solutions of Maxwell's equations. Specifically, we apply this methodology to three physical problems shock-vortex interactions, a plane free shear flow and an axisymmetric jet- with emphasis on acoustic wave propagation. Our numerical results indicate that the use of absorbing layers effectively minimizes numerical reflection in all three problems considered.