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Free electron model for electron work functions and number density distributions and surface potentials in metals
Electric fields and electron work functions, surface potentials and number density distributions in selected metals surfaces determined using free electron model
Electron work functions, surface potentials, and electron number density distributions and electric fields in the surface region of 26 metals were calculated from first principles within the free electron model. Calculation proceeded from an expression of the total energy as a functional of the electron number density, including exchange and correlation energies, as well as a first inhomogeneity term. The self-consistent solution was obtained via a variational procedure. Surface barriers were due principally to many-body effects; dipole barriers were small only for some alkali metals, becoming quite large for the transition metals. Surface energies were inadequately described by this model, which neglects atomistic effects. Reasonable results were obtained for electron work functions and surface potential characteristics, maximum electron densities varying by a factor of over 60.
The mechanical behavior and stresses inducing fracture modes of unidirectional high-modulus graphite-fiber/epoxy composites subjected to off-axis tensile loads were investigated theoretically. The investigation included the use of composite mechanics, combined-stress failure criteria, and finite-element stress analysis. The results are compared with experimental data and led to the formulation of criteria and convenient plotting procedures for identifying, characterizing, and quantifying these fracture modes.
A wind-tunnel study was conducted to determine the capability of a method combining linear theory and shock-expansion theory to design optimum camber surfaces for wings that will fly at high-supersonic/low-hypersonic speeds. Three force models (a flat-plate reference wing and two cambered and twisted wings) were used to obtain aerodynamic lift, drag, and pitching-moment data. A fourth pressure-orifice model was used to obtain surface-pressure data. All four wing models had the same planform, airfoil section, and centerbody area distribution. The design Mach number was 4.5, but data were also obtained at Mach numbers of 3.5 and 4.0. Results of these tests indicated that the use of airfoil thickness as a theoretical optimum, camber-surface design constraint did not improve the aerodynamic efficiency or performance of a wing as compared with a wing that was designed with a zero-thickness airfoil (linear-theory) constraint.
Approximation of expectation values for nonenergy properties via perturbation theory, obtaining values for molecular polarizability
The theory of functionals is used to reformulate the notions of aerodynamic indicial functions and superposition. Integral forms for the aerodynamic response to arbitrary motions are derived that are free of dependence on a linearity assumption. Simplifications of the integral forms lead to practicable nonlinear generalizations of the linear superpositions and stability derivative formulations. Applied to arbitrary nonplanar motions, the generalization yields a form for the aerodynamic response that can be compounded of the contributions from a limited number of well-defined characteristic motions, in principle reproducible in the wind tunnel. Further generalizations that would enable the consideration of random fluctuations and multivalued aerodynamic responses are indicated.
Satellite measurements are subject to a wide range of uncertainties due to their temporal, spatial, and directional sampling characteristics. An information-theory approach is suggested to examine the nonuniform temporal sampling of ERB measurements. The information (i.e., its entropy or uncertainty) before and after the measurements is determined, and information gain (IG) is defined as a reduction in the uncertainties involved. A stochastic model for the diurnal outgoing flux variations that affect the ERB is developed. Using Gaussian distributions for the a priori and measured radiant exitance fields, the IG is obtained by computing the a posteriori covariance. The IG for the monthly outgoing flux measurements is examined for different orbital parameters and orbital tracks, using the Earth Observing System orbital parameters as specific examples. Variations in IG due to changes in the orbit's inclination angle and the initial ascending node local time are investigated.
A general theory of fluidelastic instability for a tube array in crossflow is presented. Various techniques to obtain the motion-dependent fluid-force coefficients are discussed and the general instability characteristics are summarized. The theory is also used to evaluate the results of other mathematical models for crossflow-induced instability.
The phase-locked loop (PLL) is an old and widely used circuit for frequency and phase demodulation, carrier and clock recovery, and frequency synthesis [1]. Its implementations range from discrete components to fully integrated circuits and even to firmware or software. Often the PLL is a highly critical component of a system, as for example when it is used to derive the on-chip clock, but as of this writing no definitive single-event upset (SET)/single-event transient (SET) tolerant PLL circuit has been described. This chapter hopes to rectify that situation, at least in regard to PLLs that are used to generate clocks. Older literature on fault-tolerant PLLs deals with detection of a hard failure, which is recovered by replacement, repair, or manual restart of discrete component systems. Several patents exist along these lines (6349391, 6272647, and 7089442). A newer approach is to harden the parts of a PLL system, to one degree or another, such as by using a voltage-based charge pump or a triple modular redundant (TMR) voted voltage-controlled oscillator (VCO). A more comprehensive approach is to harden by triplication and voting (TMR) all the digital pieces (primarily the divider) of a frequency synthesis PLL, but this still leaves room for errors in the VCO and the loop filter. Instead of hardening or voting pieces of a system, such as a frequency synthesis system (i.e., clock multiplier), we will show how the entire system can be voted. There are two main ways of doing this, each with advantages and drawbacks. We will show how each has advantages in certain areas, depending on the lock acquisition and tracking characteristics of the PLL. Because of this dependency on PLL characteristics, we will briefly revisit the theory of PLLs. But first we will describe the characteristics of voters and their correct application, as some literature does not follow the voting procedure that guarantees elimination of errors. Additionally, we will find that voting clocks is a bit trickier than voting data where an infallible clock is assumed. It is our job here to produce (or recover) that assumed infallible clock!
The linear and the nonlinear stability of disturbances that propagate along the attachment line of a three-dimensional boundary layer is considered. The spatially evolving disturbances in the boundary layer are computed by direct numerical simulation (DNS) of the unsteady, incompressible Navier-Stokes equations. Disturbances are introduced either by forcing at the in ow or by applying suction and blowing at the wall. Quasi-parallel linear stability theory and a nonparallel theory yield notably different stability characteristics for disturbances near the critical Reynolds number; the DNS results con rm the latter theory. Previously, a weakly nonlinear theory and computations revealed a high wave-number region of subcritical disturbance growth. More recent computations have failed to achieve this subcritical growth. The present computational results indicate the presence of subcritically growing disturbances; the results support the weakly nonlinear theory. Furthermore, an explanation is provided for the previous theoretical and computational discrepancy. In addition, the present results demonstrate that steady suction can be used to stabilize disturbances that otherwise grow subcritically along the attachment line.
Some applications of the vortex-lattice theory to the preliminary aerodynamic design and analysis of subsonic aircraft were presented. These methods include the Rockwell-Tulinius vortex-lattice theory for estimating aerodynamic characteristics, a Trefftz plane optimization procedure for determining the span loads for minimum induced drag, and a modification of the Trefftz plane procedure to estimate the induced drag for specified span loads. The first two methods are used to aerodynamically design aircraft planforms, twists, and cambers, and the latter method is used to estimate the drag for components such as flaps and control surfaces. Results from the theories for predicting lift and pitching moment, drag due to lift, and the drag of control surfaces are compared with experimental data. This data was obtained on a general aviation model with flaps and a close-coupled canard-wing model.
An experimental investigation has been conducted to determine the effect of wing leading edge sweep and wing translation on the aerodynamic characteristics of a wing body configuration at a free stream Mach number of about 6 and Reynolds number (based on body length) of 17.9 x 10 to the 6th power. Seven wings with leading edge sweep angles from -20 deg to 60 deg were tested on a common body over an angle of attack range from -12 deg to 10 deg. All wings had a common span, aspect ratio, taper ratio, planform area, and thickness ratio. Wings were translated longitudinally on the body to make tests possible with the total and exposed mean aerodynamic chords located at a fixed body station. Aerodynamic forces were found to be independent of wing sweep and translation, and pitching moments were constant when the exposed wing mean aerodynamic chord was located at a fixed body station. Thus, the Hypersonic Isolation Principle was verified. Theory applied with tangent wedge pressures on the wing and tangent cone pressures on the body provided excellent predictions of aerodynamic force coefficients but poor estimates of moment coefficients.
A summary of the probable interplanetary missions for the 1970's is presented, which may prove useful in testing the general theory of relativity. Mission characteristics are discussed, as well as instrumentation. This last includes a low-level accelerometer and S-/X-band transponders and antennas.
This paper examines some basic considerations underlying dynamic shell response analysis and the impact of these considerations upon the practical aspects of solution by numerical methods. Emphasis is placed on the solution of linear problems. The present states of development of the finite difference and finite element methods are reviewed, and techniques for the treatment of temporal variation are discussed. An examination is made of the frequency parameters characteristic of thin shell theory, applied excitations, and spatial mesh geometries, and the significance of these parameters with respect to computational convergence is illustrated.
Theoretical backgrounds and digital techniques for a class of image processing problems are presented. Image formation in the context of linear system theory, image evaluation, noise characteristics, mathematical operations on image and their implementation are discussed. Various techniques for image restoration and image enhancement are presented. Methods for object extraction and the problem of pictorial pattern recognition and classification are discussed.
A technique was developed for the simulation of random wind fluctuations for use in computer studies of the space shuttle ascent control. The simulated wind fluctuations were generated using the techniques of control theory that have statistical characteristics similar to the characteristics obtained from wind data at Kennedy Space Center.
Research consisted of a theoretical analysis which attempts to predict aerodynamic characteristics using lifting surface theory and finite-element structural analysis as well as an experimental investigation using 1/5 scale elastically similar models in the NASA Ames 2m x 3m (7' x 10') wind tunnel. Experimental data were compared with theoretical results in the development of a computer program which may be used in the design and evaluation of ultralight gliders.