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Simple analytical expressions may be derived for sound velocities in cubic crystals by using lattice harmonics or functions which are invariant under the crystal symmetry operations. These expressions are in good agreement with the exact results for typical crystals such as metallic iron and potassium fluoride.
Simple analytical expressions may be derived for sound velocities in cubic crystals by using lattice harmonics or functions which are invariant under the crystal symmetry operations. These expressions are in good agreement with the exact results for typical crystals such as metallic iron and potassium fluoride.
Many types of hypersonic aircraft configurations are currently being studied for feasibility of future development. Since the control of the hypersonic configurations throughout the speed range has a major impact on acceptable designs, it must be considered in the conceptual design stage. Here, an investigation of the aerodynamic control effectiveness of highly swept delta planforms operating in ground effect is presented. A vortex-lattice computer program incorporating a free wake is developed as a tool to calculate aerodynamic stability and control derivatives. Data generated using this program are compared to experimental data and to data from other vortex-lattice programs. Results show that an elevon deflection produces greater increments in C sub L and C sub M in ground effect than the same deflection produces out of ground effect and that the free wake is indeed necessary for good predictions near the ground.
A given question can be defined in terms of the set of statements or assertions that answer it. Application of the logic of inference to this set of assertions allows one to derive the logic of inquiry among questions. There are interesting symmetries between the logics of inference and inquiry; where probability describes the degree to which a premise implies an assertion, there exists an analogous quantity that describes the bearing or relevance that a question has on an outstanding issue. These have been extended to suggest that the logic of inquiry results in functional relationships analogous to, although more general than, those found in information theory. Employing lattice theory, I examine in greater detail the structure of the space of assertions and questions demonstrating that the symmetries between the logical relations in each of the spaces derive directly from the lattice structure. Furthermore, I show that while symmetries between the spaces exist, the two lattices are not isomorphic. The lattice of assertions is described by a Boolean lattice 2(sup N) whereas the lattice of real questions is shown to be a sublattice of the free distributive lattice FD(N) = 2(sup 2(sup N)). Thus there does not exist a one-to-one mapping of assertions to questions, there is no reflection symmetry between the two spaces, and questions in general do not possess unique complements. Last, with these lattice structures in mind, I discuss the relationship between probability, relevance and entropy.
A computer program based on the Quasi-Vortex-Lattice Method of Lan is presented for calculating longitudinal and lateral-directional aerodynamic characteristics of nonplanar wing-body combination. The method is based on the assumption of inviscid subsonic flow. Both attached and vortex-separated flows are treated. For the vortex-separated flow, the calculation is based on the method of suction analogy. The effect of vortex breakdown is accounted for by an empirical method. A summary of the theoretical method, program capabilities, input format, output variables and program job control set-up are described. Three test cases are presented as guides for potential users of the code.
A significant hurdle confronts the software reuser attempting to select candidate components from a software repository - discriminating between those components without resorting to inspection of the implementation(s). We outline a mixed classification/axiomatic approach to this problem based upon our lattice-based faceted classification technique and Guttag and Horning's algebraic specification techniques. This approach selects candidates by natural language-derived classification, by their interfaces, using signatures, and by their behavior, using axioms. We briefly outline our problem domain and related work. Lattice-based faceted classifications are described; the reader is referred to surveys of the extensive literature for algebraic specification techniques. Behavioral support for reuse queries is presented, followed by the conclusions.
The relaxation, diffusion, and annihilation of split and hexagonal interstitials resulting from 10 eV Si irradiation of (2x1)-terminated Si(100) are investigated. Molecular dynamics and quasidynamics simulations, utilizing the Tersoff many-body potential are used in the investigation. The interstitials are created in layers two through six, and stable atomic configurations and total potential energies are derived as a function of site symmetry and layer depth. The interstitial Si atoms are allowed to diffuse, and the total potential energy changes are calculated. Lattice configurations along each path, as well as the starting configurations, are relaxed, and minimum energy diffusion paths are derived. The results show that the minimum energy paths are toward the surface and generally involved tetrahedral sites. The calculated interstitial migration activation energies are always less than 1.4 eV and are much lower in the near-surface region than in the bulk.
A recent potential of distributed image processing is discussed. Applications in the control of flexible spacecraft are emphasized. Devices are currently being developed at NASA and in universities and industries that allow the real-time processing of holographic images. Within 5 years, it is expected that, in real-time, one may add or subtract holographic images at optical accuracy. Images are stored and processed in crystal mediums. The accuracy of their storage and processing is dictated by the grating level of laser holograms. It is far greater than that achievable using current analog-to-digital, pixel oriented, image digitizing and computing techniques. Processors using image processing algebra can conceptually be designed to mechanize Fourier transforms, least square lattice filters, and other complex control system operations. Thus, actuator command inputs derived from complex control laws involving distributed holographic images can be generated by such an image processor. Plans are revealed for the development of a Conjugate Optics Processor for control of a flexible object.
The atomic structure of a screw dislocation core of the 110 line type in aluminum is calculated by the modified lattice-statics method developed in the preceding paper. The method includes anharmonic as well as harmonic forces and permits relaxation of the atoms in all three dimensions. All forces used in the present calculations were derived from a first-principles interatomic pair potential obtained via pseudopotential theory. Several significant differences from the ordinary lattice statics results are noted, including the displacement field, Peierl's energy barrier, and the equilibrium core-center location.
This paper derives algorithms for identifying autoregressive models, with external input, of multi-input multi-output systems from data using a fast transversal filter or a least-squares lattice filter. The autoregressive models including external inputs are used to identify state-space models and the corresponding observer/Kalman filter gains of the system. The derivation is an extension of scalar autoregressive model approaches, modified to cope with multivariables, external inputs and an extra direct-influence term. Comparisons between the fast transversal filter, the least-squares lattice filter and the classical least-squares method are made in terms of complexity, computational cost and practical applications issues. A numerical example is included to illustrate the approach.
A laser velocimeter capable of rapidly scanning a flow field while simultaneously sensing two components of the velocity was used to measure the vertical and streamwise velocity structure 1.5 spans downstream in the wake of a model typical of a large subsonic transport (Boeing 747). This flow field was modeled by a superposition of axisymmetric vortices with finite cores. This theoretical model was found to agree with the measured velocities everywhere except where two vortices were in close proximity. Vortex strengths derived from the span loading on the wing as predicted by vortex-lattice theory also agree with the present measurements. The axisymmetric vortex model used herein is a useful tool for analytically investigating the vortex wakes of aircraft.
The formulation of the Dirac equation on a discrete lattice with half-integer spacing and periodic boundary conditions is investigated analytically. The importance of lattice formulations for problems in field theory and quantum mechanics is explained; the concept of half-integer Fourier representation is introduced; the discrete Dirac equation for the two-dimensional case is derived; dispersion relations for the four-dimensional case are developed; and the spinor formulation for the Dirac fields on the half-integer lattice and the discrete time variable for the four-dimensional time-dependent Dirac equation are obtained. It is argued that the half-integer lattice, because it takes the Dirac Lagrangian into account, is more than a mere relabeling of the integer lattice and may have fundamental physical meaning (e.g., for the statistics of fermions). It is noted that the present formulation does not lead to species doubling, except in the continuum limit.
The development of low conductivity, robust thermal and environmental barrier coatings requires advanced testing techniques that can accurately and effectively evaluate coating thermal conductivity and cyclic resistance at very high surface temperatures (up to 17OOOC) under large thermal gradients. In this study, a laser high-heat-flux test approach is established for evaluating advanced low conductivity, ultra-high temperature ceramic thermal and environmental barrier coatings under the NASA Ultra Efficient Engine Technology (UEET) program. The test approach emphasizes the real-time monitoring and assessment of the coating thermal conductivity: the initial conductivity rise under a steady-state high temperature thermal gradient test due to coating sintering, and the later coating conductivity reduction under a subsequent cyclic thermal gradient test due to coating cracking/delamination. The coating system is then evaluated based on the damage accumulations and failure after the combined steady-state and cyclic thermal gradient tests. The lattice and radiation thermal conductivity of advanced ceramic coatings can also be evaluated using laser heat-flux techniques. The coating external radiation resistance is assessed based on the measured specimen temperature response under a laser heated intense radiation flux source. The coating internal radiation contribution is investigated based on the measured apparent coating conductivity increases with the coating surface test temperature under large thermal gradient test conditions. Since an increased radiation contribution is observed at these very high surface test temperatures, by varying the laser heat-flux and coating average test temperature, the complex relation between the lattice and radiation conductivity as a function of surface and interface test temperature is derived.
A new technique of high-temperature thermal-conductivity measurement is described. A CO2 gas laser is used to generate a low-frequency temperature wave at one face of a small disk-shaped sample, and an infrared detector views the opposite face to detect the phase of the emerging radiation. A mathematical expression is derived which enables phase data at several frequencies to be used for the simultaneous determination of thermal diffusivity and mean extinction coefficient. Lattice and radiative thermal conductivities are then calculated. Test results for sintered aluminum oxide at temperatures from 530 to 1924 K are within the range of error of previously existing data.
The general theory of conduction in a piezoresistive material subjected to temperature change is derived and the basic equations needed to design and apply test chips for thermal stress measurement are established. A general expression is obtained for the resistance changes which occur in an arbitrarily oriented 1D filamentary conductor subjected to general 3D stress states and arbitrary temperature changes. The derived formula is valid for crystals such as silicon which have cubic symmetry and diamond lattice structures. Basic equations are presented for the resistance changes experienced by stressed in-plane resistors fabricated on (100) silicon wafers. The established theory is applied to a simple two-element sensor rosette. A test chip containing this rosette configuration is designed and fabricated, and a suitable calibration system is constructed.
The development of low conductivity, robust thermal and environmental barrier coatings requires advanced testing techniques that can accurately and effectively evaluate coating thermal conductivity and cyclic resistance at very high surface temperatures (up to 1700 C) under large thermal gradients. In this study, a laser high-heat-flux test approach is established for evaluating advanced low conductivity, high temperature capability thermal and environmental barrier coatings under the NASA Ultra Efficient Engine Technology (UEET) program. The test approach emphasizes the real-time monitoring and assessment of the coating thermal conductivity, which initially rises under the steady-state high temperature thermal gradient test due to coating sintering, and later drops under the cyclic thermal gradient test due to coating cracking/delamination. The coating system is then evaluated based on damage accumulation and failure after the combined steady-state and cyclic thermal gradient tests. The lattice and radiation thermal conductivity of advanced ceramic coatings can also be evaluated using laser heat-flux techniques. The external radiation resistance of the coating is assessed based on the measured specimen temperature response under a laser- heated intense radiation-flux source. The coating internal radiation contribution is investigated based on the measured apparent coating conductivity increases with the coating surface test temperature under large thermal gradient test conditions. Since an increased radiation contribution is observed at these very high surface test temperatures, by varying the laser heat-flux and coating average test temperature, the complex relation between the lattice and radiation conductivity as a function of surface and interface test temperature may be derived.
We present three-dimensional Thomas-Fermi-Dirac calculations of lattice mixing energies of hydrogen with carbon and oxygen atoms, respectively. The results are used to derive effective interatomic potentials for use in liquid-state mixture calculations. We then use the potentials to derive analytic expressions for binary mixture-free energies and to map out the phase diagrams of mixtures of hydrogen with, respectively, helium, carbon, and oxygen, over a pressure range of about 5 to about 10 to the 3rd Mbar. Within this pressure range, all three of the latter elements are found to have unlimited solubility in metallic hydrogen over a temperature range which lies above their pure-element melting temperatures, and which includes likely interior temperatures in the Jovian planets.
The linearized frequency-domain method was recently implemented in the stabilized finite element solver in NASA’s FUN3D code. Previous work by the authors used this method for enforcing flutter constraints during gradient-based optimizations. More recently, the solver was expanded to account for continuous (also known as stochastic) gust responses. This paper expands on recent Common Research Model wing optimization work, which demonstrated gradient-based optimization with flutter and stochastic gust constraints, among others. While that work utilized FUN3D for static aeroelastic solutions but relied on doublet lattice aerodynamics for gust and flutter responses, the present work replaces these unsteady aerodynamic analyses with those of FUN3D’s linearized frequency-domain solver. With analytic derivatives available, gradient-based optimization is performed through the use of the OpenMDAO/MPhys libraries with over 700 shape, structural, and aerodynamic design variables and over 10 nonlinear constraints. Comparisons of analysis results and optimized designs are made between doublet lattice and linearized frequency-domain solutions.