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Mathematical models of a 5, 6, 7, and 8 coil large gap magnetic suspension system (MSDS) are presented. Some of the topics covered include: force and torque equations, reduction of state-space form, natural modes, origins of modes, effect of rotation in azimuth (yaw), future work, and n-coil ring conclusions.
Comprehensive mathematical-analysis technique developed for array of solar-photovoltaic panels equipped with truncated-pyramid concentrators. Hollow pyramidal concentrator reflects Sunlight onto panel of photovoltaic cells. Comprehensive optical, thermal, and electrical analysis performed on array of units. Technique applicable, with modifications, to analysis and design of other multiple-cell reflecting photovoltaic systems.
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A threaded multi-core implementation of the high performance dense linear algebra matrix-matrix multiply GEMM kernel is described. This kernel is widely implemented by vendors in the basic linear algebra subroutine BLAS library. The mathematics of arrays (MoA) paradigm due to Mullin (1988) results in contiguous memory accesses by employing outer-product forms. Our performance studies demonstrate that the MoA implementation of double precision DGEMM combined with optimal cache-blocking strategies results in at least a 25% performance gain on the Intel Xeon Skylake processor over the vendor supplied Intel MKL basic linear algebra libraries. Results are presented for the NREL Eagle supercomputer. The multi-core DGEMM achieves over 100 GigaFlops/sec with eight openMP threads.
The goal of this paper is to demonstrate performance enhancements of the high performance dense linear algebra matrix-matrix multiply DGEMM kernel, widely implemented by vendors in the basic linear algebra subroutine BLAS library. The mathematics of arrays (MoA) paradigm due to Mullin (1988) results in contiguous memory accesses in combination with Church-Rosser complete language constructs optimized for target processor architectures [3]. Our performance studies demonstrate that the MoA implementation of DGEMM combined with optimal cache-blocking strategies results in at least a 25% performance gain on both Intel Xeon Skylake and IBM Power-9 processors over the vendor supplied Intel MKL and IBM ESSL basic linear algebra libraries. Results are presented for the NREL Eagle and ORNL Summit supercomputers.
Beginning with the mathematical prediction of planetary orbits in the early seventeenth century up through the most recent developments in sensor fusion methods, many techniques have emerged that can be employed on the problem of endo and exoatmospheric trajectory estimation. Although early methods were ad hoc, the twentieth century saw the emergence of many systematic approaches to estimation theory that produced a wealth of useful techniques. The broad genesis of estimation theory has resulted in an equally broad array of mathematical principles, methods and vocabulary. Among the fundamental ideas and methods that are briefly touched on are batch and sequential processing, smoothing, estimation, and prediction, sensor fusion, sensor fusion architectures, data association, Bayesian and non Bayesian filtering, the family of Kalman filters, models of the dynamics of the phases of a rocket's flight, and asynchronous, delayed, and asequent data. Along the way, a few trajectory estimation issues are addressed and much of the vocabulary is defined.
Least integral square error method for antenna array synthesis
Effects of mutual coupling on thirty six element square array of crossed slots in electronically scanned tracking antenna
The Large Angle Magnetic Suspension Test Fixture (LAMSTF) is a laboratory scale proof-of-concept system. The configuration is unique in that the electromagnets are mounted in a circular planar array. A mathematical model of the system had previously been developed, but was shown to have inaccuracies. These inaccuracies showed up in the step responses. Eddy currents were found to be the major cause of the modeling errors. In the original system, eddy currents existed in the aluminum baseplate, iron cores, and the sensor support frame. An attempt to include the eddy current dynamics in the system model is presented. The dynamics of a dummy sensor ring were added to the system. Adding the eddy current dynamics to the simulation improves the way it compares to the actual experiment. Also presented is a new method of determining the yaw angle of the suspended element. From the coil currents the yaw angle can be determined and the controller can be updated to suspend at the new current. This method has been used to demonstrate a 360 degree yaw angle rotation.
A technique is proposed for designing sensor weightings, or array shading functions, for microphone phased arrays. The presented method attempts to maintain mathematical simplicity while maximizing array gain for a desired mainlobe beamwidth. It does so using the two-parameter optimization of a family of functions. The shading design process is described and applied to an array used recently in the NASA Langley Research Center 14- by 22-Foot Subsonic Tunnel. Several variants of the method are compared to an existing shading scheme for the array, along with a more general optimization formulation. Results are presented for both an idealized point source and experimental data from the wind tunnel test. The shading schemes are shown to improve the behavior of array operations, but have a stronger impact on visual interpretation of maps than on source level calculations. The study results show that the two-parameter optimization scheme provides favorable characteristics while maintaining implementation simplicity.
Mathematical cost models previously developed for hybrid microelectronic subsystems were refined and expanded. Rework terms related to substrate fabrication, nonrecurring developmental and manufacturing operations, and prototype production are included. Sample computer programs were written to demonstrate hybrid microelectric applications of these cost models. Computer programs were generated to calculate and analyze values for the total microelectronics costs. Large scale integrated (LST) chips utilizing tape chip carrier technology were studied. The feasibility of interconnecting arrays of LSU chips utilizing tape chip carrier and semiautomatic wire bonding technology was demonstrated.
New developments in infrared sensor technology have potentially made possible a new space-based system which can measure far-infrared radiation at lower costs (mass, power and expense). The Stationary Imaging Fourier Transform Spectrometer (SIFTS) proposed by NASA Langley Research Center, makes use of new detector array technology. A mathematical model which simulates resolution and spectral range relationships has been developed for analyzing the utility of such a radically new approach to spectroscopy. Calculations with this forward model emulate the effects of a detector array on the ability to retrieve accurate spectral features. Initial computations indicate significant attenuation at high wavenumbers.
Mathematical cost factors were generated for both hybrid microcircuit and printed wiring board packaging methods. A mathematical cost model was created for analysis of microcircuit fabrication costs. The costing factors were refined and reduced to formulae for computerization. Efficient methods were investigated for low cost packaging of LSI devices as a function of density and reliability. Technical problem areas such as wafer bumping, inner/outer leading bonding, testing on tape, and tape processing, were investigated.
Link Array signals emanating from different antennas must be compensated for Doppler and delay in order to achieve the N(sup 2) array gain predicted by theory. However compensation is never perfect, leaving residual errors that cause losses in array gain and degradation in signal quality. Here we develop a mathematical model for Uplink Array signals in the presence of phase and delay errors, similar to well-known multipath analyses but with features unique to this problem. The resulting losses and distortions are described, and the power spectral density of the array signal derived first conditioned on a given error vector, then averaged over distributions deemed suitable for Uplink Array applications. The impact of phase and delay errors on array gain and signal distortion are addressed, and the maximum data throughput is quantified in terms of the assumed error statistics.
Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. In the past, antenna designers have had to resort to expensive measurements in order to develop a conformal array design. This is due to the lack of rigorous mathematical models for conformal antenna arrays, and as a result the design of conformal arrays is primarily based on planar antenna design concepts. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. Herewith we shall extend this formulation for conformal arrays on large metallic cylinders. In this we develop the mathematical formulation. In particular we discuss the finite element equations, the shape elements, and the boundary integral evaluation, and it is shown how this formulation can be applied with minimal computation and memory requirements. The implementation shall be discussed in a later report.
From earlier measurements and the mathematical examples, it can be gathered that the inertia of dynamic pressure arrays can be computed with sufficient accuracy and the proper size of tubing established, provided that certain requirements are made on the inertia.
Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. In the past, antenna designers have had to resort to expensive measurements in order to develop a conformal array design. This was due to the lack of rigorous mathematical models for conformal antenna arrays. As a result, the design of conformal arrays was primarily based on planar antenna design concepts. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. We are extending this formulation to conformal arrays on large metallic cylinders. In doing so, we will develop a mathematical formulation. In particular, we discuss the finite element equations, the shape elements, and the boundary integral evaluation. It is shown how this formulation can be applied with minimal computation and memory requirements.
Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. However, due to a lack of rigorous mathematical models for conformal antenna arrays, antenna designers resort to measurement and planar antenna concepts for designing non-planar conformal antennas. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. We extend this formulation to conformal arrays on large metallic cylinders. In this report, we develop the mathematical formulation. In particular, we discuss the shape functions, the resulting finite elements and the boundary integral equations, and the solution of the conformal finite element-boundary integral system. Some validation results are presented and we further show how this formulation can be applied with minimal computational and memory resources.