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COMPLEX is workspace program designed to empower APL with complexnumber capabilities. Complex-variable methods provide analytical tools invaluable for applications in mathematics, science, and engineering. COMPLEX written in APL.
Flight systems must be validated to show that they are consistent with the requirements of their intended applications. While high reliability is difficult to validate, the additional complexity of fault tolerance further compounds the validation problem. The objective of NASA’s research is to develop a methodology for designing validatable fault-tolerant systems. Under the design-for-validation philosophy, emphasis is placed on developing validation methods that can be incorporated into the design process right from the start and design methods and guidance which, while incorporating fault tolerance, can assure validatability. This paper examines the statistical issues of validating highly reliable, fault tolerant system. There are many problems associated with traditional methods of designing and validating these potentially complex hardware and software systems. Useful design-for-validation methods, which include structured specification and design methodologies, mathematical proof techniques, analytical modeling, simulation and emulation, and physical testing, are discussed. Important design issues associated with fault tolerance are presented along with the related validation concerns which must be addressed. Experience has shown that synchronization and Byzantine resilience must accompany fault tolerance. Other design attributes associated with fault tolerance may be used by a designer on the basis of cost, weight, performance, and validation considerations.
A general method for systematizing a bulk of data on the secondary-electron spectrum into a small number of indices is shown. The method is based on thorough examination of the mathematical physics that governs the spectrum. Several examples of the analysis of recent experimental data on proton impact are presented.
The objective was to analytically and experimentally study the capabilities of adaptive material plate actuators for suppressing flutter. The validity of analytical modeling techniques for piezoelectric materials was also investigated. Piezoelectrics are materials which are characterized by their ability to produce voltage when subjected to a mechanical strain. The converse piezoelectric effect can be utilized to actuate a structure by applying a voltage. For this investigation, a two degree of freedom wind tunnel model was designed, analyzed, and tested. The model consisted of a rigid airfoil and a flexible mount system which permitted a translational and a rotational degree of freedom. It was designed such that flutter was encounted within the testing envelope of the wind tunnel. Actuators, made of piezoelectric material were affixed to leaf springs of the mount system. Each degree of freedom was controlled by a separate leaf spring. Command signals, applied to the piezoelectric actuators, exerted control over the damping and stiffness properties. A mathematical aeroservoelastic model was constructed using finite element methods, laminated plate theory, and aeroelastic analysis tools. Plant characteristics were determined from this model and verified by open loop experimental tests. A flutter suppression control law was designed and implemented on a digital control computer. Closed loop flutter testing was conducted. The experimental results represent the first time that adaptive materials have been used to actively suppress flutter. It demonstrates that small, carefully placed actuating plates can be used effectively to control aeroelastic response.
The objective of this research was to analytically and experimentally study the capabilities of adaptive material plate actuators for suppressing flutter. Piezoelectrics are materials which are characterized by their ability to produce voltage when subjected to a mechanical strain. The converse piezoelectric effect can be utilized to actuate a structure by applying a voltage. For this investigation, a two degree of freedom wind-tunnel model was designed, analyzed, and tested. The model consisted of a rigid wing and a flexible mount system which permitted translational and rotational degrees of freedom. Actuators, made of piezoelectric material were affixed to leaf springs on the mount system. Command signals, applied to the piezoelectric actuators, exerted control over the closed-loop damping and stiffness properties. A mathematical aeroservoelastic model was constructed using finite element and stiffness properties. A mathematical aeroservoelastic model was constructed using finite element methods, laminated plate theory, and aeroelastic analysis tools. A flutter suppression control law was designed, implemented on a digital control computer, and tested to conditions 20 percent above the passive flutter speed of the model. The experimental results represent the first time that adaptive materials have been used to actively suppress flutter. It demonstrates that small, carefully-placed actuating plates can be used effectively to control aeroelastic response.
A tutorial introduction to the complex structured singular value (mu) is presented, with an emphasis on the mathematical aspects of mu. The mu-based methods discussed here have been useful for analyzing the performance and robustness properties of linear feedback systems. Several tests for robust stability and performance with computable bounds for transfer functions and their state space realizations are compared, and a simple synthesis problem is studied. Uncertain systems are represented using linear fractional transformations which naturally unify the frequency-domain and state space methods.
A mathematical analysis has been made to show the method of obtaining the dimensions of the intercooler that will use the least total power for a given set of design conditions. The results of this analysis have been used in a sample calculation and, on the basis of this calculation, a new inter cooler arrangement is suggested. Because the length of the two air passages of the new arrangement is short in comparison with the third dimension, the height of the intercooler, this intercooler arrangement has unusual dimensions. These dimensions give the proposed intercooler arrangement an advantage over one of usual dimensions because less total power will be consumed by the intercooler, the weight and volume of the intercooler will be smaller, and the pressure drop of both the engine air and the cooling air in passing through the intercooler will be lower.
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Split path gearboxes can be attractive alternatives to the common planetary designs for rotorcraft, but because they have seen little use, they are relatively high risk designs. To help reduce the risk of fielding a rotorcraft with a split path gearbox, the vibration and dynamic characteristics of such a gearbox were studied. A mathematical model was developed by using the Lagrangian method, and it was applied to study the effect of three design variables on the natural frequencies and vibration energy of the gearbox. The first design variable, shaft angle, had little influence on the natural frequencies. The second variable, mesh phasing, had a strong effect on the levels of vibration energy, with phase angles of 0 deg and 180 deg producing low vibration levels. The third design variable, the stiffness of the shafts connecting the spur gears to the helical pinions, strongly influenced the natural frequencies of some of the vibration modes, including two of the dominant modes. We found that, to achieve the lowest level of vibration energy, the natural frequencies of these two dominant modes should be less than those of the main excitation sources.
This document is a compilation of papers presented at the Mechanics of Textile Composites Conference in Hampton, Virginia, December 6-8, 1994. This conference was the culmination of a 3-year program that was initiated by NASA late in 1990 to develop mechanics of textile composites in support of the NASA Advance Composites Technology Program (ACT). The goal of the program was to develop mathematical models of textile preform materials and test methods to facilitate structural analysis and design. Participants in the program were from NASA, academia, and industry.
This document is a compilation of papers presented at the Mechanics of Textile Composites Conference in Hampton, Virginia, December 6-8, 1994. This conference was the culmination of a 3-year program that was initiated by NASA late in 1990 to develop mechanics of textile composites in support of the NASA Advanced Composites Technology Program (ACT). The goal of the program was to develop mathematical models of textile preform materials and test methods to facilitate structural analysis and design. Participants in the program were from NASA, academia, and industry.
A formalism for target fragment transport is presented with application to energy loss spectra in thin silicon devices. A nuclear data base is recommended that agrees well with the measurements of McNulty et al. using surface barrier detectors. High-energy events observed by McNulty et al., which are not predicted by intranuclear cascade models, are well represented by the present work.
The results of a Monte Carlo model for calculating fragment fluences and LET spectra are compared to data taken with 600 MeV/nucleon iron ions incident on an accelerator beamline configured for irradiation of biological samples, with no target and with 2, 5 and 8 cm of polyethylene. The model uses a multi-generation nuclear fragmentation code, coupled with a formulation of ionization energy loss based on the Bethe-Bloch equation. In the region where the data are reliable and the experimental acceptance is well understood, many of the features of the experimental spectra are well replicated by the model. To obtain good agreement with the experimental data, the model must allow for at least two generations of fragment production in the target.
The device and associated analysis methodology summarized in this report were developed for the purpose of estimating the size of discontinuities in the surface of the foam that covers the Space Shuttle External Tank. These surface offsets are thought to be due to subsurface cracks in the foam insulation. The mathematical analysis and procedure described here provide a method to quantity the dimensions of the crack offset in a direction perpendicular to the surface, making use of the projected laser target device (PLTD) tool and a laser line projector. The keys to the construction and use of the PLTD are the following geometrical design requirements: Laser dots are on a square grid: length on a side. Laser beams are perpendicular to projected surface. Beams are parallel out to the distance being projected. The PLTD can be used to (1) calibrate fixed cameras of unknown magnification and orientation (far-field solution); (2) provide equivalent calibration to multiple cameras, previously achieved only by the use of known target points, for example, in 3.D foreign-object debris tracking on a fixed launch platform; (3) compute scaling for conventional 2.D images, and depth of field for 3.D images (near-field solution); and (4) in conjunction with a laser line projector, achieve accurate measurements of surface discontinuity (cracks) in a direction perpendicular to the surface.
Additional information about a mathematical model denoted the high-fidelity generalized method of cells (HFGMC) and implementation of the HFGMC within version 4.0 of the MAC/GMC software has become available. MAC/GMC (Micromechanics Analysis Code With Generalized Method of Cells) was a topic of several prior NASA Tech Briefs articles, version 4.0 having been described in "Comprehensive Micromechanics-Analysis Code - Version 4.0" (LEW-17495-1), NASA Tech Briefs, Vol. 29, No. 9 (September 2005), page 54. MAC/GMC predicts elastic and inelastic thermomechanical responses of composite materials. MAC/GMC utilizes the generalized method of cells (GMC) - a model of micromechanics that predicts macroscopic responses of a composite material as functions of the properties, sizes, shapes, and responses of its constituents (e.g., matrix and fibers). The accuracy of the GMC is limited by neglect of coupling between normal and shear stresses. The HFGMC was developed by combining elements of the GMC and a related model, denoted the higher-order theory for functionally graded materials (HOTFGM), that can account for this coupling. Hence, the HFGMC enables simulation of stress and strain with greater accuracy. Some alterations of the MAC/GMC data structure were necessitated by the greater computational complexity of the HFGMC.
With the conclusion of the Laboratory Directed Research and Development (LDRD) project on Provable Security and Resilience (PSaR) in Critical Infrastructure, we present forward-looking technical concepts and strategies that build on the project’s outcomes and INL’s long-standing expertise in infrastructure protection. The challenge is to protect critical infrastructure and functions much more efficiently at scale than capable adversaries can attack at scale. After summarizing progress and ongoing work we’ll discuss what are the challenges that remain and what are new/emerging technologies, strategies, and processes to meet those challenges. Finally, we’ll layout concepts that integrate with other protection work in the coming year and beyond. For example, building secure function-specific platforms based on the seL4 microkernel, and considering the successes of Cyber-Informed Engineering as a model for engage, collaboration, and adoption. We look forward to your feedback and collaboration as we refine and expand this vision.
Mathematical model of flooded porous electrodes under dynamic and static conditions - Methods for measuring porous electrode reaction distribution
Loosely coupled partitioned methods for multiphysics problems treat each subproblem as a separate entity and advance them independently in time. In so doing these methods enable code reuse, increase concurrency and provide a convenient framework for plug-and-play multiphysics simulations. However, mathematically loosely coupled schemes are equivalent to a single step of an iterative solution method, which can compromise their accuracy and stability. We present a new data-driven partitioned method for coupled parametric PDEs that can improve upon the accuracy of traditional loosely coupled methods without incurring a performance penalty. To that end, we replace conventional field transfers across the interface by a surrogate for the dynamics of the interface flux exchanged between the subdomains. To develop this surrogate we apply dynamic mode decomposition to a non-standard staggered-in-time state, comprising the interface flux and small solution patches near the interface. The new approach shifts the main computational burden to an offline training phase, whereas application of the surrogate in the online phase amounts to a single matrix–vector multiplication. In conclusion, we provide stability analysis of the surrogate-based partitioned scheme and include numerical results that demonstrate its potential.