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At least 451 records · Page 25

Runge-Kutta Methods for Linear Ordinary Differential Equations

Three new Runge-Kutta methods are presented for numerical integration of systems of linear inhomogeneous ordinary differential equations (ODES) with constant coefficients. Such ODEs arise in the numerical solution of the partial differential equations governing linear wave phenomena. The restriction to linear ODEs with constant coefficients reduces the number of conditions which the coefficients of the Runge-Kutta method must satisfy. This freedom is used to develop methods which are more efficient than conventional Runge-Kutta methods. A fourth-order method is presented which uses only two memory locations per dependent variable, while the classical fourth-order Runge-Kutta method uses three. This method is an excellent choice for simulations of linear wave phenomena if memory is a primary concern. In addition, fifth- and sixth-order methods are presented which require five and six stages, respectively, one fewer than their conventional counterparts, and are therefore more efficient. These methods are an excellent option for use with high-order spatial discretizations.

Zingg, David W.↗

High-Order Hyperbolic Residual-Distribution Schemes on Arbitrary Triangular Grids

In this paper, we construct high-order hyperbolic residual-distribution schemes for general advection-diffusion problems on arbitrary triangular grids. We demonstrate that the second-order accuracy of the hyperbolic schemes can be greatly improved by requiring the scheme to preserve exact quadratic solutions. We also show that the improved second-order scheme can be easily extended to third-order by further requiring the exactness for cubic solutions. We construct these schemes based on the LDA and the SUPG methodology formulated in the framework of the residual-distribution method. For both second- and third-order-schemes, we construct a fully implicit solver by the exact residual Jacobian of the second-order scheme, and demonstrate rapid convergence of 10-15 iterations to reduce the residuals by 10 orders of magnitude. We demonstrate also that these schemes can be constructed based on a separate treatment of the advective and diffusive terms, which paves the way for the construction of hyperbolic residual-distribution schemes for the compressible Navier-Stokes equations. Numerical results show that these schemes produce exceptionally accurate and smooth solution gradients on highly skewed and anisotropic triangular grids, including curved boundary problems, using linear elements. We also present Fourier analysis performed on the constructed linear system and show that an under-relaxation parameter is needed for stabilization of Gauss-Seidel relaxation.

Mazaheri, Alireza↗

Survey and Assessment of Crew Performance Evaluation Methods Applicable to Human Spacecraft Design

Space is an unforgiving environment where the actions of the crew play a critical role in their health and safety. Given the limited number of crewmembers typically onboard a spacecraft and the multitude of complex systems they must operate, the performance of each individual is of paramount importance. Spacecraft habitat layout and operations are two main drivers affecting crew performance efficiency. Having the capability to analyze and compare crew performance across various spacecraft configurations can help identify improvements early in the conceptual design process where changes are less costly to implement, ultimately reducing overall project costs and improving long-term operations of the system. Currently, there are few comprehensive methods readily available for evaluating crew integration within a spacecraft in the conceptual design phase. In order to address this shortcoming, the goal of this work was to analyze various specialized evaluation methods found in analogous industries that have potential application to human spacecraft design. A survey of more than 400 human performance evaluation methods was completed. Over twenty different attributes were identified for each method and a variety of analyses were conducted to characterize and evaluate their potential use for assessing human spacecraft design options. The analysis revealed a particular deficiency of quantitative evaluation methods that are applicable early in the systems engineering design phase. It also identified five existing methods that could be supplemented to achieve the needs of an early design evaluation method. Additional discussion describes potential issues that must be overcome when developing a method specific for use in human spacecraft evaluations.

crew performance↗

Semiclassical theory of unimolecular dissociation induced by a laser field

A semiclassical nonperturbative theory of direct photodissociation in a laser field is developed in which photon absorption and dissociation are treated in a unified fashion. This is achieved by visualizing nuclear dynamics as a representative particle moving on electronic-field surfaces. Methods are described for calculating dissociation rates and probabilities by Monte Carlo selection of initial conditions and integration of classical trajectories on these surfaces. This unified theory reduces to the golden rule expression in the weak-field and short-time limits, and predicts nonlinear behavior, i.e., breakdown of the golden rule expression in intense fields. Field strengths above which lowest-order perturbation theory fails to work have been estimated for some systems. Useful physical insights provided by the electronic-field representation have been illustrated. Intense field effects are discussed which are amenable to experimental observation. The semiclassical methods used here are also applicable to multiple-surface dynamics in fieldfree unimolecular and bimolecular reactions.

Yuan, J.-M.↗

Operational Parameters, Considerations, and Design Decisions for Resource-Constrained Ion Trap Mass Spectrometers

Mass spectrometers are increasingly finding applications in new and unique areas, often in situations where key operational resources (i.e. power, weight and size) are limited. One such example is the Mars Organic Molecule Analyzer (MOMA). This instrument is a joint venture between NASA and the European Space Agency (ESA) to develop an ion trap mass spectrometer for chemical analysis on Mars. The constraints on such an instrument are significant as are the performance requirements. While the ideal operating parameters for an ion trap are generally well characterized, methods to maintain analytical performance with limited power and system weight need to be investigated and tested. Methods Experiments have been performed on two custom ion trap mass spectrometers developed as prototypes for the MOMA instrument. This hardware consists of quadrupole ion trap electrodes that are 70% the size of common commercial instrumentation. The trapping RF voltage is created with a custom tank circuit that can be tuned over a range of RF frequencies and is driven using laboratory supplies and amplifiers. The entire instrument is controlled with custom Lab VIEW software that allows a high degree of flexibility in the definition of the scan function defining the ion trap experiment. Ions are typically generated via an internal electron ionization source, however, a laser desorption source is also in development for analysis of larger intact molecules. Preliminary Data The main goals in this work have been to reduce the power required to generate the radio frequency trapping field used in an ion trap mass spectrometer. Generally minimizing the power will also reduce the volume and mass of the electronics to support the instrument. In order to achieve optimum performance, commercial instruments typically utilize RF frequencies in the 1 MHz range. Without much concern for power usage, they simply generate the voltage required to access the mass range of interest. In order to reduce the required RF voltage (and power), operation of the ion trap at lower RF frequencies has been investigated. Surprisingly, the performance of the instrument has only been slightly degraded at RF frequencies all the way down to 500 kHz. Mass resolution is relatively stable to this point and depending on the resonant ejection point used, the peak intensity is also quite stable. To date only masses up to m/z 200 have been fully investigated, however, additional studies are planned to verify the performance with higher mass ions. The lower frequency and voltage should reduce the pseudo potential well depth, eventually affecting the trapping efficiency of the instrument -- effect that could manifest itself in significantly limiting the mass range of trapped ions. Other methods to reduce the RF power while maintaining analytical performance are also under investigation. This includes ion ejection at lower q(sub z) values to access a given mass with a lower RF voltage. The loss of mass resolution at lower q(sub eject) points has been measured and current work is underway to leverage scan speed and the use of non-linear resonances in order to counter this trend. The overall trap performance under this range of operating conditions will be presented with a goal of identifying what trade-offs are acceptable.

Danell, Ryan M.↗

Focal characteristics of spheroidal geodesic lenses for integrated optical processing

Aspheric shaping of geodesic lenses in optical waveguides is suggested as a means for correcting spherical aberrations. The technique is complementary to the method of Spiller and Harper, in which geodesic lens aberrations are reduced by thickening the waveguiding layer in the lens region. The properties of a family of oblate-spheroidal lenses with no third-order spherical aberrations are described theoretically. Diffraction-limited performance over apertures up to one-half the full lens aperture is predicted for lenses with true f/numbers (focal length divided by useful aperture) in the range 2-12. By combining spheroidal-shaping and mode-index correction techniques, geodesic lenses free from both third- and fifth-order aberrations can be designed. These lenses show diffraction-limited performance over apertures of a centimeter or more when true f/numbers are in the range 1.5-9.5.

Vahey, D. W.↗

Hybrid state vector methods for structural dynamic and aeroelastic boundary value problems

A computational technique is developed that is suitable for performing preliminary design aeroelastic and structural dynamic analyses of large aspect ratio lifting surfaces. The method proves to be quite general and can be adapted to solving various two point boundary value problems. The solution method, which is applicable to both fixed and rotating wing configurations, is based upon a formulation of the structural equilibrium equations in terms of a hybrid state vector containing generalized force and displacement variables. A mixed variational formulation is presented that conveniently yields a useful form for these state vector differential equations. Solutions to these equations are obtained by employing an integrating matrix method. The application of an integrating matrix provides a discretization of the differential equations that only requires solutions of standard linear matrix systems. It is demonstrated that matrix partitioning can be used to reduce the order of the required solutions. Results are presented for several example problems in structural dynamics and aeroelasticity to verify the technique and to demonstrate its use. These problems examine various types of loading and boundary conditions and include aeroelastic analyses of lifting surfaces constructed from anisotropic composite materials.

Lehman, L. L.↗

A Xylophone Detector of Gravitational Radiation

We discuss spacecraft Doppler tracking searches for gravitational waves in which Doppler data recorded on the ground are linearly combined with Doppler measurements made on board a spacecraft. By using the four-link radio system first proposed by Vessot and Levine, we describe a new method for removing from the combined data the frequency fluctuations due to the Earth troposphere, ionosphere, and mechanical vibrations of the antenna on the ground. This technique provides also a way for reducing by several orders of magnitude, at selected Fourier components, the frequency fluctuations due to other noise sources, such as the clock on board the spacecraft or the antenna and buffeting of the probe by nongravitational forces. In this respect spacecraft Doppler tracking can be regarded as a xylophone detector of gravitational radiation. In the assumption of calibrating the frequency fluctuations induced by the interplanetary plasma, a strain sensitivity equal to 4.7 x 10(exp -18) at 10(exp -3) Hz is estimated. This experimental technique could be extended to other tests of the theory of relativity, and to radio science experiments that rely on high-precision Doppler measurements.

Tinto, Massimo↗

Direct Detection Doppler Lidar for Spaceborne Wind Measurement

Aerosol and molecular based versions of the double-edge technique can be used for direct detection Doppler lidar spaceborne wind measurement. The edge technique utilizes the edge of a high spectral resolution filter for high accuracy wind measurement using direct detection lidar. The signal is split between an edge filter channel and a broadband energy monitor channel. The energy monitor channel is used for signal normalization. The edge measurement is made as a differential frequency measurement between the outgoing laser signal and the atmospheric backscattered return for each pulse. As a result the measurement is insensitive to laser and edge filter frequency jitter and drift at a level less than a few parts in 10(exp 10). We have developed double edge versions of the edge technique for aerosol and molecular-based lidar measurement of the wind. Aerosol-based wind measurements have been made at Goddard Space Flight Center and molecular-based wind measurements at the University of Geneva. We have demonstrated atmospheric measurements using these techniques for altitudes from 1 to more than 10 km. Measurement accuracies of better than 1.25 m/s have been obtained with integration times from 5 to 30 seconds. The measurements can be scaled to space and agree, within a factor of two, with satellite-based simulations of performance based on Poisson statistics. The theory of the double edge aerosol technique is described by a generalized formulation which substantially extends the capabilities of the edge technique. It uses two edges with opposite slopes located about the laser frequency at approximately the half-width of each edge filter. This doubles the signal change for a given Doppler shift and yields a factor of 1.6 improvement in the measurement accuracy compared to the single edge technique. The use of two high resolution edge filters substantially reduces the effects of Rayleigh scattering on the measurement, as much as order of magnitude, and allows the signal to noise ratio to be substantially improved in areas of low aerosol backscatter. We describe a method that allows the Rayleigh and aerosol components of the signal to be independently determined using the two edge channels and an energy monitor channel. The effects of Rayleigh scattering may then subtracted from the measurement and we show that the correction process does not significantly increase the measurement noise for Rayleigh to aerosol ratios up to 10. We show that for small Doppler shifts a measurement accuracy of 0.4 m/s can be obtained for 5000 detected photon, 1.2 m/s for 1000 detected photons, and 3.7 m/s for 50 detected photons for a Rayleigh to aerosol ratio of 5. Methods for increasing the dynamic range of the aerosol-based system to more than +/- 100 m/s are given.

Korb, C. Laurence↗

Model Predictive Control in the Three-body Problem Using Invariant Funnels As Terminal Sets

This paper describes a method for augmenting Model Predictive Control techniques using invariant funnels computed in the Circular Restricted Three-Body Problem. We use ellipsoids that roughly approximate the boundary of the invariant funnel as convex terminal sets for a short look-ahead optimization problem at each time step. We apply this method to a hypothetical low-thrust mission to land on Jupiter’s mooon Europa and show that including the invariant funnels as terminal sets reduces the amount of control effort required by almost an order of magnitude.

Close, Sigrid↗

Element Library for Three-Dimensional Stress Analysis by the Integrated Force Method

The Integrated Force Method, a recently developed method for analyzing structures, is extended in this paper to three-dimensional structural analysis. First, a general formulation is developed to generate the stress interpolation matrix in terms of complete polynomials of the required order. The formulation is based on definitions of the stress tensor components in term of stress functions. The stress functions are written as complete polynomials and substituted into expressions for stress components. Then elimination of the dependent coefficients leaves the stress components expressed as complete polynomials whose coefficients are defined as generalized independent forces. Such derived components of the stress tensor identically satisfy homogenous Navier equations of equilibrium. The resulting element matrices are invariant with respect to coordinate transformation and are free of spurious zero-energy modes. The formulation provides a rational way to calculate the exact number of independent forces necessary to arrive at an approximation of the required order for complete polynomials. The influence of reducing the number of independent forces on the accuracy of the response is also analyzed. The stress fields derived are used to develop a comprehensive finite element library for three-dimensional structural analysis by the Integrated Force Method. Both tetrahedral- and hexahedral-shaped elements capable of modeling arbitrary geometric configurations are developed. A number of examples with known analytical solutions are solved by using the developments presented herein. The results are in good agreement with the analytical solutions. The responses obtained with the Integrated Force Method are also compared with those generated by the standard displacement method. In most cases, the performance of the Integrated Force Method is better overall.

Kaljevic, Igor↗

Propagation of high amplitude higher order sounds in slightly soft rectangular ducts, carrying mean flow

The resonance expansion method, developed to study the propagation of sound in rigid rectangular ducts is applied to the case of slightly soft ducts. Expressions for the generation and decay of various harmonics are obtained. The effect of wall admittance is seen through a dissipation function in the system of nonlinear differential equations, governing the generation of harmonics. As the wall admittance increases, the resonance is reduced. For a given wall admittance this phenomenon is stronger at higher input intensities. Both the first and second order solutions are obtained and the results are extended to the case of ducts having mean flow.

Wang, K. S.↗

Complex eigenvalue extraction in NASTRAN by the tridiagonal reduction (FEER) method

An extension of the Tridiagonal Reduction (FEER) method to complex eigenvalue analysis in NASTRAN is described. As in the case of real eigenvalue analysis, the eigensolutions closest to a selected point in the eigenspectrum are extracted from a reduced, symmetric, tridiagonal eigenmatrix whose order is much lower than that of the full size problem. The reduction process is effected automatically, and thus avoids the arbitrary lumping of masses and other physical quantities at selected grid points. The statement of the algebraic eigenvalue problem admits mass, damping and stiffness matrices which are unrestricted in character, i.e., they may be real, complex, symmetric or unsymmetric, singular or non-singular.

Newman, M.↗

The measurement of aircraft performance and stability and control after flight through natural icing conditions

The effects of airframe icing on the performance and stability and control of a twin-engine commuter-class aircraft were measured by the NASA Lewis Research Center. This work consisted of clear air tests with artificial ice shapes attached to the horizontal tail, and natural icing flight tests in measured icing clouds. The clear air tests employed static longitudinal flight test methods to determine degradation in stability margins for four simulated ice shapes. The natural icing flight tests employed a data acquisition system, which was provided under contract to NASA by Kohlman Systems Research Incorporated. This system used a performance modeling method and modified maximum likelihood estimation (MMLE) technique to determine aircraft performance degradation and stability and control. Flight test results with artificial ice shapes showed that longitudinal, stick-fixed, static margins are reduced on the order of 5 percent with flaps up. Natural icing tests with the KSR system corroborated these results and showed degradation in the elevator control derivatives on the order of 8 to 16 percent depending on wing flap configuration. Performance analyses showed the individual contributions of major airframe components to the overall degration in lift and drag.

Ranaudo, R. J.↗

The measurement of aircraft performance and stability and control after flight through natural icing conditions

The effects of airframe icing on the performance and stability and control of a twin-engine commuter-class aircraft were measured by the NASA Lewis Research Center. This work consisted of clear air tests with artificial ice shapes attached to the horizontal tail, and natural icing flight tests in measured icing clouds. The clear air tests employed static longitudinal flight test methods to determine degradation in stability margins for four simulated ice shapes. The natural icing flight tests employed a data acquisition system, which was provided under contract to NASA by Kohlman Systems Research Incorporated. This system used a performance modeling method and modified maximum likelihood estimation (MMLE) technique to determine aircraft performance degradation and stability and control. Flight test results with artificial ice shapes showed that longitudinal, stick-fixed, static margins are reduced on the order of 5 percent with flaps up. Natural icing tests with the KSR system corroborated these results and showed degradation in the elevator control derivatives on the order of 8 to 16 percent depending on wing flap configuration. Performance analyses showed the individual contributions of major airframe components to the overall degradation in lift and drag.

Ranaudo, R. J.↗

Systematic generation of multibody equations of motion suitable for recursive and parallel manipulation

The formulation of a method known as the joint coordinate method for automatic generation of the equations of motion for multibody systems is summarized. For systems containing open or closed kinematic loops, the equations of motion can be reduced systematically to a minimum number of second order differential equations. The application of recursive and nonrecursive algorithms to this formulation, computational considerations and the feasibility of implementing this formulation on multiprocessor computers are discussed.

Nikravesh, Parviz E.↗

Connectivity strategies for higher-order neural networks applied to pattern recognition

Different strategies for non-fully connected HONNs (higher-order neural networks) are discussed, showing that by using such strategies an input field of 128 x 128 pixels can be attained while still achieving in-plane rotation and translation-invariant recognition. These techniques allow HONNs to be used with the larger input scenes required for practical pattern-recognition applications. The number of interconnections that must be stored has been reduced by a factor of approximately 200,000 in a T/C case and about 2000 in a Space Shuttle/F-18 case by using regional connectivity. Third-order networks have been simulated using several connection strategies. The method found to work best is regional connectivity. The main advantages of this strategy are the following: (1) it considers features of various scales within the image and thus gets a better sample of what the image looks like; (2) it is invariant to shape-preserving geometric transformations, such as translation and rotation; (3) the connections are predetermined so that no extra computations are necessary during run time; and (4) it does not require any extra storage for recording which connections were formed.

Spirkovska, Lilly↗

Optimal Control Modification Adaptive Law for Time-Scale Separated Systems

Recently a new optimal control modification has been introduced that can achieve robust adaptation with a large adaptive gain without incurring high-frequency oscillations as with the standard model-reference adaptive control. This modification is based on an optimal control formulation to minimize the L2 norm of the tracking error. The optimal control modification adaptive law results in a stable adaptation in the presence of a large adaptive gain. This study examines the optimal control modification adaptive law in the context of a system with a time scale separation resulting from a fast plant with a slow actuator. A singular perturbation analysis is performed to derive a modification to the adaptive law by transforming the original system into a reduced-order system in slow time. A model matching conditions in the transformed time coordinate results in an increase in the actuator command that effectively compensate for the slow actuator dynamics. Simulations demonstrate effectiveness of the method.

Nguyen, Nhan T.↗