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All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

A dual-input nonlinear system analysis of autonomic modulation of heart rate

Linear analyses of fluctuations in heart rate and other hemodynamic variables have been used to elucidate cardiovascular regulatory mechanisms. The role of nonlinear contributions to fluctuations in hemodynamic variables has not been fully explored. This paper presents a nonlinear system analysis of the effect of fluctuations in instantaneous lung volume (ILV) and arterial blood pressure (ABP) on heart rate (HR) fluctuations. To successfully employ a nonlinear analysis based on the Laguerre expansion technique (LET), we introduce an efficient procedure for broadening the spectral content of the ILV and ABP inputs to the model by adding white noise. Results from computer simulations demonstrate the effectiveness of broadening the spectral band of input signals to obtain consistent and stable kernel estimates with the use of the LET. Without broadening the band of the ILV and ABP inputs, the LET did not provide stable kernel estimates. Moreover, we extend the LET to the case of multiple inputs in order to accommodate the analysis of the combined effect of ILV and ABP effect on heart rate. Analyzes of data based on the second-order Volterra-Wiener model reveal an important contribution of the second-order kernels to the description of the effect of lung volume and arterial blood pressure on heart rate. Furthermore, physiological effects of the autonomic blocking agents propranolol and atropine on changes in the first- and second-order kernels are also discussed.

NASA Discipline Regulatory Physiology↗
NASA NTRS1996

Mixing and Transition Control Studied

Considerable progress in understanding nonlinear phenomena in both unbounded and wallbounded shear flow transition has been made through the use of a combination of high- Reynolds-number asymptotic and numerical methods. The objective of this continuing work is to fully understand the nonlinear dynamics so that ultimately (1) an effective means of mixing and transition control can be developed and (2) the source terms in the aeroacoustic noise problem can be modeled more accurately. Two important aspects of the work are that (1) the disturbances evolve from strictly linear instability waves on weakly nonparallel mean flows so that the proper upstream conditions are applied in the nonlinear or wave-interaction streamwise region and (2) the asymptotic formulations lead to parabolic problems so that the question of proper out-flow boundary conditions--still a research issue for direct numerical simulations of convectively unstable shear flows--does not arise. Composite expansion techniques are used to obtain solutions that account for both mean-flow-evolution and nonlinear effects. A previously derived theory for the amplitude evolution of a two-dimensional instability wave in an incompressible mixing layer (which is in quantitative agreement with available experimental data for the first nonlinear saturation stage for a plane-jet shear layer, a circular-jet shear layer, and a mixing layer behind a splitter plate) have been extended to include a wave-interaction stage with a three-dimensional subharmonic. The ultimate wave interaction effects can either give rise to explosive growth or an equilibrium solution, both of which are intimately associated with the nonlinear self-interaction of the three dimensional component. The extended theory is being evaluated numerically. In contrast to the mixing-layer situation, earlier comparisons of theoretical predictions based on asymptotic methods and experiments in wall-bounded shear-flow transition have been somewhat lacking in one aspect or another. The current work strongly suggests that the main weakness is the underlying asymptotic representation of the linear "part" of the problem and not the explicit modeling of the nonlinear/wave-interaction effects. Consequently, the long-wave-length/high-Reynolds-number asymptotic limit for the Blasius boundary-layer stability problem was reexamined, and a new dispersion relationship for the instability waves that is uniformly valid for both the upper- and lower branch regions to the required order of approximation was obtained. A comparison with numerical results, obtained by solving the Orr-Sommerfeld stability problem, shows that the asymptotic formula provides surprisingly good results, even for values of the frequency parameter usually encountered in experimental investigations. This is particularly evident in the dynamically important upper-branch region, where much of the nonlinear interactions in transition experiments are believed to take place. The result is important in that it can be used to greatly improve the accuracy of weakly nonlinear critical-layer-based theories, and a consistent nonlinear theory is currently under evaluation.

Source record↗
NASA NTRS2023

Quantification of Global Cloud Properties with Use of Spherical Harmonic Functions

Spherical harmonic (SH) expansion is a useful tool to study any variable that has valid values at all latitudes and longitudes. The variable can be quantified as a sum of different spherical harmonic components, which are the spherical harmonic functions multiplied by their expansion coefficients. We find that the SH components of cloud radiative effect (CRE) have correlations with El Niño-Southern Oscillation (ENSO) and the Hadley Circulation (HC). In particular, the expansion degree 2 (l = 2) SH power spectrum component anomaly of CRE is strongly correlated with ENSO. The two dipole patterns appearing in the l = 2 SH component anomaly map can be reasonably explained by a known mechanism of ENSO’s impact on cloud properties. The l = 3 and l = 5 SH power spectrum components are correlated with HC intensity, whereas the l = 6 and l = 8 components are correlated with HC latitudinal widths. In ENSO warm and cold phases, the HC-correlated SH components have opposite anomalies, which suggests the impact of ENSO on HC. This study illustrates that the SH expansion technique provides a different perspective to study the impacts of large-scale atmospheric circulation on global cloud properties and radiative effects.

clouds↗
NASA NTRS1989

Expansion and orthogonalization of measured modes for structure identification

The purpose was to investigate a new simultaneous expansion/orthogonalization method in comparison with two previously published expansion methods and a widely used orthogonalization technique. Each expansion method uses data from an analytical model of the structure to complete the estimate of the mode shape vectors. Berman and Nagy used Guyan expansion in their work with improving analytical models. In this method, modes are expanded one at a time, producing a set not orthogonal with respect to the mass matrix. Baruch and Bar Itzhack's optimal orthogonalization procedure was used to subsequently adjust the expanded modes. A second expansion technique was presented by O'Callahan, Avitabile, and Reimer and separately by Kammer. Again, modes are expanded individually and orthogonalized after expansion with the same optimal technique as above. Finally, a simultaneous expansion/orthogonalization method was developed from the orthogonal Procrustes problem of computational mathematics. In this method modes are optimally expanded as a set and orthogonal with respect to the mass matrix as a result. Two demonstation problems were selected for the comparison of the methods described. The first problem is an 8 degree of freedom spring-mass problem first presented by Kabe. Several conditions were examined for expansion method including the presence of errors in the measured data and in the analysis models. As a second demonstration problem, data from tests of laboratory scale model truss structures was expanded for system identification. Tests with a complete structure produced a correlated analysis model and the stiffness and mass matrices. Tests of various damaged configurations produced measured data for 6 modes at 14 dof locations.

Smith, Suzanne Weaver↗
NASA NTRS1989

Techniques for measurement of the thermal expansion of advanced composite materials

Techniques available to measure small thermal displacements in flat laminates and structural tubular elements of advanced composite materials are described. Emphasis is placed on laser interferometry and the laser interferometric dilatometer system used at the National Aeronautics and Space Administration (NASA) Langley Research Center. Thermal expansion data are presented for graphite-fiber reinforced 6061 and 2024 aluminum laminates and for graphite fiber reinforced AZ91 C and QH21 A magnesium laminates before and after processing to minimize or eliminate thermal strain hysteresis. Data are also presented on the effects of reinforcement volume content on thermal expansion of silicon-carbide whisker and particulate reinforced aluminum.

Tompkins, Stephen S.↗
NASA NTRS1989

A hybrid-perturbation-Galerkin technique which combines multiple expansions

A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be sued to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Geer, James F.↗
NASA NTRS1990

A hybrid perturbation-Galerkin technique that combines multiple expansions

A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be used to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Geer, James F.↗
NASA NTRS1996

A Noncontact Measurement Technique for the Density and Thermal Expansion Coefficient of Solid and Liquid Materials

A noncontact measurement technique for the density and the thermal expansion refractory materials in their molten as well as solid phases is presented. This technique is based on the video image processing of a levitated sample. Experiments were performed using the high-temperature electrostatic levitator (HTESL) at the Jet Propulsion Laboratory in which 2-3 mm diameter samples can be levitated, melted, and radiatively cooled in a vacuum. Due to the axisymmetric nature of the molten samples when levitated in the HTESL, a rather simple digital image analysis can be employed to accurately measure the volumetric change as a function of temperature. Density and the thermal expansion coefficient measurements were made on a pure nickel sample to test the accuracy of the technique in the temperature range of 1045-1565 C. The result for the liquid phase density can be expressed by p = 8.848 + (6.730 x 10(exp -4)) x T (degC) g/cu cm within 0.8% accuracy, and the corresponding thermal expansion coefficient can be expressed by Beta=(9.419 x 10(exp -5)) - (7.165 x 10(exp -9) x T (degC)/K within 0.2% accuracy.

Chung, Sang K.↗
NASA NTRS1992

Order reduction of z-transfer functions via multipoint Jordan continued-fraction expansion

The order reduction problem of z-transfer functions is solved by using the multipoint Jordan continued-fraction expansion (MJCFE) technique. An efficient algorithm that does not require the use of complex algebra is presented for obtaining an MJCFE from a stable z-transfer function with expansion points selected from the unit circle and/or the positive real axis of the z-plane. The reduced-order models are exactly the multipoint Pade approximants of the original system and, therefore, they match the (weighted) time-moments of the impulse response and preserve the frequency responses of the system at some characteristic frequencies, such as gain crossover frequency, phase crossover frequency, bandwidth, etc.

Lee, Ying-Chin↗
NASA NTRS1982

A Computer Code for Swirling Turbulent Axisymmetric Recirculating Flows in Practical Isothermal Combustor Geometries

A primitive pressure-velocity variable finite difference computer code was developed to predict swirling recirculating inert turbulent flows in axisymmetric combustors in general, and for application to a specific idealized combustion chamber with sudden or gradual expansion. The technique involves a staggered grid system for axial and radial velocities, a line relaxation procedure for efficient solution of the equations, a two-equation k-epsilon turbulence model, a stairstep boundary representation of the expansion flow, and realistic accommodation of swirl effects. A user's manual, dealing with the computational problem, showing how the mathematical basis and computational scheme may be translated into a computer program is presented. A flow chart, FORTRAN IV listing, notes about various subroutines and a user's guide are supplied as an aid to prospective users of the code.

Lilley, D. G.↗
NASA NTRS2013

Extended Analytic Device Optimization Employing Asymptotic Expansion

Analytic optimization of a thermoelectric junction often introduces several simplifying assumptionsincluding constant material properties, fixed known hot and cold shoe temperatures, and thermallyinsulated leg sides. In fact all of these simplifications will have an effect on device performance,ranging from negligible to significant depending on conditions. Numerical methods, such as FiniteElement Analysis or iterative techniques, are often used to perform more detailed analysis andaccount for these simplifications. While numerical methods may stand as a suitable solution scheme,they are weak in gaining physical understanding and only serve to optimize through iterativesearching techniques. Analytic and asymptotic expansion techniques can be used to solve thegoverning system of thermoelectric differential equations with fewer or less severe assumptionsthan the classic case. Analytic methods can provide meaningful closed form solutions and generatebetter physical understanding of the conditions for when simplifying assumptions may be valid.In obtaining the analytic solutions a set of dimensionless parameters, which characterize allthermoelectric couples, is formulated and provide the limiting cases for validating assumptions.Presentation includes optimization of both classic rectangular couples as well as practically andtheoretically interesting cylindrical couples using optimization parameters physically meaningful toa cylindrical couple. Solutions incorporate the physical behavior for i) thermal resistance of hot andcold shoes, ii) variable material properties with temperature, and iii) lateral heat transfer through legsides.

Thermoelectric Generators↗
NASA NTRS1974

Microwave interferometry technique for obtaining gas interface velocity measurements in an expansion tube facility

A microwave interferometer technique to determine the front interface velocity of a high enthalpy gas flow, is described. The system is designed to excite a standing wave in an expansion tube, and to measure the shift in this standing wave as it is moved by the test gas front. Data, in the form of a varying sinusoidal signal, is recorded on a high-speed drum camera-oscilloscope combination. Measurements of average and incremental velocities in excess of 6,000 meters per second were made.

Laney, C. C., Jr.↗
NASA NTRS1990

An optical technique to measure ion engine grid distortion due to differential thermal expansion

This paper describes an optical technique developed for measuring small differential grid displacements due to thermal expansion of an ion thruster accelerator system. The technique is based on confocal scanning optical microscope type II. For the measurements of small displacements where there are distances on the order of a meter or more between the lens plane and the sample, some of the optical components are moved while the sample is kept fixed. The feasibility of applying this technique to measure the thermally induced ion thruster grid displacements was demonstrated in a bench-top simulation. It is noted that this technique can also provide information on grid movement resulting from thermal transients such as the start-up.

Trava-Airoldi, V. J.↗
NASA NTRS1976

Time-dependent perturbation of a two-state quantum system by a sinusoidal field

Different methods for solving the 'two-level problem' are discussed, namely, the problem of what happens to a material system having only two nondegenerate energy levels when it is perturbed by an electromagnetic field that varies with time in a monochromatic sinusoidal fashion. The various methods discussed include: (1) the Sen Gupta technique using nondegenerate Rayleigh-Schroedinger perturbation theory, (2) the Salwen-Winter-Shirley partitioning perturbation technique, (3) the Shirley and series degenerate Rayleigh-Schroedinger expansion, (4) the degenerate Rayleigh-Schroedinger technique for considering high frequency fields, and (5) the singular perturbation expansion technique.

Dion, D. R.↗