Search NASA⌕ Search

SEARCH · Search NASA

Results for “Variational Analysis”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Drive tube 60009 - A chemical study of magnetic separates of size fractions from five strata

Each bulk soil and both the magnetic and nonmagnetic components of the 90-150 micron and below 20 micron fractions of five soils from drive tube 60009 were analyzed. Samples were analyzed for FeO, Na2O, Sc, Cr, Co, Ni, Hf, Ta, Th, La, Ce, Sm, Eu, Tb, Yb, and Lu by neutron activation analysis. Several samples were fused and analyzed for major elements by electron microprobe analysis. Compositional variations are not systematically related to depth. The compositions of the five soils studied are well explained by a two-component mixing model whose end members are a submature Apollo 16-type soil and an extremely immature anorthositic material similar to 60025. There is evidence that the anorthositic component had received a small amount of exposure before these soils were mixed. After mixing, the soils received little exposure suggesting mixing and deposition on a rapid time scale.

Blanchard, D. P.↗
NASA NTRS1977

A finite element simulation of sound attenuation in a finite duct with a peripherally variable liner

Using multimodal analysis, a variational finite element method is presented for analyzing sound attenuation in a three-dimensional finite duct with a peripherally variable liner in the absence of flow. A rectangular element, with cubic shaped functions, is employed. Once a small portion of a peripheral liner is removed, the attenuation rate near the frequency where maximum attenuation occurs drops significantly. The positioning of the liner segments affects the attenuation characteristics of the liner. Effects of the duct termination are important in the low frequency ranges. The main effect of peripheral variation of the liner is a broadening of the attenuation characteristics in the midfrequency range. Because of matrix size limitations of the presently available computer program, the eigenvalue equations should be solved out of core in order to handle realistic sources.

Watson, W. R.↗
NASA NTRS1977

Analysis of magnetic fields using variational principles and CELAS2 elements

Prospective techniques for analyzing magnetic fields using NASTRAN are reviewed. A variational principle utilizing a vector potential function is presented which has as its Euler equations, the required field equations and boundary conditions for static magnetic fields including current sources. The need for an addition to this variational principle of a constraint condition is discussed. Some results using the Lagrange multiplier method to apply the constraint and CELAS2 elements to simulate the matrices are given. Practical considerations of using large numbers of CELAS2 elements are discussed.

Frye, J. W.↗
NASA NTRS1981

The stability of solar coronal loops with realistic photospheric boundary conditions

Finite-length effects are the primary influence for the MHD stability of coronal loops. This paper gives a new physical description of the photospheric boundary conditions, and the first complete and uniformly convergent initial-perturbation set. A general energy-principle (or variational) stability analysis is then developed. The results of this calculation show that large classes of cylindrical-symmetry perturbations, those with separable contributions to the energy integral, are completely stable. Comparisons are also made with other more restrictive formulations of this problem.

Van Hoven, G.↗
NASA NTRS1985

On the similarity and differences for N2 and CO on Ni

The computed dipole derivatives for the N-N and C-O stretches are found to be quite similar, while the Ni-N derivative is much larger than for the corresponding Ni-C stretch; this is in agreement with experiment. A constrained space orbital variation (CSOV) analysis shows shows that the NiN2 bonding is more similar to that in NiCO than was concluded based upon the experimental dipole derivatives and binding energy shifts.

Bauschlicher, C. W., Jr.↗
NASA NTRS1985

Analysis of all-frequency variational behavior of the Kirchhoff approximation for a classic surface-scattering model

In testing a stochastic variational principle at high frequencies by using a Kirchhoffean trial function in an idealized model for surface scattering - a randomly embossed plane - we have found not only the predicted high-frequency improvement but also an unexpected low-frequency improvement in the calculated scattering amplitudes. To investigate systematically the all-frequency variational behavior, we consider here the deterministic one-boss case - Rayleigh's classic model whose exact solution is available for comparison - over all wavelengths, polarizations, and configurations of incidence and scattering. We examine analytically in particular the long-wave limit of the variational-Kirchhoff amplitudes; the results demonstrate improvements in both wavelength and angle depedence for horizontal (TM) polarization and some variational improvements for vertical (TE) polarization. This low-frequency behavior in tandem with the foreseen high-frequency improvement leads to good variational-Kirchhoff results through the intermediate resonance-frequency regime for this model.

Bird, J. F.↗
NASA NTRS1985

Unification of color postprocessing techniques for 3-dimensional computational mechanics

To facilitate the understanding of complex three-dimensional numerical models, advanced interactive color postprocessing techniques are introduced. These techniques are sufficiently flexible so that postprocessing difficulties arising from model size, geometric complexity, response variation, and analysis type can be adequately overcome. Finite element, finite difference, and boundary element models may be evaluated with the prototype postprocessor. Elements may be removed from parent models to be studied as independent subobjects. Discontinuous responses may be contoured including responses which become singular, and nonlinear color scales may be input by the user for the enhancement of the contouring operation. Hit testing can be performed to extract precise geometric, response, mesh, or material information from the database. In addition, stress intensity factors may be contoured along the crack front of a fracture model. Stepwise analyses can be studied, and the user can recontour responses repeatedly, as if he were paging through the response sets. As a system, these tools allow effective interpretation of complex analysis results.

Bailey, Bruce Charles↗
NASA NTRS1988

The relationship of satellite-inferred stratospheric aerosol extinction to the position of the 50-mb north polar jet stream

The relationship between stratospheric aerosols and the location of the north polar night stratospheric jet stream was investigated for selected periods of four successive winters (1979-1982), using measurements from SAM II (Stratospheric Aerosol Measurement II) and SAGE I (Stratospheric Aerosol and Gas Experiment I) satellite-borne sun photometers and corresponding meteorological observations. Each period investigated included a polar stratospheric warming during which major dynamic meteorological changes are known to have perturbed the structure of the polar vortex. The analysis of variations in aerosol extinction mixing ratio patterns among winters and during major stratospheric warming events within separate winters showed a well-defined positive gradient in extinction mixing ratio and temperature across the jet stream from the cyclonic side to the anticyclonic side at altitudes between 20 and 30 km during each winter period. Estimates of extinction mixing ratio profiles measured near the center of the polar vortex suggest that a gradual subsidence took place within the polar vortex during at least three of the four winter periods.

Livingston, John M.↗
NASA NTRS1988

Development and experimental test of an analytical model of the orifice pulse tube refrigerator

An analytical model for the orifice pulse tube is developed, in which the system is described in terms of average enthalpy flow with such simplifying assumptions as an ideal gas and sinusoidal pressure variation. Phasor analysis is used to represent temperature, pressure, and mass-flow rate waves in vector form. The model predictions, namely, that the refrigeration power of a pulse-tube refrigerator is proportional to the average pressure, the pulse frequency, the mass-flow ratio, and the square of the dynamic pressure ratio, were verified by experimental measurements. It was found that, as a result of the simplifying assumptions, the magnitudes of the refrigeration power predicted by the model were between three and five times greater than experimental values.

Storch, Peter J.↗
NASA NTRS1991

A Variational Assimilation Method for Satellite and Conventional Data: a Revised Basic Model 2B

A variational objective analysis technique that modifies observations of temperature, height, and wind on the cyclone scale to satisfy the five 'primitive' model forecast equations is presented. This analysis method overcomes all of the problems that hindered previous versions, such as over-determination, time consistency, solution method, and constraint decoupling. A preliminary evaluation of the method shows that it converges rapidly, the divergent part of the wind is strongly coupled in the solution, fields of height and temperature are well-preserved, and derivative quantities such as vorticity and divergence are improved. Problem areas are systematic increases in the horizontal velocity components, and large magnitudes of the local tendencies of the horizontal velocity components. The preliminary evaluation makes note of these problems but detailed evaluations required to determine the origin of these problems await future research.

Achtemeier, Gary L.↗
NASA NTRS1992

The formation and effect of outer-ply microcracks in cross-ply laminates - A variational approach

The paper presents a variational mechanics analysis of the stresses and energy release rate in a (90m/0n)s laminate, with account taken of the observed existence of staggered microcracks. It is found that the load required to initiate microcracks is significantly lower for (90m/0n)s laminates than for (0n/90m)s laminates. It is also found that (90m/0n)s laminates are characterized by a lower saturation crack density and that no bending effects tend to promote mode I delamination in (90m/0n)s laminates.

Nairn, John A.↗
NASA NTRS1991

The initiation, propagation, and effect of matrix microcracks in cross-ply and related laminates

Recently, a variational mechanics approach was used to determine the thermoelastic stress state in cracked laminates. Described here is a generalization of the variational mechanics techniques to handle other cross-ply laminates, related laminates, and to account for delaminations emanating from microcrack tips. Microcracking experiments on Hercules 3501-6/AS4 carbon fiber/epoxy laminates show a staggered cracking pattern. These results can be explained by the variational mechanics analysis. The analysis of delaminations emanating from microcrack tips has resulted in predictions about the structural and material variables controlling competition between microcracking and delamination failure modes.

Nairn, John A.↗
NASA NTRS1992

The initiation and growth of delaminations induced by matrix microcracks in laminated composites

A recent variational mechanics analysis of microcracking damage in cross-ply laminates of the form /(S)/90n/s, where (S) is any orthotropic sublaminate much stiffer than /90n/, has been extended to account for the presence of delaminations emanating from the tips of microcracks in the /90 2n/T sublaminate. The new two-dimensional stress analysis is used to calculate the total strain energy, effective modulus, and longitudinal thermal expansion coefficient for a laminate having microcracks and delaminations. These results are used to calculate the energy release rate for the initiation and growth of a delamination induced by a matrix microcrack. At low crack densities, /(S)/90n/s laminates are expected to fail by microcracking and to show little or no delamination. At some critical crack density, which is a function of laminate structure and material properties, the energy release rate for delamination exceeds that for microcracking and delamination is predicted to dominate over microcracking. A quasi-three-dimensional model is used to predict the propagation of arbitrarily shaped delamination fronts. All predictions agree with experimental observations.

Nairn, J. A.↗
NASA NTRS1993

A critical evaluation of theories for predicting microcracking in composite laminates

We present experimental results on 21 different layups of Hercules AS4 carbon fiber/3501-6 epoxy laminates. All laminates had 90 deg plies; some had them in the middle, while some had them on a free surface. During tensile loading, the first form of damage in all laminates was microcracking of the 90 deg plies. For each laminate, we recorded both the crack density and the complete distribution of crack spacings as a function of the applied load. By rearranging various microcracking theories, we developed a master-curve approach that permitted plotting the results from all laminates on a single plot. By comparing master-curve plots for different theories, it was possible to critically evaluate the quality of those theories. We found that a critical-energy-release-rate criterion calculated using a 2D variational stress analysis gave the best results. All microcracking theories based on a strength-failure criteria gave poor results. All microcracking theories using 1D stress analyses, regardless of the failure criterion, also gave poor results.

Nairn, John A.↗
NASA NTRS1994

Analysis and comparison of diurnal variations of cloud radiative forcing: Earth Radiation Budget Experiment and International Satellite Cloud Climatology Project results

Cloud radiative forcing (CRF) is the radiative impact of clouds on the Earth's radiation budget. This study examines the diurnal variations of CRF using the Earth Radiation Budget Experiment (ERBE) monthly hourly flux data and the flux data derived from the International Satellite Cloud Climatology Project (ISCCP) using the Goddard Institute for Space Studies general circulation model radiation code. The results for the months of April, July, and October 1985 and January 1986 are analyzed. We found that, in general, two data sets agreed. For longwave (LW) CRF the diurnal range over land is generally greater than that observed over oceans. For the 4-month averages the ERBE values are 15.8 W/sq m and 6.8 W/sq m for land and ocean, respectively, compared with the ISCCP calculated values of 18.4 W/sq m and 8.0 W/sq m, respectively. The land/ocean contrast is largely associated with changes in cloud amount and the temperature difference between surface and cloud top. It would be more important to note that the clear-sky flux (i.e., surface temperature) variabilities are shown to be a major contributor to the large variabilities over land. The maximum diurnal range is found to be in the summer hemisphere, and the minimum values in the winter hemisphere. It is also shown that the daytime maximum and the nighttime minimum are seen over large portions of land, whereas they occur at any local hour over most oceans. For shortwave (SW) CRF the daytime maximum values are about twice as large as monthly averages, and their highest frequency occurs at local noon, indicating that solar insolation is a primary factor for the diurnal variation of SW CRF. However, the comparison of the ERBE data with the ISCCP results demonstrated that the largest differences in the diurnal range and monthly mean of LW CRF were associated with tropical convergence zones, where clear-sky fluxes could be easily biased by persistent cloudiness and the inadequate treatment of the atmospheric water vapor.

Kim, Yongseung↗
NASA NTRS1994

Improvement of the photometric sunspot index and changes of the disk-integrated sunspot contrast with time

The photometric sunspot index (PSI) was developed to study the effects of sunspots on solar irradiance. It is calculated from the sunspot data published in the Solar-Geophysical Data catalog. It has been shown that the former PSI models overestimate the effect of dark sunspots on solar irradiance; furthermore results of direct sunspot photometry indicate that the contrast of spots depends on their area. An improved PSI calculation is presented; it takes into account the area dependence of the contrast and calculates `true' daily means for each observation using the differential rotation of the spots. Moreover, the observations are screened for outliers which improves the homogeneity of the data set substantially, at least for the period after December 1981 when NOAA started to report data from a few instead of one to two stations. A detailed description of the method is provided. The correlation between the newly calculated PSI and total solar irradiance is studied for different phases of the solar cycles 21 and 22 using bi-variate spectral analysis. The results can be used as a `calibration' of PSI in terms of gain, the factor by which PSI has to be multiplied to yield the observed irradiance change. The factor changes with time from about 0.6 in 1980 to 1.1 in 1990. This unexpected result cannot be interpreted by a change of the contrast relative to the quiet Sun (as it is normally defined and determined by direct photometry) but rather as a change of the contrast between the spots and their surrounding as seen in total irradiance (integrated over the solar disk). This may partly be explained by a change in the ratio between the areas of the spots and the surrounding faculae.

Froehlich, Claus↗
NASA NTRS1997

The Preparation and Structural Characterization of Three Structural Types of Gallium Compounds Derived from Gallium (II) Chloride

The three compounds Ga2Cl4(4-mepy)2 (1),[GaCl2(4-mepy)4]GaCl4x1/2(4-mepy); (2) and GaCl2(4-mepy)2(S2CNEt2); (3) (4-mepy= 4-methylpyridine) have been prepared from reactions of gallium (II) chloride in 4-methylpyridine and characterized by single-crystal X-ray analysis. Small variations in the reaction conditions for gallium(II) chloride can produce crystals with substantially different structural properties. The three compounds described here encompass a neutral gallium(II) dimer in which each gallium is four-coordinate, an ionic compound containing both anionic and cationic gallium complex ions with different coordination numbers and a neutral six-coordinate heteroleptic

Gordon, Edward M.↗
NASA NTRS2003

Cloud Modeling Using Field Project Data for the Study of Precipitation Processes

The use of cloud-resolving models (CRMs) in the study of precipitation process and their relation to the large-scale environment can be generally categorized into two approaches. The first approach is so called "cloud ensemble modeling". In this approach, many clouds of different size in various stages of their lifecycles can be present at any model simulation time. Large-scale effects are derived from observations and imposed into the model as the main forcing. The advantage of this approach is that the modeled convection will be forced to have the same intensity, thermodynamic budget and organization as the obserations.This approach will also allow CRMs to perform multi-day or multi-week time integrations. The second approach usually requires initial temperature and water vapor profiles that have a medium to large CAPE, and open lateral boundary conditions are used. The modeled clouds could be termed "self-forced convection". Model improvements, such as in the microphysics, are achieved using the second approach. In cloud ensemble modeling, accurate large-scale advective tendencies for temperature and water vapor are the main forcing for the CRMs. We found that the large-scale advective terms for temperature and water vapor are not always consistent, For example, large-scale forcing could indicate strong drying which would produce cooling in the model through evaporation but not contain large-scale advective heating to compensate. This discrepancy in forcing would cause differences between the observed and modeled latent heating profiles. Good measurements of other quantities (i.e., surface fluxes and radiation) are also required to perform variational objective analysis that computes and minimizes a "cost function" that constrains the difference between the large-scale advective forcing in temperature and water vapor. With self-forced convection, accurate vertical distributions of temperature, moisture (water vapor), and horizontal winds are required. The timing of the measurements relative to cloud development is crucial (i.e., prior to cloud triggering). Microphysical measurements (i.e., the cloud number concentration and size distribution) can also be used in this second approach but are of secondary importance with cloud ensemble modeling. In this paper, data collected during TRMM field campaigns (FCs; i.e., SCSMEX, LBA and KWAJEX) which were aimed at validating TRMM products (i.e., rainfall and the vertical distribution of latent heating) will be used to examine the impact of errors in the initial conditions (e.g.., soundings an large-scale forcing) on simulated rainfall distributions and brightness. Rainfall and precipitations simulated from a CRM will also be compared with those estimated by a schocastic model.

Tao, W.-K.↗