Physics of planetary atmospheres. i- ray- leigh scattering by helium
Physics of planetary atmospheres - Variation method used to calculate Rayleigh scattering cross sections of helium as wavelength function
HELIUM↗
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Results for “Variational methods”
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A modified sweep method for control optimization
Modified sweep second-order variational method for solving two-point boundary value trajectory optimization problem
Colunga, D.↗
Use of a transcendental approximation in transient conduction analysis
Variation method applied to transient thermal conductivity in semiinfinite slab with nonlinear boundary condition
TRANSIENT HEATING↗
Three-dimensional inversion of satellite observed radiances A proposal
Fully three-dimensional temperature fields are obtained from observed satellite radiances through the use of variational methods which generalize the method of Wahba and Wendelberger (1980). This variational formalism allows a variety of different information types to contribute to the inversion process. Full use can be made of the horizontal smoothness of the temperature field in the calculation of three-dimensional retrievals. The present method facilitates the acquisition of maximum vertical resolution, accomplishes cloud effect filtering, and minimizes the effects of instrument noise, to yield horizontally coherent retrievals.
Hoffman, R. N.↗
A Multifunctional Interface Method for Coupling Finite Element and Finite Difference Methods: Two-Dimensional Scalar-Field Problems
A multifunctional interface method with capabilities for variable-fidelity modeling and multiple method analysis is presented. The methodology provides an effective capability by which domains with diverse idealizations can be modeled independently to exploit the advantages of one approach over another. The multifunctional method is used to couple independently discretized subdomains, and it is used to couple the finite element and the finite difference methods. The method is based on a weighted residual variational method and is presented for two-dimensional scalar-field problems. A verification test problem and a benchmark application are presented, and the computational implications are discussed.
Ransom, Jonathan B.↗
Absence of diurnal variation of C-reactive protein concentrations in healthy human subjects
BACKGROUND: The concentration of C-reactive protein (CRP) in otherwise healthy subjects has been shown to predict future risk of myocardial infarction and stroke. CRP is synthesized by the liver in response to interleukin-6, the serum concentration of which is subject to diurnal variation. METHODS: To examine the existence of a time-of-day effect for baseline CRP values, we determined CRP concentrations in hourly blood samples drawn from healthy subjects (10 males, 3 females; age range, 21-35 years) during a baseline day in a controlled environment (8 h of nighttime sleep). RESULTS: Overall CRP concentrations were low, with only three subjects having CRP concentrations >2 mg/L. Comparison of raw data showed stability of CRP concentrations throughout the 24 h studied. When compared with cutoff values of CRP quintile derived from population-based studies, misclassification of greater than one quintile did not occur as a result of diurnal variation in any of the subjects studied. Nonparametric ANOVA comparing different time points showed no significant differences for both raw and z-transformed data. Analysis for rhythmic diurnal variation using a method fitting a cosine curve to the group data was negative. CONCLUSIONS: Our data show that baseline CRP concentrations are not subject to time-of-day variation and thus help to explain why CRP concentrations are a better predictor of vascular risk than interleukin-6. Determination of CRP for cardiovascular risk prediction may be performed without concern for diurnal variation.
Non-NASA Center↗
A design method for minimizing sensitivity to plant parameter variations
A method is described for minimizing the sensitivity of multivariable systems to parameter variations. The variable parameters are considered as random variables and their effect is included in a quadratic performance index. The performance index is a weighted sum of the state and control covariances that stem from both the random system disturbances and the parameter uncertainties. The numerical solution of the problem is described and application of the method to several initially sensitive tracking systems is discussed. The sensitivity factor of reduction was typically 2 or 3 over a system based on random system noise only, and yet resulted in state RMS increases of only about a factor of two.
Hadass, Z.↗
Partial spline models for the inclusion of tropopause and frontal boundary information in otherwise smooth two- and three-dimensional objective analysis
A new method, based on partial spline models, is developed for including specified discontinuities in otherwise smooth two- and three-dimensional objective analyses. The method is appropriate for including tropopause height information in two- and three-dimensinal temperature analyses, using the O'Sullivan-Wahba physical variational method for analysis of satellite radiance data, and may in principle be used in a combined variational analysis of observed, forecast, and climate information. A numerical method for its implementation is described and a prototype two-dimensional analysis based on simulated radiosonde and tropopause height data is shown. The method may also be appropriate for other geophysical problems, such as modeling the ocean thermocline, fronts, discontinuities, etc.
Shiau, Jyh-Jen↗
Positron-atom scattering by the Kohn and Harris methods
S wave scattering from H and He positron systems at low energies, applying Kohn and Harris variational methods
Drachman, R. J.↗
Computing Highly Accurate Spectroscopic Line Lists for Characterization of Planetary Atmospheres: CO2 and SO2 Line Lists Needed for Modeling Venus
Over the last decade, it has become apparent that the most effective approach for determining highly accurate rotational and rovibrational line lists for molecules of interest in planetary atmospheres and other astrophysical environments is through a combination of highresolution laboratory experiments coupled with state-of-the art ab initio quantum chemistry methods. The approach involves computing the most accurate potential energy surface (PES) possible using state-of-the art electronic structure methods, followed by computing rotational and rovibrational energy levels using an exact variational method to solve the nuclear Schrödinger equation. Then, reliable experimental data from high-resolution experiments is used to refine the ab initio PES in order to improve the accuracy of the computed energy levels and transition energies. From the refinement step, we have been able to achieve an accuracy of approximately 0.015 cm-1 for rovibrational transition energies, and even better for purely rotational transitions. This combined "experiment / theory" approach allows for determination of essentially a complete line list, with hundreds of millions of transitions, and having the transition energies and intensities be highly accurate. Our group has successfully applied this approach to determine highly accurate line lists for NH3, CO2 and isotopologues, and SO2 and isotopologues. Here I will report our latest results for CO2 and SO2 including all isotopologues. Comparisons to the available data in HITRAN2012 and other available databases will be shown, though we note that our line lists for SO2 are significantly more complete than any other databases. Since it is important to span a large temperature range in order to model the spectral signature of Venus as well as exoplanets, we will demonstrate how the spectra change on going from low temperatures (100 K) to higher temperatures (500 K to 1500 K).
potential energy surface (PES)5405 PLANETARY SCIEN↗
Transformation of two and three-dimensional regions by elliptic systems
Grid smoothing and orthogonalization procedures were developed and implemented in the construction of two and three dimensional grids. The procedures are based on the variational methods of grid generation. The two-dimensional examples were computed using the MSU IRIS Graphics Workstation. It was demonstrated that the elliptic grid generation equations, with arbitrary forcing functions, can be solved, in their variational formulation, using a gradient method. Since gradient methods have a global convergence property, the divergence problems often encountered when using SOR iterative methods can be avoided. It is not to be concluded, however, that SOR methods should be abandoned, since gradient methods tend to converge very slowly. In fact, slow convergence was the major problem encountered in the three-dimensional grids. Further progress was made on the continuing effort to develop conservative interpolation formulas for overlapping grids.
Mastin, C. Wayne↗
Coupling finite and boundary element methods for 2-D elasticity problems
A finite element-boundary element (FE-BE) coupling method for two-dimensional elasticity problems is developed based on a weighted residual variational method in which a portion of the domain of interest is modeled by FEs and the remainder of the region by BEs. The performance of the FE-BE coupling method is demonstrated via applications to a simple 'patch test' problem and three-crack problems. The method passed the patch tests for various modeling configurations and yielded accurate strain energy release rates for the crack problems studied.
Krishnamurthy, T.↗
Muscle recruitment variations during wrist flexion exercise: MR evaluation
OBJECTIVE: Many exercise protocols used in physiological studies assume homogeneous and diffuse muscle recruitment. To test this assumption during a "standard" wrist flexion protocol, variations in muscle recruitment were assessed using MRI in eight healthy subjects. MATERIALS AND METHODS: Variations were assessed by comparing the right to the left forearms and the effect of slight (15 degrees) pronation or supination at the wrist. RESULTS: Postexercise imaging showed focal regions of increased signal intensity (SI), indicating relatively strong recruitment, most often in entire muscles, although occasionally only in subvolumes of muscles. In 15 of 26 studies, flexor carpi radialis (FCR) showed more SI than flexor carpi ulnaris, while in 11 studies SI in these muscles increased equivalently. Relatively greater FCR recruitment was seen during pronation and/or use of the nondominant side. Palmaris longus, a wrist flexor, did not appear recruited in 4 of 11 forearms in which it was present. A portion of the superficial finger flexor became hyperintense in 89% of studies, while recruitment of the deep finger flexor was seen only in 43%. CONCLUSION: Inter- and intraindividual variations in forearm muscle recruitment should be anticipated in physiological studies of standard wrist flexion exercise protocols.
NASA Discipline Cardiopulmonary↗
A comparison of digital flight control design methods
Many variations in design methods for aircraft digital flight control have been proposed in the literature. In general, the methods fall into two categories: those where the design is done in the continuous domain (or s-plane), and those where the design is done in the discrete domain (or z-plane). This paper evaluates several variations of each category and compares them for various flight control modes of the Langley TCV Boeing 737 aircraft. Design method fidelity is evaluated by examining closed loop root movement and the frequency response of the discretely controlled continuous aircraft. It was found that all methods provided acceptable performance for sample rates greater than 10 cps except the 'uncompensated s-plane design' method which was acceptable above 20 cps. A design procedure based on optimal control methods was proposed that provided the best fidelity at very slow sample rates and required no design iterations for changing sample rates.
Powell, J. D.↗
A new formulation for anisotropic radiative transfer problems. I - Solution with a variational technique
The equations of radiative transfer in anisotropically scattering media are reformulated as linear operator equations in a single independent variable. The resulting equations are suitable for solution by a variety of standard mathematical techniques. The operators appearing in the resulting equations are in general nonsymmetric; however, it is shown that every bounded linear operator equation can be embedded in a symmetric linear operator equation and a variational solution can be obtained in a straightforward way. For purposes of demonstration, a Rayleigh-Ritz variational method is applied to three problems involving simple phase functions. It is to be noted that the variational technique demonstrated is of general applicability and permits simple solutions for a wide range of otherwise difficult mathematical problems in physics.
Cheyney, H., III↗
Variational approaches to CFD: Applications to potential Euler and Navier-Stokes equations
Flow simulations based on variational techniques are discussed. Variational techniques are applied for the problem formulation, for the construction of discrete schemes, and for the solution procedures. Inviscid transonic flows, as well as viscous incompressible and compressible flows, are analyzed by several methods. Variational techniques to solve the discrete systems of equations are well known. The most popular one is the conjugate gradient method. Extensions to nonsymmetric and nonpositive definite systems were under investigation for the last two decades. Variational techniques were used for convergence acceleration of iterative procedures. Some of these ideas based on recent work are examined. The lectures are organized in three parts including numerical simulation of inviscid as well as viscous incompressible and compressible flows.
Hafez, M.↗
Solution of an optimal control lifting body entry problem by an improved method of perturbation functions
This paper presents a solution to a complex lifting reentry three-degree-of-freedom problem by using the calculus of variations to minimize the integral of the sum of the aerodynamics loads and heat rate input to the vehicle. The entry problem considered does not have state and/or control constraints along the trajectory. The calculus of variations method applied to this problem gives rise to a set of necessary conditions which are used to formulate a two point boundary value (TPBV) problem. This TPBV problem is then numerically solved by an improved method of perturbation functions (IMPF) using several starting co-state vectors. These vectors were chosen so that each one had a larger norm with respect to show how the envelope of convergence is significantly increased using this method and cases are presented to point this out.
Garcia, F., Jr.↗
Variational calculations of vibrational properties of ozone
A variational method is used to obtain vibrational-rotational properties for ozone from an experimental quartic force field. Band positions, average structures, matrix elements for calculating infrared intensities, and effective rotational constants are reported for (O-16)3 and its O-18 isotopic species. Also, the degree to which the vibrational energies and properties are converged is investigated as a function of the basis set parameters and basis set size, and of the method of obtaining the Hamiltonian matrix elements. A convenient procedure for assigning the vibrational states is developed for variational vibrational wavefunction expansions.
Carney, G. D.↗