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.↗
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Results for “VARIATION METHOD”
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.
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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.↗
Differential games and manual control.
Simulation of pursuit-evasion differential game using variational method, comparing performance of human pilot to optimal pursuer
MANUAL CONTROL↗
Theoretical calculation of ozone vibrational infrared intensities
An ab initio dipole moment function for ozone has been computed using the CASSCF (complete active space self-consistent field) method, and forms the basis for a calculation of ozone infrared band intensities. Vibrational wave functions were generated using the variational method with potential energy surfaces derived from experimental force constants. Computed values of the permanent dipole moment, dipole moment derivatives, and infrared band strengths are all found to be in remarkably good agreement with experiment. Intensities are predicted for hot bands for which experimental values are unavailable, and implications for atmospheric ozone spectroscopy are discussed. As the dipole moment matrix element signs are now established for nearly all of the observed bands, further refinement of the dipole moment function is possible.
Adler-Golden, S. M.↗
Skin Friction Extracted from Surface Pressure in Incident Shock-Wave/Boundary-Layer Interaction
High-resolution skin-friction fields are extracted from pressure-sensitive paint (PSP) data obtained in shock-wave/boundary-layer interaction (SWBLI). The method of extracting skin friction from surface pressure is described, including the fundamental relation between skin friction and surface pressure, the variational method, error analysis, and an approximate iterative method. The proposed method is based on a coupling relation between skin friction and surface pressure, where the boundary enstrophy flux is suitably modeled or approximated. This method is applied to unsteady PSP data obtained in incident SWBLIs at Mach 2.5 for different Reynolds numbers, revealing the skin-friction structures of the flows: particularly, the separation bubble induced by the incident shock wave. The extracted results are in good agreement with the data obtained by the surface-stress-sensitive film.
skin friction↗
Finite element analysis of time-independent superconductivity
The development of electromagnetic (EM) finite elements based upon a generalized four-potential variational principle is presented. The use of the four-potential variational principle allows for downstream coupling of EM fields with the thermal, mechanical, and quantum effects exhibited by superconducting materials. The use of variational methods to model an EM system allows for a greater range of applications than just the superconducting problem. The four-potential variational principle can be used to solve a broader range of EM problems than any of the currently available formulations. It also reduces the number of independent variables from six to four while easily dealing with conductor/insulator interfaces. This methodology was applied to a range of EM field problems. Results from all these problems predict EM quantities exceptionally well and are consistent with the expected physical behavior.
Schuler, James J.↗
Control optimization of a lifting body entry problem by an improved and a modified method of perturbation function
A study of the solution problem of a complex entry optimization was studied. The problem was transformed into a two-point boundary value problem by using classical calculus of variation methods. Two perturbation methods were devised. These methods attempted to desensitize the contingency of the solution of this type of problem on the required initial co-state estimates. Also numerical results are presented for the optimal solution resulting from a number of different initial co-states estimates. The perturbation methods were compared. It is found that they are an improvement over existing methods.
Garcia, F., Jr.↗
Synthesis of spherical minimum-weight proton shields
A systematic method has been developed for minimizing spherical shield weights for protection against proton radiation, including secondary neutron production, subject to various specified dose constraints. Variational methods are applied to a radiation model yielding the choice of optimum shielding materials and their mixtures, together with a prescription for their disposition in a multilayer spherical shield.
Spherical Shell↗
Active Control of Fan Noise-Feasibility Study. Volume 2: Canceling Noise Source-Design of an Acoustic Plate Radiator Using Piezoceramic Actuators
The feasibility of using acoustic plate radiators powered by piezoceramic thin sheets as canceling sources for active control of aircraft engine fan noise is demonstrated. Analytical and numerical models of actuated beams and plates are developed and validated. An optimization study is performed to identify the optimum combination of design parameters that maximizes the plate volume velocity for a given resonance frequency. Fifteen plates with various plate and actuator sizes, thicknesses, and bonding layers were fabricated and tested using results from the optimization study. A maximum equivalent piston displacement of 0.39 mm was achieved with the optimized plate samples tested with only one actuator powered, corresponding to a plate deflection at the center of over 1 millimeter. This is very close to the deflection required for a full size engine application and represents a 160-fold improvement over previous work. Experimental results further show that performance is limited by the critical stress of the piezoceramic actuator and bonding layer rather than by the maximum moment available from the actuator. Design enhancements are described in detail that will lead to a flight-worthy acoustic plate radiator by minimizing actuator tensile stresses and reducing nonlinear effects. Finally, several adaptive tuning methods designed to increase the bandwidth of acoustic plate radiators are analyzed including passive, active, and semi-active approaches. The back chamber pressurization and volume variation methods are investigated experimentally and shown to be simple and effective ways to obtain substantial control over the resonance frequency of a plate radiator. This study shows that piezoceramic-based plate radiators can be a viable acoustic source for active control of aircraft engine fan noise.
Pla, F. G.↗
Determination of optimum nozzle contours for the expansion of dissociated gases by methods of the variational calculus.
Optimum nozzle contours for expansion of Lighthill idealized dissociating gas in one- dimensional flow determined by methods of variational calculus
ONE-DIMENSIONAL FLOW↗