Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “perturbation methods”

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 541 records · Page 30
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Temperature effects in first-principles solid state calculations of the chemical shielding tensor made simple

We study the effects of atomic vibrations on the solid-state chemical shielding tensor using first principles density functional theory calculations. At the harmonic level, we use a Monte Carlo method and a perturbative expansion. The Monte Carlo method is accurate but computationally expensive, while the perturbative method is computationally more efficient, but approximate. We find excellent agreement between the two methods for both the isotropic shift and the shielding anisotropy. The effects of zero-point quantum mechanical nuclear motion are important up to relatively high temperatures: at 500 K they still represent about half of the overall vibrational contribution. We also investigate the effects of anharmonic vibrations, finding that their contribution to the zero-point correction to the chemical shielding tensor is small. We exemplify these ideas using magnesium oxide and the molecular crystals L-alanine and β-aspartyl-L-alanine. We therefore propose as the method of choice to incorporate the effects of temperature in solid state chemical shielding tensor calculations using the perturbative expansion within the harmonic approximation. This approach is accurate and requires a computational effort that is about an order of magnitude smaller than that of dynamical or Monte Carlo approaches, so these effects might be routinely accounted for.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1972

On optimizing the treatment of exchange perturbations

A method using the zeroth plus first order wave functions, obtained by optimizing the basic equation used in exchange perturbation treatments, is utilized in an attempt to determine the exact energy and wave function in the exchange process. Attempts to determine the first order perturbation solution by optimizing the sum of the first and second order energies were unsuccessful.

Hirschfelder, J. O.↗
DOE OSTI2014

SU-E-T-429: Uncertainties of Cell Surviving Fractions Derived From Tumor-Volume Variation Curves

Purpose: To evaluate uncertainties of cell surviving fraction reconstructed from tumor-volume variation curves during radiation therapy using sensitivity analysis based on linear perturbation theory. Methods: The time dependent tumor-volume functions V(t) have been calculated using a twolevel cell population model which is based on the separation of entire tumor cell population in two subpopulations: oxygenated viable and lethally damaged cells. The sensitivity function is defined as S(t)=[δV(t)/V(t)]/[δx/x] where δV(t)/V(t) is the time dependent relative variation of the volume V(t) and δx/x is the relative variation of the radiobiological parameter x. The sensitivity analysis was performed using direct perturbation method where the radiobiological parameter x was changed by a certain error and the tumor-volume was recalculated to evaluate the corresponding tumor-volume variation. Tumor volume variation curves and sensitivity functions have been computed for different values of cell surviving fractions from the practically important interval S{sub 2}=0.1-0.7 using the two-level cell population model. Results: The sensitivity functions of tumor-volume to cell surviving fractions achieved a relatively large value of 2.7 for S{sub 2}=0.7 and then approached zero as S{sub 2} is approaching zero Assuming a systematic error of 3-4% we obtain that the relative error in S{sub 2} is less that 20% in the range S2=0.4-0.7. This Resultis important because the large values of S{sub 2} are associated with poor treatment outcome should be measured with relatively small uncertainties. For the very small values of S2<0.3, the relative error can be larger than 20%; however, the absolute error does not increase significantly. Conclusion: Tumor-volume curves measured during radiotherapy can be used for evaluation of cell surviving fractions usually observed in radiation therapy with conventional fractionation.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1984

Methodology for predictive testing of fuel cells

A perturbation testing method has been developed and tested for predictive testing of fuel cells. This method involves application of small changes to the operating conditions of the cell in a predetermined sequence. The resultant response of the cell is then measured and statistically correlated with the corresponding test conditions. This method has been applied to the phosphoric acid fuel cell, and the effect of operating and cell-component variables on cell-performance degradation has been studied. A strong effect of the cell temperature and cathode potential on fuel-cell-performance degradation has been observed. A cell-performance degradation model has been formulated, and the unknown parameters in the model have been estimated by a regression analysis of the experimental data. A reasonable agreement between the fuel cell performance predicted by this model (derived from the perturbation experiments) and the unperturbed test data supports fthe applicability of the perturbation method.

Patel, D. N.↗
NASA NTRS1975

Special Perturbations Using Back-Correction Methods of Numerical Integration

A new class of linear multistep methods for numerical integration of differential equations is reported that permits satellite computation solutions to be corrected at certain points in the past as the integration advances in time. Algorithms have been developed for the solution of both first- and second-order differential equations. The back correction method appears to be more efficient than classical methods when dominant and perturbing forces can be separated.

Feagin, T.↗
DOE OSTI2014

Perturbational treatment of spin-orbit coupling for generally applicable high-level multi-reference methods

An efficient perturbational treatment of spin-orbit coupling within the framework of high-level multi-reference techniques has been implemented in the most recent version of the COLUMBUS quantum chemistry package, extending the existing fully variational two-component (2c) multi-reference configuration interaction singles and doubles (MRCISD) method. The proposed scheme follows related implementations of quasi-degenerate perturbation theory (QDPT) model space techniques. Our model space is built either from uncontracted, large-scale scalar relativistic MRCISD wavefunctions or based on the scalar-relativistic solutions of the linear-response-theory-based multi-configurational averaged quadratic coupled cluster method (LRT-MRAQCC). The latter approach allows for a consistent, approximatively size-consistent and size-extensive treatment of spin-orbit coupling. The approach is described in detail and compared to a number of related techniques. The inherent accuracy of the QDPT approach is validated by comparing cuts of the potential energy surfaces of acrolein and its S, Se, and Te analoga with the corresponding data obtained from matching fully variational spin-orbit MRCISD calculations. The conceptual availability of approximate analytic gradients with respect to geometrical displacements is an attractive feature of the 2c-QDPT-MRCISD and 2c-QDPT-LRT-MRAQCC methods for structure optimization and ab inito molecular dynamics simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Generalized Sensitivity Calculation in the Monte Carlo Wielandt Method

Recently the Monte Carlo (MC) adjoint-weighted perturbation (AWP) methods with k-adjoint have been developed for the k sensitivity calculations. In order to extend the MC AWP methods to estimate sensitivities of a ratio of two reaction rates, Perfetti and Rearden devised a MC sensitivity calculation method with the generalized adjoint expressed by the intra-generational and intergenerational effects. Aufiero et al. suggested the collision history-based approach to calculate sensitivities of responses in the form of ratios of linear or bilinear functions by applying the correlated sampling for multi-generational collisions. However these methods may require a huge size of computer memory to save inter-generational contributions proportional to the number of the sensitivity tallies. In order to reduce memories required for the k-adjoint estimation, the present authors proposed the AWP algorithm in the MC Wielandt method where multiple generations from a fission source neutron are simulated in single history calculations. In this paper, we present perturbation formulations to estimate sensitivities for general tallies such as volume flux, reaction rates, etc. in the MC Wielandt calculations. The proposed method has been implemented into the Seoul National University MC code, McCARD and tested in two-group infinite homogeneous problems. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1992

A doubly averaging method for third body perturbations in planet equator coordinates

The first order doubly averaged potential due to third-body gravity is derived in any arbitrary coordinates. The equations of motion are nonsingular at zero eccentricity. The derivation uses a recursive method which allows easy expansion to higher order terms. Instead of using analytical quadrature to obtain the doubly averaged potential, the method presented in this paper simply eliminates the mean anomaly of the perturbed and perturbing bodies by inspection of the recursive formulation. The derivatives of the orbital elements can be numerically integrated rapidly. When a planet equator coordinate system is used, they can be added directly to the derivatives due to gravity harmonics without any coordinate transformation. The method is applied to various high altitude missions. The results are compared with a high precision numerical integration method and are found to provide excellent agreement.

Hwok, Johnny H.↗
NASA NTRS1979

Application of singular perturbation techniques /SPT/ and continuation methods for on-line aircraft trajectory optimization

The singular perturbation theory (SPT) approximation of optimal feedback control laws is presented and methods for on-line application of these approximations are discussed. It is demonstrated that SPT control laws break down when the current state is near the terminal target state. The use of continuation methods to improve the accuracy of the SPT approximation and to obtain global solutions of two-point boundary value problems is also discussed. As an illustration, consideration is given to the minimum-time control of a supersonic aircraft for a three-dimensional intercept problem.

Washburn, R. B.↗
DOE OSTI2017

The Laplace transformed divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation (DEC-LT-RIMP2) theory method

The divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation (DEC-RI-MP2) theory method introduced in Baudin et al. [J. Chem. Phys. 144, 054102 (2016)] is greatly improved by introducing the Laplace transform of the orbital energy denominator in order to construct the double amplitudes directly in the local basis. Moreover, our paper introduces the auxiliary reduction procedure, which reduces the set of the auxiliary functions employed in the individual fragments. The resulting Laplace transformed divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation method is applied to the insulin molecule where we obtain a factor 9.5 speedup compared to the DEC-RI-MP2 method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1982

Subsonic panel method for the efficient analysis of multiple geometry perturbations

An accurate and efficient method was developed for the aerodynamic analysis of a series of arbitrary small geometry perturbations to a given baseline configuration. The method is appropriate for wing-fuselage configurations in incompressible potential flow. Mathematical formulations are presented for three computer programs that are employed. The first program is a conventional surface panel method for calculating the baseline singularity distribution. The second program calculates a partial derivative matrix. Each element of the matrix is the rate of change of singularity strength at one point with respect to a surface coordinate of a different point. For each baseline configuration, the calculated quantities from the first two programs establish an input file for the third. The third program calculates the surface pressure distribution and forces and moments for a series of geometry perturbations.

Bristow, D. R.↗
DOE OSTI2014

Beryllium Dynamic Strength Measurements (Report on Task 3, Agreement #B590737)

The goal of the work under Agreement #B590737 consisted in the development of the experimentally justified model of beryllium shear strength of American production ( Be S200F ) in the pressure range of ~10÷60 GPa and at strain rates up to $\dot{ε_i}$ ≈10 6 s -1 . The Be shear strength models, which were available in this range of parameters, had no sufficiently reliable experimental justification. The purpose of the third final phase consisted in the performance of tests by using the method of perturbations and with recovery of samples Be S200F and parametric verification of a model of beryllium strength on their basis. In the course of the works of the third phase six experiments were performed with the use of the dynamic method of perturbations with shock-free loading of the Be S200F samples under investigation up to the pressure P m ≈50 GPa. The growth of the specified perturbations was recorded by means of the radiographic technique. In addition, each experiment includes measurements of free surface velocities of a liner by using a laser interferometer of the VISAR type. Two experiments were implemented with loading of beryllium samples up to the pressure P~25÷60 GPa with recovery followed by metallographic investigation. The objective of the metallographic investigation consisted of determination of peculiarities of high-rate deformation of Be . Measurements were carried out in each experiment by using the technique of a manganin-based pressure sensor. Numerical simulation of experiments was implemented with the use of Eulerian technique and Lagrangian technique. In accordance with the results of numerical simulation the authors performed verification of parameters of a relaxation model of beryllium strength.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Size consistent formulations of the perturb-then-diagonalize Møller-Plesset perturbation theory correction to non-orthogonal configuration interaction

In this paper we introduce two size consistent forms of the non-orthogonal configuration interaction with second-order Møller-Plesset perturbation theory method, NOCI-MP2. We show that the original NOCI-MP2 formulation [S. R. Yost, T. Kowalczyk, and T. VanVoorh, J. Chem. Phys. 193, 174104 (2013)], which is a perturb-then-diagonalize multi-reference method, is not size consistent. We also show that this causes significant errors in large systems like the linear acenes. By contrast, the size consistent versions of the method give satisfactory results for singlet and triplet excited states when compared to other multi-reference methods that include dynamic correlation. For NOCI-MP2 however, the number of required determinants to yield similar levels of accuracy is significantly smaller. These results show the promise of the NOCI-MP2 method, though work still needs to be done in creating a more consistent black-box approach to computing the determinants that comprise the many-electron NOCI basis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗