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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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Discrete Morse Theory for the Barycentric Subdivision

Let F be a discrete Morse function on a simplicial complex L. We construct a discrete Morse function Δ(F) on the barycentric subdivision Δ(L). The constructed function Δ(F) “behaves the same way” as F, i.e., has the same number of critical simplices and the same gradient path structure.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Classical ladder functions for Rosen–Morse and curved Kepler–Coulomb systems

Ladder functions in classical mechanics are defined in a similar way as ladder operators in the context of quantum mechanics. In the present paper, we develop a new method for obtaining ladder functions of one dimensional systems by means of a product of two ‘factor functions’. We apply this method to the curved Kepler–Coulomb and Rosen–Morse II systems whose ladder functions were not found yet. The ladder functions here obtained are applied to get the motion of the systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1976

Diatomic molecule variations

The rotational energy is separated from vibrational energy in the two-particle, steady-state wave equation and to first order the solutions are harmonic oscillator functions. The classical phase integral gives a partition function valid only at high temperature, but the quantum summation is easily performed to give analytic expressions for all the thermodynamic properties of the harmonic oscillator at all temperatures. Anharmonic effects are treated by small perturbation solutions to the wave equation and the relation between energy levels and a series expansion of the perturbation potential is derived. Next, the quantum solutions for an oscillator with a Morse-function potential are derived in terms of Laguerre polynomials.

Source record↗
NASA NTRS1988

Theoretical studies of solar-pumped lasers

The investigation of stimulated emission causing transitions from the B(1) pi sub u state of sodium to the overlapping 2(1) sigma(+) sub g electronic state has been continued. A new method of estimating the Franck-Condon factors has been developed which instead of fitting the molecular potential curves with Morse functions, estimates the V(r) dependence by interpolation from given potential curves. The results for the sum of the rates from one vibrational level in the upper state to all the levels in the lower state show good agreement with the previous method, implying that curve crossing by stimulated emission due to photons from the oven is an important mechanism in sodium.

Harries, Wynford L.↗
NASA NTRS1960

Vacancy Relaxation in Cubic Crystals

The configuration of the atoms surrounding a vacancy in four face-centered cubic and three body-centered cubic metals has been computed, using a pairwise, central-force model in which the energy of interaction between two atoms was taken to have the form of a Morse function. Only radial relaxations were considered. The first and second nearest-neighbor relaxations for the face-centered systems were found to be: Pb (1.42,−0.43), Ni (2.14,−0.39), Cu(2.24,−0.40) and Ca (2.73,−0.41, expressed in percentages of normal distances. For the body-centered systems the relaxations out to the fourth nearest neighbors to the vacancy were: Fe (6.07,−2.12, −0.25, −), Ba (7.85, −2.70, 0.70, −0.33) and Na (10.80, −3.14, 3.43, −0.20). The positive signs indicate relaxation toward the vacancy and the negative signs indicate relaxation away from the vacancy. The energies of relaxation (eV) are: Pb (0.162), Ni (0.626), Cu (0.560), Ca (0.400), Fe (1.410), Ba (0.950) and Na (0.172).

Girifalco, L. A.↗
NASA NTRS1960

Vacancy-Vacancy Interaction in Copper

The binding energy of two vacancies in a static lattice as a function of their separation and the positions of their displaced neighboring atoms has been calculated using a Morse potential function model for copper. It was found that two vacancies attract one another at separation less than about 7 A. At separations greater than 7 A the vacancies do not interact appreciably. The most stable separation was found to be the first nearest- neighbor separation or the divacancy configuration, for which the binding energy was found to be 0.64 ev. Based on these calculations, it is shown that third-stage annealing in irradiated copper may be accounted for by divacancy migration. The role of the divacancy in copper self-diffusion is also explained.

Girifalco, L. A.↗
DOE OSTI2016

Effects of guest atomic species on the lattice thermal conductivity of type-I silicon clathrate studied via classical molecular dynamics

The effects of guest atomic species in Si clathrates on the lattice thermal conductivity were studied using classical molecular dynamics calculations. The interaction between a host atom and a guest atom was described by the Morse potential function while that between host atoms was described by the Tersoff potential. The parameters of the potentials were newly determined for this study such that the potential curves obtained from first-principles calculations for the insertion of a guest atom into a Si cage were successfully reproduced. The lattice thermal conductivities were calculated by using the Green-Kubo method. The experimental lattice thermal conductivity of Ba{sub 8}Ga{sub 16}Si{sub 30} can be successfully reproduced using the method. As a result, the lattice thermal conductivities of type-I Si clathrates, M{sub 8}Si{sub 46} (M = Na, Mg, K, Ca Rb, Sr, Cs, or Ba), were obtained. It is found that the lattice thermal conductivities of M{sub 8}Si{sub 46}, where M is IIA elements (i.e., M = Mg, Ca, Sr, or Ba) tend to be lower than those of M{sub 8}Si{sub 46}, where M is IA elements (i.e., M = Na, K, Rb, or Cs). Those of {sup m}M{sub 8}Si{sub 46}, where m was artificially modified atomic weight were also obtained. The obtained lattice thermal conductivity can be regarded as a function of a characteristic frequency, f{sub c}. That indicates minimum values around f{sub c}=2-4 THz, which corresponds to the center of the frequencies of the transverse acoustic phonon modes associated with Si cages.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Parameterization Strategies for Intermolecular Potentials for Predicting Trajectory-Based Collision Parameters

The accuracy of separable strategies for constructing full-dimensional potential energy surfaces for collisional energy transfer and collision rate calculations is studied systematically for three alcohols (A = methanol, ethanol, and butanol) and three bath gases (M = Ar, N 2 , and H 2 O). The fitting efficiency (defined as the number of ab initio data required to achieve parametrizations of a desired accuracy) is quantified for both pairwise (Buckingham or "exp6") and nonpairwise (permutationally invariant polynomials, PIPs, of Morse variables) functional forms, for four sampling strategies, and as a function of the complexity and anisotropy of the interaction potential. We find that convergence with respect to the number of sampled ab initio data is largely independent of the choice of functional form but instead varies nearly linearly with the number of adjustable parameters and depends strongly on the sampling strategy. Specifically, the use of biased Sobol quasirandom sampling is similar to 7X more efficient than using unbiased pseudorandom sampling, on average, requiring just similar to 3 computed ab initio energies per adjustable fitting parameter. The pairwise exp6 functional form is shown to provide accurate and transferable parametrizations for M = Ar but is unable to accurately describe alcohol interactions with M = N 2 and H 2 O. The nonpairwise PIP functional form, which is systematically improvable, can produce separable parametrizations with arbitrarily small fitting errors. However, these can suffer from overfitting, which is demonstrated using dynamics calculations of collision parameters for a large number of exp6 and PIP parametrizations. The tests described here validate a robust strategy for automatically generating A + M potential energy surfaces with minimal human intervention, including a quantifiable out of sample metric for judging the accuracy of the fitted surface. We further analyze this set of automatically generated potential energy surfaces to identify areas where more sophisticated fitting strategies may be desired, including pruning of the PIP expansions for large systems and improved sampling strategies more closely coupled with the description of the functional form.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1979

A calculation of the diffusion energies for adatoms on surfaces of F.C.C. metals

The activation energies for diffusion were determined for gold, platinum and iridium adatoms on plane and plane PT surfaces and were found to be in good agreement with the measurements reported by Bassett and Webber. The Lennard-Jones pair potentials were used to model the interatomic forces, and relaxation of the substrate atoms in near proximity to the adatom was considered in detail. The present calculations clarify the mechanism of the observed two-dimensional diffusion of platinum and iridium atoms on a plane PT surface. The results are compared with those obtained using Morse potential functions and different relaxation techniques.

Halicioglu, T.↗
NASA NTRS1992

Schroedinger's radial equation - Solution by extrapolation

A high-accuracy numerical method for the solution of a 1D Schroedinger equation that is suitable for a diatomic molecule, obtained by combining a finite-difference method with iterative extrapolation to the limit, is presently shown to have several advantages over more conventional methods. Initial guesses for the term values are obviated, and implementation of the algorithm is straightforward. The method is both less sensitive to round-off error, and faster than conventional methods for equivalent accuracy. These advantages are illustrated through the solution of Schroedinger's equation for a Morse potential function suited for HCl and a numerically derived Rydberg-Klein-Rees potential function for the X 1Sigma(+) state of CO.

Goorvitch, D.↗
DOE OSTI2017

Morse oscillator propagator in the high temperature limit I: Theory

In an earlier work of the author the time evolution of Morse oscillator was studied analytically and exactly at low temperatures whereupon optical correlation functions were calculated using Morse oscillator coherent states were employed. Morse oscillator propagator in the high temperature limit is derived and a closed form of its corresponding canonical partition function is obtained. Both diagonal and off-diagonal forms of Morse oscillator propagator are derived in the high temperature limit. Partition functions of diatomic molecules are calculated. - Highlights: • Derives the quantum propagator of Morse oscillator in the high temperature limit. • Uses the resulting diagonal propagator to derive a closed form of Morse oscillator partition function. • Provides a more sophisticated formula of the quantum propagator to test the accuracy of the herein results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗