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All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Real-time obstacle avoidance using harmonic potential functions

This paper presents a new formulation of the artificial potential approach to the obstacle avoidance problem for a mobile robot or a manipulator in a known environment. Previous formulations of artificial potentials for obstacle avoidance have exhibited local minima in a cluttered environment. To build an artificial potential field, harmonic functions that completely eliminate local minima even for a cluttered environment are used. The panel method is employed to represent arbitrarily shaped obstacles and to derive the potential over the whole space. Based on this potential function, an elegant control strategy is proposed for the real-time control of a robot. The harmonic potential, the panel method, and the control strategy are tested with a bar-shaped mobile robot and a three-degree-of-freedom planar redundant manipulator.

Kim, Jin-Oh↗
NASA NTRS1993

Wave packet motion in harmonic potential and computer visualization

Wave packet motions of a single electron in harmonic potentials or a magnetic field are obtained analytically. The phase of the wave function which depends on both time and space is also presented explicitly. The probability density of the electron changes its width and central position periodically. These results are visualized using computer animation techniques.

Tsuru, Hideo↗
NASA NTRS1995

A possible generalization of the harmonic oscillator potential

A four-parameter potential is analyzed, which contains the three-dimensional harmonic oscillator as a special case. This potential is exactly solvable and retains several characteristics of the harmonic oscillator, and also of the Coulomb problem. The possibility of similar generalizations of other potentials is also pointed out.

Levai, Geza↗
NASA NTRS1988

Accuracy of analytic energy level formulas applied to hadronic spectroscopy of heavy mesons

Linear and harmonic potential models are used in the nonrelativistic Schroedinger equation to obtain article mass spectra for mesons as bound states of quarks. The main emphasis is on the linear potential where exact solutions of the S-state eigenvalues and eigenfunctions and the asymptotic solution for the higher order partial wave are obtained. A study of the accuracy of two analytical energy level formulas as applied to heavy mesons is also included. Cornwall's formula is found to be particularly accurate and useful as a predictor of heavy quarkonium states. Exact solution for all partial waves of eigenvalues and eigenfunctions for a harmonic potential is also obtained and compared with the calculated discrete spectra of the linear potential. Detailed derivations of the eigenvalues and eigenfunctions of the linear and harmonic potentials are presented in appendixes.

Badavi, Forooz F.↗
DOE OSTI2023

An asymptotic approach for the statistical thermodynamics of certain model systems

In classical statistical thermodynamics, calculating the configuration integral is both vital and elusive. Analytic relations for configuration integrals are desirable for modeling purposes, but it is typically impossible to obtain them. Certain systems become analytically tractable after replacing steep potential energies with harmonic potentials or athermal rigid constraints, but these approximations are often inadequate, especially when modeling the stretching of molecules. It is therefore necessary to develop a systematic approach to improve upon the approximations provided by these reference systems. Here, a general asymptotic approach is introduced, where the configuration integral for the full system is obtained in terms of that of the reference system and several corrections. This asymptotic approach is first demonstrated using the simple example of a classical three-dimensional oscillator. Next, the approach is applied to modeling the stretching of single polymer chains and to modeling thermally assisted crack growth, where results are verified with respect to numerical calculations. Overall, this asymptotic approach is a valid and effective tool for statistical thermodynamics in general.

Buche, Michael Robert↗
DOE OSTI2021

Spatiotemporal spread of perturbations in power-law models at low temperatures: Exact results for classical out-of-time-order correlators

Here, we present exact results for the classical version of the out-of-time-order commutator (OTOC) for a family of power-law models consisting of N particles in one dimension and confined by an external harmonic potential. These particles are interacting via power-law interaction of the form ∝ $Σ_{i,j=(i≠j)}^{N}$ |x i -x j | -k for every k>1 where x i is the position of the i th particle. We present numerical results for the OTOC for finite N at low temperatures and short enough times so that the system is well approximated by the linearized dynamics around the many-body ground state. In the large-N limit, we compute the ground-state dispersion relation in the absence of external harmonic potential exactly and use it to arrive at analytical results for OTOC. We find excellent agreement between our analytical results and the numerics. We further obtain analytical results in the limit where only linear and leading nonlinear (in momentum) terms in the dispersion relation are included. The resulting OTOC is in agreement with numerics in the vicinity of the edge of the “light cone.” We find remarkably distinct features in OTOC below and above k=3 in terms of going from non-Airy behavior (1 < k < 3) to an Airy universality class (k>3). We present certain additional rich features for the case k=2 that stem from the underlying integrability of the Calogero-Moser model. We present a field theory approach that also assists in understanding certain aspects of OTOC such as the sound speed. Our findings are a step forward towards a more general understanding of the spatiotemporal spread of perturbations in long-range interacting systems.

1-dimensional systems↗
DOE OSTI2024

Quantum Liouville theorem based on Haar measure

Liouville theorem (L theorem) reveals robust incompressibility of the distribution function in phase space, given arbitrary potentials. However, its quantum generalization, Wigner flow, is compressible, i.e., L theorem is only conditionally true (e.g., for perfect Harmonic potential). Here, we develop quantum L theorem (rigorous incompressibility) for arbitrary potentials (interacting or not) in Hamiltonians. Haar measure, instead of symplectic measure dp$\bigwedge$dq used in Wigner’s scheme, plays a central role. The argument is based on general measure theory, independent of specific spaces or coordinates. Comparison of classical and quantum is made: for instance, here we address why Haar measure and metric preservation do not work in the classical case. Applications of the theorems in statistics, topological phase transition, ergodic theory, etc., are discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1980

Reducing the error of geoid undulation computations by modifying Stokes' function

The truncation theory as it pertains to the calculation of geoid undulations based on Stokes' integral, but from limited gravity data, is reexamined. Specifically, the improved procedures of Molodenskii et al. are shown through numerical investigations to yield substantially smaller errors than the conventional method that is often applied in practice. In this improved method, as well as in a simpler alternative to the conventional approach, the Stokes' kernel is suitably modified in order to accelerate the rate of convergence of the error series. These modified methods, however, effect a reduction in the error only if a set of low-degree potential harmonic coefficients is utilized in the computation. Consider, for example, the situation in which gravity anomalies are given in a cap of radius 10 deg and the GEM 9 (20,20) potential field is used. Then, typically, the error in the computed undulation (aside from the spherical approximation and errors in the gravity anomaly data) according to the conventional truncation theory is 1.09 m; with Meissl's modification it reduces to 0.41m, while Molodenskii's improved method gives 0.45 m. A further alteration of Molodenskii's method is developed and yields an RMS error of 0.33 m. These values reflect the effect of the truncation, as well as the errors in the GEM 9 harmonic coefficients. The considerable improvement, suggested by these results, of the modified methods over the conventional procedure is verified with actual gravity anomaly data in two oceanic regions, where the GEOS-3 altimeter geoid serves as the basis for comparison. The optimal method of truncation, investigated by Colombo, is extremely ill-conditioned. It is shown that with no corresponding regularization, this procedure is inapplicable.

Jekeli, C.↗
NASA NTRS1979

Global accuracy estimates of point and mean undulation differences obtained from gravity disturbances, gravity anomalies and potential coefficients

Through the method of truncation functions, the oceanic geoid undulation is divided into two constituents: an inner zone contribution expressed as an integral of surface gravity disturbances over a spherical cap; and an outer zone contribution derived from a finite set of potential harmonic coefficients. Global, average error estimates are formulated for undulation differences, thereby providing accuracies for a relative geoid. The error analysis focuses on the outer zone contribution for which the potential coefficient errors are modeled. The method of computing undulations based on gravity disturbance data for the inner zone is compared to the similar, conventional method which presupposes gravity anomaly data within this zone.

Jekeli, C.↗
DOE OSTI2025

Extended molecular eigenmodes treatment of dipole–dipole NMR relaxation in real fluids

Traditional models of NMR relaxation fail to account for the complex, multi-exponential behavior of the autocorrelation function in realistic systems characterized by soft-interactions and molecules that are chemically and physically complex. Here, in this study, we describe the relative diffusion of the spin dipoles by means of a Fokker–Planck equation that includes an interaction potential of mean force to account for the response of the physical/chemical environment around the dipoles. By numerically solving the Fokker–Planck equation for the diffusion propagator, we estimate dipole–dipole NMR relaxation for like- and unlike-spin systems via its eigenmode solution. We test the model against molecular simulations of diffusing dipoles with harmonic potentials and also validate using experimental longitudinal relaxation data from real systems, including Gd(III)–aqua and Gd(III)–DO3A–butrol complexes, the latter being an important MRI contrast agent. Using this novel approach, we predict both the inner- and outer-shell contributions to the relaxivity rates with excellent accuracy at frequencies relevant to MRI. We also show that, under the appropriate assumptions, our framework naturally recovers the Bloembergen–Purcell–Pound, the Solomon–Bloembergen–Morgan, and the Hwang–Freed models. Our implementation is general and publicly available for application to a broad range of systems.

Pinheiro dos Santos, Thiago J. [Rice Univ., Housto↗
NASA NTRSDate not supplied

Human Factors and Behavioral Performance Exploration Measures Harmonized Across HERA, NEK, and ISS: Teams Risk

BACKGROUNDThe Human Factors and Behavioral Performance Exploration Measures (HFBP-EM) suite is a set of standardized measures to assess behavioral health and performance risk related to future exploration class missions, and to support reduction of the Human Research Program’s (HRP) Behavioral Medicine (BMed), Team, Sleep, and Human Systems Integration Architecture risks. HFBP-EM were collected during Human Exploration Research Analogs (HERA) campaigns 4 (C4) and 5 (C5), and during SIRIUS 17 and 19 missions in the Russian Ground Based Experiment Complex, NEK, to document the feasibility, flexibility, and acceptability of these measures in analogsof the spaceflight environment. A subset of the HFBP-EM suite was collected during spaceflight as part HRP’s Standard Measures in Spaceflight Project. Whenever possible, the HFBP-EM protocol and measures are kept the same across studies, however, differences across research settings (e.g., experimental manipulations, mission scenarios, mission length) and implementation of the measures require the data are harmonized to ensure comparable views across missions. The purpose of our project is to develop a harmonized database of HFBP-EM data from different settings, and to summarize the trajectory of behavioral health and performance within and between research settings. In this presentation, we will summarize the harmonized dataset and the trajectory of measures related to the Team Risk, including team performance, team cohesion, team processes, and psychological safety, over time and between and within settings.METHODSWe followed best practices for data harmonization. Characteristics of each research setting were assessed for harmonization potential, and we deemed NEK-SIRIUS 17 as inappropriate due to study aims, length, and data quality. Common variables of interest were identified. Study characteristics and key variables with which datafiles could be merged were defined as “meta-data.” HFBP-EM data from all settings were processed under a common format. We then created a harmonized team-level database designed to facilitate analyses that address HRP research gaps related to HRP’s Team risk. In this database, team cohesion, processes, performance, psychological safety, and group living were operationalized as the team mean of the crew responses for each data collection (e.g., on mission day 7). Data collected on the International Space Station (ISS) included a subset of scale items administered to participants. Data collected from ISS team members within +/- 7 days of the first data collection and every following 30 +/-4 days were aggregated to the team level. We generated figures that display the mean and variability of team constructs across research settings. We also generated plots of changes in team constructs with mission day and with percentage of the mission completed. Where possible, we compared data from spaceflight analogs with data from astronauts aboard the ISS. RESULTS AND DISCUSSIONThe team-level harmonized database was structured such that each row represents data for a team on a specific mission day. Team constructs (e.g., team cohesion) were included as columns (i.e., wide format) with repeated measures across mission days given in rows (i.e., long format). The database included data from 18 crews: five, 4-person American crews in HERA C4, four 4-person American crews in HERA C5, one 6-person multinational crew in NEK-SIRIUS 19, and eight, 2–11-person multinational crews aboard the ISS. Results provide insights into mission and campaign differences in team functioning and performance. For example, between campaign differences were observed for team processes—the interdependent team actions that orchestrate taskwork in pursuit of the team’s goals [1]. Greater between-team variability on team processes was detected during HERA C4 than during C5, and a downward trend was observed over the duration of C4, but not C5 or SIRIUS 19. This may be due to the campaign-level differences such as the sleep deprivation implemented during C4. Responses on the subset of team process items administered on the ISS indicate between-crew variability more like those observed in C4 than C5 and NEK, with some, but not all ISS crews demonstrating a downward trend over time. Additional findings will be presented. REFERENCESMarks, M. A., et al (2001) Academy of Management Review, 26(3), 356-376.

S T Bell↗
DOE OSTI2022

Causality and dimensionality in geometric scattering

We report the scattering matrix which describes low-energy, non-relativistic scattering of spin-1/2 fermions interacting via finite-range potentials can be obtained from a geometric action principle in which space and time do not appear explicitly. In the case of zero-range forces, causality leads to constraints on scattering trajectories in the geometric picture. The effect of spatial dimensionality is also investigated by considering scattering in two and three dimensions. In the geometric formulation it is found that dimensionality is encoded in the phase of the harmonic potential that appears in the geometric action.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Bonding and Acidity of the Formal Hydride in the Prototypical Au 9 (PPh 3 ) 8 H 2+ Nanocluster

Abstract The role of hydrogen atoms as surface ligands on metal nanoclusters is of profound importance but remains difficult to directly study. While hydrogen atoms often appear to be incorporated formally as hydrides, evidence suggests that they donate electrons to the cluster's delocalized superatomic orbitals and may consequently behave as acidic protons that play key roles in synthetic or catalytic mechanisms. Here we directly test this assertion for the prototypical Au 9 (PPh 3 ) 8 H 2+ nanocluster, formed by addition of a hydride to the well‐characterized Au 9 (PPh 3 ) 8 3+ . Using gas‐phase infrared spectroscopy, we were able to unambiguously isolate Au 9 (PPh 3 ) 8 H 2+ and Au 9 (PPh 3 ) 8 D 2+ , revealing an Au−H stretching mode at 1528 cm −1 that shifts to 1038 cm −1 upon deuteration. This shift is greater than the maximum expected for a typical harmonic potential, suggesting a potential governing cluster‐H bonding that has some square‐well character consistent with the hydrogen nucleus behaving as a metal atom in the cluster core. Complexing this cluster with very weak bases reveals a redshift of 37 cm −1 in the Au−H vibration, consistent with those typically seen for moderately acidic groups in gas phase molecules and providing an estimate of the acidity of Au 9 (PPh 3 ) 8 H 2+ , at least with regard to its surface reactivity.

Hernández, Hanna Morales↗
DOE OSTI2023

Bonding and Acidity of the Formal Hydride in the Prototypical Au 9 (PPh 3 ) 8 H 2+ Nanocluster

The role of hydrogen atoms as surface ligands on metal nanoclusters is of profound importance but remains difficult to directly study. While hydrogen atoms often appear to be incorporated formally as hydrides, evidence suggests that they donate electrons to the cluster's delocalized superatomic orbitals and may consequently behave as acidic protons that play key roles in synthetic or catalytic mechanisms. Here we directly test this assertion for the prototypical Au 9 (PPh 3 ) 8 H 2+ nanocluster, formed by addition of a hydride to the well-characterized Au 9 (PPh 3 ) 8 3+ . Using gas-phase infrared spectroscopy, we were able to unambiguously isolate Au 9 (PPh 3 ) 8 H 2+ and Au 9 (PPh 3 ) 8 D 2+ , revealing an Au–H stretching mode at 1528 cm –1 that shifts to 1038 cm –1 upon deuteration. This shift is greater than the maximum expected for a typical harmonic potential, suggesting a potential governing cluster-H bonding that has some square-well character consistent with the hydrogen nucleus behaving as a metal atom in the cluster core. Complexing this cluster with very weak bases reveals a redshift of 37 cm –1 in the Au–H vibration, consistent with those typically seen for moderately acidic groups in gas phase molecules and providing an estimate of the acidity of Au 9 (PPh 3 ) 8 H 2+ , at least with regard to its surface reactivity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Pynta-An Automated Workflow for Calculation of Surface and Gas-Surface Kinetics

Many important industrial processes rely on heterogeneous catalytic systems. However, given all possible catalysts and conditions of interest, it is impractical to optimize most systems experimentally. Automatically generated microkinetic models can be used to efficiently consider many catalysts and conditions. However, these microkinetic models require accurate estimation of many thermochemical and kinetic parameters. Manually calculating these parameters is tedious and error prone, involving many interconnected computations. Here, we present Pynta, a workflow software for automating the calculation of surface and gas–surface reactions. Pynta takes the reactants, products, and atom maps for the reactions of interest, generates sets of initial guesses for all species and saddle points, runs all optimizations, frequency, and IRC calculations, and computes the associated thermochemistry and rate coefficients. It is able to consider all unique adsorption configurations for both adsorbates and saddle points, allowing it to handle high index surfaces and bidentate species. Pynta implements a new saddle point guess generation method called harmonically forced saddle point searching (HFSP). HFSP defines harmonic potentials based on the optimized adsorbate geometries and which bonds are breaking and forming that allow initial placements to be optimized using the GFN1-xTB semiempirical method to create reliable saddle point guesses. This method is reaction class agnostic and fast, allowing Pynta to consider all possible adsorbate site placements efficiently. We demonstrate Pynta on 11 diverse reactions involving monodenate, bidentate, and gas-phase species, many distinct reaction classes, and both a low and a high index facet of Cu. Our results suggest that it is very important to consider reactions between adsorbates adsorbed in all unique configurations for interadsorbate group transfers and reactions on high index surfaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Lattice simulations of inflation

The scalar field theory of cosmological inflation constitutes nowadays one of the preferred scenarios for the physics of the early universe. In this paper we aim at studying the inflationary universe making use of a numerical lattice simulation. Various lattice codes have been written in the last decades and have been extensively used for understating the reheating phase of the universe, but they have never been used to study the inflationary phase itself far from the end of inflation (i.e. about 50 e-folds before the end of inflation). In this paper we use a lattice simulation to reproduce the well-known results of some simple models of single-field inflation, particularly for the scalar field perturbation. The main model that we consider is the standard slow-roll inflation with an harmonic potential for the inflaton field. We explore the technical aspects that need to be accounted for in order to reproduce with precision the nearly scale invariant power spectrum of inflaton perturbations. We also consider the case of a step potential, and show that the simulation is able to correctly reproduce the oscillatory features in the power spectrum of this model. Even if a lattice simulation is not needed in these cases, that are well within the regime of validity of linear perturbation theory, this sets the basis to future work on using lattice simulations to study more complicated models of inflation.

79 ASTRONOMY AND ASTROPHYSICS↗