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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 721 records · Page 40
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Theoretical calculations of rotationally inelastic collisions of He with NaK(A {sup 1}Σ{sup +}): Transfer of population, orientation, and alignment

We have performed extensive calculations to investigate thermal energy, rotationally inelastic collisions of NaK (A{sup 1}Σ{sup +}) with He. We determined a potential energy surface using a multi-reference configuration interaction wave function as implemented by the GAMESS electronic structure code, and we have performed coupled channel scattering calculations using the Arthurs and Dalgarno formalism. We also calculate the Grawert coefficients B{sub λ}(j, j′) for each j → j′ transition. These coefficients are used to determine the probability that orientation and alignment are preserved in collisions taking place in a cell environment. The calculations include all rotational levels with j or j′ between 0 and 50, and total (translational and rotational) energies in the range 0.0002–0.0025 a.u. (∼44–550 cm{sup −1}). The calculated cross sections for transitions with even values of Δj tend to be larger than those for transitions with odd Δj, in agreement with the recent experiments of Wolfe et al. (J. Chem. Phys. 134, 174301 (2011)). The calculations of the energy dependence of the cross sections and the calculations of the fraction of orientation and alignment preserved in collisions also exhibit distinctly different behaviors for odd and even values of Δj. The calculations also indicate that the average fraction of orientation or alignment preserved in a transition becomes larger as j increases. We interpret this behavior using the semiclassical model of Derouard, which also leads to a simple way of visualizing the distribution of the angles between the initial and final angular momentum vectors j and j′. Finally, we compare the exact quantum results for j → j′ transitions with results based on the simpler, energy sudden approximation. That approximation is shown to be quite accurate.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2015

Experimental Study of Fillets to Reduce Corner Effects in an Oblique Shock-Wave/Boundary Layer Interaction

A test was conducted in the 15 cm x 15 cm supersonic wind tunnel at NASA Glenn Research Center that focused on corner effects of an oblique shock-wave/boundary-layer interaction. In an attempt to control the interaction in the corner region, eight corner fillet configurations were tested. Three parameters were considered for the fillet configurations: the radius, the fillet length, and the taper length from the square corner to the fillet radius. Fillets effectively reduced the boundary-layer thickness in the corner; however, there was an associated penalty in the form of increased boundary-layer thickness at the tunnel centerline. Larger fillet radii caused greater reductions in boundary-layer thickness along the corner bisector. To a lesser, but measureable, extent, shorter fillet lengths resulted in thinner corner boundary layers. Overall, of the configurations tested, the largest radius resulted in the best combination of control in the corner, evidenced by a reduction in boundary-layer thickness, coupled with minimal impacts at the tunnel centerline.

Fillets↗
DOE OSTI2024

Time-resolved biphase signatures of quadratic nonlinearity observed in coupled Alfvén eigenmodes on the DIII-D tokamak

We report the detection of nonstationary quadratic coupling between toroidicity-induced Alfvén eigenmodes (TAEs) on sub-millisecond time scales. Identification of phase coherency between multiple TAEs and nonlinearly generated modes is facilitated by wavelet-based bicoherence analysis of time-series from inductive coils, taken from a DIII-D discharge heated by neutral beam injection (NBI). Characterization of nonlinear three-wave interaction is inferred by stationary local bispectrum phase (biphase) and confirmed via bandpass filtering. Biphase dynamics associated with prominent bispectral features are well-resolved in time and consistent with transient quadratic coupling. Onset and duration of nonlinearity are correlated with enhanced amplitude of participating TAEs; coincident changes in amplitude are observed for modes at difference frequency |f TAE,1 - f TAE,2 |.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Collaboration with NSTX in Calculations of Radiofrequency and Neutral Beam Heating and Current Drive

The overall objective of this project was to advance the understanding of heating and current drive necessary for toroidal magnetic confinement fusion energy reactors, and to provide accurate models for these sources to aid in understanding magneto-hydrodynamic, transport and boundary physics issues. Increased understanding is provided by computer simulation using the underlying physics laws, and will lead to greater reliability and increased efficiency of a power producing fusion reactor. The proposed work entailed applications of existing CompX Fokker-Planck, ray tracing, full-wave microwave, and particle diffusion calculator codes to the National Spherical Torus Experiment at Princeton Plasma Physics Laboratory. Special features of NSTX include that large ion orbits are emphasized in its geometry and thus offer a major opportunity within fusion research for focused exploration of their ubiquitous effects, including comparison with simulation codes. The CompX CQL3D Fokker-Planck code was be further adapted to the finite-orbit-width physics. Comparison with experiment ensured that the computer codes have sufficient accuracy to accurately model the experiments. Nonthermal distributions of energetic ions are produced in experiments-- and modeled with the codes-- exhibiting the signatures of auxiliary heating, transport, and radiation processes within the plasma. Using physics-based modeling, in conjunction with experimental data, nonthermal distributions can provide keys to validation and quantification of auxiliary heating physics. Nonthermal distributions also hold particular information on radial transport processes, not obscured by the smoothing Maxwellization effects of Coulomb collisions. Generally, radial transport is not well understood but is a key to efficient fusion energy production. By comparison with Fokker-Planck modeling, the velocity dependence of radial transport coefficients becomes experimentally accessible, particularly in cases of well-modeled sources such as neutral beams, fast wave power, or the toroidal electric field. It is clear from modeling of fast-wave interactions with ions that finite-orbit-width effects play a significant role. For example, a different set of ions is computed to intersect a given cyclotron resonance depending on whether or not radial orbit drifts are taken into account. Also, radial transport, associated bootstrap current, and alpha channeling depend on radial drifts. Ion cyclotron heating above the first harmonic interacts preferentially with higher velocity ions, giving large radial drifts. The CQL3D Fokker-Planck code, maintained by the proposers, is a physics based model used extensively within the US fusion community to compare with and interpret experimental observations. At the beginning of this grant, bounce-averages of the rf quasilinear and other operators have been performed neglecting the radial drifts which give finite orbit widths to the particle orbits. The proposed work included a major upgrade to CQL3D to include finite-orbit-width effects be accounted for by performing the bounce-averages of rf and neutral beam fast ions along guiding center orbits. This CQL3D enhancement provided microwave and neutral beam contributions to neoclassical radial transport coefficients for nonthermal distributions, and substantially increased the comprehensiveness of the ion model. Additional work validated Fokker-Planck and ray tracing modeling of neutral beam and high harmonic fast wave absorption and current drive against the NSTX experiment, as had been very successful for electron cyclotron current drive in the DIII-D tokamak at General Atomics and lower hybrid waves on C-Mod at MIT. The validation work was in conjunction with staff and graduate students at Princeton Plasma Physics Laboratory. This DOE grant supported fusion energy research, a potential long-term solution to the world's energy needs. The research grant under consideration, DE-SC0006614, provided research support at the 0.3 Full-Time-Equivalent level for application of computer models to aid in understanding and projecting efficacy of heating and current drive sources in the National Spherical Torus Experiment, a tokamak variant, at the Princeton Plasma Physics Laboratory. The NSTX experiment explores the physics of very tight aspect ratio, almost spherical tokamaks, aiming at producing steady-state fusion plasmas. The current drive is an integral part of the steady-state concept, maintaining the magnetic geometry in the steady-state tokamak.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Characteristics of SBS dynamics in single-mode optical fibres

The characteristics of the gain of Stokes pulses in single-mode optical fibres by stimulated Brillouin scattering (SBS) of monochromatic and nonmonochromatic pump signals have been investigated by numerical simulation using a spectral approach. Conditions under which 'slow light' (caused by a group delay) can be implemented are found (it is reasonable to apply this term to a process in which a pulse is delayed with conservation of its shape). The plane-wave interaction model is shown to describe adequately the dynamics of this process in single-mode fibres. A number of gain modes are investigated for Stokes pulses with different time structures upon monochromatic and nonmonochromatic excitation. A new data transfer technique is proposed, which is based on the conversion of stepwise phase modulation of the input Stokes signal into amplitude modulation of the output signal. (nonlinear optical phenomena)

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Unsupervised discovery of nonlinear plasma physics using differentiable kinetic simulations

Plasma supports collective modes and particle–wave interactions that lead to complex behaviour in, for example, inertial fusion energy applications. While plasma can sometimes be modelled as a charged fluid, a kinetic description is often crucial for studying nonlinear effects in the higher-dimensional momentum–position phase space that describes the full complexity of the plasma dynamics. We create a differentiable solver for the three-dimensional partial-differential equation describing the plasma kinetics and introduce a domain-specific objective function. Using this framework, we perform gradient-based optimization of neural networks that provide forcing function parameters to the differentiable solver given a set of initial conditions. We apply this to an inertial-fusion-relevant configuration and find that the optimization process exploits a novel physical effect.

plasma nonlinear phenomena↗
DOE OSTI2022

Nondestructive Evaluation of Stress Corrosion Cracking in a Welded Steel Plate Using Guided Ultrasonic Waves

Stress corrosion cracking (SCC) had occurred in early-generation high-level nuclear waste tanks constructed by welding carbon steel. This paper describes an ultrasonic inspection system and its fundamental ability to detect and quantify the length of SCC on thick welded steel plates. The finite element method (FEM) was applied to simulate the welding process to estimate the welding residual stress field. Growth of stress corrosion cracks is driven by crack stress intensities exceeding the subcritical cracking threshold intensity. The subject plate was experimentally inspected with ultrasonic nondestructive evaluation (NDE) techniques to characterize the extent of SCC. The NDE system uses a piezoelectric transducer to generate guided waves in the thick steel plate, and a scanning laser Doppler vibrometer (SLDV) to measure multidimensional time–space wavefield data over a user-defined scanning area in the plate surface. The measured wavefield data can show wave interactions in a localized area in the plate due to the presence of the discontinuities of the SCC. To generate an inspection image that can precisely show the crack’s location and/or the dimension, the wavefield data are further processed to generate inspection image that maps the entire sample plate so the crack can be clearly identified in the plate while its length can be readily estimated. In conclusion, the ultrasonic test results for crack length agree well with the visually estimated length and are close to that predicted by the FEM for cracks in the weld residual stress field.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Characterization of nonlinear ultrasonic waves behavior while interacting with poor interlayer bonds in large-scale additive manufactured materials

Over the past decades, researchers have developed several nonlinear ultrasonic techniques for quality control of materials commonly used in different applications. Owing to the superior sensitivity of nonlinear ultrasound waves to small defects such as micro-cracks, their applicability in different nondestructive testing (NDT) problems has been investigated in numerous studies. These studies utilize frequency domain analysis to detect the generation of higher harmonics because of the formation of defects in the inspected medium. Frequency domain analysis based on the Fourier transform is a significant approach used in linear systems; however, it may not perform adequately on nonlinear systems. Hence, studies on nonlinear dynamics and physics consider analyzing systems' behavior in the phase-space domain. In contrast to the frequency domain analysis, which can result in information loss, analysis in the phase-space domain retains all the information regarding a system's states. Here, we investigate the nonlinearities induced by poor interlayer bonding in polymer-based additive manufactured parts in the phase-space domain. It is convenient to characterize the nonlinearity in the phase-space domain because it provides a geometrical representation of a system's states. Two types of low quality interlayer bond are considered. The first type is simulated artificially while the second type is manufactured by reducing the bond quality during the printing process. The analysis verified that the received ultrasonic signals exhibit classical nonlinear behavior in the phase-space domain while interacting with simulated poor interlayer bonds. In addition, the results showed that the behavior of ultrasonic waves is amplitude-dependent and evolves into models that have not been previously reported. Furthermore, Largest Lyapunov Exponent (LLE) is used to quantify the behavior of nonlinear ultrasonic waves while interacting with poor interlayer bonds. Using LLE, it was observed that the divergence rate of the phase-space trajectories depends on the amplitude of the excitation. This observation quantitatively proves that nonlinear behavior of ultrasound while interacting with poor interlayer bonds can be amplitude-dependent. The results of both simulated and inherent poor interlayer bond cases showed that LLE can be used as a reliable quantitative damage-sensitive feature to detect and potentially characterize weak bonds, which are difficult to detect using conventional approaches. Additionally, the reported results in the phase-space domain provide a basis for proposing a new mathematical model for ultrasonic waves interacting with poor interlayer bonds.

36 MATERIALS SCIENCE↗
DOE OSTI2025

An experimental study of the existence regions and non-linear interactions of drift wave and Kelvin–Helmholtz instabilities in a linear magnetized plasma

Experimental observations of the intrinsic excitation and non-linear interactions of drift wave (DW) and Kelvin–Helmholtz (KH) instabilities in a linear magnetized plasma column are presented. The experiments are carried out in the inverse mirror plasma experimental device (IMPED)—a cylindrical, magnetized, linear plasma machine designed to study low-frequency waves and instabilities in plasma. A novel feature of IMPED is the ability to control plasma profiles, such as the density n(r)⁠, electron temperature T e (r)⁠, and plasma potential V p (r) by varying the ratio Rm of the magnetic field in the main chamber to that in the source chamber. At high values of Rm, higher-density gradient scale length promotes the drift wave (DW) instability while lower Rm value results in a higher radial electric field, inducing a sheared poloidal flow that enhances the dominance of the Kelvin–Helmholtz (KH) mode. The background and fluctuating plasma parameters are characterized using various configurations of multiple in situ electric probes at different spatial locations to quantify the local gradients that excite the low-frequency primary instabilities. Statistical, spectral, and bispectral analysis of the density and potential signals help identify these modes in terms of wave number, frequency, phase, and amplitude and also delineate the nature of their non-linear interactions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1995

Observational and numerical studies of extreme frontal scale contraction

The general objective of this effort is to increase understanding of how frontal scale contraction processes may create and sustain intense mesoscale precipitation along intensifying cold fronts. The five-part project (an expansion of the originally proposed two-part project) employed conventional meteorological data, special mesoscale data, remote sensing measurements, and various numerical models. First an idealized hydrostatic modeling study of the scale contraction effects of differential cloud cover on low-level frontal structure and dynamics was completed and published in a peer-reviewed journal. The second objective was to complete and publish the results from a three dimensional numerical model simulation of a cold front in which differential sensible heating related to cloud coverage patterns was apparently crucial in the formation of a severe frontal squall line. The third objective was to use a nonhydrostatic model to examine the nonlinear interactions between the transverse circulation arising from inhomogeneous cloud cover, the adiabatic frontal circulation related to semi-geostrophic forcing, and diabatic effects related to precipitation processes, in the development of a density current-like microstructure at the leading edge of cold fronts. Although the development of a frontal model that could be used to initialize such a primitive equation model was begun, we decided to focus our efforts instead on a project that could be successfully completed in this short time, due to the lack of prospects for continued NASA funding beyond this first year (our proposal was not accepted for future funding). Thus, a fourth task was added, which was to use the nonhydrostatic model to test tentative hypotheses developed from the most detailed observations ever obtained on a density current (primarily sodar and wind profiler data). These simulations were successfully completed, the findings were reported at a scientific conference, and the results have recently been submitted to a peer-reviewed journal. The fifth objective was to complete the analysis of data collected during the Cooperative Oklahoma Profiler Studies (COPS-91) field project, which was supported by NASA. The analysis of the mesoscale surface and sounding data, Doppler radar imagery, and other remote sensing data from multi frequency wind profiler, microwave radiometer, and the Radio Acoustic Sounding System has been completed. This study is a unique investigation of processes that caused the contraction of a cold front to a microscale zone exhibiting an undular bore-like structure. Results were reported at a scientific conference and are being prepared for publication. In summary, considerable progress has been achieved under NASA funding in furthering our understanding of frontal scale contraction and density current - gravity wave interaction processes, and in utilizing models and remotely sensed data in such studies.

Koch, Steven E.↗
DOE OSTI2019

Dust survival rates in clumps passing through the Cas A reverse shock – I. Results for a range of clump densities

ABSTRACT The reverse shock in the ejecta of core-collapse supernovae is potentially able to destroy newly formed dust material. In order to determine dust survival rates, we have performed a set of hydrodynamic simulations using the grid-based code astrobear in order to model a shock wave interacting with clumpy supernova ejecta. Dust motions and destruction rates were computed using our newly developed external, post-processing code paperboats, which includes gas drag, grain charging, sputtering, and grain–grain collisions. We have determined dust destruction rates for the oxygen-rich supernova remnant Cassiopeia A as a function of initial grain sizes and clump gas density. We found that up to $30\,\mathrm{{{\ \rm per\ cent}}}$ of the carbon dust mass is able to survive the passage of the reverse shock if the initial grain size distribution is narrow with radii around ∼10–50 nm for high gas densities, or with radii around $\sim 0.5\!-\!1.5\,\mathrm{\mu m}$ for low and medium gas densities. Silicate grains with initial radii around 10–30 nm show survival rates of up to $40\,\mathrm{{{\ \rm per\ cent}}}$ for medium- and high-density contrasts, while silicate material with micron-sized distributions is mostly destroyed. For both materials, the surviving dust mass is rearranged into a new size distribution that can be approximated by two components: a power-law distribution of small grains and a lognormal distribution of grains having the same size range as the initial distribution. Our results show that grain–grain collisions and sputtering are synergistic and that grain–grain collisions can play a crucial role in determining the surviving dust budget in supernova remnants.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1986

Shock-wave boundary layer interactions

Presented is a comprehensive, up-to-date review of the shock-wave boundary-layer interaction problem. A detailed physical description of the phenomena for transonic and supersonic speed regimes is given based on experimental observations, correlations, and theoretical concepts. Approaches for solving the problem are then reviewed in depth. Specifically, these include: global methods developed to predict sudden changes in boundary-layer properties; integral or finite-difference methods developed to predict the continuous evolution of a boundary-layer encountering a pressure field induced by a shock wave; coupling methods to predict entire flow fields; analytical methods such as multi-deck techniques; and finite-difference methods for solving the time-dependent Reynolds-averaged Navier-Stokes equations used to predict the development of entire flow fields. Examples are presented to illustrate the status of the various methods and some discussion is devoted to delineating their advantages and shortcomings. Reference citations for the wide variety of subject material are provided for readers interested in further study.

Delery, J.↗
DOE OSTI2014

The Effect of Pore Morphology on Hot Spot Temperature

Composite explosives contain pores that collapse under shock wave interaction generating localized regions of heat known to be important in the initiation of high explosives. Understanding pore collapse under shock loading is essential to create predictive reactive flow models to simulate the initiation process. While spherical pore collapse has been thoroughly simulated, other geometries have been relatively neglected. By simulating microoscale hot spot nucleation in this study, we analyze the effect of pore morphology on the post-shock hot spot temperature. Several pore morphologies that yield higher temperatures than the spherical case are revealed and discussed.

42 ENGINEERING↗
DOE OSTI2019

Implementing the three-particle quantization condition including higher partial waves

We present an implementation of the relativistic three-particle quantization condition including both s - and d -wave two-particle channels. For this, we develop a systematic expansion of the three-particle K matrix, \( \mathcal{K} \) df,3 , about threshold, which is the generalization of the effective range expansion of the two-particle K matrix, \( \mathcal{K} \) 2 . Relativistic invariance plays an important role in this expansion. We find that d -wave two-particle channels enter first at quadratic order. We explain how to implement the resulting multichannel quantization condition, and present several examples of its application. We derive the leading dependence of the threshold three-particle state on the two-particle d -wave scattering amplitude, and use this to test our implementation. We show how strong two-particle d -wave interactions can lead to significant effects on the finite-volume three-particle spectrum, including the possibility of a generalized three-particle Efimov-like bound state. We also explore the application to the 3 π + system, which is accessible to lattice QCD simulations, where we study the sensitivity of the spectrum to the components of \( \mathcal{K} \) df,3 . Finally, we investigate the circumstances under which the quantization condition has unphysical solutions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Optical Characterization of the Keck Array and BICEP3 CMB Polarimeters from 2016 to 2019

The BICEP/Keck experiment (BK) is a series of small-aperture refracting telescopes observing degree-scale cosmic microwave background (CMB) polarization from the South Pole in search of a primordial B-mode signature. This B-mode signal arises from primordial gravitational waves interacting with the CMB and has amplitude parametrized by the tensor-to-scalar ratio r. Since 2016, BICEP3 and the Keck Array have been observing with 4800 total antenna-coupled transition-edge sensor detectors, with frequency bands spanning 95, 150, 220, and 270 GHz. Here we present the optical performance of these receivers from 2016 to 2019, including far-field beams measured in situ with an improved chopped thermal source and instrument spectral response measured with a field-deployable Fourier transform spectrometer. As a pair differencing experiment, an important systematic that must be controlled is the differential beam response between the co-located, orthogonally polarized detectors. We generate per-detector far-field beam maps and the corresponding differential beam mismatch that is used to estimate the temperature-to-polarization leakage in our CMB maps and to give feedback on detector and optics fabrication. The differential beam parameters presented here were estimated using improved low-level beam map analysis techniques, including efficient removal of non-Gaussian noise as well as improved spatial masking. These techniques help minimize systematic uncertainty in the beam analysis, with the goal of constraining the bias on r induced by temperature-to-polarization leakage to be subdominant to the statistical uncertainty. This is essential as we progress to higher detector counts in the next generation of CMB experiments.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

The Role of Kinetic Instabilities and Waves in Collisionless Magnetic Reconnection

Magnetic reconnection converts magnetic field energy into particle energy by breaking and reconnecting magnetic field lines. Magnetic reconnection is a kinetic process that generates a wide variety of kinetic waves via wave-particle interactions. Kinetic waves have been proposed to play an important role in magnetic reconnection in collisionless plasmas by, for example, contributing to anomalous resistivity and diffusion, particle heating, and transfer of energy between different particle populations. These waves range from below the ion cyclotron frequency to above the electron plasma frequency and from ion kinetic scales down to electron Debye length scales. This review aims to describe the progress made in understanding the relationship between magnetic reconnection and kinetic waves. We focus on the waves in different parts of the reconnection region, namely, the diffusion region, separatrices, outflow regions, and jet fronts. Particular emphasis is placed on the recent observations from the Magnetospheric Multiscale (MMS) spacecraft and numerical simulations, which have substantially increased the understanding of the interplay between kinetic waves and reconnection. Some of the ongoing questions related to waves and reconnection are discussed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

On the Bonding Nature of Ozone (O 3 ) and Its Sulfur-Substituted Analogues SO 2 , OS 2 , and S 3 : Correlation between Their Biradical Character and Molecular Properties

We investigate the bonding mechanism in ozone (O 3 ) and its sulfur-substituted analogues, SO 2 , OS 2 , and S 3 . By analyzing their ground-state multireference configuration interaction wave functions, we demonstrate that the bonding in these systems can be represented as a mixture of a closed-shell structure with one and a half bonds between the central and terminal atoms and an open-shell structure with a single bond and two lone electrons on each terminal atom (biradical). The biradical character (β) further emerges as a simple measure of the relative contribution of those two classical Lewis structures emanating from the interpretation of the respective wave functions. Our analysis yields a biradical character of 3.5% for OSO, 4.4% for SSO, 11% for S 3 , 18% for O 3 , 26% for SOO, and 35% for SOS. The size/electronegativity of the end atoms relative to the central one is the prevalent factor for determining the magnitude of β: smaller and more electronegative central atoms better accommodate a pair of electrons facilitating the localization of the remaining two lone π-electrons on each of the end atoms, therefore increasing the weight of the second picture in the mixed bonding scenario (larger β). The proposed mixture of these two bonding scenarios allows for the definition of the bond order of the covalent bonds being (3-β)/2, and this accounts for the different O–O, S–S, or S–O bond lengths in the triatomic series. The biradical character was furthermore found to be a useful concept for explaining several structural and energetic trends in the series: larger values of β mark a smaller singlet–triplet splitting, closer bond lengths in the ground 1 A' and the first excited 3 A' states, and larger bond dissociation and atomization energies in the ground state. Finally, the latter explains the relative energy difference between the OSS/SOS and OOS/OSO isomers due to their different β values.

Miliordos, Evangelos↗