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NASA NTRS1990

Theory of biaxial graded-index optical fiber

A biaxial graded-index fiber with a homogeneous cladding is studied. Two methods, wave equation and matrix differential equation, of formulating the problem and their respective solutions are discussed. For the wave equation formulation of the problem it is shown that for the case of a diagonal permittivity tensor the longitudinal electric and magnetic fields satisfy a pair of coupled second-order differential equations. Also, a generalized dispersion relation is derived in terms of the solutions for the longitudinal electric and magnetic fields. For the case of a step-index fiber, either isotropic or uniaxial, these differential equations can be solved exactly in terms of Bessel functions. For the cases of an istropic graded-index and a uniaxial graded-index fiber, a solution using the Wentzel, Krammers and Brillouin (WKB) approximation technique is shown. Results for some particular permittivity profiles are presented. Also the WKB solutions is compared with the vector solution found by Kurtz and Streifer. For the matrix formulation it is shown that the tangential components of the electric and magnetic fields satisfy a system of four first-order differential equations which can be conveniently written in matrix form. For the special case of meridional modes, the system of equations splits into two systems of two equations. A general iterative technique, asymptotic partitioning of systems of equations, for solving systems of differential equations is presented. As a simple example, Bessel's differential equation is written in matrix form and is solved using this asymptotic technique. Low order solutions for particular examples of a biaxial and uniaxial graded-index fiber are presented. Finally numerical results obtained using the asymptotic technique are presented for particular examples of isotropic and uniaxial step-index fibers and isotropic, uniaxial and biaxial graded-index fibers.

Kawalko, Stephen F.↗
DOE OSTI2024

A data-driven framework for predicting machining stability: employing simulated data, operational modal analysis, and enhanced transfer learning

Chatter, a self-excited vibration phenomenon, presents a significant challenge in machining operations, particularly in high-speed milling, where it can degrade tool life, reduce material removal efficiency, and compromise workpiece quality. Addressing this challenge requires a reliable predictive model that can accommodate the complex dynamics of various machining scenarios. This study introduces a novel, data-driven approach to predicting machining stability, leveraging over 140,000 simulated datasets and employing advanced techniques such as operational modal analysis (OMA), enhanced transfer learning (TL), and receptance coupling substructure analysis (RCSA). By integrating these methodologies, the framework effectively classifies and predicts chatter across diverse operational modes, achieving robust and accurate outcomes. Our model utilizes a Random Forest (RF) classifier trained with the comprehensive dataset, which demonstrates substantial improvements in both predictive accuracy and robustness. Specifically, the RF model achieved an accuracy rate of 85%, an area under the curve (AUC) of 0.90, and an F1 score of 0.88, underscoring its capability to adapt to varying machining configurations. These results highlight the framework’s potential to enhance operational efficiency and machining quality by providing reliable chatter predictions across a broad range of machining parameters. In conclusion, this research thus offers a significant advancement in predictive maintenance for machining processes, enabling more stable and efficient manufacturing operations.

42 ENGINEERING↗
DOE OSTI2023

Search for Higgs boson pairs decaying to WW*WW*, WW* ττ , and ττττ in proton-proton collisions at $ \sqrt{s} $ = 13 TeV

The results of a search for Higgs boson pair (HH) production in the WW*WW*, WW*$ττ$, and $ττττ$ decay modes are presented. The search uses 138 fb –1 of proton-proton collision data recorded by the CMS experiment at the LHC at a center-of-mass energy of 13 TeV from 2016 to 2018. Analyzed events contain two, three, or four reconstructed leptons, including electrons, muons, and hadronically decaying tau leptons. No evidence for a signal is found in the data. Upper limits are set on the cross section for nonresonant HH production, as well as resonant production in which a new heavy particle decays to a pair of Higgs bosons. For nonresonant production, the observed (expected) upper limit on the cross section at 95% confidence level (CL) is 21.3 (19.4) times the standard model (SM) prediction. The observed (expected) ratio of the trilinear Higgs boson self-coupling to its value in the SM is constrained to be within the interval –6.9 to 11.1 (–6.9 to 11.7) at 95% CL, and limits are set on a variety of new-physics models using an effective field theory approach. The observed (expected) limits on the cross section for resonant HH production range from 0.18 to 0.90 (0.08 to 1.06) pb at 95% CL for new heavy-particle masses in the range 250–1000 GeV.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Higgs-confinement transitions in QCD from symmetry protected topological phases

In gauge theories with fundamental matter there is typically no sharp way to distinguish confining and Higgs regimes, e.g. using generalized global symmetries acting on loop order parameters. It is standard lore that these two regimes are continuously connected, as has been explicitly demonstrated in certain lattice and continuum models. We point out that Higgsing and confinement sometimes lead to distinct symmetry protected topological (SPT) phases -- necessarily separated by a phase transition -- for ordinary global symmetries. We present explicit examples in 3+1 dimensions, obtained by adding elementary Higgs fields and Yukawa couplings to QCD while preserving parity P and time reversal T. In a suitable scheme, the confining phases of these theories are trivial SPTs, while their Higgs phases are characterized by non-trivial P- and T-invariant theta-angles θ f , θ g = π for flavor or gravity background gauge fields, i.e. they are topological insulators or superconductors. Finally, we consider conventional three-flavor QCD (without elementary Higgs fields) at finite U(1) B baryon-number chemical potential μ B , which preserves P and T. At very large μ B , three-flavor QCD is known to be a completely Higgsed color superconductor that also spontaneously breaks U(1) B . We argue that this high-density phase is in fact a gapless SPT, with a gravitational theta-angle θ g = π that safely co-exists with the U(1) B Nambu-Goldstone boson. We explain why this SPT motivates unexpected transitions in the QCD phase diagram, as well as anomalous surface modes at the boundary of quark-matter cores inside neutron stars.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Quasiparticle description of angle-resolved photoemission spectroscopy for SrCuO 2

SrCuO 2 has long been considered a near-archetypal realization of a quasi-one-dimensional (1D) system of interacting electrons with short-range interactions. Within this framework, experimental observations - interpreted through the lens of the 1D Hubbard model - suggest that electron and hole excitations decay into two types of (unphysical) collective bosonic modes: "spinons", which carry the spin degree of freedom, and "holons", which carry the charge degree of freedom. This model, known as spin-charge separation, is most directly evidenced by angle-resolved photoemission spectroscopy (ARPES), where a photo-induced hole decays into a continuum of these excitations. Here we present an alternative perspective grounded in first-principles, self-consistent, and parameter-free many-body perturbation theory. In this revised quasiparticle framework, ARPES can be understood as a one-body effect arising from mild disorder in a long-range antiferromagnetic ground state. the emergence of the so-called spinon branch arises naturally from spin disorder, the anomalous linewidths are accurately captured, and we provide a compelling explanation for the spectral weight observed at the non-magnetic zone boundary. This reinterpretation provides a unified explanation for key experimental signatures previously attributed to spin-charge separation, including features observed in optical conductivity. Additionally, we show that SrCuO 2 exhibits a nontrivial interchain coupling that significantly influences both its one-particle and two-particle spectral functions. By comparing the spectral features of SrCuO 2 with those of La 2 CuO 4 , we argue that SrCuO 2 shares notable similarities with the two-dimensional cuprates-both being rooted in a common CuO 4 plaquette-based molecular orbital framework.

1D cuprates↗
NASA NTRS1993

A numerical study of wave propagation in a confined mixing layer by eigenfunction expansions

It is well known that the growth rate of instability waves of a two-dimensional free shear layer is reduced greatly at supersonic convective Mach numbers. In previous works, it has been shown that new wave modes exist when the shear layers are bounded by a channel due to the coupling effect between the acoustic wave modes and the motion of the mixing layer. The present work studies the simultaneous propagation of multiple stability waves using numerical simulation. It is shown here that the coexistence of two wave modes in the flow field can lead to an oscillatory growth of disturbance energy with each individual wave mode propagating linearly. This is particularly important when the growth rates of the unstable waves are small. It is also shown here that the propagation of two neutrally stable wave modes can lead to a stationary periodic structure of rms fluctuations. In the numerical simulations presented here the forced wave modes are propagating at same frequency, but with different phase velocities. In order to track the growth of each wave mode as it propagates downstream, a numerical method that can effectively detect and separate the contribution of the individual wave is given. It is demonstrated that by a least square fitting of the disturbance field with eigenfunctions the amplitude of each wave mode can be found. Satisfactory results as compared to linear theory are obtained.

Hu, Fang Q.↗
DOE OSTI2026

Propagation of elastic waves in a flexomagnetic solid

Flexomagnetism is the coupling between magnetism and strain gradients and is a technologically relevant phenomenon. We present a theory of elastic wave propagation in a linear elastic flexomagnetic material with microstructure and strain gradient elastic interactions. The expressions of frequency, phase velocity, and group velocity of longitudinal and transverse waves are derived and are shown to depend on the flexomagnetic coefficient and microstructure. We also show that the effect of flexomagnetism and microstructure can lead to some interesting phenomena in wave propagation, which are not observed in classical linear elasticity theory of waves. Specifically, in contrast to classical linear elastic materials, where wave propagation is non-dispersive, flexomagnetic materials with microstructure can exhibit both normal and abnormal dispersion. It is also noteworthy that, in flexomagnetic materials with gradient elasticity, the phase velocities of transverse waves can exceed those of longitudinal waves, which is atypical in classical elasticity. Furthermore, waves can also attenuate for a certain range of wavenumbers that depend on the flexomagnetic coefficient and microstructural parameters. Finally, we explore the possibility of waves exhibiting zero group velocity modes, where waves are non-propagating but have strong local energy confinement, negative group velocity modes, where the wave packet moves in the opposite direction to that of wave propagation, and the phenomenon of wave freezing, where a propagating wave stops in space without diffusing or spreading.

Ghosh, Swarnava [ORNL] (ORCID:0000000338005264)↗
DOE OSTI2026

Fingerprinting Uranium Oxides with Electron Energy Loss Spectroscopy Supported by Theoretical Computations

Uranium oxides occur in a variety of phases that differ in crystal structure and uranium oxidation states. Electron energy loss spectroscopy (EELS) is one of the few techniques that has sufficient spatial resolution and sensitivity to electronic structure to distinguish amongst phases at the nanoscale. However, beam-sensitive materials such as uranium oxides are subject to spectral modification due to interactions with the electron beam. Therefore, theory support is essential to reliably exclude the impact of beam damage and generate true reference datasets. Here we use a comparison of theoretical and experimental spectra to probe the impact of beam damage on O K-edge and U N-edge (N6,7 and N4,5) EELS spectra of various single-valent and mixed-valence uranium oxide bulk phases. Using a low-dose experimental set-up, we show that the O K-edge theoretical spectra are in excellent agreement with experiment for both peak positions and relative intensities of respective peaks. In contrast, U N-edge features are less distinguishing due to the partially localized nature of the U 5f orbitals and overlapping multiplet and spin–orbit coupling effects. This work demonstrates that O K-edge EELS is sufficiently diagnostic to distinguish a wide range of uranium oxides and that the experimental approach used here minimizes beam damage and allows valence state discrimination across the U(IV), U(V) and U(VI) series. When combined with imaging modes available in electron mi-croscopy, the work enables detailed investigation and characterization of uranium redox transformations at the nanoscale.

Carbone, Jacopo↗
DOE OSTI2025

Direct reactions with the AT-TPC

Direct reactions are crucial tools for accessing properties of the atomic nucleus. Fundamental and exotic phenomena such as collective modes, pairing, weakbinding effects and evolution of single-particles energies can be investigated in peripheral collisions between a heavy nucleus and a light target. The necessity of using inverse kinematics to reveal how these structural properties change with isospin imbalance renders direct reactions a challenging technique when using the missing mass method. In this scenario, Active Target Time Projection Chambers (AT-TPC) have demonstrated an outstanding performance in enabling these types of reactions even under conditions of very low beam intensities. The AT-TPC of the Facility for Rare Isotope Beams (FRIB) is a next generation multipurpose Active Target. When operated inside a solenoidal magnet, direct reactions benefit from the measurement of the magnetic rigidity that enables particle identification and the determination of the excitation energy with high resolution without the need of auxiliary detectors. Additionally, the AT-TPC can be coupled to a magnetic spectrometer improving even further its spectroscopic investigation capability. In this contribution, we discuss inelastic scattering and transfer reaction data obtained via the AT-TPC and compare them to theory. In particular, we present the results for the 14 C(p,p′) and 12 Be (p,d) 11 Be reactions. For 14 C, we compare the experimental excitation energy of the first 1 – excited state with coupled-cluster calculationsbased on nuclear interactions from chiral effective field theory and with available shell-model predictions. For 12 Be, we determine the theoretical spectroscopic factors of the 12 Be (p,d) 11 Be transfer reaction in the shell modeland compare them to the experimental excitation spectrum from a qualitative standpoint.

active target↗
NASA NTRS2005

Influence of Compression and Shear on the Strength of Composite Laminates With Z-Pinned Reinforcement

The influence of compression and shear loads on the strength of composite laminates with z-pins is evaluated parametrically using a 2D Finite Element Code (FLASH) based on Cosserat couple stress theory. Meshes were generated for three unique combinations of z-pin diameter and density. A laminated plate theory analysis was performed on several layups to determine the bi-axial stresses in the zero degree plies. These stresses, in turn, were used to determine the magnitude of the relative load steps prescribed in the FLASH analyses. Results indicated that increasing pin density was more detrimental to in-plane compression strength than increasing pin diameter. Compression strengths of lamina without z-pins agreed well with a closed form expression derived by Budiansky and Fleck. FLASH results for lamina with z-pins were consistent with the closed form results, and FLASH results without z-pins, if the initial fiber waviness due to z-pin insertion was added to the fiber waviness in the material to yield a total misalignment. Addition of 10% shear to the compression loading significantly reduced the lamina strength compared to pure compression loading. Addition of 50% shear to the compression indicated shear yielding rather than kink band formation as the likely failure mode. Two different stiffener reinforced skin configurations with z-pins, one quasi-isotropic and one orthotropic, were also analyzed. Six unique loading cases ranging from pure compression to compression plus 50% shear were analyzed assuming material fiber waviness misalignment angles of 0, 1, and 2 degrees. Compression strength decreased with increased shear loading for both configurations, with the quasi-isotropic configuration yielding lower strengths than the orthotropic configuration.

OBrien, T. Kevin↗
NASA NTRS2005

Influence of Compression and Shear on the Strength of Composite Laminates with Z-Pinned Reinforcement

The influence of compression and shear loads on the strength of composite laminates with z-pins is evaluated parametrically using a 2D Finite Element Code (FLASH) based on Cosserat couple stress theory. Meshes were generated for three unique combinations of z-pin diameter and density. A laminated plate theory analysis was performed on several layups to determine the bi-axial stresses in the zero degree plies. These stresses, in turn, were used to determine the magnitude of the relative load steps prescribed in the FLASH analyses. Results indicated that increasing pin density was more detrimental to in-plane compression strength than increasing pin diameter. Compression strengths of lamina without z-pins agreed well with a closed form expression derived by Budiansky and Fleck. FLASH results for lamina with z-pins were consistent with the closed form results, and FLASH results without z-pins, if the initial fiber waviness due to z-pin insertion was added to the fiber waviness in the material to yield a total misalignment. Addition of 10% shear to the compression loading significantly reduced the lamina strength compared to pure compression loading. Addition of 50% shear to the compression indicated shear yielding rather than kink band formation as the likely failure mode. Two different stiffener reinforced skin configurations with z-pins, one quaiisotropic and one orthotropic, were also analyzed. Six unique loading cases ranging from pure compression to compression plus 50% shear were analyzed assuming material fiber waviness misalignment angles of 0, 1, and 2 degrees. Compression strength decreased with increased shear loading for both configurations, with the quasi-isotropic configuration yielding lower strengths than the orthotropic configuration.

O'Brien, T. Kevin↗
DOE OSTI2024

First-principles investigation of elastic, vibrational, and thermodynamic properties of kagome metals CsM 3 Te 5 (M = Ti, Zr, Hf)

Kagome metals are a unique class of quantum materials characterized by their distinct atomic lattice arrangement, featuring interlocking triangles and expansive hexagonal voids. These lattice structures impart exotic properties, including superconductivity, interaction-driven topological many-body phenomena, and magnetism, among others. The kagome metal CsM 3 ⁢Te 5 (where M = Ti, Zr, or Hf) exhibits both superconductivity and nontrivial topological electronic properties, offering a promising platform for exploring topological superconductivity. This study employs first-principles density functional theory calculations to systematically analyze the elastic, mechanical, vibrational, thermodynamic, and electronic properties of CsM 3 ⁢Te 5 (M = Ti, Zr, Hf). Our calculations reveal that the studied compounds—CsTi 3 ⁢Te 5 , CsZr 3 ⁢Te 5 , and CsHf 3 ⁢Te 5 —are ductile metals with elastic properties akin to the hexagonal Bi and Sb, with average elastic constants, including a bulk modulus of 27 GPa, a shear modulus of 11 GPa, and Young's modulus of 29 GPa. We observe peculiar dispersionless, flat, phonon branches in the vibrational spectra of these metals. Additionally, we thoroughly analyze the symmetries of the zone-center phonon eigenvectors and predict vibrational fingerprints of the Raman- and infrared-active phonon modes. The analysis of thermodynamic properties reveals the Einstein temperature for CsTi 3 ⁢Te 5 , CsZr 3 ⁢Te 5 , and CsHf 3 ⁢Te 5 to be 66, 54, and 53 K, respectively. Our orbital-decomposed electronic structure calculations reveal significant in-plane steric interactions and multiple Dirac band crossings near the Fermi level. We further investigate the role of spin-orbit coupling effect on the studied properties. Furthermore, this theoretical investigation sheds light on the intriguing quantum behavior of kagome metals.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Predictive Design of Hybrid Improper Ferroelectric Double Perovskite Oxides

The computational design of suitable multiferroic double perovskite oxides requires finding materials that exhibit sizable polarization, magnetization, and coupling between them. Oxides with the chemical formula of AA'BB'O 6 with building blocks of ABO 3 single perovskite oxides in centrosymmetric Pnma symmetry are strong candidates that have been reported to satisfy such criteria. The system lowers to noncentrosymmetric, polar P2 1 symmetry if A/A' layered and B/B' rocksalt cation orderings are imposed. A detailed compositional search over a variety of chemical spaces followed by evaluating their polarization may lead to the identification of more of these compounds with ferroelectric ordering. The standard density functional theory practices to estimate polarization within the Berry phase formalism require the systems to be perfectly insulating. The number of compounds that can be evaluated using this method is therefore limited. In this work, we introduce a predictive learning strategy based on importance sampling to build a series of machine learning models using results from first-principles simulations to predict polarization and the corresponding switching barrier. The geometry-driven features related to charge states and cationic radii play key roles in predicting the switching barrier with complementary contributions from the key structural mode-based order parameters. These modes become important to draw reasonable predictions of polarization components from machine learning models. In conclusion, our predictive models identify candidates with high polarizations and low switching barriers from a pool of double perovskite oxides, suitable for future investigation for their potential applications in spintronic devices.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Stabilization of kink/peeling modes by coupled rotation and ion diamagnetic drift effects in quiescent H-mode plasmas in DIII-D and JT-60U

Magnetohydrodynamic stability at the edge pedestal in several quiescent H-mode (QH-mode) plasmas in DIII-D and JT-60U experiments was analyzed by considering plasma rotation and ion diamagnetic drift effects. It was identified that a kink/peeling mode, which is a prime candidate for a trigger of edge harmonic oscillation in QH-mode, is stabilized by plasma rotation when considering the ion diamagnetic drift simultaneously in both experiments. Furthermore, the stabilizing effect by rotation becomes more effective in case using the rotation profile of the main ion species evaluated by assuming radial force balance. In addition, when inverting the rotation direction, it was found that the kink/peeling mode is more stabilized when considering the rotation of the main ion species, though the mode is less stabilized by the rotation of impurity ion species. The result implies that the kink/peeling mode stability in QH-mode plasmas is sensitive to how the rotation profile is evaluated, but it is shown that a qualitative trend stabilizing the kink/peeling mode by rotation can be reproduced with the poloidal rotation profile of an impurity predicted numerically based on the neoclassical theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Spin pumping from antiferromagnetic insulator spin-orbit-proximitized by adjacent heavy metal: a first-principles Floquet-nonequilibrium Green function study

Motivated by the recent experiment on spin pumping from sub-THz radiation-driven uniaxial antiferromagnetic insulator (AFI) MnF 2 into heavy metal (HM) Pt hosting strong spin-orbit (SO) coupling, we compute and compare pumped spin currents in Cu/MnF 2 /Cu and Pt/MnF 2 /Cu heterostructures. Recent theories of spin pumping by AFI have relied on simplistic Hamiltonians (such as tight-binding) and the scattering approach to quantum transport yielding the so-called interfacial spin mixing conductance (SMC), but the concept of SMC ceases to be applicable when SO coupling is present directly at the interface. In contrast, we use a more general first-principles quantum transport approach which combines noncollinear density functional theory with Floquet-nonequilibrium Green's functions in order to take into account: SO-proximitized AFI as a new type of quantum material, different from isolated AFI and brought about by AFI hybridization with adjacent HM layer; strong SO coupling at the interface; and evanescent wavefunctions penetrating from Pt or Cu into AFI layer to make its interfacial region conducting rather than insulating as in the isolated AFI. The DC component of pumped spin current $I_\mathrm{DC}^{S_z}$ vs. precession cone angle $\theta_{\boldsymbol{l}}$ of the Néel vector l of AFI does not follow putative $I^{S_z}_\mathrm{DC} \propto \sin^2 \theta_{\boldsymbol{l}}$, except for very small angles $\theta_{\boldsymbol{l}} \lesssim 10^\circ$ for which we define an effective SMC from the prefactor and find that it doubles from MnF2/Cu to MnF2/Pt interface. In addition, the angular dependence $I^{S_z}_\mathrm{DC}(\theta_{\boldsymbol{l}})$ differs for opposite directions of precession of the Néel vector, leading to twice as large SMC for the right-handed than for the left-handed chirality of the precession mode.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Designing a validation experiment for radio frequency condensation

Abstract Theoretical studies have suggested that nonlinear effects can lead to ‘radio frequency (RF) condensation’, where an initially broad current profile can coalesce in islands when they reach sufficient width. In suitable conditions, RF condensation can ‘self-focus’ the driven current to the center of an island, improving stabilization efficiency and reducing control complexity. In unsuitable conditions, the effect can prematurely deplete the RF energy before it reaches the island center, impairing stabilization. It is predicted that the RF condensation effect can significantly impact reactor-scale tokamaks. This paper presents a set of simulations investigating the conditions under which RF condensation might be encountered in present-day tokamaks. For concreteness, the calculations use equilibrium reconstructions for two shots from DIII-D and AUG. The Current Condensation Amid Magnetic Islands (OCCAMI) simulation code has been used for this investigation. The code takes as its input a numerically specified axisymmetric EFIT equilibrium solution, and it perturbatively constructs a 3D field with an island embedded at the appropriate rational surface. In the OCCAMI code, the GENRAY code is used for ray tracing and for calculating the power deposition along a ray trajectory, and GENRAY is coupled self-consistently to a solution of the thermal diffusion equation in the island. The simulation results described in the paper illuminate the conditions required for experimental validation of the theory of RF condensation. The simulations also provide an explanation of why the effect was not noticed in experiments prior to the publication of theoretical papers on the subject.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Aeroelastic oscillations of a pitching flexible wing with structural geometric nonlinearities: Theory and numerical simulation

In this paper, we focus on the derivation of an analytical model of the aeroelastic dynamics of an elastically mounted flexible wing. This equations of motion obtained serve to help understand the behaviour of the aeroelastic wind tunnel setup in question, which consists of a rectangular wing with a uniform NACA 0012 airfoil profile, whose base is free to rotate rigidly about a longitudinal axis. Of particular interest are the structural geometric nonlinearities primarily introduced by the coupling between the rigid body pitch degree-of-freedom and the continuous system. A coupled system of partial differential equations (PDEs) coupled with an ordinary differential equation (ODE) describing axial-bending-bending-torsion-pitch motion is derived using Hamilton's principle. A finite dimensional approximation of the system of coupled differential equations is obtained using the Galerkin method, leading to a system of coupled nonlinear ODEs. Subsequently, these nonlinear ODEs are solved numerically using Houbolt's method. The results that are obtained are verified by comparison with the results obtained by direct integration of the equations of motion using a finite difference scheme. Adopting a linear unsteady aerodynamic model, it is observed that the system undergoes coalescence flutter due to coupling between the rigid body pitch rotation dominated mode and the first flapwise bending dominated mode. Finally, the behaviour of the limit cycle oscillations is primarily influenced by the structural geometric nonlinear terms in the coupled system of PDEs and ODE.

42 ENGINEERING↗
NASA NTRS1997

Positive Anharmonicities: The Oxonide Anion as an Example

An accurate ab initio quartic force field for the ozonide anion has been determined at the singles and doubles coupled-cluster level of theory that includes a perturbational estimate of the effects of connected triple excitations, denoted CCSD(T), using the augmented valence triple-zeta correlation consistent one-particle basis set. Convergence of the harmonic frequencies with respect to the one-particle basis set has been demonstrated by computing quadratic force fields at the CCSD(T) level using augmented valence double-zeta and quadruple-zeta basis sets. Fundamental vibrational frequencies have been determined via second-order ro-vibrational perturbation theory and also using exact variational methods. Agreement is very good, and they both show that the antisymmetric O-O stretch, v 3, possesses a positive anharmonic correction (that is, the fundamental frequency is predicted to be higher in energy than the harmonic frequency). Comparison of the O_3 and O3 quartic force fields shows that the positive anharmonic correction is the result of a particularly large F3333 symmetry internal coordinate force constant. The reasonableness of this force constant has been tested by computing both F33 and F3333 at the CCSD, CCSD(T), and CASPT2 levels of theory. A discussion of known positive anharmonicities for stretching modes is presented.

Lee, Timothy J.↗