Search NASA⌕ Search

SEARCH · Search NASA

Results for “Angular Reference”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 325 records · Page 18

Transport of absolute angular momentum in quasi-axisymmetric equatorial jet streams

It is well known that prograde equatorial jet stresses cannot occur in an axisymmetric inviscid fluid, owing to the constraints of local angular momentum conservation. For a viscous fluid, the constraints of mass conservation prevent the formation of any local maximum of absolute angular momentum (m) without a means of transferring m against its gradient (delta m) in the meridional plane. The circumstances under which m can be diffused up-gradient by normal molecular viscosity are derived, and illustrated with reference to numerical simulations of axisymmetric flows in a cylindrical annulus. Viscosity is shown to act so as to tend to expel m from the interior outwards from the rotation axis. Such an effect can produce local super-rotation even in a mechanically isolated fluid. The tendency of viscosity to result in the expulsion of m is shown to be analogous in certain respects to a vorticity-mixing hypothesis for the effects of non-axisymmetric eddies of the zonally-averaged flow. It is shown how the advective and diffusive transport of m by non-axisymmetric eddies can be represented by the Transformed Eulerian Mean meridional circulation and the Eliassen-Palm (EP) flux of Andrews and McIntyre respectively, in the zonal mean. Constraints on the form and direction of the EP flux in an advective/diffusive flow for such eddies are derived, by analogy with similar constraints on the diffusive flux of m due to viscosity.

Read, P. L.↗

Method for determining shear direction using liquid crystal coatings

A method is provided for determining shear direction wherein a beam of white light is directed onto the surface of a liquid crystal coating to cause the white light to be dispersed (reflected) from the surface in a spectrum having bands of different colors in a fixed spatial 2 (angular) sequence. The system is calibrated by locating an observer, e.g., a video and movie camera, such that a particular color band (preferably at or near the center of the reflected spectrum) is observed to thereby provide a reference color band. Because the application of shear causes either clockwise or counterclockwise rotation of the reflected spectrum dependent on the direction of the shear, a determination is then made of the reflected color band observed by the observer when the surface of the liquid crystal is subjected to shear to thereby determine the direction of the shear based on the directional (rotation) relation of the observed color band with respect to the reference color band in the spatial sequence of color bands.

Reda, Daniel C.↗

Consequences of air around an ionization chamber: Are existing solid phantoms suitable for reference dosimetry on an MR-linac?

Purpose: A protocol for reference dosimetry for the MR-linac is under development. The 1.5 T magnetic field changes the mean path length of electrons in an air-filled ionization chamber but has little effect on the electron trajectories in a surrounding phantom. It is therefore necessary to correct the response of an ionization chamber for the influence of the magnetic field. Solid phantoms are used for dosimetry measurements on the MR-linac, but air is present between the chamber wall and phantom insert. This study aimed to determine if this air influences the ion chamber measurements on the MR-linac. The absolute response of the chamber and reproducibility of dosimetry measurements were assessed on an MR-linac in solid and water phantoms. The sensitivity of the chamber response to the distribution of air around the chamber was also investigated. Methods: Measurements were performed on an MR-linac and replicated on a conventional linac for five chambers. The response of three waterproof chambers was measured with air and with water between the chamber and the insert to measure the influence of the air volume on absolute chamber response. The distribution of air around the chamber was varied indirectly by rotating each chamber about the longitudinal chamber axis in a solid phantom and a water phantom (waterproof chambers only) and measuring the angular dependence of the chamber response, and varied directly by displacing the chamber in the phantom insert using a paper shim positioned at different orientations between the chamber casing and the insert. Results: The responses of the three waterproof chambers measured on the MR-linac were 0.7%–1.2% higher with water than air in the chamber insert. The responses of the chambers on the conventional linac changed by less than 0.3% when air in the insert was replaced with water. The angular dependence of the chambers ranged from 0.6% to 1.9% in the solid phantom on the MR-linac but was less than 0.5% in water on the MR-linac and less than 0.3% in the solid phantom on the conventional linac. Inserting a shim around the chamber induced changes of the chamber response in a magnetic field of up to 2.2%, but the change in chamber response on the conventional linac was less than 0.3%. Conclusions: The interaction between the magnetic field and secondary electrons in the air around the chamber reduces the charge collected from 0.7% to 1.2%. The large angular dependence of ion chambers measured in the plastic phantom in a magnetic field appears to arise from a change of air distribution as the chamber is moved within the insert, rather than an intrinsic isotropy of the chamber sensitivity to radiation. It is recommended that reference dosimetry measurements on the MR-linac can be performed only in water, rather than in existing plastic phantoms.

60 APPLIED LIFE SCIENCES↗

A computational procedure for the dynamics of flexible beams within multibody systems

The dynamic analysis of three dimensional elastic beams which experience large rotational and large deformational motions are examined. The beam motion is modeled using an inertial reference for the translational displacements and a body-fixed reference for the rotational quantities. Finite strain rod theories are then defined in conjunction with the beam kinematic description which accounts for the effects of stretching, bending, torsion, and transverse shear deformations. A convected coordinate representation of the Cauchy stress tensor and a conjugate strain definition is introduced to model the beam deformation. To treat the beam dynamics, a two-stage modification of the central difference algorithm is presented to integrate the translational coordinates and the angular velocity vector. The angular orientation is then obtained from the application of an implicit integration algorithm to the Euler parameter/angular velocity kinematical relation. The combined developments of the objective internal force computation with the dynamic solution procedures result in the computational preservation of total energy for undamped systems. The present methodology is also extended to model the dynamics of deployment/retrieval of the flexible members. A moving spatial grid corresponding to the configuration of a deployed rigid beam is employed as a reference for the dynamic variables. A transient integration scheme which accurately accounts for the deforming spatial grid is derived from a space-time finite element discretization of a Hamiltonian variational statement. The computational results of this general deforming finite element beam formulation are compared to reported results for a planar inverse-spaghetti problem.

Downer, Janice Diane↗

A synthetic diamond diode in volumetric modulated arc therapy dosimetry

Purpose: The aim of this work is to investigate the behavior of a single crystal diamond diode (SCDD) for volumetric modulated arc therapy (VMAT) dose verifications. This delivery technique is one of the most severe test of a dosimeter performance due to the modulation of the dose rate achieved by simultaneously changing the velocity of the gantry and the position of the collimator leaves. The performed measurements with VMAT photon beams can therefore contribute to an overall global validation of the device to be used in dose distribution verifications.Methods: The SCDD response to 6 MVRX has been tested and compared with reference ionization chambers and treatment planning system (TPS) calculations in different experiments: (a) measurements of output factors for small field sizes (square fields of side ranging between 8 mm and 104 mm) by SCDD and A1SL ionization chamber; (b) angular dependence evaluation of the entire experimental set-up by SCDD, A1SL, and Farmer ionization chambers; and (c) acquisition of dose profiles for a VMAT treatment of a pulmonary disease in latero-lateral and gantry-target directions by SCDD and A1SL ionization chamber.Results: The output factors measured by SCDD favorably compare with the ones obtained by A1SL, whose response is affected by the lack of charged particle equilibrium and by averaging effect when small fields are involved. From the experiment on angular dependence, a good agreement is observed among the diamond diode, the ion chambers, and the TPS. In VMAT profiles, the absorbed doses measured by SCDD and A1SL compare well with the TPS calculated ones. An overall better agreement is observed in the case of the diamond dosimeter, which is also showing a better accuracy in terms of distance to agreement in the high gradient regions.Conclusions: Synthetic diamond diodes, whose performance were previously studied for conformal and IMRT radiotherapy techniques, were found to be suitable detectors also for dosimetric measurements in volumetric arc therapy treatments.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Decentralized control experiments on NASA's flexible grid

Methods arising from the area of decentralized control are emerging for analysis and control synthesis for large flexible structures. In this paper the control strategy involves a decentralized model reference adaptive approach using a variable structure control. Local models are formulated based on desired damping and response time in a model-following scheme for various modal configurations. Variable structure controllers are then designed employing co-located angular rate and position feedback. In this scheme local control forces the system to move on a local sliding mode in some local error space. An important feature of this approach is that the local subsystem is made insensitive to dynamical interactions with other subsystems once the sliding surface is reached. Experiments based on the above have been performed for NASA's flexible grid experimental apparatus. The grid is designed to admit appreciable low-frequency structural dynamics, and allows for implementation of distributed computing components, inertial sensors, and actuation devices. A finite-element analysis of the grid provides the model for control system design and simulation; results of several simulations are reported on here, and a discussion of application experiments on the apparatus is presented.

Ozguner, U.↗

Rotor control system

A helicopter rotor control system (13) including a stop azimuth controller (32) for establishing the value of a deceleration command (15') to a deceleration controller (23), a transition azimuth predictor (41) and a position reference generator (55), which are effective during the last revolution of said rotor (14) to establish a correction indication (38) to adjust the deceleration command (15') to ensure that one of the rotor blades (27) stops at a predetermined angular position.

Bradford, Michael P.↗

Generalization of Equivalent Crystal Theory to Include Angular Dependence

In the original Equivalent Crystal Theory, each atomic site in the real crystal is assigned an equivalent lattice constant, in general different from the ground state one. This parameter corresponds to a local compression or expansion of the lattice. The basic method considers these volumetric transformations and, in addition, introduces the possibility that the reference lattice is anisotropically distorted. These distortions however, were introduced ad-hoc. In this work, we generalize the original Equivalent Crystal Theory by systematically introducing site-dependent directional distortions of the lattice, whose corresponding distortions account for the dependence of the energy on anisotropic local density variations. This is done in the spirit of the original framework, but including a gradient term in the density. This approach is introduced to correct a deficiency in the original Equivalent Crystal Theory and other semiempirical methods in quantitatively obtaining the correct ratios of the surface energies of low index planes of cubic metals (100), (110), and (111). We develop here the basic framework, and apply it to the calculation of Fe (110) and Fe (111) surface energy formation. The results, compared with first principles calculations, show an improvement over previous semiempirical approaches.

Ferrante, John↗

ACOUSTIC SCALE FROM THE ANGULAR POWER SPECTRA OF SDSS-III DR8 PHOTOMETRIC LUMINOUS GALAXIES

We measure the acoustic scale from the angular power spectra of the Sloan Digital Sky Survey III (SDSS-III) Data Release 8 imaging catalog that includes 872, 921 galaxies over {approx}10,000 deg{sup 2} between 0.45 < z < 0.65. The extensive spectroscopic training set of the Baryon Oscillation Spectroscopic Survey luminous galaxies allows precise estimates of the true redshift distributions of galaxies in our imaging catalog. Utilizing the redshift distribution information, we build templates and fit to the power spectra of the data, which are measured in our companion paper, to derive the location of Baryon acoustic oscillations (BAOs) while marginalizing over many free parameters to exclude nearly all of the non-BAO signal. We derive the ratio of the angular diameter distance to the sound horizon scale D{sub A} (z)/r{sub s} = 9.212{sup +0.416}{sub -{sub 0.404}} at z = 0.54, and therefore D{sub A} (z) = 1411 {+-} 65 Mpc at z = 0.54; the result is fairly independent of assumptions on the underlying cosmology. Our measurement of angular diameter distance D{sub A} (z) is 1.4{sigma} higher than what is expected for the concordance {Lambda}CDM, in accordance to the trend of other spectroscopic BAO measurements for z {approx}> 0.35. We report constraints on cosmological parameters from our measurement in combination with the WMAP7 data and the previous spectroscopic BAO measurements of SDSS and WiggleZ. We refer to our companion papers (Ho et al.; de Putter et al.) for investigations on information of the full power spectrum.

79 ASTRONOMY AND ASTROPHYSICS↗

Estimating the Inertia Matrix of a Spacecraft

A paper presents a method of utilizing some flight data, aboard a spacecraft that includes reaction wheels for attitude control, to estimate the inertia matrix of the spacecraft. The required data are digitized samples of (1) the spacecraft attitude in an inertial reference frame as measured, for example, by use of a star tracker and (2) speeds of rotation of the reaction wheels, the moments of inertia of which are deemed to be known. Starting from the classical equations for conservation of angular momentum of a rigid body, the inertia-matrix-estimation problem is formulated as a constrained least-squares minimization problem with explicit bounds on the inertia matrix incorporated as linear matrix inequalities. The explicit bounds reflect physical bounds on the inertia matrix and reduce the volume of data that must be processed to obtain a solution. The resulting minimization problem is a semidefinite optimization problem that can be solved efficiently, with guaranteed convergence to the global optimum, by use of readily available algorithms. In a test case involving a model attitude platform rotating on an air bearing, it is shown that, relative to a prior method, the present method produces better estimates from few data.

Acikmese, Behcet↗

Dark Energy Survey Year 6 results: Clustering redshifts and importance sampling of self-organized-maps 𝑛⁡(𝑧) realizations for 3 × 2 ⁢pt samples

This work is part of a series establishing the redshift framework for the 3 × 2 ⁢pt analysis of the Dark Energy Survey Year 6 (DES Y6). For DES Y6, photometric redshift distributions are estimated using self-organizing maps (SOMs), calibrated with spectroscopic and many-band photometric data. To overcome limitations from color-redshift degeneracies and incomplete spectroscopic coverage, we enhance this approach by incorporating clustering-based redshift constraints (clustering-z, or WZ) from angular cross-correlations with BOSS and eBOSS galaxies and eBOSS quasar samples. We define a WZ likelihood and apply importance sampling to a large ensemble of SOM-derived 𝑛⁡(𝑧) realizations, selecting those consistent with the clustering measurements to produce a posterior sample for each lens and source bin. The analysis uses angular scales corresponding to 1.5–5 Mpc to optimize signal-to-noise ratio while mitigating modeling uncertainties and marginalizes over redshift-dependent galaxy bias and other systematics informed by the N-body simulation CARDINAL . While a sparser spectroscopic reference sample limits WZ constraining power at 𝑧 >1.1, particularly for source bins, we demonstrate that combining SOM with WZ improves redshift accuracy and enhances the overall cosmological constraining power of DES Y6. As a result, we estimate an improvement in 𝑆 8 of approximately 10% for cosmic shear and 3 ×2⁢pt analysis, primarily due to the WZ calibration of the source samples.

Cosmological parameters↗

Planar reorientation of a free-free beam in space using embedded electromechanical actuators

It is demonstrated that the planar reorientation of a free-free beam in zero gravity space can be accomplished by periodically changing the shape of the beam using embedded electromechanical actuators. The dynamics which determine the shape of the free-free beam is assumed to be characterized by the Euler-Bernoulli equation, including material damping, with appropriate boundary conditions. The coupling between the rigid body motion and the flexible motion is explained using the angular momentum expression which includes rotatory inertia and kinematically exact effects. A control scheme is proposed where the embedded actuators excite the flexible motion of the beam so that it rotates in the desired sense with respect to a fixed inertial reference. Relations are derived which relate the average rotation rate to the amplitudes and the frequencies of the periodic actuation signal and the properties of the beam. These reorientation maneuvers can be implemented by using feedback control.

Kolmanovsky, Ilya V.↗

Reference Earth Orbital Research and Applications Investigations (Blue Book). Volume 2: Astronomy

Representative astronomy objectives, experiments, facilities, and instruments for use in the space station are discussed. The specific program elements describe a coordinated multiwavelength, multisensor approach needed to locate, observe, and interpret radiation from extragalactic, galactic, solar, and planetary sources in the different parts of the spectrum with spectral, angular, and temporal resolution not achievable from earth sites. Items of astronomy equipment are identified for the experiments to be conducted.

Source record↗

On the use of DSCOVR EPIC to monitor the visible calibration stability of polar orbiting imagers to improve the next edition of the CERES climate data record.

The NASA CERES project has provided the climate quality observed TOA and computed surface fluxes to the scientific community. CERES instruments are onboard the Terra, Aqua, NPP, and NOAA-20 spacecraft. CERES uses MODIS and VIIRS imagers to retrieve cloud properties needed to convert CERES footprint radiance observations into fluxes using empirically derived angular directional models obtained during early CERES record. CERES utilizes geostationary sensors to infer the regional diurnal fluxes in between Terra and Aqua CERES observations. The imagers are also used to radiometrically scale the geostationary sensors (GEO) radiances to the imager calibration reference to ensure that the GEO derived cloud properties and broadband TOA fluxes are consistent in both space and time. Both the imager and GEO retrieved cloud properties are used to compute the surface fluxes. The Aqua-MODIS, SNPP-VIIRS, and NOAA-20 VIIRS afternoon imagers will also need to be radiometrically scaled to the same common calibration reference. Although all three imagers employ onboard solar diffusers, the calibration is not consistent over time due to instrument anomalies and ageing of the onboard calibrators. The CERES imager and GEO calibration group (IGCG) has been tasked to remove the imager channel calibration drifts for the next CERES reprocessing effort. The team will rely primarily on deep convective clouds, desert, and polar ice invariant targets to monitor the imager channel stability. The team uses ray-matched radiance pairs to radiometrically scale the SNPP and NOAA-20 VIIRS sensors to Aqua-MODIS. The radiometric scaling is further validated using geostationary imagers as transfer radiometers. The DSCOVR satellite was launched on February 25, 2015 and orbits around the L1 Lagrange point directly between the Earth and the sun. The EPIC instrument onboard DSCOVR employs a CCD array to image the Earth approximately every 2-hours. The EPIC sensor contains no onboard calibration systems. However, multiple inter-calibration studies have shown that the EPIC imager is very stable in time. This is likely due to the DSCOVR satellite being located about a 1.5M km from the Earth, where very little Earth reflected solar radiation degrades the optics. The excellent radiometric stability of EPIC allows the CERES IGCG to utilize the EPIC observations as a stable reference for monitoring the calibration stability of the three afternoon imagers, as well as to validate the radiometric scaling factors between them. Examples of the imager relative calibration using EPIC before and after radiometric scaling will be shown along with the results from the use of invariant targets to remove imager calibration drifts.

DSCOVR-EPIC↗

Raytracing the long trace profiler

The optical design of the Long Trace Profiler optical system is explored with a commercial raytrace program, Zemax OpticStudio™ (ZOS)1, with the intent of finding and correcting sources of systematic error. ZOS provides both geometric raytracing tools and physical optics Gaussian beam propagation and diffraction image calculation tools, and two design modes, sequential component (SC) and non-sequential component (NSC) that are optimized for different aspects of the design process. The original LTP-II system employs a singlet lens with a 1250 mm focal length. It is optimized to provide minimum distortion over a surface slope angle range of ±5 mrad. Using the ZOS tools, we are able to simulate ghost rays that produce distortion in the beam spot image and can minimize the distortion by deliberate misalignment of the beamsplitter (BS) components. Unfortunately, the reference beam is compromised because of the component tilts. The most recent LTP500 system design simplifies the optical system and makes the reference beam usable again, even with misalignment of the polarizing beamsplitter (PBS). Two lenses are designed for the LTP500 - a cemented doublet that has been fabricated, and a singlet with one aspheric surface. Both have focal distances of 500 mm with an expanded angular measurement range of ±10 mrad. The aspheric singlet provides superior performance. ZOS allows the import of wavefront measurement data produced by commercial interferometer software. We apply the wavefront error measurement from the cemented doublet to the model to show that the 19nm RMS wavefront error needs to be improved by at least a factor of ten in order to reduce the systematic error to a level that will allow the LTP to approach its design limit of a few tens of nanoradians.

Takacs, Peter Z.↗

SU-C-201-07: Towards Clinical Cherenkov Emission Dosimetry: Stopping Power-To-Cherenkov Power Ratios and Beam Quality Specification of Clinical Electron Beams

Purpose: We propose a Cherenkov emission (CE)-based reference dosimetry method, which in contrast to ionization chamber-based dosimetry, employs spectrum-averaged electron restricted mass collision stopping power-to-Cherenkov power ratios (SCRs), and we examine Monte Carlo-calculated SCRs and beam quality specification of clinical electron beams. Methods: The EGSnrc user code SPRRZnrc was modified to compute SCRs instead of stopping-power ratios (single medium: water; cut-off: CE threshold (observing Spencer-Attix conditions); CE power: Frank-Tamm). SCRs are calculated with BEAMnrc for realistic electron beams with nominal energies of 6–22 MeV from three Varian accelerators (TrueBeam Clinac 21EX, Clinac 2100C/D) and for mono-energetic beams of energies equal to the mean electron energy at the water surface. Sources of deviation between clinical and mono-energetic SCRs are analyzed quantitatively. A universal fit for the beam-quality index R{sub 50} in terms of the depth of 50% CE C{sub 50} is carried out. Results: SCRs at reference depth are overestimated by mono-energetic values by up to 0.2% for a 6-MeV beam and underestimated by up to 2.3% for a 22-MeV beam. The variation is mainly due to the clinical beam spectrum and photon contamination. Beam angular spread has a small effect across all depths and energies. The influence of the electron spectrum becomes increasingly significant at large depths, while at shallow depths and high beam energies photon contamination is predominant (up to 2.0%). The universal data fit reveals a strong linear correlation between R{sub 50} and C{sub 50} (ρ > 0.99999). Conclusion: CE is inherent to radiotherapy beams and can be detected outside the beam with available optical technologies, which makes it an ideal candidate for out-of-beam high-resolution 3D dosimetry. Successful clinical implementation of CE dosimetry hinges on the development of robust protocols for converting measured CE to radiation dose. Our findings constitute a key step towards clinical CE dosimetry.

60 APPLIED LIFE SCIENCES↗

Rapidly rotating neutron stars in general relativity: Realistic equations of state

We construct equilibrium sequences of rotating neutron stars in general relativity. We compare results for 14 nuclear matter equations of state. We determine a number of important physical parameters for such stars, including the maximum mass and maximum spin rate. The stability of the configurations to quasi-radial perturbations is assessed. We employ a numerical scheme particularly well suited to handle rapid rotation and large departures from spherical symmetry. We provide an extensive tabulation of models for future reference. Two classes of evolutionary sequences of fixed baryon rest mass and entropy are explored: normal sequences, which behave very much like Newtonian sequences, and supramassive sequences, which exist for neutron stars solely because of general relativistic effects. Adiabatic dissipation of energy and angular momentum causes a star to evolve in quasi-stationary fashion along an evolutionary sequence. Supramassive sequences have masses exceeding the maximum mass of a nonrotating neutron star. A supramassive star evolves toward eventual catastrophic collapse to a black hole. Prior to collapse, the star actually spins up as it loses angular momentum, an effect that may provide an observable precursor to gravitational collapse to a black hole.

Cook, Gregory B.↗

Ab initio Bogoliubov coupled cluster theory for open-shell nuclei

Background: Ab initio many-body methods have been developed over the past 10 yr to address closed-shell nuclei up to mass A≈130 on the basis of realistic two- and three-nucleon interactions. A current frontier relates to the extension of those many-body methods to the description of open-shell nuclei. Several routes to address open-shell nuclei are currently under investigation, including ideas that exploit spontaneous symmetry breaking. Purpose: Singly open-shell nuclei can be efficiently described via the sole breaking of U(1) gauge symmetry associated with particle-number conservation as a way to account for their superfluid character. While this route was recently followed within the framework of self-consistent Green's function theory, the goal of the present work is to formulate a similar extension within the framework of coupled cluster theory. Methods: We formulate and apply Bogoliubov coupled cluster (BCC) theory, which consists of representing the exact ground-state wave function of the system as the exponential of a quasiparticle excitation cluster operator acting on a Bogoliubov reference state. Equations for the ground-state energy and the cluster amplitudes are derived at the singles and doubles level (BCCSD) both algebraically and diagrammatically. The formalism includes three-nucleon forces at the normal-ordered two-body level. The first BCC code is implemented in m scheme, which will permit the treatment of doubly open-shell nuclei via the further breaking of SU(2) symmetry associated with angular momentum conservation. Results: Proof-of-principle calculations in an N max =6 spherical harmonic oscillator basis for 16,18 O and 18 Ne in the BCCD approximation are in good agreement with standard coupled cluster results with the same chiral two-nucleon interaction, while 20 O and 20 Mg display underbinding relative to experiment. The breaking of U(1) symmetry, monitored by computing the variance associated with the particle-number operator, is relatively constant for all five nuclei, in both the Hartree-Fock-Bogoliubov and BCCD approximations. Conclusions: The newly developed many-body formalism increases the potential span of ab initio calculations based on single-reference coupled cluster techniques tremendously, i.e., potentially to reach several hundred additional midmass nuclei. The new formalism offers a wealth of potential applications and further extensions dedicated to the description of ground and excited states of open-shell nuclei. Short-term goals include the implementation of three-nucleon forces at the normal-ordered two-body level. Midterm extensions include the approximate treatment of triples corrections and the development of the equation-of-motion methodology to treat both excited states and odd nuclei. Long-term extensions include exact restoration of U(1) and SU(2) symmetries.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗