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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Periodic Korteweg–de Vries soliton potentials generate quasisymmetric magnetic field strength in a finite plasma- β equilibrium

Quasisymmetry (QS) is a hidden symmetry of the magnetic field strength, B , that enables effective confinement of charged particles in a fully three-dimensional (3D) toroidal plasma equilibrium. Such equilibria are typically modeled by the ideal magnetohydrostatic (MHS) equations. The nonlinear, overdetermined nature of the QS MHS equations severely complicates our understanding of the interplay between 3D shaping, equilibrium properties such as pressure and rotational transform, and B . Progress has been made through expansions near the magnetic axis; however, a more comprehensive theory is desirable. Using a combination of analysis and regression on a large dataset of numerically optimized quasisymmetric stellarators, we demonstrate that there is a hidden lower dimensionality of B on a magnetic flux surface with connections to the theory of periodic solitons. We show that B on a flux surface is determined by three or at most four flux functions, each of which determines a critical value of the derivative of B along the field line. While being consistent with the near-axis models, our results are global and hold even on the last closed flux surface.

Differential geometry↗
DOE OSTI2025

The absence of ray-effects in the discrete ordinate solution to the transport equation in spherical coordinates in multi-dimensions

The streaming operator of the transport equation is derived for spherical coordinates by starting from Newton’s second law for a free particle expressed in spherical coordinates. We shall show that the partial derivatives with respect to the velocity variables of the particle, which are absent in the Cartesian coordinate formulation of the transport equation, arise in the spherical coordinate formulation of the transport equation in response to the centrifugal force which prevents a free particle from ‘falling into the origin’ of the coordinate system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2003

Geometric differences of the mitral apparatus between ischemic and dilated cardiomyopathy with significant mitral regurgitation: real-time three-dimensional echocardiography study

BACKGROUND: This study was conducted to elucidate the geometric differences of the mitral apparatus in patients with significant mitral regurgitation caused by ischemic cardiomyopathy (ICM-MR) and by idiopathic dilated cardiomyopathy (DCM-MR) by use of real-time 3D echocardiography (RT3DE). METHODS AND RESULTS: Twenty-six patients with ICM-MR caused by posterior infarction, 18 patients with DCM-MR, and 8 control subjects were studied. With the 3D software, commissure-commissure plane and 3 perpendicular anteroposterior (AP) planes were generated for imaging the medial, central, and lateral sides of the mitral valve (MV) during mid systole. In 3 AP planes, the angles between the annular plane and each leaflet (anterior, Aalpha; posterior, Palpha) were measured. In ICM-MR, Aalpha measured in the medial and central planes was significantly larger than that in the lateral plane (39+/-5 degrees, 34+/-6 degrees, and 27+/-5 degrees, respectively; P<0.01), whereas Palpha showed no significant difference in any of the 3 AP planes (61+/-7 degrees, 57+/-7 degrees, and 56+/-7 degrees, P>0.05). In DCM-MR, both Aalpha (38+/-8 degrees, 37+/-9 degrees, and 36+/-7 degrees, P>0.05) and Palpha (59+/-6 degrees, 58+/-5 degrees, and 57+/-6 degrees, P>0.05) revealed no significant differences in the 3 planes. CONCLUSIONS: The pattern of MV deformation from the medial to the lateral side was asymmetrical in ICM-MR, whereas it was symmetrical in DCM-MR. RT3DE is a helpful tool for differentiating the geometry of the mitral apparatus between these 2 different types of functional mitral regurgitation.

Evaluation Studies↗
NASA NTRS2020

SCExAO/CHARIS Near-infrared Integral Field Spectroscopy of the HD 15115 Debris Disk

We present new, near-infrared (1.1–2.4 μm) high-contrast imaging of the debris disk around HD 15115 with the Subaru Coronagraphic Extreme Adaptive Optics (SCExAO) system coupled with the Coronagraphic High Angular Resolution Imaging Spectrograph (CHARIS). The SCExAO/CHARIS resolves the disk down to ρ ∼ 0."2 (r(proj) ∼ 10 au), a factor of ∼3–5 smaller than previous recent studies. We derive a disk position angle of PA ∼ 279.°4–280.°5 and an inclination of i ∼ 85.°3–86.2.°. While recent SPHERE/IRDIS imagery of the system could suggest a significantly misaligned two-ring disk geometry, CHARIS imagery does not reveal conclusive evidence for this hypothesis. Moreover, optimizing models of both one- and two-ring geometries using differential evolution, we find that a single ring having a Hong-like scattering phase function matches the data equally well within the CHARIS field of view (ρ ≲ 1''). The disk's asymmetry, well evidenced at larger separations, is also recovered; the west side of the disk appears, on average, around 0.4 mag brighter across the CHARIS bandpass between 0farcs25 and 1''. Comparing Space Telescope Imaging Spectrograph (STIS) 50CCD optical photometry (2000–10500 Å) with CHARIS near-infrared photometry, we find a red (STIS/50CCD−CHARIS broadband) color for both sides of the disk throughout the 0farcs4–1'' region of overlap, in contrast to the blue color reported at similar wavelengths for regions exterior to ∼2''. Further, this color may suggest a smaller minimum grain size than previously estimated at larger separations. Finally, we provide constraints on planetary companions and discuss possible mechanisms for the observed inner disk flux asymmetry and color.

Kellen Lawson↗
DOE OSTI2024

Loops of loops expansion in the amplituhedron

We study a novel geometric expansion for scattering amplitudes in the planar sector of $\mathcal{N}$ = 4 super Yang-Mills theory, in the context of the Amplituhedron which reproduces the all-loop integrand as a canonical differential form on the positive geometry. In a paper by Arkani-Hamed, Henn and one of the authors, it was shown that this result can be recast in terms of negative geometries with a certain hierarchy of loops (closed cycles) in the space of loop momenta, represented by lines in momentum twistor space. One can then calculate an all-loop order result in the approximation where only tree graphs in the space of all loops are considered. Furthermore, using differential equation methods, it is possible to calculate and resum integrated expressions and obtain strong coupling results. In this paper, we provide a more general framework for the ‘loops of loops’ expansion and outline a powerful method for the determination of differential forms for higher-order geometries. We solve the problem completely for graphs with one internal cycle, but the method can be used more generally for other geometries.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1983

Parallel architectures for iterative methods on adaptive, block structured grids

A parallel computer architecture well suited to the solution of partial differential equations in complicated geometries is proposed. Algorithms for partial differential equations contain a great deal of parallelism. But this parallelism can be difficult to exploit, particularly on complex problems. One approach to extraction of this parallelism is the use of special purpose architectures tuned to a given problem class. The architecture proposed here is tuned to boundary value problems on complex domains. An adaptive elliptic algorithm which maps effectively onto the proposed architecture is considered in detail. Two levels of parallelism are exploited by the proposed architecture. First, by making use of the freedom one has in grid generation, one can construct grids which are locally regular, permitting a one to one mapping of grids to systolic style processor arrays, at least over small regions. All local parallelism can be extracted by this approach. Second, though there may be a regular global structure to the grids constructed, there will be parallelism at this level. One approach to finding and exploiting this parallelism is to use an architecture having a number of processor clusters connected by a switching network. The use of such a network creates a highly flexible architecture which automatically configures to the problem being solved.

Gannon, D.↗
NASA NTRS1992

Ejecta patterns of Meteor Crater, Arizona derived from the linear un-mixing of TIMS data and laboratory thermal emission spectra

Accurate interpretation of thermal infrared data depends upon the understanding and removal of complicating effects. These effects may include physical mixing of various mineralogies and particle sizes, atmospheric absorption and emission, surficial coatings, geometry effects, and differential surface temperatures. The focus is the examination of the linear spectral mixing of individual mineral or endmember spectra. Linear addition of spectra, for particles larger than the wavelength, allows for a straight-forward method of deconvolving the observed spectra, predicting a volume percent of each endmember. The 'forward analysis' of linear mixing (comparing the spectra of physical mixtures to numerical mixtures) has received much attention. The reverse approach of un-mixing thermal emission spectra was examined with remotely sensed data, but no laboratory verification exists. Understanding of the effects of spectral mixing on high resolution laboratory spectra allows for the extrapolation to lower resolution, and often more complicated, remotely gathered data. Thermal Infrared Multispectral Scanner (TIMS) data for Meteor Crater, Arizona were acquired in Sep. 1987. The spectral un-mixing of these data gives a unique test of the laboratory results. Meteor Crater (1.2 km in diameter and 180 m deep) is located in north-central Arizona, west of Canyon Diablo. The arid environment, paucity of vegetation, and low relief make the region ideal for remote data acquisition. Within the horizontal sedimentary sequence that forms the upper Colorado Plateau, the oldest unit sampled by the impact crater was the Permian Coconino Sandstone. A thin bed of the Toroweap Formation, also of Permian age, conformably overlays the Coconino. Above the Toroweap lies the Permian Kiabab Limestone which, in turn, is covered by a thin veneer of the Moenkopi Formation. The Moenkopi is Triassic in age and has two distinct sub-units in the vicinity of the crater. The lower Wupatki member is a fine-grained sandstone, while the upper Moqui member is a fissile siltstone. Ejecta from these units are preserved as inverted stratigraphy up to 2 crater radii from the rim. The mineralogical contrast between the units, relative lack of post-emplacement erosion and ejecta mixing provide a unique site to apply the un-mixing model. Selection of the aforementioned units as endmembers reveals distinct patterns in the ejecta of the crater.

Ramsey, Michael S.↗
NASA NTRS2006

Dynamic Features in and nearby a Prominence

We will discuss the thermal and dynamic properties of dynamic structures in and around a prominence channel observed on the limb on 17 April 2003. Observations were taken with the Solar and Heliospheric Observatory's Solar Ultraviolet Measurements of Emitted Radiation (SOHO/SUMER) in lines formed at temperatures from 80,000 to 1.6 million K. The instrument was pointed to a single location and took a series of 90 s exposures. Two-dimensional context was provided by the Transition Region and Coronal Explorer (TRACE) in the UV and EUV and by the Kanzelhohe Solar Observatory in H-alpha. Two dynamic features were studied in depth: a prominence activation and repeated motions in a loop nearby the prominence. We were able to calculate three-dimensional geometries and trajectories, differential emission measure, and limits on the average density, kinetic and thermal energies. These observations provide important tests for models of dynamics in prominences and cool (approx.10(exp 5) K) loops.

Kucera, T.↗
NASA NTRS2006

UV Observations of Prominence Activation and Cool Loop Dynamics

In this paper we investigate the thermal and dynamic properties of dynamic structures in and around a prominence channel observed on the limb on 17 April 2003. Observations were taken with the Solar and Heliospheric Observatory's Solar Ultraviolet Measurements of Emitted Radiation (SOHO/SUMER) in lines formed at temperatures from 80,000 to 1.6 MK. The instrument was pointed to a single location and took a series of 90 s exposures. Two-dimensional context was provided by the Transition Region and Coronal Explorer (TRACE) in the UV and EUV and the Kanzelhohe Solar Observatory in H-alpha. Two dynamic features were studied in depth: an activated prominence and repeated motions in a loop near the prominence. We calculated three-dimensional geometries and trajectories, differential emission measure, and limits on the mass, pressure, average density, and kinetic and thermal energies. These observations provide important tests for models of dynamics in prominences and cool (approx. 10(exp 5) K)loops, which will ultimately lead to a better understanding the mechanism(s) leading to energy and mass flow in these solar features.

Kucera, Therese A.↗
NASA NTRS1982

Recent advances in electromagnetic synthesis and analysis of dual-shaped reflector antennas

Dual-shaped reflectors have been used for many years. Thus, these reflectors have been used as high gain antennas on Voyagers 1 and 2. The objectives of the geometrical optics (GO) dual shaped synthesis are considered. Concerning the synthesis of dual shaped reflectors, it has been shown for circular symmetric reflectors that an exact GO solution can be found to the problem of transforming, by two reflections, any feed pattern into any aperture distribution. This problem involves solving two simultaneous nonlinear ordinary differential equations. The same approach for offset geometry leads to two simultaneous nonlinear partial differential equations. It is shown that these equations could also be integrated numerically, except that in general these equations are not total and therefore, in general, they do not have a 'smooth' solution. It is further shown that the offset partial differentials often very nearly form a total differential in many cases of practical importance.

Galindo-Israel, V.↗
NASA NTRS1980

Absolute elastic differential electron scattering cross sections for He - A proposed calibration standard from 5 to 200 eV

Absolute differential, integral, and momentum-transfer cross sections for electrons elastically scattered from helium are reported for the impact energy range of 5 to 200 eV. Angular distributions for elastically scattered electrons are measured in a crossed-beam geometry using a collimated, differentially pumped atomic-beam source which requires no effective-path-length correction. Below the first inelastic threshold the angular distributions were placed on an absolute scale by use of a phase-shift analysis. Above this threshold, the angular distributions from 10 to 140 deg were fitted using the phase-shift technique, and the resulting integral cross sections were normalized to a semiempirically derived integral elastic cross section. Depending on the impact energy, the data are estimated to be accurate to within 5 to 9%.

Register, D. F.↗
NASA NTRS1990

Radiative interactions in laminar duct flows

Analyses and numerical procedures are presented for infrared radiative energy transfer in gases when other modes of energy transfer occur simultaneously. Two types of geometries are considered, a parallel plate duct and a circular duct. Fully developed laminar incompressible flows of absorbing-emitting species in black surfaced ducts are considered under the conditions of uniform wall heat flux. The participating species considered are OH, CO, CO2, and H2O. Nongray as well as gray formulations are developed for both geometries. Appropriate limiting solutions of the governing equations are obtained and conduction-radiation interaction parameters are evaluated. Tien and Lowder's wide band model correlation was used in nongray formulation. Numerical procedures are presented to solve the integro-differential equations for both geometries. The range of physical variables considered are 300 to 2000 K for temperature, 0.1 to 100.0 atm for pressure, and 0.1 to 100 cm spacings between plates/radius of the tube. An extensive parametric study based on nongray formulation is presented. Results obtained for different flow conditions indicate that the radiative interactions can be quite significant in fully developed incompressible flows.

Trivedi, P. A.↗