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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Symmetries of the Gas Dynamics Equations using the Differential Form Method

Here, a brief review of the theory of exterior differential systems and isovector symmetry analysis methods is presented in the context of the one-dimensional inviscid compressible flow equations. These equations are formulated as an exterior differential system with equation of state (EOS) closure provided in terms of an adiabatic bulk modulus. The scaling symmetry generators—and corresponding EOS constraints—otherwise appearing in the existing literature are recovered through the application and invariance under Lie derivative dragging operations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Chiral algebra, localization, modularity, surface defects, and all that

We study the 2D vertex operator algebra (VOA) construction in 4D N = 2 superconformal field theories on S 3 × S 1 , focusing on both old puzzles and new observations. The VOA lives on a two-torus T 2 ⊂ S 3 × S 1 , it is 1 2 Z -graded, and this torus is equipped with the natural choice of spin structure (1,0) for the Z + 1 2 -graded operators, corresponding to the NS sector vacuum character. By analyzing the possible refinements of the Schur index that preserves the VOA, we find that it admits discrete deformations, which allows access to the remaining spin structures (1,1), (0,1), and (0,0), of which the latter two involve the inclusion of a particular surface defect. For Lagrangian theories, we perform the detailed analysis: we describe the natural supersymmetric background, perform localization, and derive the gauged symplectic boson action on a torus in any spin structure. In the absence of flavor fugacities, the 2D and 4D path integrals precisely match, including the Casimir factors. We further analyze the 2D theory: we identify its integration cycle and the two-point functions and interpret flavor holonomies as screening charges in the VOA. Next, we make some observations about modularity; the T-transformation acts on our four partition functions and lifts to a large diffeomorphism on S 3 × S 1 . More interestingly, we generalize the four partition functions on the torus to an infinite family labeled by both the spin structure and the integration cycle inside the complexified maximal torus of the gauge group. Members of this family transform into one another under the full modular group, and we confirm the recent observation that the S-transform of the Schur index in Lagrangian theories exhibits logarithmic behavior. Finally, we comment on how locally our background reproduces the Ω-background.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Generalized Grad–Shafranov equation for non-axisymmetric MHD equilibria

The structure of static MHD equilibria that admit continuous families of Euclidean symmetries is well understood. Such field configurations are governed by the classical Grad–Shafranov equation, which is a single elliptic partial differential equation in two space dimensions. By revealing a hidden symmetry, here we show that in fact all smooth solutions of the equilibrium equations with non-vanishing pressure gradients away from the magnetic axis satisfy a generalization of the Grad–Shafranov equation. In contrast to solutions of the classical Grad–Shafranov equation, solutions of the generalized equation are not automatically equilibria, but instead only satisfy force balance averaged over the one-parameter hidden symmetry. We then explain how the generalized Grad–Shafranov equation can be used to reformulate the problem of finding exact three-dimensional smooth solutions of the equilibrium equations as finding an optimal volume-preserving symmetry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Normal stability of slow manifolds in nearly periodic Hamiltonian systems

Kruskal [J. Math. Phys. 3, 806 (1962)] showed that each nearly periodic dynamical system admits a formal U(1) symmetry, generated by the so-called roto-rate. We prove that such systems also admit nearly invariant manifolds of each order, near which rapid oscillations are suppressed. We study the nonlinear normal stability of these slow manifolds for nearly periodic Hamiltonian systems on barely symplectic manifolds—manifolds equipped with closed, non-degenerate 2-forms that may be degenerate to leading order. In particular, we establish a sufficient condition for long-term normal stability based on second derivatives of the well-known adiabatic invariant. We use these results to investigate the problem of embedding guiding center dynamics of a magnetized charged particle as a slow manifold in a nearly periodic system. Here, we prove that one previous embedding and two new embeddings enjoy long-term normal stability and thereby strengthen the theoretical justification for these models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Comparison of private flux region instability in conventional and super-X divertor configurations

Understanding turbulence in the divertor leg of tokamaks is essential to predicting the heat deposition profile on the divertor plate. This in turn is important for evaluating advanced divertor configurations, such as the super-X divertor. Within the divertor region, the private flux region is of interest because it is relatively unaffected by turbulence extending from the outboard midplane, so instabilities in this region could have a particularly pronounced effect on transport. These instabilities are modeled using the Arbitrary Topology Equation Reader (ArbiTER) eigenvalue code. Eigenmodes are examined further by comparing physics models to determine the fundamental mechanisms behind their formation, and quantifying the effect of individual terms. This analysis is conducted on both conventional and super-X divertors to compare these effects. Here, the resulting analysis reveals the presence of a geodesic curvature driven instability that is significantly more pronounced in the super-X configuration.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Pressure–strain interaction. II. Decomposition in magnetic field-aligned coordinates

In weakly collisional and collisionless magnetized plasmas, the pressure–strain interaction describes the rate of conversion between bulk flow and thermal energy density. In this study, we derive an analytical expression for the pressure–strain interaction in a coordinate system with an axis aligned with the local magnetic field. The result is eight groups of terms corresponding to different physical mechanisms that can contribute to the pressure–strain interaction. We provide a physical description of each term. Here, the results are immediately of interest to weakly collisional and collisionless magnetized plasmas and the fundamental processes that happen therein, including magnetic reconnection, magnetized plasma turbulence, and collisionless shocks. The terms in the field-aligned coordinate decomposition are likely accessible to measurement with satellite observations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Multiscale modeling of solute diffusion in triblock copolymer membranes

We develop a multiscale simulation model for diffusion of solutes through porous triblock copolymer membranes. The approach combines two techniques: self-consistent field theory (SCFT) to predict the structure of the self-assembled, solvated membrane and on-lattice kinetic Monte Carlo (kMC) simulations to model diffusion of solutes. Solvation is simulated in SCFT by constraining the glassy membrane matrix while relaxing the brush-like membrane pore coating against the solvent. The kMC simulations capture the resulting solute spatial distribution and concentration-dependent local diffusivity in the polymer-coated pores; we parameterize the latter using particle-based simulations. We apply our approach to simulate solute diffusion through nonequilibrium morphologies of a model triblock copolymer, and we correlate diffusivity with structural descriptors of the morphologies. We also compare the model’s predictions to alternative approaches based on simple lattice random walks and find our multiscale model to be more robust and systematic to parameterize. Furthermore, our multiscale modeling approach is general and can be readily extended in the future to other chemistries, morphologies, and models for the local solute diffusivity and interactions with the membrane.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Symmetry and scaling in one-dimensional compressible two-phase flow

Investigations of shock compression of heterogeneous materials often focus on the shock front width and overall profile. The number of experiments required to fully characterize the dynamic response of a material often belie the structure–property relationships governing these aspects of a shock wave. Recent observations measured a pronounced shock-front width on the order of 10 s of ns in particulate composites. We focus on particulate composites with disparate densities and investigate whether the mechanical interactions between the phases are adequate to describe this emergent behavior. The analysis proceeds with a general Mie–Grüneisen equation of state for the matrix material, a general drag force law with general power-law scaling for the particle-matrix coupling of the phases, and a volume fraction-dependent viscosity. Lie group analysis is applied to one-dimensional hydrodynamic flow equations for the self-consistent interaction of particles embedded in a matrix material. The particle phase is characterized by a particle size and volume fraction. The Lie group analysis results in self-similar solutions reflecting the symmetries of the flow. The symmetries lead to well-defined scaling laws, which may be used to characterize the propagation of shock waves in particle composites. An example of the derived scaling laws for shock attenuation and rise time is shown for experimental data on shock-driven tungsten-loaded polymers. A key result of the Lie analysis is that there is a relationship between the exponents characterizing the form of the drag force and the exponent characterizing the shock velocity and its attenuation in a particulate composite. Comparison to recent experiments results in a single exponent that corresponds to a conventional drag force.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
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 OSTI2016

Quasitoric manifolds and small covers over properly coloured polytopes: immersions and embeddings

We construct small covers and quasitoric manifolds over n-dimensional simple polytopes which allow proper colourings of facets with n colours. We calculate the Stiefel-Whitney classes of these manifolds as obstructions to immersions and embeddings into Euclidean spaces. The largest dimension required for embedding is achieved in the case n is a power of two.Bibliography: 11 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

RESONANCE IN FORCED FLUX-TRANSPORT DYNAMOS

We show that simple two- and three-layer flux-transport dynamos, when forced at the top by a poloidal source term, can produce a widely varying amplitude of toroidal field at the bottom, depending on how close the meridional flow speed of the bottom layer is to the propagation speed of the forcing applied above the top layer, and how close the amplitude of the {alpha}-effect is to two values that give rise to a resonant response. This effect should be present in this class of dynamo model no matter how many layers are included. This result could have implications for the prediction of future solar cycles from the surface magnetic fields of prior cycles. It could be looked for in flux-transport dynamos that are more realistic for the Sun, done in spherical geometry with differential rotation, meridional flow, and {alpha}-effect that vary with latitude and time as well as radius. Because of these variations, if resonance occurs, it should be more localized in time, latitude, and radius.

79 ASTRONOMY AND ASTROPHYSICS↗
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↗
DOE OSTI2020

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 {sub 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 0.″25 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 0.″4–1″ 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.

79 ASTRONOMY AND ASTROPHYSICS↗
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↗