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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Hyperbolic vacua in Minkowski space

Families of Lorentz, but not Poincare, invariant vacua are constructed for a massless scalar field in 4D Minkowski space. These are generalizations of the Rindler vacuum with a larger symmetry group. Explicit expressions are given as squeezed excitations of the Poincare vacuum. The effective reduced vacua on the 3D hyperbolic de Sitter slices are the well-known de Sitter α-vacua with antipodal singularities in the Wightman function. Several special interesting cases are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Geodesic acoustic modes in toroidally rotating tokamaks with an arbitrary β

Theoretical research on the geodesic acoustic mode (GAM) induced by the equilibrium toroidal rotation flow (ETRF) in the tokamak plasmas with an arbitrary β is performed by using the ideal magnetohydrodynamic model, where β is the ratio of the plasma pressure and magnetic field pressure. Two equations determining the poloidal displacement ξ{sub θ} and the divergence of the Lagrangian perturbation are obtained and suitable for arbitrary cross-section tokamaks with large-aspect-ratios. The dispersion relations are then derived for two different coupling patterns by assuming ξ{sub ±2}=0 and ξ{sub ±4}=0, respectively, where ξ{sub m}=(1/2π)∫ξ{sub θ}e{sup imθ}dθ with θ being the poloidal angle under the circular cross-section condition. In both patterns, the ETRF will increase the frequencies of the GAMs but β can decrease them. The GAM for ξ{sub ±2}=0 has a larger frequency than GAM for ξ{sub ±4}=0.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Emergence of complex and spinor wave functions in scale relativity. I. Nature of scale variables

One of the main results of scale relativity as regards the foundation of quantum mechanics is its explanation of the origin of the complex nature of the wave function. The scale relativity theory introduces an explicit dependence of physical quantities on scale variables, founding itself on the theorem according to which a continuous and non-differentiable space-time is fractal (i.e., scale-divergent). In the present paper, the nature of the scale variables and their relations to resolutions and differential elements are specified in the non-relativistic case (fractal space). We show that, owing to the scale-dependence which it induces, non-differentiability involves a fundamental two-valuedness of the mean derivatives. Since, in the scale relativity framework, the wave function is a manifestation of the velocity field of fractal space-time geodesics, the two-valuedness of velocities leads to write them in terms of complex numbers, and yields therefore the complex nature of the wave function, from which the usual expression of the Schrödinger equation can be derived.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Extension of Chern-Simons forms

We investigate metric independent, gauge invariant, and closed forms in the generalized Yang-Mills (YM) theory. These forms are polynomial on the corresponding fields strength tensors – curvature forms and are analogous to the Pontryagin-Chern densities in the YM gauge theory. The corresponding secondary characteristic classes have been expressed in integral form in analogy with the Chern-Simons form. Because they are not unique, the secondary forms can be dramatically simplified by the addition of properly chosen differentials of one-step-lower-order forms. Their gauge variation can also be found yielding the potential anomalies in the gauge field theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Differential geometric invariants for time-reversal symmetric Bloch-bundles: The “Real” case

Topological quantum systems subjected to an even (resp. odd) time-reversal symmetry can be classified by looking at the related “Real” (resp. “Quaternionic”) Bloch-bundles. If from one side the topological classification of these time-reversal vector bundle theories has been completely described in De Nittis and Gomi [J. Geom. Phys. 86, 303–338 (2014)] for the “Real” case and in De Nittis and Gomi [Commun. Math. Phys. 339, 1–55 (2015)] for the “Quaternionic” case, from the other side it seems that a classification in terms of differential geometric invariants is still missing in the literature. With this article and its companion [G. De Nittis and K. Gomi (unpublished)] we want to cover this gap. More precisely, we extend in an equivariant way the theory of connections on principal bundles and vector bundles endowed with a time-reversal symmetry. In the “Real” case we generalize the Chern-Weil theory and we show that the assignment of a “Real” connection, along with the related differential Chern class and its holonomy, suffices for the classification of “Real” vector bundles in low dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Analysis of X-ray adsorption edges: L 2,3 edge of FeCl 4 –

We describe a detailed analysis of the features of the X-ray adsorption spectra at the Fe L 2,3 edge of FeCl 4 . The objective of this analysis is to explain the origin of the complex features in relation to properties of the wavefunctions, especially for the excited states. These properties include spin-orbit and ligand field splittings where a novel aspect of the dipole selection rules is applied to understand the influence of these splittings on the spectra. We also explicitly take account of the intermediate coupling of the open core and valence shell electrons. Our analysis also includes comparison of theory and experiment for the Fe L 2,3 edge and comparison of theoretical predictions for the Fe 3+ cation and FeCl 4 -. Here, the electronic structure is obtained from theoretical wavefunctions for the ground and excited states.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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 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↗