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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
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DOE OSTI2014

A new approach for magnetic curves in 3D Riemannian manifolds

A magnetic field is defined by the property that its divergence is zero in a three-dimensional oriented Riemannian manifold. Each magnetic field generates a magnetic flow whose trajectories are curves called as magnetic curves. In this paper, we give a new variational approach to study the magnetic flow associated with the Killing magnetic field in a three-dimensional oriented Riemann manifold, (M{sup 3}, g). And then, we investigate the trajectories of the magnetic fields called as N-magnetic and B-magnetic curves.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Short-time asymptotics of a rigorous path integral for N = 1 supersymmetric quantum mechanics on a Riemannian manifold

Following Feynman's prescription for constructing a path integral representation of the propagator of a quantum theory, a short-time approximation to the propagator for imaginary-time, N = 1 supersymmetric quantum mechanics on a compact, even-dimensional Riemannian manifold is constructed. The path integral is interpreted as the limit of products, determined by a partition of a finite time interval, of this approximate propagator. The limit under refinements of the partition is shown to converge uniformly to the heat kernel for the Laplace-de Rham operator on forms. A version of the steepest descent approximation to the path integral is obtained, and shown to give the expected short-time behavior of the supertrace of the heat kernel.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Killing vector fields and harmonic superfield theories

The harmonic action functional allows a natural generalisation to semi-Riemannian supergeometry, also referred to as harmonic, which resembles the supersymmetric sigma models studied in high energy physics. We show that Killing vector fields are infinitesimal supersymmetries of this harmonic action and prove three different Noether theorems in this context. En passant, we provide a homogeneous treatment of five characterisations of Killing vector fields on semi-Riemannian supermanifolds, thus filling a gap in the literature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

A new version of circular symmetrization with applications to p-valent functions

A new version of circular symmetrization of sets, functions and condensers is proposed, which is different from classical symmetrization in the following respect: the symmetrized sets and condensers lie on the Riemann surface of the inverse function of a Chebyshev polynomial. As applications, Hayman's well-known results for nonvanishing p-valent holomorphic functions are supplemented as well as results for p-valent functions in a disc which have a zero of order p at the origin. Bibliography: 20 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Reducing quasilinear systems to block triangular form

The paper is concerned with systems of n quasilinear partial differential equations of the first order with 2 independent variables. Using a geometric formalism for such equations, which goes back to Riemann, it is possible to assign a field of linear operators on an appropriate vector bundle to this type of quasilinear system. Several tests for a quasilinear system to be reducible to triangular or block triangular form are obtained in terms of this field; they supplement well known results on diagonalization and block diagonalization due to Haantjes and Bogoyavlenskij. Bibliography: 10 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Topology of codimension-one foliations of nonnegative curvature

We show that a transversely oriented C{sup 2}-foliation of codimension one with nonnegative Ricci curvature on a closed orientable manifold is a foliation with almost no holonomy. This allows us to decompose the manifold into blocks on which this foliation has a simple structure. We also show that a manifold homeomorphic to a 5-dimensional sphere does not admit a codimension-one C{sup 2}-foliation with nonnegative sectional curvature. Bibliography: 29 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Closeness to spheres of hypersurfaces with normal curvature bounded below

For a Riemannian manifold M{sup n+1} and a compact domain Ω⊂ M{sup n+1} bounded by a hypersurface ∂Ω with normal curvature bounded below, estimates are obtained in terms of the distance from O to ∂Ω for the angle between the geodesic line joining a fixed interior point O in Ω to a point on ∂Ω and the outward normal to the surface. Estimates for the width of a spherical shell containing such a hypersurface are also presented. Bibliography: 9 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

A holomorphic version of the Tate-Iwasawa method for unramified L-functions. I

Using the Tate-Iwasawa method the problem of meromorphic continuation and of the existence of a functional equation can be solved for the zeta and L-functions of one-dimensional arithmetical schemes. A new version of this method is put forward, which looks at the case of curves over a finite field and of unramified L-functions. The proof is based on a reduction of the problem to a Cousin problem on the Riemann sphere which is related to the curve under consideration. Bibliography: 16 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

On a criterion of conformal parabolicity of a Riemannian manifold

The paper relates to the circle of problems concerning the connection between the conformal type of a Riemannian manifold and the canonical form of its isoperimetric function. Two special examples of 2-manifolds are constructed, which explain the meaning, role and importance of the conditions involved in the criterion, previously obtained by the author, which decides whether a noncompact Riemannian n-manifold is conformally parabolic. Bibliography: 8 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Mechanical systems with closed orbits on manifolds of revolution

We study natural mechanical systems describing the motion of a particle on a two-dimensional Riemannian manifold of revolution in the field of a central smooth potential. We obtain a classification of Riemannian manifolds of revolution and central potentials on them that have the strong Bertrand property: any nonsingular (that is, not contained in a meridian) orbit is closed. We also obtain a classification of manifolds of revolution and central potentials on them that have the 'stable' Bertrand property: every parallel is an 'almost stable' circular orbit, and any nonsingular bounded orbit is closed. Bibliography: 14 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Steiner minimal trees in small neighbourhoods of points in Riemannian manifolds

In contrast to the Euclidean case, almost no Steiner minimal trees with concrete boundaries on Riemannian manifolds are known. A result describing the types of Steiner minimal trees on a Riemannian manifold for arbitrary small boundaries is obtained. As a consequence, it is shown that for sufficiently small regular n-gons with n⩾7 their boundaries without a longest side are Steiner minimal trees. Bibliography: 22 titles. (paper)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Constraining smoothness parameter and the DD relation of Dyer-Roeder equation with supernovae

Our real universe is locally inhomogeneous. Dyer and Roeder introduced the smoothness parameter α to describe the influence of local inhomogeneity on angular diameter distance, and they obtained the angular diameter distance-redshift approximate relation (Dyer-Roeder equation) for locally inhomogeneous universe. Furthermore, the Distance-Duality (DD) relation, D{sub L}(z)(1+z){sup −2}/D{sub A}(z) = 1, should be valid for all cosmological models that are described by Riemannian geometry, where D{sub L} and D{sub A} are, respectively, the luminosity and angular distance distances. Therefore, it is necessary to test whether if the Dyer-Roeder approximate equation can satisfy the Distance-Duality relation. In this paper, we use Union2.1 SNe Ia data to constrain the smoothness parameter α and test whether the Dyer-Roeder equation meet the DD relation. By using χ{sup 2} minimization, we get α = 0.92{sub −0.32}{sup +0.08} at 1σ and 0.92{sub −0.65}{sup +0.08} at 2σ, and our results show that the Dyer-Roeder equation is in good consistency with the DD relation at 1σ.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

GravitoMagnetic force in modified Newtonian dynamics

We introduce the Gauge Vector-Tensor (GVT) theory by extending the AQUAL's approach to the GravitoElectroMagnetism (GEM) approximation of gravity. GVT is a generally covariant theory of gravity composed of a pseudo Riemannian metric and two U(1) gauge connections that reproduces MOND in the limit of very weak gravitational fields while remains consistent with the Einstein-Hilbert gravity in the limit of strong and Newtonian gravitational fields. GVT also provides a simple framework to study the GEM approximation to gravity. We illustrate that the gravitomagnetic force at the edge of a galaxy can be in accord with either GVT or ΛCDM but not both. We also study the physics of the GVT theory around the gravitational saddle point of the Sun and Jupiter system. We notice that the conclusive refusal of the GVT theory demands measuring either both of the gravitoelectric and gravitomagnetic fields inside the Sun-Jupiter MOND window, or the gravitoelectric field inside two different solar GVT MOND windows. The GVT theory, however, will be favored by observing an anomaly in the gravitoelectric field inside a single MOND window.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Randers geometry as MOND/dark matter

We consider a deviation of the physical length from the Riemann geometry toward the Randers'. We construct a consistent second-order relativistic theory of gravity that dynamically reduces to the Einstein-Hilbert theory for the strong and Newtonian gravity while its weak gravitational regime reproduces MOND and the gravitational lensing attributed to the dark matter halo. It also naturally accommodates the observed value of the cosmological constant. We show that it predicts a few percent deviation for the post Newtonian parameter γ in a part of the regime that interpolates the Newtonian regime to the MOND regime. The deviation is consistent with the reported observations but can possibly be detected by fine-tuned refinements of the current data or specified future observations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Cosmological backreaction in higher-derivative gravity expansions

We calculate a general effective stress-energy tensor induced by cosmological inhomogeneity in effective theories of gravity where the action is Taylor-expandable in the Riemann tensor and covariant derivatives of the Riemann tensor. This is of interest as an effective fluid that might provide an alternative to the cosmological constant, but it also applies to gravitational waves. We use an adaptation of Green and Wald's weak-averaging framework, which averages over perturbations in the field equation where the perturbation length scales are small compared to the averaging scale. In this adaptation, the length scale of the effective theory, 1/ M , is also taken to be small compared with the averaging scale. This ensures that the perturbation length scales remain in fixed proportion to the length scale of the effective theory as the cosmological averaging scale is taken to be large. We find that backreaction from higher-derivative terms in the effective action can continue to be important in the late universe, given a source of sufficiently high-frequency metric perturbations. This backreaction might also provide a window on exotic particle physics in the far ultraviolet.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Finite-Aperture Riemann’s Wave

The Riemann compression wave describes a 2D flow behind an infinite wave front, but is used for describing its propagation in channels. The effect of walls on the process of its propagation is disregarded in this case. However, friction against the walls and diffraction divergence of elementary plane waves compensating the friction change the conditions of wave propagation. These effects, which are inevitable in a channel, violate the constancy of entropy and the jet nature of the flow, which contradicts the definition of a “simple wave.” Analysis of diffraction divergence makes it possible to solve the problem of formation of a finite-aperture simple wave (a wave beam with a large Rayleigh length). The evolution of friction processes explains the emergence of a turbulent flow and makes it possible to describe the mechanism of a spontaneous transition of deflagration into detonation more accurately.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Integrable string models of WZNW model type with constant SU(2), SO(3), SP(2) and SU(3) torsion and hydrodynamic chains

The integrability of string model of WZNW model type with constant SU (2), SO (3), SP (2) torsion is investigated. The closed boson string model in the background gravity and antisymmetric B-field is considered as integrable system in terms of initial chiral currents. The model is considered under assumption that internal torsion related with metric of Riemann-Cartan space and external torsion related with antisymmetric B-field are (anti)coincide. New equation of motion and exact solution this equation was obtained for string model with constant SU (2), SO (3), SP (2) torsion. New equations of motion and new Poisson brackets (PB) for infinite dimensional hydrodynamic chains was obtained for string model with constant SU (n ), SO (n ), SP (n ) torsion for n → ∞.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Solving 3d gravity with Virasoro TQFT

We propose a precise reformulation of 3d quantum gravity with negative cosmological constant in terms of a topological quantum field theory based on the quantization of the Teichmüller space of Riemann surfaces that we refer to as “Virasoro TQFT”. This TQFT is similar, but importantly not equivalent, to SL(2, \mathbb{R} ℝ ) Chern-Simons theory. This sharpens the folklore that 3d gravity is related to SL(2, \mathbb{R} ℝ ) Chern-Simons theory into a precise correspondence, and resolves some well-known issues with this lore at the quantum level. Our proposal is computationally very useful and provides a powerful tool for the further study of 3d gravity. In particular, we explain how together with standard TQFT surgery techniques this leads to a fully algorithmic procedure for the computation of the gravity partition function on a fixed topology exactly in the central charge. Mathematically, the relation leads to many nontrivial conjectures for hyperbolic 3-manifolds, Virasoro conformal blocks and crossing kernels.

Collier, Scott↗