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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Boundary Value Problems for Nonclassical Systems of Second Order Differential Equations

We study boundary value problems for systems of second order differential equations with principal part in the form of the squared first order differential operator. We establish the unique solvability of the boundary value problem for a nonclassical system in the plane, which can be regarded as the Riemann–Hilbert problem with discontinuous boundary conditions. Similar problems are considered in the space.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

The Virasoro minimal string

We introduce a critical string theory in two dimensions and demonstrate that this theory, viewed as two-dimensional quantum gravity on the worldsheet, is equivalent to a double-scaled matrix integral. The worldsheet theory consists of Liouville CFT with central charge c ≥ ≥ 25 coupled to timelike Liouville CFT with central charge 26-c. The double-scaled matrix integral has as its leading density of states the universal Cardy density of primaries in a two-dimensional CFT, thus motivating the name Virasoro minimal string. The duality holds for any value of the continuous parameter c c and reduces to the JT gravity/matrix integral duality in the large central charge limit. It thus provides a precise stringy realization of JT gravity. The main observables of the Virasoro minimal string are quantum analogues of the Weil-Petersson volumes, which are computed as absolutely convergent integrals of worldsheet CFT correlators over the moduli space of Riemann surfaces. By exploiting a relation of the Virasoro minimal string to three-dimensional gravity and intersection theory on the moduli space of Riemann surfaces, we are able to give a direct derivation of the duality. We provide many checks, such as explicit numerical - and in special cases, analytic - integration of string diagrams, the identification of the CFT boundary conditions with asymptotic boundaries of the two-dimensional spacetime, and the matching between the leading non-perturbative corrections of the worldsheet theory and the matrix integral. As a byproduct, we discover natural conformal boundary conditions for timelike Liouville CFT.

Physics↗
DOE OSTI2010

Founding Gravitation in 4D Euclidean Space-Time Geometry

The Euclidean interpretation of special relativity which has been suggested by the author is a formulation of special relativity in ordinary 4D Euclidean space-time geometry. The natural and geometrically intuitive generalization of this view involves variations of the speed of light (depending on location and direction) and a Euclidean principle of general covariance. In this article, a gravitation model by Jan Broekaert, which implements a view of relativity theory in the spirit of Lorentz and Poincare, is reconstructed and shown to fulfill the principles of the Euclidean approach after an appropriate reinterpretation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

Affine Kac-Moody symmetric spaces related with A{sub 1}{sup (1)}, A{sub 2}{sup (1)}, A{sub 2}{sup (2)}

Symmetric spaces associated with Lie algebras and Lie groups which are Riemannian manifolds have recently got a lot of attention in various branches of Physics for their role in classical/quantum integrable systems, transport phenomena, etc. Their infinite dimensional counter parts have recently been discovered which are affine Kac-Moody symmetric spaces. In this paper we have (algebraically) explicitly computed the affine Kac-Moody symmetric spaces associated with affine Kac-Moody algebras A{sub 1}{sup (1)},A{sub 2}{sup (1)},A{sub 2}{sup (2)}. We hope these types of spaces will play similar roles as that of symmetric spaces in many physical systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2010

Dyson-Schwinger equations with a parametrized metric

We construct and solve the Dyson-Schwinger equation of a quark propagator with a parameterized metric, which connects the Euclidean metric with the Minkowskian one. We show, in some models, that the Minkowskian vacuum is different from the Euclidean vacuum. The usual analytic continuation of the Green function does not make sense in these cases. While with the algorithm we proposed and the quark-gluon vertex ansaetz which preserves the Ward-Takahashi identity, the vacuum keeps being unchanged in the evolution of the metric. In this case, analytic continuation becomes meaningful and can be fully carried out.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2010

Bekenstein bound in asymptotically free field theory

For spatially bounded free fields, the Bekenstein bound states that the specific entropy satisfies the inequality (S/E){<=}2{pi}R, where R stands for the radius of the smallest sphere that circumscribes the system. The validity of the Bekenstein bound in the asymptotically free side of the Euclidean ({lambda}{phi}{sup 4}){sub d} scalar field theory is investigated. We consider the system in thermal equilibrium with a reservoir at temperature {beta}{sup -1} and defined in a compact spatial region without boundaries. Using the effective potential, we discuss the thermodynamic of the model. For low and high temperatures the system presents a condensate. We present the renormalized mean energy E and entropy S for the system and show in which situations the specific entropy satisfies the quantum bound.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Dual instantons in antimembranes theory

We introduce two ansatzs for the 3-form potential of Euclidean 11d supergravity on skew-whiffed AdS{sub 4}xS{sup 7} background which results in two scalar modes with m{sup 2}=-2 on AdS{sub 4}. Being conformally coupled with a quartic interaction, it is possible to find the exact solutions of the scalar equation on this background. These modes turn out to be invariant under the SU(4) subgroup of the SO(8) isometry group, whereas there are no corresponding SU(4) singlet Bogomol'nyi-Prasad-Sommerfeld operators of dimensions one or two on the boundary theory constructed by Aharony, Bergman, Jafferis, and Maldacena. Noticing the interchange of 8{sub s} and 8{sub c} representations under skew-whiffing in the bulk, we propose the theory of antimembranes should similarly be obtained from Aharony, Bergman, Jafferis, and Maldacena's theory by swapping these representations. In particular, this enables us to identify the dual boundary operators of the two scalar modes. We deform the boundary theory by the dual operators and examine the fermionic field equations, and compare the solutions of the deformed theory with those of the bulk.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

On small values of the Riemann zeta-function at Gram points

In this paper, we prove the existence of a large set of Gram points t{sub n} such that the values ζ(0.5+it{sub n}) are 'anomalously' close to zero. A lower bound for the negative 'discrete' moment of the Riemann zeta-function on the critical line is also given. Bibliography: 13 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Riemann quasi-invariants

The notion of Riemann quasi-invariants is introduced and their applications to several conservation laws are considered. The case of nonisentropic flow of an ideal polytropic gas is analysed in detail. Sufficient conditions for gradient catastrophes are obtained. Bibliography: 16 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

The Effective Dynamics of the Volume Preserving Mean Curvature Flow

We consider the dynamics of small closed submanifolds (‘bubbles’) under the volume preserving mean curvature flow. We construct a map from (n+1)-dimensional Euclidean space into a given (n+1)-dimensional Riemannian manifold which characterizes the existence, stability and dynamics of constant mean curvature submanifolds. This is done in terms of a reduced area function on the Euclidean space, which is given constructively and can be computed perturbatively. This allows us to derive adiabatic and effective dynamics of the bubbles. The results can be mapped by rescaling to the dynamics of fixed size bubbles in almost Euclidean Riemannian manifolds.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Classical mechanics on noncommutative space with Lie-algebraic structure

Highlights: > Suggest a useful method to look for new Lie-algebraic noncommutative spaces. > Find out two new Lie-algebraic noncommutative spaces. > Derive Newton and Hamilton equations that present unimaginable extra forces. > Analyse the source of unimaginable extra forces from space noncummutativity. > Provide various intriguing classical trajectories. - Abstract: We investigate the kinetics of a nonrelativistic particle interacting with a constant external force on a Lie-algebraic noncommutative space. The structure constants of a Lie algebra, also called noncommutative parameters, are constrained in general due to some algebraic properties, such as the antisymmetry and Jacobi identity. Through solving the constraint equations the structure constants satisfy, we obtain two new sorts of algebraic structures, each of which corresponds to one type of noncommutative spaces. Based on such types of noncommutative spaces as the starting point, we analyze the classical motion of the particle interacting with a constant external force by means of the Hamiltonian formalism on a Poisson manifold. Our results not only include that of a recent work as our special cases, but also provide new trajectories of motion governed mainly by marvelous extra forces. The extra forces with the unimaginable tx-dot-,(xx-dot)-, and (xx-double dot)-dependence besides with the usual t-, x-, and x-dot-dependence, originating from a variety of noncommutativity between different spatial coordinates and between spatial coordinates and momenta as well, deform greatly the particle's ordinary trajectories we are quite familiar with on the Euclidean (commutative) space.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Spin(7)-structures on complex linear bundles and explicit Riemannian metrics with holonomy group SU(4)

A system of differential equations with 5 unknowns is fully investigated; this system is equivalent to the existence of a parallel Spin(7)-structure on a cone over a 3-Sasakian manifold. A continuous one-parameter family of solutions to this system is explicitly constructed; it corresponds to metrics with a special holonomy group, SU(4), which generalize Calabi's metrics. Bibliography: 10 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Curvature and Tachibana numbers

The aim of this paper is to define the rth Tachibana number t{sub r} of an n-dimensional compact oriented Riemannian manifold as the dimension of the space of conformally Killing r-forms, for r=1,2,...,n-1. We also describe properties of these numbers, by analogy with properties of the Betti numbers b{sub r} of a compact oriented Riemannian manifold. Bibliography: 25 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2010

Fields in nonaffine bundles. IV. Harmonious non-Abelian currents in string defects

This article continues the study of the category of harmonious field models that was recently introduced as a kinetically nonlinear generalization of the well-known harmonic category of multiscalar fields over a supporting brane world sheet in a target space with a curved Riemannian metric. Like the perfectly harmonious case of which a familiar example is provided by ordinary barotropic perfect fluids, another important subcategory is the simply harmonious case, for which it is shown that as well as 'wiggle' modes of the underlying brane world sheet, and sound type longitudinal modes, there will also be transverse shake modes that propagate at the speed of light. Models of this type are shown to arise from a non-Abelian generalization of the Witten mechanism for conducting string formation by ordinary scalar fields with a suitable quartic self-coupling term in the action.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

Noncommutative spherically symmetric spaces

We examine some noncommutative spherically symmetric spaces in three space dimensions. A generalization of Snyder's noncommutative (Euclidean) space allows the inclusion of the generator of dilations into the defining algebra of the coordinate and rotation operators. We then construct a spherically symmetric noncommutative Laplacian on this space having the correct limiting spectrum. This is presented via a creation and annihilation operator realization of the algebra, which may lend itself to a truncation of the Hilbert space.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Kubo Formulas for Second-Order Hydrodynamic Coefficients

At second order in gradients, conformal relativistic hydrodynamics depends on the viscosity {eta} and on five additional ''second-order'' hydrodynamical coefficients {tau}{sub {Pi}}, {kappa}, {lambda}{sub 1}, {lambda}{sub 2}, and {lambda}{sub 3}. We derive Kubo relations for these coefficients, relating them to equilibrium, fully retarded three-point correlation functions of the stress tensor. We show that the coefficient {lambda}{sub 3} can be evaluated directly by Euclidean means and does not in general vanish.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗