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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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Principal fiber bundle description of number scaling for scalars and vectors: application to gauge theory

The purpose of this paper is to put the description of number scaling and its effects on physics and geometry on a firmer foundation, and to make it more understandable. A main point is that two different concepts, number and number value are combined in the usual representations of number structures. This is valid as long as one structure of each number type is being considered. It is not valid when different structures of each number type are being considered. Elements of base sets of number structures, considered by themselves, have no meaning. They acquire meaning or value as elements of a number structure. Fiber bundles over a space or space time manifold, M, are described. The fiber consists of a collection of many real or complex scaling factor, s. A vector space at a fiber level, s, has as scalars, real or complex number structures at the same level. Connections are described that relate scalar and vector space structures at both neighbor M locations and at neighbor scaling levels. Scalar and vector structure valued fields are described and covariant derivatives of these fields are obtained. Two complex vector fields, each with one real and one imaginary field, appear, with one complex field associated with positions in M and the other with position dependent scaling factors. A derivation of the covariant derivative for scalar and vector values fields gives the same vector fields. The derivation shoes that complex vector field associated with scaling fiber levels is the gradient of a complex scalar field. Use of these results in gauge theory shows that the imaginary part of the vector field associated with M positions acts like the electromagnetic field. The physical relevance of the other three fields, if any, is not known.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Model of Four-Dimensional Sub-Proton Euclidean Space with Real Time for Valence Quarks. Lagrangian Mechanics

The model of Euclidean space with imaginary time used in sub-hadron physics uses only part of it since this part is isomorphic to Minkowski space and has the velocity limit 0 ≤ ||v{sub Ei}|| ≤ 1. The model of four-dimensional Euclidean space with real time (Е space), in which 0 ≤ ||v{sub E}|| ≤ ∞ is investigated. The vectors of this space have Е-invariants, equal or analogous to the invariants of Minkowski space. All relations between physical quantities in Е-space, after they are mapped into Minkowski space, satisfy the principles of SRT and are Lorentz-invariant, and the velocity of light corresponds to infinite velocity. Results obtained in the model are different from the physical laws in Minkowski space. Thus, from the model of the Lagrangian mechanics of quarks in a centrally symmetric attractive potential it follows that the energy-mass of a quark decreases with increase of the velocity and is equal to zero for v = ∞. This made it possible to establish the conditions of emission and absorption of gluons by quarks. The effect of emission of gluons by high-energy quarks was discovered experimentally significantly earlier. The model describes for the first time the dynamic coupling of the masses of constituent and current quarks and reveals new possibilities in the study of intrahardon space. The classical trajectory of the oscillation of quarks in protons is described.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Theory and application of the vector pair correlation function for real-space crystallographic analysis of order/disorder correlations from STEM images

Deviations of local structure and chemistry from the average crystalline unit cell are increasingly recognized to have a significant influence on the properties of many technologically important materials. Here, we present the vector pair correlation function (vPCF) as a new real-space crystallographic analysis method, which can be applied to atomic-resolution scanning transmission electron microscopy (STEM) images to quantify and analyze structural order/disorder correlations. Our STEM-based vPCFs have several advantages over radial PCFs and/or 3D pair distribution functions from x-ray total scattering: vPCFs explicitly retain crystallographic orientation information, are spatially resolved, can be applied directly on a sublattice basis, and are suitable for any material that can be imaged with STEM. To show the utility of our approach, we measure partial vPCFs in Ba 5 SmSn 3 Nb 7 O 30 (BSSN), a tetragonal tungsten bronze (TTB) structured complex oxide. Many TTBs are known to be classical or relaxor ferroelectrics, and these properties have been correlated with the presence of superlattice ordering. BSSN, specifically, exhibits relaxor behavior and an incommensurate structural modulation. From the vPCF data, we observe that, of the cation sites, only the Ba (A2) sublattice is structurally modulated. We then infer the local modulation vector and reveal a marked anisotropy in its correlation length. Finally, short-range correlated polar displacements on the B2 cation sites are observed. This work introduces the vPCF as a powerful real-space crystallography technique, which enables direct, robust quantification of short-to-long range order on a sublattice-specific basis and is applicable to a wide range of complex material types.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2013

Mimetic discretization of the Abelian Chern-Simons theory and link invariants

A mimetic discretization of the Abelian Chern-Simons theory is presented. The study relies on the formulation of a theory of differential forms in the lattice, including a consistent definition of the Hodge duality operation. Explicit expressions for the Gauss Linking Number in the lattice, which correspond to their continuum counterparts are given. A discussion of the discretization of metric structures in the space of transverse vector densities is presented. The study of these metrics could serve to obtain explicit formulae for knot an link invariants in the lattice.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Geometry of matrix product states: Metric, parallel transport, and curvature

We study the geometric properties of the manifold of states described as (uniform) matrix product states. Due to the parameter redundancy in the matrix product state representation, matrix product states have the mathematical structure of a (principal) fiber bundle. The total space or bundle space corresponds to the parameter space, i.e., the space of tensors associated to every physical site. The base manifold is embedded in Hilbert space and can be given the structure of a Kähler manifold by inducing the Hilbert space metric. Our main interest is in the states living in the tangent space to the base manifold, which have recently been shown to be interesting in relation to time dependence and elementary excitations. By lifting these tangent vectors to the (tangent space) of the bundle space using a well-chosen prescription (a principal bundle connection), we can define and efficiently compute an inverse metric, and introduce differential geometric concepts such as parallel transport (related to the Levi-Civita connection) and the Riemann curvature tensor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Coherent orthogonal polynomials

We discuss a fundamental characteristic of orthogonal polynomials, like the existence of a Lie algebra behind them, which can be added to their other relevant aspects. At the basis of the complete framework for orthogonal polynomials we include thus–in addition to differential equations, recurrence relations, Hilbert spaces and square integrable functions–Lie algebra theory. We start here from the square integrable functions on the open connected subset of the real line whose bases are related to orthogonal polynomials. All these one-dimensional continuous spaces allow, besides the standard uncountable basis (|x〉), for an alternative countable basis (|n〉). The matrix elements that relate these two bases are essentially the orthogonal polynomials: Hermite polynomials for the line and Laguerre and Legendre polynomials for the half-line and the line interval, respectively. Differential recurrence relations of orthogonal polynomials allow us to realize that they determine an infinite-dimensional irreducible representation of a non-compact Lie algebra, whose second order Casimir C gives rise to the second order differential equation that defines the corresponding family of orthogonal polynomials. Thus, the Weyl–Heisenberg algebra h(1) with C=0 for Hermite polynomials and su(1,1) with C=−1/4 for Laguerre and Legendre polynomials are obtained. Starting from the orthogonal polynomials the Lie algebra is extended both to the whole space of the L{sup 2} functions and to the corresponding Universal Enveloping Algebra and transformation group. Generalized coherent states from each vector in the space L{sup 2} and, in particular, generalized coherent polynomials are thus obtained. -- Highlights: •Fundamental characteristic of orthogonal polynomials (OP): existence of a Lie algebra. •Differential recurrence relations of OP determine a unitary representation of a non-compact Lie group. •2nd order Casimir originates a 2nd order differential equation that defines the corresponding OP family. •Generalized coherent polynomials are obtained from OP.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Multicanonical sampling of the space of states of ℋ(2, n)-vector models

Problems of temperature behavior of specific heat are solved by the entropy simulation method for Ising models on a simple square lattice and a square spin ice (SSI) lattice with nearest neighbor interaction, models of hexagonal lattices with short-range (SR) dipole interaction, as well as with long-range (LR) dipole interaction and free boundary conditions, and models of spin quasilattices with finite interaction radius. It is established that systems of a finite number of Ising spins with LR dipole interaction can have unusual thermodynamic properties characterized by several specific-heat peaks in the absence of an external magnetic field. For a parallel multicanonical sampling method, optimal schemes are found empirically for partitioning the space of states into energy bands for Ising and SSI models, methods of concatenation and renormalization of histograms are discussed, and a flatness criterion of histograms is proposed. It is established that there is no phase transition in a model with nearest neighbor interaction on a hexagonal lattice, while the temperature behavior of specific heat exhibits singularity in the same model, in case of LR interaction. A spin quasilattice is found that exhibits a nonzero value of residual entropy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Dynamic plasmonic beam shaping by vector beams with arbitrary locally linear polarization states

Vector beams, which have space-variant state of polarization (SOP) comparing with scalar beams with spatially homogeneous SOP, are used to manipulate surface plasmon polarizations (SPPs). We find that the excitation, orientation, and distribution of the focused SPPs excited in a high numerical aperture microscopic configuration highly depend on the space-variant polarization of the incident vector beam. When it comes to vector beam with axial symmetry, multi-foci of SPPs with the same size and uniform intensity can be obtained, and the number of foci is depending on the polarization order n. Those properties can be of great value in biological sensor and plasmonic tweezers applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

GenMod: A generative modeling approach for spectral representation of PDEs with random inputs

Here, we propose a method for quantifying uncertainty in high-dimensional PDE systems with random parameters, where the number of solution evaluations is small. Parametric PDE solutions are often approximated using a spectral decomposition based on polynomial chaos expansions. For the class of systems we consider (i.e., high dimensional with limited solution evaluations) the coefficients are given by an underdetermined linear system in a regression formulation. This implies additional assumptions, such as sparsity of the coefficient vector, are needed to approximate the solution. Here, we present an approach where we assume the coefficients are close to the range of a generative model that maps from a low to a high dimensional space of coefficients. Our approach is inspired be recent work examining how generative models can be used for compressed sensing in systems with random Gaussian measurement matrices. Using results from PDE theory on coefficient decay rates, we construct an explicit generative model that predicts the polynomial chaos coefficient magnitudes. The algorithm we developed to find the coefficients, which we call GenMod, is composed of two main steps. First, we predict the coefficient signs using Orthogonal Matching Pursuit. Then, we assume the coefficients are within a sparse deviation from the range of a sign-adjusted generative model. This allows us to find the coefficients by solving a nonconvex optimization problem, over the input space of the generative model and the space of sparse vectors. We obtain theoretical recovery results for a Lipschitz continuous generative model and for a more specific generative model, based on coefficient decay rate bounds. We examine three high-dimensional problems and show that, for all three examples, the generative model approach outperforms sparsity promoting methods at small sample sizes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Light beams with general direction and polarization: Global description and geometric phase

We construct the manifold describing the family of plane monochromatic light waves with all directions, polarizations, phases and intensities. A smooth description of polarization, valid over the entire sphere S{sup 2} of directions, is given through the construction of an orthogonal basis pair of complex polarization vectors for each direction; any light beam is then uniquely and smoothly specified by giving its direction and two complex amplitudes. This implies that the space of all light beams is the six dimensional manifold S{sup 2}×C{sup 2}∖(0), the (untwisted) Cartesian product of a sphere and a two dimensional complex vector space minus the origin. A Hopf map (i.e. mapping the two complex amplitudes to the Stokes parameters) then leads to the four dimensional manifold S{sup 2}×S{sup 2} which describes beams with all directions and polarization states. This product of two spheres can be viewed as an ordered pair of two points on a single sphere, in contrast to earlier work in which the same system was represented using Majorana’s mapping of the states of a spin one quantum system to an unordered pair of points on a sphere. This is a different manifold, CP{sup 2}, two dimensional complex projective space, which does not faithfully represent the full space of all directions and polarizations. Following the now-standard framework, we exhibit the fibre bundle whose total space is the set of all light beams of non-zero intensity, and base space S{sup 2}×S{sup 2}. We give the U(1) connection which determines the geometric phase as the line integral of a one-form along a closed curve in the total space. Bases are classified as globally smooth, global but singular, and local, with the last type of basis being defined only when the curve traversed by the system is given. Existing as well as new formulae for the geometric phase are presented in this overall framework. -- Highlights: • We construct a polarization basis for light which is smooth in all directions. • Proof that the manifold of all polarizations and directions is S{sup 2}×S{sup 2}. • Formula for the geometric phase for paths in S{sup 2}×S{sup 2}, generalizing earlier work.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Femtosecond photoemission electron microscopy of surface plasmon polariton beam steering via nanohole arrays

Directional control over surface plasmon polariton (SPP) waves is a prerequisite for the development of miniaturized optical circuitry. Here, the efficacy of single and dual component SPP steering elements is explored through photoemission electron microscopy. Our imaging scheme relies on two-color photoemission and counter-propagating SPP generation, which collectively allow SPPs to be visualized in real space. Wave-vector difference mixing between two-dimensional arrays of nanoholes and photon momenta enables SPP steering with directionality governed by the array lattice constant. The magnitude of grating momentum required to achieve counter-propagation guarantees efficient steering over the full range of the negative half-space. In our dual component configuration, separate SPP generation and Bragg diffraction based steering optics are employed. We find that array Bragg planes principally influence the SPP angles through the array band structure, which allows us to visualize both positive and negative refractory waves.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

Two-mode Ginzburg-Landau theory of crystalline anisotropy for fcc-liquid interfaces

Here we develop a Ginzburg-Landau (GL) theory for fcc crystal-melt systems at equilibrium by employing two sets of order parameters that correspond to amplitudes of density waves of principal reciprocal lattice vectors and amplitudes of density waves of a second set of reciprocal lattice vectors. The choice of the second set of reciprocal lattice vectors is constrained by the condition that this set must form closed triangles with the principal reciprocal lattice vectors in reciprocal space to make the fcc-liquid transition first order. The capillary anisotropy of fcc-liquid interfaces is investigated by GL theory with amplitudes of $\langle$111$\rangle$ and $\langle$200$\rangle$ density waves. Furthermore, we explore the dependence of the anisotropy of the excess free energy of the solid-liquid interface on density waves of higher-order reciprocal lattice vectors such as $\langle$311$\rangle$ by extending the two-mode GL theory with an additional mode. The anisotropy calculated using GL theory with input parameters from molecular dynamics (MD) simulations for fcc Ni is compared to that measured in MD simulations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2013

Klein-Gordon equations for energy-momentum of the relativistic particle in rapidity space

The notion of four-rapidity is defined as a four-vector with one time-like and three space-like coordinates. It is proved, the energy and momentum defined in the space of four-rapidity obey Klein-Gordon equations constrained by the classical trajectory of a relativistic particle. It is shown, for small values of a proper mass influence of the constraint is weakened and the classical motion gains features of a wave motion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Quantitative comparison of self-healing ability between Bessel–Gaussian beam and Airy beam

The self-healing ability during propagation process is one of the most important properties of non-diffracting beams. This ability has crucial advantages to light sheet-based microscopy to reduce scattering artefacts, increase the quality of the image and enhance the resolution of microscopy. Based on similarity between two infinite-dimensional complex vectors in Hilbert space, the ability to a Bessel–Gaussian beam and an Airy beam have been studied and compared. Comparing the evolution of the similarity of Bessel–Gaussian beam with Airy beam under the same conditions, we find that Bessel–Gaussian beam has stronger self-healing ability and is more stable than that of Airy beam. To confirm this result, the intensity profiles of Bessel–Gaussian beam and Airy beam with different similarities are numerically calculated and compared.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Accelerating eigenvalue computation for nuclear structure calculations via perturbative corrections

Subspace projection methods utilizing perturbative corrections have been proposed for computing the lowest few eigenvalues and corresponding eigenvectors of large Hamiltonian matrices. In this paper, we build upon these methods and introduce the term Subspace Projection with Perturbative Corrections (SPPC) method to refer to this approach. We tailor the SPPC for nuclear many-body Hamiltonians represented in a truncated configuration interaction subspace, i.e., the no-core shell model (NCSM). We use the hierarchical structure of the NCSM Hamiltonian to partition the Hamiltonian as the sum of two matrices. The first matrix corresponds to the Hamiltonian represented in a small configuration space, whereas the second is viewed as the perturbation to the first matrix. Eigenvalues and eigenvectors of the first matrix can be computed efficiently. Because of the split, perturbative corrections to the eigenvectors of the first matrix can be obtained efficiently from the solutions of a sequence of linear systems of equations defined in the small configuration space. These correction vectors can be combined with the approximate eigenvectors of the first matrix to construct a subspace from which more accurate approximations of the desired eigenpairs can be obtained. We show by numerical examples that the SPPC method can be more efficient than conventional iterative methods for solving large-scale eigenvalue problems such as the Lanczos, block Lanczos and the locally optimal block preconditioned conjugate gradient (LOBPCG) method. The method can also be combined with other methods to avoid convergence stagnation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

Quantitative analysis of magnetic spin and orbital moments from an oxidized iron (1 1 0) surface using electron magnetic circular dichroism

Understanding the ramifications of reduced crystalline symmetry on magnetic behavior is a critical step in improving our understanding of nanoscale and interfacial magnetism. However, investigations of such effects are often controversial largely due to the challenges inherent in directly correlating nanoscale stoichiometry and structure to magnetic behavior. Here, we describe how to use Transmission Electron Microscope (TEM) to obtain Electron Magnetic Circular Dichroism (EMCD) signals as a function of scattering angle to locally probe the magnetic behavior of thin oxide layers grown on an Fe (1 1 0) surface. Experiments and simulations both reveal a strong dependence of the magnetic orbital to spin ratio on its scattering vector in reciprocal space. We exploit this variation to extract the magnetic properties of the oxide cladding layer, showing that it locally may exhibit an enhanced orbital to spin moment ratio. This finding is supported here by both spatially and angularly resolved EMCD measurements, opening up the way for compelling investigations into how magnetic properties are affected by nanoscale features.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Efficient Execution of Recursive Programs on Commodity Vector Hardware

The pursuit of computational efficiency has led to the proliferation of throughput-oriented hardware, from GPUs to increasingly-wide vector units on commodity processors and accelerators. This hardware is designed to efficiently execute data-parallel computations in a vectorized manner. However, many algorithms are more naturally expressed as divide-and-conquer, recursive, task-parallel computations; in the absence of data parallelism, it seems that such algorithms are not well-suited to throughput-oriented architectures. This paper presents a set of novel code transformations that expose the data-parallelism latent in recursive, task-parallel programs. These transformations facilitate straightforward vectorization of task-parallel programs on commodity hardware. We also present scheduling policies that maintain high utilization of vector resources while limiting space usage. Across several task-parallel benchmarks, we demonstrate both efficient vector resource utilization and substantial speedup on chips using Intel's SSE4.2 vector units as well as accelerators using Intel's AVX512 units.

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