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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 541 records · Page 30
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NASA NTRSDate not supplied

Efficient and Singularity-Aware Inverse Kinematics for 6-DOF and 7-DOF Revolute Manipulators

Inverse kinematics (IK) for 6-DOF and 7-DOF revolute robot manipulators may be decomposed into canonical subproblems which find the angles on circles where they intersect with other geometric objects. We present new algebraic solutions and geometric interpretations for six subproblems. We demonstrate significant performance improvements over existing IK methods. 7-DOF manipulators have one redundant DOF to parameterize, so we introduce the general SEW angle, which generalizes the conventional SEW angle but with an arbitrary reference direction function. One special choice, the stereographic SEW angle, has a singularity when the wrist is on a half-line instead of a full line.

Computational Geometry↗
DOE OSTI2018

Multiphase Optimal and Non-Singular Power Flow by Successive Linear Approximations: Preprint

We propose an optimal power flow method for multiphase power systems. The method works for both radial and meshed networks, and is able to accommodate different types of load/source connections such as wye, delta, etc. Moreover, the method generates a sequence of non-singular points in the electrical state space and a corresponding sequence of power injections, which can be used in real-time control settings. Under certain conditions, the sequences attain the local minimum. The method has been tested using several typical networks, including the IEEE 37-bus and 123-bus test feeders.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Novel Solver Algorithms for Nearly Singular Linear Systems Arising in Combustion Modelling

Direct Numerical Simulations of realistic combustion devices are extremely challenging due to the wide separation of scales in the simulation, for example an internal combustion (IC) engine chamber, and the flame thickness of a high-pressure flame. The PeleLMeX solver uses adaptive mesh refinement (AMR) to evolve multi-species reacting flows in the low Mach number limit at the Exascale and relies on an embedded boundary (EB) approach to represent complex geometries. In that framework, the EB geometries often give rise to very small cut-cells along the boundary, which translate into extreme ill-conditioning of the pressure-projection, with eigenvalues that span 15-16 orders of magnitude. In this talk, we focus on the case of a typical IC piston bowl geometry for which we present on a novel approach towards solving these nearly singular linear systems with ILU-based, C-AMG smoothers on massively parallel architectures. In particular, we use scaling and equilibration algorithms to handle the non-normality of the upper triangular factors. This enables us to approximate the highly sequential triangular solve algorithm, embedded in the AMG smoothing-solve phase, with Jacobi iterations. This approximation can be written as a convergent Neumann series whose terms are composed of highly parallel sparse matrix vector multiplications. The result is an algorithm that substantially decreases setup and solve time, compared to state-of-the-art, for these challenging linear systems.

combustion modelling↗
DOE OSTI2018

Singular Temperature Dependence of the Equation of State of Superconductors with Spin-Orbit Interaction in Low-Temperature Region – II

We extend a previous study of the space and temperature dependence of the order parameter in an ultrathin superconducting film in a longitudinal magnetic field to the vicinity of the critical transition surface. In these films, the spin-orbit interaction can be sizeable. The calculations are restricted to the low-temperature regime. Special attention is given to the zero temperature limit where the state with the maximum value of the critical field is investigated for the given strength of the spin-orbit interaction.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Effective construction of eigenvectors for a class of singular sparse matrices

Fundamental results and an efficient algorithm for constructing eigenvectors corresponding to non-zero eigenvalues of matrices with zero rows and/or columns are developed. The formulation is built on the relation between eigenvectors of such matrices and the eigenvectors of their submatrices after removing all zero rows and columns. While being easily utilized, the algorithm decreases the computation time needed for numerical eigenanalysis, and resolves potential numerical eigensolver instabilities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Discretizing singular point sources in hyperbolic wave propagation problems

Here, we develop high order accurate source discretizations for hyperbolic wave propagation problems in first order formulation that are discretized by finite difference schemes. By studying the Fourier series expansions of the source discretization and the finite difference operator, we derive sufficient conditions for achieving design accuracy in the numerical solution. Only half of the conditions in Fourier space can be satisfied through moment conditions on the source discretization, and we develop smoothness conditions for satisfying the remaining accuracy conditions. The resulting source discretization has compact support in physical space, and is spread over as many grid points as the number of moment and smoothness conditions. In numerical experiments we demonstrate high order of accuracy in the numerical solution of the 1-D advection equation (both in the interior and near a boundary), the 3-D elastic wave equation, and the 3-D linearized Euler equations.

58 GEOSCIENCES↗
DOE OSTI2015

Complex-time singularity and locality estimates for quantum lattice systems

We present and prove a well-known locality bound for the complex-time dynamics of a general class of one-dimensional quantum spin systems. Then we discuss how one might hope to extend this same procedure to higher dimensions using ideas related to the Eden growth process and lattice trees. Finally, we demonstrate with a specific family of lattice trees in the plane why this approach breaks down in dimensions greater than one and prove that there exist interactions for which the complex-time dynamics blows-up in finite imaginary time. .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Current singularities in line-tied three-dimensional magnetic fields

This paper considers the current distributions that derive from finite amplitude perturbations of line-tied magnetic fields comprising hyperbolic field structures. The initial equilibrium on which we principally focus is a planar magnetic X-point threaded by a uniform axial field. This field is line-tied on all surfaces but subject to three-dimensional (3D) disturbances that alter the initial topology. Results of ideal relaxation simulations are presented which illustrate how intense current structures form that can be related, through the influence of line-tying, to the quasi-separatrix layers (QSLs) of the initial configuration. It is demonstrated that the location within the QSL that attracts the current, and its scaling properties, are strongly dependent on the relative dimensions of the QSL with respect to the line-tied boundaries. These results are contrasted with the behavior of a line-tied 3D field containing an isolated null point. In this case, it is found that the dominant current always forms at the null, but that the collapse is inhibited when the null is closer to a line-tied boundary.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Singularities of Silicon Surface Nanostructuring due to Ultrafast Heating in Water by a Femtosecond Laser Pulse

Silicon surface morphology induced by a femtosecond laser pulse at near-threshold fluences in water environment is investigated by means of atomic-force microscopy (AFM). With increasing fluence, the silicon surface transforms into nanoscale ring-shaped and blister structures, as well as smooth and nanostructured microcraters with a minimum depth of 1 nm. The formation of starlike patterns imprinted at the surface of microcraters at fluences above the ablation threshold is observed.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2022

Singularity-EOS XCAP Report

Solving the Euler equations is a fundamental component of simulating many physical phenomena ranging from high explosives to astrophysics. An equation of state (EOS) is a required piece that relates any two thermodynamic quantities to all other thermodynamic values. The presence of multiple materials within a control volume further complicates the solution requiring additional equations to describe the interaction of materials at a sub-grid level. Equations of state themselves can also come in many forms ranging from simple algebraic relations to more complicated differential equation models that describe material interactions over a broad range of physical conditions. In the latter case, the EOS is often pre-computed at a given set of grid points and provided in a tabular form where additional properties can be derived from the interpolation functions.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1995

Application of Singular Spectrum Analysis to Solar Irradiance Variability

Studies of solar variability improve our knowledge of the internal structure and dynamical processes taking place within the Sun that lead to solar irradiance changes. Becuase of the astrophysical and climatic significance of irradiance variability, considerable effort has been devoted to model and understand its physical origin.

Singular Spectrum Analysis↗
DOE OSTI2024

Multicollinear singularities in celestial CFT

The purpose of this paper is to study the holomorphic multicollinear limit of (celestial) amplitudes and use it to further investigate the double residue condition for (hard celestial) amplitudes and the celestial operator product expansion. We first set up the notion of holomorphic multicollinear limits of amplitudes and derive the 3-collinear splitting functions for Yang-Mills theory, Einstein gravity, and massless ϕ 3 theory. In particular, we find that in ϕ 3 theory the celestial 3-OPE contains a term with a branch cut. This explicit example confirms that branch cuts can obstruct the double residue condition for hard celestial amplitudes, which is the underlying cause of the celestial Jacobi identities not holding for certain theories. This addresses an ongoing debate in the literature about associativity of the celestial OPEs and concretely demonstrates a new (multi-particle) term in the celestial OPE coming from the multi-particle channel in the amplitudes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Open string amplitudes: singularities, asymptotics and new representations

Open string amplitudes at tree level have been studied for over fifty years. However, there is no known analytic form for general n-point amplitudes, and their conventional representation in terms of worldsheet integrals does not make many of their most basic physical properties manifest. Recently, a formulation of these amplitudes exposing the underlying “binary geometry” via the use of “u” variables has given us many insights into their basic features. In this paper, we initiate a systematic exploration of fundamental aspects of open string amplitudes from this new point of view. We begin by finding explicit expressions for the factorization of amplitudes at general massive levels, which are seen to be determined by products of lower-point massless amplitudes with shifted kinematics. We then study the asymptotic behavior when subsets of kinematic variables become large, delineating regimes with exponential (generalized hard scattering) and power-law (generalized Regge) behavior. We also give precise expressions for the asymptotics, which reveal another example of the recently observed property of factorization away from poles. We derive new recursion relations for the amplitude, which when repeatedly applied reduce to infinite series representations with a wider domain of convergence than the usual integral representations. For the five-point case, we present a new closed-form expression for the amplitude that for the first time gives its analytic continuation to all of kinematic space. We also discuss novel relations between amplitudes at different kinematic points following from the recently observed “split” factorizations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗