Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Arbitrary functions”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Materializing Inter-Channel Relationships With Multi-Density Woodcock Tracking

Volume rendering techniques for scientific visualization have recently shifted toward Monte Carlo (MC) methods for their flexibility and robustness, but their use in multi-channel visualization remains underexplored. Traditional multi-channel volume rendering often relies on arbitrary, non-physically based color blending functions that hinder interpretation. Here, we introduce multi-density Woodcock tracking, a simple extension of Woodcock tracking that leverages an MC method to produce high-fidelity, physically grounded multi-channel renderings without arbitrary blending. By generalizing Woodcock’s distance tracking, we provide a unified blending modality that also integrates blending functions from prior works. We further implement effects that enhance boundary and feature recognition. By accumulating frames in real-time, our approach delivers high-quality visualizations with perceptual benefits, demonstrated on diverse datasets.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

Global functions in global-local finite-element analysis of localized stresses in prismatic structures

An important consideration in the global local finite-element method (GLFEM) is the availability of global functions for the given problem. The role and mathematical requirements of these global functions in a GLFEM analysis of localized stress states in prismatic structures are discussed. A method is described for determining these global functions. Underlying this method are theorems due to Toupin and Knowles on strain energy decay rates, which are related to a quantitative expression of Saint-Venant's principle. It is mentioned that a mathematically complete set of global functions can be generated, so that any arbitrary interface condition between the finite element and global subregions can be represented. Convergence to the true behavior can be achieved with increasing global functions and finite-element degrees of freedom. Specific attention is devoted to mathematically two-dimensional and three-dimensional prismatic structures. Comments are offered on the GLFEM analysis of NASA flat panel with a discontinuous stiffener. Methods for determining global functions for other effects are also indicated, such as steady-state dynamics and bodies under initial stress.

Dong, Stanley B.↗
NASA NTRS1987

The electron distribution function upstream from the earth's bow shock

A general analytic theory for the distribution function of particles backstreaming from an arbitrary shock in a magnetized plasma is presented. Particle motions are shown to be restricted to two-dimensional planes. A general form for the source term describing upstreaming particles accelerated at the shock is presented along with explicit source terms for planar and parabolic shocks. The origin and form of the escape velocity cutoff for a shock in a magnetized plasma are discussed. The distribution function upstream of a finite planar shock and a parabolic shock in two dimensions is calculated, and an analytic approximation of the cutoff velocity at points in the upstream region is derived. The theory is then applied to the earth's bow shock, calculating distribution functions and the nature and spatial variation of the cutoff velocity. The theory for the particle distribution upstream of the bow shock is compared with the model of Filbert and Kellogg (1979).

Cairns, Iver H.↗
DOE OSTI2024

Bootstrapping smooth conformal defects in Chern-Simons-matter theories

Abstract The expectation value of a smooth conformal line defect in a CFT is a conformal invariant functional of its path in space-time. For example, in largeNholographic theories, these fundamental observables are dual to the open-string partition function in AdS. In this paper, we develop a bootstrap method for studying them and apply it to conformal line defects in Chern-Simons matter theories. In these cases, the line bootstrap is based on three minimal assumptions — conformal invariance of the line defect, largeNfactorization, and the spectrum of the two lowest-lying operators at the end of the line. On the basis of these assumptions, we solve the one-dimensional CFT on the line and systematically compute the defect expectation value in an expansion around the straight line. We find that the conformal symmetry of a straight defect is insufficient to fix the answer. Instead, imposing the conformal symmetry of the defect along an arbitrary curved line leads to a functional bootstrap constraint. The solution to this constraint is found to be unique.

Physics↗
DOE OSTI2020

Convergent momentum-space OPE and bootstrap equations in conformal field theory

General principles of quantum field theory imply that there exists an operator product expansion (OPE) for Wightman functions in Minkowski momentum space that converges for arbitrary kinematics. This convergence is guaranteed to hold in the sense of a distribution, meaning that it holds for correlation functions smeared by smooth test functions. The conformal blocks for this OPE are conceptually extremely simple: they are products of 3-point functions. We construct the conformal blocks in 2-dimensional conformal field theory and show that the OPE in fact converges pointwise to an ordinary function in a specific kinematic region. Using microcausality, we also formulate a bootstrap equation directly in terms of momentum space Wightman functions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1985

Grundy - Parallel processor architecture makes programming easy

The hardware, software, and firmware of the parallel processor, Grundy, are examined. The Grundy processor uses a simple processor that has a totally orthogonal three-address instruction set. The system contains a relative and indirect processing mode to support the high-level language, and uses pseudoprocessors and read-only memory. The system supports high-level language in which arbitrary degrees of algorithmic parallelism is expressed. The functions of the compiler and invocation frame are described. Grundy uses an operating system that can be accessed by an arbitrary number of processes simultaneously, and the access time grows only as the logarithm of the number of active processes. Applications for the parallel processor are discussed.

Meier, R. J., Jr.↗
NASA NTRS1995

A General Method for Solving Systems of Non-Linear Equations

The method of steepest descent is modified so that accelerated convergence is achieved near a root. It is assumed that the function of interest can be approximated near a root by a quadratic form. An eigenvector of the quadratic form is found by evaluating the function and its gradient at an arbitrary point and another suitably selected point. The terminal point of the eigenvector is chosen to lie on the line segment joining the two points. The terminal point found lies on an axis of the quadratic form. The selection of a suitable step size at this point leads directly to the root in the direction of steepest descent in a single step. Newton's root finding method not infrequently diverges if the starting point is far from the root. However, the current method in these regions merely reverts to the method of steepest descent with an adaptive step size. The current method's performance should match that of the Levenberg-Marquardt root finding method since they both share the ability to converge from a starting point far from the root and both exhibit quadratic convergence near a root. The Levenberg-Marquardt method requires storage for coefficients of linear equations. The current method which does not require the solution of linear equations requires more time for additional function and gradient evaluations. The classic trade off of time for space separates the two methods.

Nachtsheim, Philip R.↗
DOE OSTI2024

Dynamical edge modes and entanglement in Maxwell theory

Abstract Previous work on black hole partition functions and entanglement entropy suggests the existence of “edge” degrees of freedom living on the (stretched) horizon. We identify a local and “shrinkable” boundary condition on the stretched horizon that gives rise to such degrees of freedom. They can be interpreted as the Goldstone bosons of gauge transformations supported on the boundary, with the electric field component normal to the boundary as their symplectic conjugate. Applying the covariant phase space formalism for manifolds with boundary, we show that both the symplectic form and Hamiltonian exhibit a bulk-edge split. We then show that the thermal edge partition function is that of a codimension-two ghost compact scalar living on the horizon. In the context of a de Sitter static patch, this agrees with the edge partition functions found by Anninos et al. in arbitrary dimensions. It also yields a 4D entanglement entropy consistent with the conformal anomaly. Generalizing to Proca theory, we find that the prescription of Donnelly and Wall reproduces existing results for its edge partition function, while its classical phase space does not exhibit a bulk-edge split.

Physics↗
DOE OSTI2022

Efficient computation of N -point correlation functions in D dimensions

We present efficient algorithms for computing the N-point correlation functions (NPCFs) of random fields in arbitrary D-dimensional homogeneous and isotropic spaces. Such statistics appear throughout the physical sciences and provide a natural tool to describe stochastic processes. Typically, algorithms for computing the NPCF components have $\mathscr O$(n N ) complexity (for a dataset containing n particles); their application is thus computationally infeasible unless N is small. By projecting the statistic onto a suitably defined angular basis, we show that the estimators can be written in a separable form, with complexity $\mathscr O$(n 2 ) or $\mathscr O$(n g log n g ) if evaluated using a Fast Fourier Transform on a grid of size n g . Our decomposition is built upon the D-dimensional hyperspherical harmonics; these form a complete basis on the (D – 1) sphere and are intrinsically related to angular momentum operators. Concatenation of (N – 1) such harmonics gives states of definite combined angular momentum, forming a natural separable basis for the NPCF. As N and D grow, the number of basis components quickly becomes large, providing a practical limitation to this (and all other) approaches: However, the dimensionality is greatly reduced in the presence of symmetries; for example, isotropic correlation functions require only states of zero combined angular momentum. We provide a Julia package implementing our estimators and show how they can be applied to a variety of scenarios within cosmology and fluid dynamics. The efficiency of such estimators will allow higher-order correlators to become a standard tool in the analysis of random fields.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

funcX: Federated Function as a Service for Science

Here, funcX is a distributed function as a service (FaaS) platform that enables flexible, scalable, and high performance remote function execution. Unlike centralized FaaS systems, funcX decouples the cloud-hosted management functionality from the edge-hosted execution functionality. funcX's endpoint software can be deployed, by users or administrators, on arbitrary laptops, clouds, clusters, and supercomputers, in effect turning them into function serving systems. funcX's cloud-hosted service provides a single location for registering, sharing, and managing both functions and endpoints. It allows for transparent, secure, and reliable function execution across the federated ecosystem of endpoints-enabling users to route functions to endpoints based on specific needs. funcX uses containers (e.g., Docker, Singularity, and Shifter) to provide common execution environments across endpoints. funcX implements various container management strategies to execute functions with high performance and efficiency on diverse funcX endpoints. funcX also integrates with an in-memory data store and Globus for managing data that may span endpoints. We motivate the need for funcX, present our prototype design and implementation, and demonstrate, via experiments on two supercomputers, that funcX can scale to more than 130000 concurrent workers. We show that funcX's container warming-aware routing algorithm can reduce the completion time for 3,000 functions by up to 61% compared to a randomized algorithm and the in-memory data store can speed up data transfers by up to 3x compared to a shared file system.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Phlex: Parallel, Hierarchical, and Layered EXecution of data-processing algorithms

Phlex is a computing framework supporting the parallel, hierarchical, and layered execution of data-processing algorithms. It is based on the functional-programming paradigm, thus guaranteeing thread-safety when invoking user-defined pure functions. Phlex allows users to specify arbitrary graph-based hierarchies of data organization, enabling more flexible processing of data as required by the constraints of the program.

Knoepfel, KyleJ. [Fermi National Accelerator Labor↗
NASA NTRS1983

High frequency green function for aerodynamic noise in moving media. I - General theory. II - Noise from a spreading jet

It is shown how a high frequency analysis can be made for general problems involving flow-generated noise. In the parallel shear flow problem treated by Balsa (1976) and Goldstein (1982), the equation governing sound propagation in the moving medium could be transformed into a wave equation for a stationary medium with an inhomogeneous index of refraction. It is noted that the procedure of Avila and Keller (1963) was then used to construct a high frequency Green function. This procedure involves matching a solution valid in an inner region around the point source to an outer, ray-acoustics solution. This same procedure is used here to construct the Green function for a source in an arbitrary mean flow. In view of the fact that there is no restriction to parallel flow, the governing equations cannot be transformed into a wave equation; the analysis therefore proceeds from the equations of motion themselves.

Durbin, P. A.↗
NASA NTRS1986

Random scattering approach to gravitational microlensing

Small random deflections of a narrow beam of radiation due to gravitational scattering by stars randomly distributed within the deflector plane are considered. Using a Fouriere transform method, the probability of scattering is obtained as a function of scattering angle for an arbitrary number of stars with an arbitrary distribution of masses. The probability density, expressed in proper units, depends on one parameter only: the effective number of stars. At small scattering angles the density is a Gaussian, and at large angles it falls off as the scattering angle to the minus fourth power. The probability distribution for scatterings is simply related to the angular distribution of the surface brightness of a macroimage, averaged over many microimages. The isophotes are ellipses, with the ratio of the major axis to the minor axis, determined by the dimensionless surface mass density and the shear of the lensing system. The number of stars that has to be included in the modeling of microlensing is proportional to the amplification due to the macrolens, and to the square of the dimensionless surface mass density.

Katz, N.↗
NASA NTRS1990

A finite element-boundary integral formulation for scattering by three-dimensional cavity-backed apertures

A numerical technique is proposed for the electromagnetic characterization of the scattering by a three-dimensional cavity-backed aperture in an infinite ground plane. The technique combines the finite element and boundary integral methods to formulate a system of equations for the solution of the aperture fields and those inside the cavity. Specifically, the finite element method is employed to formulate the fields in the cavity region and the boundary integral approach is used in conjunction with the equivalence principle to represent the fields above the ground plane. Unlike traditional approaches, the proposed technique does not require knowledge of the cavity's Green's function and is, therefore, applicable to arbitrary shape depressions and material fillings. Furthermore, the proposed formulation leads to a system having a partly full and partly sparse as well as symmetric and banded matrix which can be solved efficiently using special algorithms.

Jin, Jian-Ming↗