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.

SourceResearch connectionFrom yearThrough year

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

At least 325 records · Page 18

All sources NASA NTRS DOE OSTI

NASA NTRS1973

Liapunov stability analysis of spinning flexible spacecraft.

The attitude stability of a class of spinning flexible spacecraft in a force-free environment is analyzed. The spacecraft is modeled as a rigid core having attached to it a flexible appendage idealized as a collection of elastically interconnected particles. Liapunov stability theorems are employed with the Hamiltonian of the system, constrained through the angular momentum integral so as to admit complete damping, used as a testing function. The Hamiltonian is written in terms of modal coordinates as interpreted by the hybrid coordinate formulation, thus allowing truncation to a level amenable to literal stability analysis. Testing functions are constructed for a spacecraft with an arbitrary (discretized) appendage, and closed form stability criteria are generated for the first mode of a restricted appendage model lying in a plane which contains the center of mass and is orthogonal to the spin axis. The criteria are (except for idealized cases on the stability boundary line in the parameter space) both necessary and sufficient for stability for any spacecraft characterized by the planar appendage model, such as a spacecraft containing solar panels and/or radial booms.

Barbera, F. J.↗

NASA NTRS1975

Steady subsonic flow around finite-thickness wings

The general method for analyzing steady subsonic potential aerodynamic flow around a lifting body having arbitrary shape is presented. By using the Green function method, an integral representation for the potential is obtained. Under small perturbation assumption, the potential at any point, P, in the field depends only upon the values of the potential and its normal derivative on the surface of the body. Hence if the point P approaches the surface of the body, the representation reduces to an integral equation relating the potential and its normal derivative (which is known from the boundary conditions) on the surface. The question of uniqueness is examined and it is shown that, for thin wings, the operator becomes singular as the thickness approaches zero. This fact may yield numerical problems for very thin wings. However, numerical results obtained for a rectangular wing in subsonic flow show that these problems do not appear even for thickness ratio tau = .001. Comparison with existing results shows that the proposed method is at least as fast and accurate as the lifting surface theories.

Kuo, C. C.↗

NASA NTRS1977

Unsteady aerodynamic modeling for arbitrary motions

Results indicating that unsteady aerodynamic loads derived under the assumption of simple harmonic motions executed by airfoil or wing can be extended to arbitrary motions are summarized. The generalized Theodorsen (1953) function referable to loads due to simple harmonic oscillations of a wing section in incompressible flow, the Laplace inversion integral for unsteady aerodynamic loads, calculations of root loci of aeroelastic loads, and analysis of generalized compressible transient airloads are discussed.

Edwards, J. W.↗

NASA NTRS1990

Development of a defect stream function, law of the wall/wake method for compressible turbulent boundary layers

The method presented is designed to improve the accuracy and computational efficiency of existing numerical methods for the solution of flows with compressible turbulent boundary layers. A compressible defect stream function formulation of the governing equations assuming an arbitrary turbulence model is derived. This formulation is advantageous because it has a constrained zero-order approximation with respect to the wall shear stress and the tangential momentum equation has a first integral. Previous problems with this type of formulation near the wall are eliminated by using empirically based analytic expressions to define the flow near the wall. The van Driest law of the wall for velocity and the modified Crocco temperature-velocity relationship are used. The associated compressible law of the wake is determined and it extends the valid range of the analytical expressions beyond the logarithmic region of the boundary layer. The need for an inner-region eddy viscosity model is completely avoided. The near-wall analytic expressions are patched to numerically computed outer region solutions at a point determined during the computation. A new boundary condition on the normal derivative of the tangential velocity at the surface is presented; this condition replaces the no-slip condition and enables numerical integration to the surface with a relatively coarse grid using only an outer region turbulence model. The method was evaluated for incompressible and compressible equilibrium flows and was implemented into an existing Navier-Stokes code using the assumption of local equilibrium flow with respect to the patching. The method has proven to be accurate and efficient.

Wahls, Richard A.↗

NASA NTRS1990

An endorsement-based approach to student modeling for planner-controlled intelligent tutoring systems

An approach is described to student modeling for intelligent tutoring systems based on an explicit representation of the tutor's beliefs about the student and the arguments for and against those beliefs (called endorsements). A lexicographic comparison of arguments, sorted according to evidence reliability, provides a principled means of determining those beliefs that are considered true, false, or uncertain. Each of these beliefs is ultimately justified by underlying assessment data. The endorsement-based approach to student modeling is particularly appropriate for tutors controlled by instructional planners. These tutors place greater demands on a student model than opportunistic tutors. Numerical calculi approaches are less well-suited because it is difficult to correctly assign numbers for evidence reliability and rule plausibility. It may also be difficult to interpret final results and provide suitable combining functions. When numeric measures of uncertainty are used, arbitrary numeric thresholds are often required for planning decisions. Such an approach is inappropriate when robust context-sensitive planning decisions must be made. A TMS-based implementation of the endorsement-based approach to student modeling is presented, this approach is compared to alternatives, and a project history is provided describing the evolution of this approach.

Murray, William R.↗

NASA NTRS2002

Application of the generalized vertical coordinate ocean model for better representing satellite data

It is found that two adaptive parametric functions can be introduced into the basic ocean equations for utilizing the optimal or hybrid features of commonly used z-level, terrain- following, isopycnal, and pressure coordinates in numerical ocean models. The two parametric functions are formulated by combining three techniques: the arbitrary vertical coordinate system of Kasahara (1 974), the Jacobian pressure gradient formulation of Song (1 998), and a newly developed metric factor that permits both compressible (non-Boussinesq) and incompressible (Boussinesq) approximations. Based on the new formulation, an adaptive modeling strategy is proposed and a staggered finite volume method is designed to ensure conservation of important physical properties and numerical accuracy. Implementation of the combined techniques to SCRUM (Song and Haidvogel1994) shows that the adaptive modeling strategy can be applied to any existing ocean model without incurring computational expense or altering the original numerical schemes. Such a generalized coordinate model is expected to benefit diverse ocean modelers for easily choosing optimal vertical structures and sharing modeling resources based on a common model platform. Several representing oceanographic problems with different scales and characteristics, such as coastal canyons, basin-scale circulation, and global ocean circulation, are used to demonstrate the model's capability for multiple applications. New results show that the model is capable of simultaneously resolving both Boussinesq and non-Boussinesq, and both small- and large-scale processes well. This talk will focus on its applications of multiple satellite sensing data in eddy-resolving simulations of Asian Marginal Sea and Kurosio. Attention will be given to how Topex/Poseidon SSH, TRMM SST; and GRACE ocean bottom pressure can be correctly represented in a non- Boussinesq model.

numerical ocean model generalized coordinate syste↗

NASA NTRS2010

Nonlinear Dynamics of Cantilever-Sample Interactions in Atomic Force Microscopy

The interaction of the cantilever tip of an atomic force microscope (AFM) with the sample surface is obtained by treating the cantilever and sample as independent systems coupled by a nonlinear force acting between the cantilever tip and a volume element of the sample surface. The volume element is subjected to a restoring force from the remainder of the sample that provides dynamical equilibrium for the combined systems. The model accounts for the positions on the cantilever of the cantilever tip, laser probe, and excitation force (if any) via a basis set of set of orthogonal functions that may be generalized to account for arbitrary cantilever shapes. The basis set is extended to include nonlinear cantilever modes. The model leads to a pair of coupled nonlinear differential equations that are solved analytically using a matrix iteration procedure. The effects of oscillatory excitation forces applied either to the cantilever or to the sample surface (or to both) are obtained from the solution set and applied to the to the assessment of phase and amplitude signals generated by various acoustic-atomic force microscope (A-AFM) modalities. The influence of bistable cantilever modes of on AFM signal generation is discussed. The effects on the cantilever-sample surface dynamics of subsurface features embedded in the sample that are perturbed by surface-generated oscillatory excitation forces and carried to the cantilever via wave propagation are accounted by the Bolef-Miller propagating wave model. Expressions pertaining to signal generation and image contrast in A-AFM are obtained and applied to amplitude modulation (intermittent contact) atomic force microscopy and resonant difference-frequency atomic force ultrasonic microscopy (RDF-AFUM). The influence of phase accumulation in A-AFM on image contrast is discussed, as is the effect of hard contact and maximum nonlinearity regimes of A-AFM operation.

Cantrell, John H.↗

NASA NTRS1981

Comparison of a barotropic blocking theory with observation

Hart (1979) showed that the truncated spectral equations obtained by Charney and Devore (1979) could be derived merely by assuming that the cross-stream scale of the topography was large compared to the downstream scale. Since actual topography does not have the large y scales postulated by Hart, his model was modified in the current investigation to obtain equations with arbitrary zonal variations of topography by projecting all variable functions onto the first topographic cross-stream mode. The topographic heights and streamfunctions are expanded as Fourier series in the cross-stream coordinate and the series are truncated after the first term. This accomplishes Hart's results but permits more realistic y variations in the topography. The present investigation is the first in a two-part series. The second part will deal with a two-layer baroclinic channel flow, again with arbitrary zonal variations of topography.

Charney, J. G.↗

DOE OSTI2024

Inclusive reactions from finite Minkowski spacetime correlation functions

The need to determine scattering amplitudes of few-hadron systems for arbitrary kinematics expands a broad set of subfields of modern-day nuclear and hadronic physics. In this work, we expand upon previous explorations on the use of real-time methods, like quantum computing or tensor networks, to determine few-body scattering amplitudes. Such calculations must be performed in a finite Minkowski spacetime, where scattering amplitudes are not well defined. Our previous work presented a conjecture of a systematically improvable estimator for scattering amplitudes constructed from finite-volume correlation functions. Here we provide further evidence that the prescription works for larger kinematic regions than previously explored as well as a broader class of scattering amplitudes. Finally, we devise a new method for estimating the order of magnitude of the error associated with finite time separations needed for such calculations. In units of the lightest mass of the theory, we find that to constrain amplitudes using real-time methods within O ( 10 % ) , the spacetime volumes must satisfy m L ∼ O ( 10 – 10 2 ) ) and m T ∼ O ( 10 2 – 10 4 ) . Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Minimally entangled state preparation of localized wave functions on quantum computers

Initializing a single site of a lattice scalar field theory into an arbitrary state with support throughout the quantum register requires $O(2^{nQ})$ entangling gates on a quantum computer with $n_Q$ qubits per site. It is conceivable that instead initializing to functions that are good approximations to states may have utility in reducing the number of required entangling gates. In the case of a single site of a noninteracting scalar field theory, initializing to a symmetric exponential wave function requires $n_Q – 1$ entangling gates, the minimal number necessary to create an entangled state of all $n_Q$ qubits. This is compared with the $2^{nQ – 1} + n_Q – 3 + δ_{nQ, 1}$ required for a symmetric Gaussian wave function. In this work, we explore the initialization of one-site $(n_Q = 4)$, two-site $(n_Q = 3)$, and three-site ( n Q = 3 ) noninteracting scalar field theories with symmetric exponential wave functions using IBM's quantum simulators and quantum devices (Poughkeepsie and Tokyo). With the digitizations attainable with $n_Q = 3,4$, these tensor-product wave functions are found to have large overlap with a Gaussian wave function and provide a suitable low-noise initialization for improvement and Somma inflation. Further, in performing these simulations, we have employed a workflow that interleaves calibrations to mitigate systematic errors in production. The calibrations allow tolerance cuts on gate performance including the fidelity of the symmetrizing Hadamard gate, both in vacuum $(|\textbf{0}\gg^{\bigotimes nQ})$ and in medium ($n_Q –1$ qubits initialized to an exponential function). The results obtained in this work are relevant to systems beyond scalar field theories, such as the deuteron radial wave function, two- and three-dimensional Cartesian-space wave functions, and nonrelativistic multinucleon systems built on a localized eigenbasis.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1998

Automatic Molecular Design using Evolutionary Techniques

Molecular nanotechnology is the precise, three-dimensional control of materials and devices at the atomic scale. An important part of nanotechnology is the design of molecules for specific purposes. This paper describes early results using genetic software techniques to automatically design molecules under the control of a fitness function. The fitness function must be capable of determining which of two arbitrary molecules is better for a specific task. The software begins by generating a population of random molecules. The population is then evolved towards greater fitness by randomly combining parts of the better individuals to create new molecules. These new molecules then replace some of the worst molecules in the population. The unique aspect of our approach is that we apply genetic crossover to molecules represented by graphs, i.e., sets of atoms and the bonds that connect them. We present evidence suggesting that crossover alone, operating on graphs, can evolve any possible molecule given an appropriate fitness function and a population containing both rings and chains. Prior work evolved strings or trees that were subsequently processed to generate molecular graphs. In principle, genetic graph software should be able to evolve other graph representable systems such as circuits, transportation networks, metabolic pathways, computer networks, etc.

Globus, Al↗

NASA NTRS1988

Bayes classification of terrain cover using normalized polarimetric data

The normalized polarimetric classifier (NPC) which uses only the relative magnitudes and phases of the polarimetric data is proposed for discrimination of terrain elements. The probability density functions (PDFs) of polarimetric data are assumed to have a complex Gaussian distribution, and the marginal PDF of the normalized polarimetric data is derived by adopting the Euclidean norm as the normalization function. The general form of the distance measure for the NPC is also obtained. It is demonstrated that for polarimetric data with an arbitrary PDF, the distance measure of NPC will be independent of the normalization function selected even when the classifier is mistrained. A complex Gaussian distribution is assumed for the polarimetric data consisting of grass and tree regions. The probability of error for the NPC is compared with those of several other single-feature classifiers. The classification error of NPCs is shown to be independent of the normalization function.

Yueh, H. A.↗

NASA NTRS1937

Potential flow about arbitrary biplane wing sections

A rigorous treatment is given of the problem of determining the two-dimensional potential flow around arbitrary biplane cellules. The analysis involves the use of elliptic functions and is sufficiently general to include the effects of such elements as the section shapes, the chord ratio, gap, stagger, and decalage, which elements may be specified arbitrarily. The flow problem is resolved by making use of the methods of conformal representation. Thus the solution of the problem of transforming conformally two arbitrary contours into two circles is expressed by a pair of simultaneous integral equations, for which a method of numerical solution is outlined. As an example of the numerical process, the pressure distribution over certain arrangements of the NACA 4412 airfoil in biplane combinations is presented and compared with the monoplane pressure distribution.

Garrick, I E↗

DOE OSTI2020

Extremum seeking for optimal control problems with unknown time-varying systems and unknown objective functions

We consider the problem of optimal feedback control of an unknown, noisy, time-varying, dynamic system that is initialized repeatedly. Examples include a robotic manipulator which must perform the same motion, such as assisting a human, repeatedly and accelerating cavities in particle accelerators which are turned on for a fraction of a second with given initial conditions and vary slowly due to temperature fluctuations. In this paper, we present an approach that applies to systems of practical interest. The method presented here is model independent; does not require knowledge of the objective function; is robust to measurement noise; is applicable for any set of initial conditions; is applicable to simultaneously controlling an arbitrary number of parameters; and may be implemented with a broad range of continuous or discontinuous functions such as sine or square waves. For systems with convex cost functions we prove that our algorithm will produce controllers that approach the minimal cost. For linear systems we reproduce the cost minimizing linear quadratic regulator optimal controller that could have been designed analytically had the system and cost function been known. We demonstrate the effectiveness of the algorithm with simulation studies of noisy and time-varying systems.

42 ENGINEERING↗

DOE OSTI2020

The cosmological bootstrap: inflationary correlators from symmetries and singularities

Scattering amplitudes at weak coupling are highly constrained by Lorentz invariance, locality and unitarity, and depend on model details only through coupling constants and the particle content of the theory. For example, four-particle amplitudes are analytic for contact interactions and have simple poles with appropriately positive residues for tree-level exchange. In this paper, we develop an understanding of inflationary correlators which parallels that of flat-space scattering amplitudes. Specifically, we study slow-roll inflation with weak couplings to extra massive particles, for which all correlation functions are controlled by an approximate conformal symmetry on the boundary of the spacetime. After systematically classifying all possible contact terms in de Sitter space, we derive an analytic expression for the four-point function of conformally coupled scalars mediated by the tree-level exchange of massive scalars. Conformal symmetry implies that the correlator satisfies a pair of differential equations with respect to spatial momenta, encoding bulk time evolution in purely boundary terms. The absence of unphysical singularities (and the correct normalization of physical ones) completely fixes this correlator. Moreover, a “spin-raising” operator relates it to the correlators associated with the exchange of particles with spin, while “weight-shifting” operators map it to the four-point function of massless scalars. We explain how these de Sitter four-point functions can be perturbed to obtain inflationary three-point functions. Using our formalism, we reproduce many classic results in the literature, such as the three-point function of slow-roll inflation, and provide a complete classification of all inflationary three- and four-point functions arising from weakly broken conformal symmetry. Remarkably, the inflationary bispectrum associated with the exchange of particles with arbitrary spin is completely characterized by the soft limit of the simplest scalar-exchange four-point function of conformally coupled scalars and a series of contact terms. Finally, we demonstrate that the inflationary correlators contain flat-space scattering amplitudes via a suitable analytic continuation of the external momenta, which can also be directly connected with the signals for particle production seen in the squeezed limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

A fitting algorithm for optimizing ion implantation energies and fluences

In this work we describe a method to automatically generate an ion implantation recipe, a set of energies and fluences, to produce a desired defect density profile in a solid using the fewest required energies. We simulate defect density profiles for a range of ion energies, fit them with an appropriate function, and interpolate to yield defect density profiles at arbitrary ion energies. Given Ν energies, we then optimize a set of Ν energy-fluence pairs to match a given target defect density profile. Finally, we find the minimum Ν such that the error between the target defect density profile and the defect density profile generated by the Ν energy-fluence pairs is less than a given threshold. Inspired by quantum sensing applications with nitrogen-vacancy centers in diamond, we apply our technique to calculate optimal ion implantation recipes to create uniform-density 1 μm surface layers of 15 N or vacancies (using 4 He).

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2024

Interlayer Coupling Controlled Ordering and Phases in Polar Vortex Superlattices

The recent discovery of polar topological structures has opened the door for exciting physics and emergent properties. There is, however, little methodology to engineer stability and ordering in these systems, properties of interest for engineering emergent functionalities. Notably, when the surface area is extended to arbitrary thicknesses, the topological polar texture becomes unstable. Here we show that this instability of the phase is due to electrical coupling between successive layers. We demonstrate that this electrical coupling is indicative of an effective screening length in the dielectric, similar to the conductor–ferroelectric interface. Controlling the electrostatics of the superlattice interfaces, the system can be tuned between a pure topological vortex state and a mixed classical-topological phase. This coupling also enables engineering coherency among the vortices, not only tuning the bulk phase diagram but also enabling the emergence of a 3D lattice of polar textures.

3D ordering↗

DOE OSTI2021

SILIA: software implementation of a multi-channel, multi-frequency lock-in amplifier for spectroscopy and imaging applications

In this work, we describe a software implementation of a multi-channel, multi-frequency Lock-in Amplifier (SILIA) to extract modulated signals from noisy data distributed over multiple channels of arbitrary number and size. This software implementation emulates the functionality of a multi-channel, multi-frequency lock-in amplifier in a post-processing step following data acquisition. Unlike most traditional lock-in amplifiers, SILIA can work with any number of input channels and is especially useful to analyze data distributed over many channels. We demonstrate the versatility and performance for extracting weak signals in spectroscopy and fluorescence microscopy. We also discuss more general applications and exhibit a method to automatically estimate error from a lock-in result.

47 OTHER INSTRUMENTATION↗