Search NASA⌕ Search

SEARCH · Search NASA

Results for “DISCRETE FUNCTION”

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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Loop transfer recovery for general nonminimum phase discrete time systems. II - Design

The authors consider the design of controllers for the recovery of target loop transfer function or sensitivity and complementary sensitivity functions for general nonminimum phase discrete time systems. The necessary design constraints and the available design freedom are reviewed. In view of the available freedom, possible specifications on the eigenstructure of the observer dynamic matrix are formulated. Three different types of controllers which are respectively based on prediction, current, and reduced-order estimators are considered. For each one of those controllers, three different design techniques are developed. The first one is an eigenstructure assignment scheme, while the other two are optimization-based designs. The eigenstructure assignment method yields a controller design which achieves any chosen recovery error matrix among a set of admissible recovery error matrices. On the other hand, one of the optimization-based design methods leads to a controller that achieves a recovery error matrix having the infimum H-infinity norm, while the other does the same except it achieves a recovery error matrix having the infimum H2 norm.

Chen, Ben M.↗
NASA NTRS1977

An investigation of rotor noise generation by aerodynamic disturbance

An open rotor was considered as a process for converting an unsteady velocity inflow into sound radiation. With the aid of crude assumptions, aero-acoustic transfer functions were defined theoretically for both discrete frequency and broad band noise. A study of the validity of these transfer functions yielded results which show good agreement at discrete frequencies though slightly less good for broad band noise. Agreement in both cases holds over three or more decades of the relevant parameters. A rotating hot wire anemometry system consisting of a single hot wire probe mounted in the nose cone of the rotor was used to quantify fluctuations in the airflow onto a single rotor blade for the transfer function results. Further theoretical analysis revealed that the sound field can be expressed in terms of blade-to-blade correlations in the airflow, and results from two probes rotating simultaneously were modelled mathematically and inserted in the theory. Preliminary results snow encouraging agreement with experimental data.

Whitfield, C. E.↗
NASA NTRS1983

Explicit Hilbert-space representations of atomic and molecular photoabsorption spectra - Computational studies of Stieltjes-Tchebycheff functions

Computational methods are reported for construction of discrete and continuum Schroedinger states in atoms and molecules employing explicit Hilbert space procedures familiar from bound state studies. As theoretical development, the Schroedinger problem of interest is described, the Cauchy-Lanczos bases and orthonormal polynomials used in constructing L-squared Stieltjes-Tchebycheff (ST) approximations to the discrete and continuum states are defined, and certain properties of these functions are indicated. Advantages and limitations of the ST approach to spectral studies relative to more conventional calculations are discussed, and aspects of the approach in single-channel approximations to larger molecules are described. Procedures are indicated for construction of photoejection anisotropies and for performing coupled-channel calculations employing the ST formalism. Finally, explicit descriptive intercomparisons are made of the nature and diagnostic value of ST functions with more conventional scattering functions.

Hermann, M. R.↗
NASA NTRS1995

Nonlinear Control and Discrete Event Systems

As the operation of large systems becomes ever more dependent on extensive automation, the need for an effective solution to the problem of design and validation of the underlying software becomes more critical. Large systems possesses much detailed structure, typically hierarchical, and they are hybrid. Information processing at the top of the hierarchy is by means of formal logic and sentences; on the bottom it is by means of simple scalar differential equations and functions of time; and in the middle it is by an interacting mix of nonlinear multi-axis differential equations and automata, and functions of time and discrete events. The lecture will address the overall problem as it relates to flight vehicle management, describe the middle level, and offer a design approach that is based on Differential Geometry and Discrete Event Dynamic Systems Theory.

Meyer, George↗
NASA NTRS2004

Improved Ionospheric Electrodynamic Models and Application to Calculating Joule Heating Rates

Improved techniques have been developed for empirical modeling of the high-latitude electric potentials and magnetic field aligned currents (FAC) as a function of the solar wind parameters. The FAC model is constructed using scalar magnetic Euler potentials, and functions as a twin to the electric potential model. The improved models have more accurate field values as well as more accurate boundary locations. Non-linear saturation effects in the solar wind-magnetosphere coupling are also better reproduced. The models are constructed using a hybrid technique, which has spherical harmonic functions only within a small area at the pole. At lower latitudes the potentials are constructed from multiple Fourier series functions of longitude, at discrete latitudinal steps. It is shown that the two models can be used together in order to calculate the total Poynting flux and Joule heating in the ionosphere. An additional model of the ionospheric conductivity is not required in order to obtain the ionospheric currents and Joule heating, as the conductivity variations as a function of the solar inclination are implicitly contained within the FAC model's data. The models outputs are shown for various input conditions, as well as compared with satellite measurements. The calculations of the total Joule heating are compared with results obtained by the inversion of ground-based magnetometer measurements. Like their predecessors, these empirical models should continue to be a useful research and forecast tools.

Weimer, D. R.↗
NASA NTRS2008

Adjoint-Based Methodology for Time-Dependent Optimization

This paper presents a discrete adjoint method for a broad class of time-dependent optimization problems. The time-dependent adjoint equations are derived in terms of the discrete residual of an arbitrary finite volume scheme which approximates unsteady conservation law equations. Although only the 2-D unsteady Euler equations are considered in the present analysis, this time-dependent adjoint method is applicable to the 3-D unsteady Reynolds-averaged Navier-Stokes equations with minor modifications. The discrete adjoint operators involving the derivatives of the discrete residual and the cost functional with respect to the flow variables are computed using a complex-variable approach, which provides discrete consistency and drastically reduces the implementation and debugging cycle. The implementation of the time-dependent adjoint method is validated by comparing the sensitivity derivative with that obtained by forward mode differentiation. Our numerical results show that O(10) optimization iterations of the steepest descent method are needed to reduce the objective functional by 3-6 orders of magnitude for test problems considered.

Yamaleev, N. K.↗
DOE OSTI2026

FunDiff: diffusion models over function spaces for physics-informed generative modeling

Recent advances in generative modeling-particularly diffusion models and flow matching-have been widely used for synthesizing discrete data such as images and videos. However, adapting these models to physical applications remains challenging, as the quantities of interest are continuous functions governed by complex physical laws. To address this, we introduce FunDiff, an efficient and robust framework for generative modeling in function spaces. FunDiff combines a latent diffusion process with a function autoencoder architecture to handle input functions with varying discretizations, generates continuous functions that can be evaluated at arbitrary locations, and seamlessly incorporate physical priors. These priors are enforced through architectural constraints or physics-informed loss functions, ensuring that generated samples satisfy fundamental physical laws. We theoretically establish minimax optimality guarantees for density estimation in function spaces, demonstrating that diffusion-based estimators achieve optimal convergence rates under suitable regularity conditions. We further demonstrate the practical effectiveness of FunDiff across diverse applications in fluid dynamics and solid mechanics. Empirical results indicate that our method can generate physically consistent samples with high fidelity to the target distribution, and exhibit robustness to noisy and low-resolution data.

Wang, Sifan [Yale University, New Haven, CT (Unite↗
NASA NTRS1997

Finite Element Aircraft Simulation of Turbulence

A turbulence model has been developed for realtime aircraft simulation that accommodates stochastic turbulence and distributed discrete gusts as a function of the terrain. This model is applicable to conventional aircraft, V/STOL aircraft, and disc rotor model helicopter simulations. Vehicle angular activity in response to turbulence is computed from geometrical and temporal relationships rather than by using the conventional continuum approximations that assume uniform gust immersion and low frequency responses. By using techniques similar to those recently developed for blade-element rotor models, the angular-rate filters of conventional turbulence models are not required. The model produces rotational rates as well as air mass translational velocities in response to both stochastic and deterministic disturbances, where the discrete gusts and turbulence magnitudes may be correlated with significant terrain features or ship models. Assuming isotropy, a two-dimensional vertical turbulence field is created. A novel Gaussian interpolation technique is used to distribute vertical turbulence on the wing span or lateral rotor disc, and this distribution is used to compute roll responses. Air mass velocities are applied at significant centers of pressure in the computation of the aircraft's pitch and roll responses.

McFarland, R. E.↗
NASA NTRS2004

Discrete X-Ray Source Populations and Star-Formation History in Nearby Galaxies

This program aims in understanding the connection between the discrete X-ray source populations observed in nearby galaxies and the history of star-formation in these galaxies. The ultimate goal is to use this knowledge in order to constrain X-ray binary evolution channels. For this reason although the program is primarily observational it has a significant modeling component. During the first year of this study we focused on the definition of a pilot sample of galaxies with well know star-formation histories. A small part of this sample has already been observed and we performed initial analysis of the data. However, the majority of the objects in our sample either have not been observed at all, or the detection limit of the existing observations is not low enough to probe the bulk of their young X-ray binary populations. For this reason we successfully proposed for additional Chandra observations of three targets in Cycle-5. These observations are currently being performed. The analysis of the (limited) archival data for this sample indicated that the X-ray luminosity functions (XLF) of the discrete sources in these galaxies may not have the same shape as is widely suggested. However, any solid conclusions are hampered by the small number of detected sources. For this reason during the second year of this study, we will try to extend the sample in order to include more objects in each evolutionary stage. In addition we are completing the analysis of the Chandra monitoring observations of the Antennae galaxies. The results from this work, apart from important clues on the nature of the most luminous sources (Ultra-luminous X-ray sources; ULXs) provide evidence that source spectral and/or temporal variability does not significantly affect the shape of their X-ray luminosity functions. This is particularly important for comparisons between the XLFs of different galaxies and comparisons with predictions from theoretical models. Results from this work have been presented in several conferences. Refereed journal papers presenting these conclusions are currently in preparation. An important part of this study is the Chandra survey of the Small Magellanic Cloud, our second nearest star- forming galaxy. So far we have been awarded 5 Chandra observations of the central youngest part of the galaxy. These observations will help to study the very faint end of the young X-ray binary populations which is not possible to probe in more distant objects. Results from this study have been presented in several conferences and two papers are in preparation. In addition during year-2 we are planning of undertaking the task of identifying optical counterparts to the X-ray sources, which will help us to isolate interlopers (sources not associated with the SMC) and classify the X-ray binaries which are found to be associated with the SMC. In the theoretical front, the Star-Track X-ray binary population synthesis code which will be used for the modeling of the X-ray binary populations (led by co-I V. Kalogera and C. Belczynski), is complete. A first test using the XLF of the star-forming galaxy NGC-1569 showed remarkable agreement between the observed and the modeled XLF. These results are presented in an ApJ. Letters paper (Belczynski et al, 2004, 601, 147). During year-2 of this study we are planning of performing a parameter study in order to investigate which parameters are most important for the shape of the XLF. In addition we will perform comparisons with observations of other galaxies from our sample as they become available.

Zezas, Andreas↗
DOE OSTI2024

Sublattice modulated superconductivity in the kagome Hubbard model

Here we identify a superconducting order featuring spatial pair modulations on the kagome lattice subject to onsite Hubbard U and nearest neighbor V interactions. Within our functional renormalization group analysis, this state appears with a concomitant d-wave superconducting (SC) instability at zero lattice momentum, where it distinguishes itself through intra-unit cell modulations of the pairing function thus breaking the discrete space group symmetry. The relative weight of the sublattice modulated superconductor (SMS) and d-wave SC is influenced by the absolute interaction strength and coupling ratio V/U. Parametrically adjacent to this domain at weak coupling, we find an intra-unit cell modulated vestigial charge density wave and an s-wave SC instability. Our study provides a microscopic setting and thorough description of this novel SMS arising within a translation symmetry broken background.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Odd-Parity Magnetism Driven by Antiferromagnetic Exchange

Realizing odd-parity, time-reversal-preserving, nonrelativistic spin splitting is a central goal for spintronics applications. We propose a group-theory-based microscopic framework to induce odd-parity spin splitting from coplanar antiferromagnetic (AFM) states without spin-orbit coupling (SOC). We develop phenomenological models for 421 conventional period-doubling AFM systems in nonsymmorphic space groups and construct minimal microscopic models for 119 of these. We find that these AFM states can attain three possible competing ground states. These ground states all break symmetries in addition to those broken by the usual AFM order. Specifically, they give rise to either odd-parity spin-splitting, nematic order, or scalar odd-parity order related to multiferroicity. Our microscopic theories reveal that the odd-parity spin-splitting energy scale is generically large and further reveal that the scalar odd-parity order gives a nonzero Berry curvature dipole without SOC. We identify 67 materials in the Magndata database for which our theory applies. We provide density-functional theory (DFT) calculations on Fe-based materials that reveal an ℎ-wave spin splitting consistent with our symmetry arguments and apply our microscopic model to determine the nonrelativistic Edelstein response for CeNiAsO.

Antiferromagnets↗
DOE OSTI2024

Development of an Optical Library for Coevaporated CdSe x Te 1– x

The conversion efficiency of CdTe solar cells may be improved by bandgap engineering, i.e., changing the bandgap value through the addition of Se in the absorber. The Se alloying enables a short-circuit current density improvement, as it leads to a bandgap energy value decrease. Furthermore, it has been associated with increased minority carrier lifetimes, assuring high open-circuit voltage values. An Se gradient profile control can further optimize the solar cell performance. Thus, an optical model baseline of the CdSe x Te 1–x (CST) compound was developed. Spectroscopic ellipsometry measurements were conducted to accurately extract the optical constants of ten CST layers deposited through coevaporation with x varying from 0 to 1. Using the measured dielectric function spectra from the discrete CST layers with varying x, and considering the composition-induced shift in the critical point energies, an energy-shift model was employed to develop the accurate optical library for the CST compound for any x value to provide data for future modeling and optimization. Furthermore, the library accuracy was validated through optical simulations of the quantum efficiency of a graded CST solar cell using the finite-difference time-domain method by replicating the Se profile in the absorber layer measured through secondary ion mass spectrometry.

14 SOLAR ENERGY↗
DOE OSTI2026

An Approach for Simulating Transport of Nonspherical, Sublimating Particles in Rarefied Gas Flows via the Direct Simulation Monte Carlo Method

This paper extends the particle Green’s function approach of Gallis et al. [Phys. Fluids 13, 3482–3492 (2001)] to compute the force and heat transfer on nonspherical, sublimating particles in rarefied gas flows. Green’s functions are derived for rods and plates, which are representative of ice particle shapes, and a numerical procedure is developed for computing the Green’s functions for a general discretized convex shape. Additionally, a sublimation model is developed to simulate the evolution of ice particles in rarefied gas flows. These models are implemented in a direct simulation Monte Carlo code and demonstrated for the case of ice-particle-laden hypersonic flow over a ramp.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Hybrid Basis and Multi-Center Grid Method for Strong-Field Processes

We present a time-dependent framework that combines a hybrid basis, consisting of Gaussian-type orbitals (GTOs) and finite-element discrete-variable representation (FEDVR) functions, with a multicenter grid to simulate strong-field and attosecond dynamics in atoms and molecules. The method incorporates the construction of the orthonormal hybrid basis, the evaluation of electronic integrals, a unitary time-propagation scheme, and the extraction of optical and photoelectron observables. Its accuracy and robustness are benchmarked on one-electron systems such as atomic hydrogen and the dihydrogen cation (H$^+_2$) through comparisons with essentially-exact reference results for bound-state energies, high-harmonic generation spectra, photoionization cross sections, and photoelectron momentum distributions. This work establishes the groundwork for its integration with quantum-chemistry methods, which is already operational but will be detailed in future work, thereby enabling ab initio simulations of correlated polyatomic systems in intense ultrafast laser fields.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1973

Energy-like Liapunov functionals for linear elastic systems on a Hilbert space.

An approach is presented for generating energy-like functionals for linear elastic dynamic systems on a Hilbert space. The objective is to obtain a family of functionals which may be used for stability analysis of the equilibrium, i.e., Liapunov functionals. Although the energy functional, when one exists, is always a member of this family, the family is shown to exist even when an energy functional does not. Several discrete and distributed-parameter examples are presented, as are certain specific techniques for utilizing this approach.

Walker, J. A.↗
NASA NTRS1983

Design considerations for a real-time ocular counterroll instrument

A real-time algorithm for measuring three-dimensional movement of the human eye, especially torsional movement, is presented. As its input, the system uses images of the eyeball taken at video rate. The amount of horizontal and vertical movement is extracted using a pupil tracking technique. The torsional movement is then measured by computing the discrete cross-correlation function between the circular samples of successive images of the iris patterns and searching for the position of the peak of the function. A local least square interpolation around the peak of the cross-correlation function is used to produce nearly unbiased estimates of torsion angle with accuracy of about 3-4 arcmin. Accuracies of better than 0.03 deg are achievable in torsional measurement with SNR higher than 36 dB. Horizontal and vertical rotations of up to + or - 13 deg can occur simultaneously with torsion without introducing any appreciable error in the counterrolling measurement process.

Hatamian, M.↗
NASA NTRS1984

Physical fitness and cardiovascular response to lower body negative pressure

Klein et al. (1977) have questioned the concept of endurance training as an appropriate means of preparing for prolonged space flights. Their opinion was mainly based on reports of endurance athletes who had a decreased tolerance to orthostatic or gravitational stress induced by lower body negative pressure (LBNP), upright tilt, or whole body water immersion. The present investigation had the objective to determine if the hemodynamic response to LBNP is different between a high and average fit group of subjects. In addition, the discrete aspect of cardiovascular function which had been altered by chronic training was to be identified. On the basis of the results of experiments conducted with 14 young male volunteers, it is concluded that the reflex response to central hypovolemia is altered by endurance exercise training.

Raven, P. B.↗