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Results for “symbolic calculation”

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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

An experimental and analytical investigation of isolated rotor flap-lag stability in forward flight

The flap-lag stability of an isolated hingeless rotor is investigated, both experimentally and analytically, in hover and in forward flight. The effects of forward flight aerodynamics on regressing lead-lag mode stability are the focus of the investigation. The soft-inplane, three-bladed, isolated model rotor was operated untrimmed at advance ratios from hover to 0.55 and at shaft angles as high as 20 deg. The experimental data base includes forward flight damping data for two lead-lag natural frequencies, for three values of collective pitch, and for both zero and full-lag structural coupling. With the aid of computerized symbolic manipulation, a rigid-blade lag-flap model analysis was developed to calculate the Floquent eigenvalues and to identify the modes. Good correlation is shown for some cases, but other cases show large discrepancies between the theory and experiment.

Gaonkar, Gopal H.↗
NASA NTRS1977

Application of symbolic/numeric matrix solution techniques to the NASTRAN program

The matrix solving algorithm of any finite element algorithm is extremely important since solution of the matrix equations requires a large amount of elapse time due to null calculations and excessive input/output operations. An alternate method of solving the matrix equations is presented. A symbolic processing step followed by numeric solution yields the solution very rapidly and is especially useful for nonlinear problems.

Buturla, E. M.↗
DOE OSTI2024

Quasilinear theory: the lost ponderomotive effects and why they matter

Quasilinear theory (QLT) has been used for modeling wave–plasma interactions for decades but remains largely heuristic. Plasma inhomogeneity, ponderomotive effects, microscopic fluctuations, and collisions are not easily accommodated from first principles in QLT, and typically are ignored entirely, due to the limitations of the standard Fourier–Laplace global-mode approach. This results in inconsistencies, for example, violation of the action conservation for nonresonant waves. However, these issues can be avoided, and the theory can be substantially generalized and corrected, if QLT is formulated using more suitable analytical tools, particularly, the Weyl symbol calculus. Here, an attempt is made to deliver an accessible review of this modern formulation, provide intuitive calculations for special cases, and elaborate on the connection with the ‘oscillation-center QLT’ originally proposed by Dewar (Phys Fluids 16:1102, 1973). A Fokker–Planck equation for a ‘dressed’ distribution is derived from the Klimontovich equation and captures quasilinear diffusion, ponderomotive forces, and interactions with background fields for a generic Hamiltonian, so many known formulations of QLT for specific plasma models become corollaries of a single unifying theory. Also, waves are allowed to be off-shell (not constrained by a dispersion relation), which allows them to accommodate microscopic fluctuations. This leads to a collision integral of the Balescu–Lenard type that has all the usual properties but is not restricted to any specific plasma model. For on-shell waves, a generalized version of the classic oscillation-center QLT is obtained. Finally, combined with the wave-kinetic equation, this formulation not only conserves particles, momentum, and energy, like the classic QLT but also reinstates the action conservation for nonresonant waves.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Modeling of the metal–insulator transition temperature in alio-valently doped VO 2 through symbolic regression

The correlated semiconductor vanadium dioxide (VO 2 ) exhibits an insulator–metal transition (IMT) near room temperature, which is of interest in various device applications. Precise IMT temperature control is crucial to determine the use cases across technologies such as thermochromic windows, actuators for robots or neuronal oscillators. Doping the cation or anion sites can modulate the IMT by several tens of degrees and control hysteresis. However, modeling the effects of control parameters (e.g., doping concentration, type of dopants) is challenging due to complex experimental procedures and limited data, hindering the use of traditional data-driven machine learning approaches. Symbolic regression (SR) can bridge this gap by identifying nonlinear expressions connecting key input parameters to target properties, even with small data sets. In this work, we develop SR models to capture the IMT trends in VO 2 influenced by different dopant parameters. Using experimental data from the literature, our study reveals a dual nature of the IMT temperature with varying tungsten (W) doping concentrations. The symbolic model captures data trends and accounts for experimental variability, providing a complementary approach to first-principles calculations. Our feature-driven analysis across a broader class of dopants informs selectivity and provides qualitative insights into tuning phase transition properties valuable for neuromorphic computing and thermochromic windows.

36 MATERIALS SCIENCE↗
DOE OSTI2023

SYMBA: symbolic computation of squared amplitudes in high energy physics with machine learning

The cross section is one of the most important physical quantities in high-energy physics and the most time consuming to compute. While machine learning has proven to be highly successful in numerical calculations in high-energy physics, analytical calculations using machine learning are still in their infancy. In this work, we use a sequence-to-sequence model, specifically, a transformer, to compute a key element of the cross section calculation, namely, the squared amplitude of an interaction. We show that a transformer model is able to predict correctly 97.6% and 99% of squared amplitudes of quantum chromodynamics and quantum electrodynamics processes, respectively, at a speed that is up to orders of magnitude faster than current symbolic computation frameworks. We discuss the performance of the current model, its limitations and possible future directions for this work.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

SA-GAT-SR: self-adaptable graph attention networks with symbolic regression for high-fidelity material property prediction

Recent advances in machine learning have demonstrated an enormous utility of deep learning approaches, particularly Graph Neural Networks (GNNs) for materials science. These methods have emerged as powerful tools for high-throughput prediction of material properties, offering a compelling enhancement and alternative to traditional first-principles calculations. While the community has predominantly focused on developing increasingly complex and universal models to enhance predictive accuracy, such approaches often lack physical interpretability and insights into materials behavior. Here, we introduce a novel computational paradigm—Self-Adaptable Graph Attention Networks integrated with Symbolic Regression (SA-GAT-SR)—that synergistically combines the predictive capability of GNNs with the interpretative power of symbolic regression. Our framework employs a self-adaptable encoding algorithm that automatically identifies and adjust attention weights so as to screen critical features from an expansive 180-dimensional feature space while maintaining O(n) computational scaling. The integrated SR module subsequently distills these features into compact analytical expressions that explicitly reveal quantum-mechanically meaningful relationships, achieving 23 × acceleration compared to conventional SR implementations that heavily rely on first-principle calculations-derived features as input. This work suggests a new framework in computational materials science, bridging the gap between predictive accuracy and physical interpretability, offering valuable physical insights into material behavior.

36 MATERIALS SCIENCE↗
NASA NTRS1982

Detection of aspen-conifer forest mixes from LANDSAT digital data

Aspen, conifer and mixed aspen/conifer forests were mapped for a 15-quadrangle study area in the Utah-Idaho Bear River Range using LANDSAT multispectral scanner data. Digital classification and statistical analysis of LANDSAT data allowed the identification of six groups of signatures which reflect different types of aspen/conifer forest mixing. Photo interpretations of the print symbols suggest that such classes are indicative of mid to late seral aspen forests. Digital print map overlays and acreage calculations were prepared for the study area quadrangles. Further field verification is needed to acquire additional information about the nature of the forests. Single date LANDSAT analysis should be a cost effective means to index aspen forests which are at least in the mid seral phase of conifer invasion. Since aspen canopies tend to obscure understory conifers for early seral forests, a second date analysis, using data taken when aspens are leafless, could provide information about early seral aspen forests.

Jaynes, R. A.↗
NASA NTRS1984

Detection of aspen/conifer forest mixes from multitemporal Landsat digital data

Aspen, conifer and mixed aspen/conifer forests were mapped for a 15-quadrangle study area in the Utah-Idaho Bear River Range using Landsat multispectral scanner data. Digital classification and statistical analysis of Landsat data allowed the identification of six groups of signatures which reflect different types of aspen/conifer forest mixing. Photo interpretations of the print symbols suggest that such classes are indicative of mid to late seral aspen forests. Digital print map overlayes and acreage calculations were prepared for the study area quadrangles. Further field verification is needed to acquire additional information about the nature of the forests. Single data Landsat analysis should be a cost effective means to index aspen forests which are at least in the mid seral phase of conifer invasion. Since aspen canopies tend to obscure understory conifers for early seral forests, a second data analysis, using data taken when aspens are leafless, could provide information about early seral aspen forests.

Merola, J. A.↗
NASA NTRS1971

Calculation of inviscid surface streamlines and heat transfer on shuttle type configurations. Part 2: Description of computer program

A description of the computer program used for heating rate calculation for blunt bodies in hypersonic flow is given. The main program and each subprogram are described by defining the pertinent symbols involved and presenting a detailed flow diagram and complete computer program listing. Input and output parameters are discussed in detail. Listings are given for the computation of heating rates on (1) a blunted 15 deg half-angle cone at 20 deg incidence and Mach 10.6, (2) a blunted 70 deg slab delta wing at 10 deg incidence and Mach 8, and (3) the HL-10 lifting body at 20 deg incidence and Mach 10. In addition, the computer program output for two streamlines on the blunted 15 deg half-angle cone is listed. For Part 1, see N71-36186.

Dejarnette, F. R.↗
DOE OSTI2021

Deterministic symbolic regression with derivative information: General methodology and application to equations of state

Symbolic regression methods simultaneously determine the model functional form and the regression parameter values by generating expression trees. Symbolic regression can capture the complexity of real–world phenomena but the use of deterministic optimization for symbolic regression has been limited due to the complexity of the search space of existing formulations. Herein we present a novel deterministic mixed–integer nonlinear programming formulation for symbolic regression that incorporates derivative constraints through auxiliary expression trees. By applying the chain rule to mathematical operations, binary expression trees are capable of representing the calculation of first and second derivatives. We apply this formulation to illustrative examples using derivative information to show increased model discrimination capability. In addition, we perform a case study of a thermodynamic equation of state to gain insight on valid functional forms with thermodynamics–based constraints on the first and second derivatives.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2000

Digital Channel Simulator Developed and Tested

The Digital Channel Simulator (DCS) is a real-time test set developed in-house by the NASA Glenn Research Center at Lewis Field that simulates the characteristics of the modulator, demodulator, and transmission medium in a typical communications system to enable controlled laboratory testing of codec pairs. The DCS can support data rates up to 100 megasymbols per second (Msymbols/sec) with symbol sizes up to 10 bits and is compatible with both TTL (transistor transistor logic) and ECL (emitter coupled logic) interfaces. Because of its use of digital integrated circuits (IC's), the DCS offers the user accurate and repeatable testing while maintaining a simple reconfiguration of the modulation scheme and noise characteristics. The PC-based graphical user interface (GUI) assures user friendly operation for configuring, controlling, and monitoring the DCS and system during tests. In a typical communications system, the modulator places a symbol in constellation space and puts it on a carrier to be sent to the demodulator. Because of noise on the channel, the I and Q position in constellation space cannot be recovered exactly, and the received coordinates shift. To mimic this process in the laboratory, the DCS uses a mapper to place the symbol in constellation space. It simulates the shift in coordinates by digitally adding "noise" to the I and Q values. The mapper and noise source are implemented in lookup tables. Modulation schemes and noise characteristics are set by the values loaded in these tables. The mapper also has a pass-through mode to facilitate modulator testing, allowing noise to be added to 8-bit I and Q values of modulated data without a second mapping. To achieve high symbol rates, eight processing circuits are placed in parallel between an ECL demultiplexer and multiplexer. A graphical user interface was developed to calculate, load, and verify the values for the lookup tables. This interface can also be used to debug and verify proper operation of the channel simulator or to control an experiment. Operation of the DCS has been verified through three tests: a low-speed comprehensive system test, a high-speed (20 Msymbols/sec) test of the TTL interface, and a high-speed (100 Msymbols/sec) test of the ECL interface. The DCS is now ready for use by NASA and external customers.

Bizon, Thomas P.↗
NASA NTRS1980

Analysis and calculation of macrosegregation in a casting ingot. MPS solidification model. Volume 1: Formulation and analysis

The physical and numerical formulation of a model for the horizontal solidification of a binary alloy is described. It can be applied in an ingot. The major purpose of the model is to calculate macrosegregation in a casting ingot which results from flow of interdendritic liquid during solidification. The flow, driven by solidification contractions and by gravity acting on density gradients in the interdendritic liquid, was modeled as flow through a porous medium. The symbols used are defined. The physical formulation of the problem leading to a set of equations which can be used to obtain: (1) the pressure field; (2) the velocity field: (3) mass flow and (4) solute flow in the solid plus liquid zone during solidification is presented. With these established, the model calculates macrosegregation after solidification is complete. The numerical techniques used to obtain solution on a computational grid are presented. Results, evaluation of the results, and recommendations for future development of the model are given. The macrosegregation and flow field predictions for tin-lead, aluminum-copper, and tin-bismuth alloys are included as well as comparisons of some of the predictions with published predictions or with empirical data.

Maples, A. L.↗
DOE OSTI2020

Quadrupolar interactions between acceptor pairs in $\mathcal{p}$-doped semiconductors

Here, we consider the interaction between acceptor pairs in doped semiconductors in the limit of large interacceptor separation relevant for low doping densities. Modeling individual acceptors via the spherical model of Baldereschi and Lipari, we calculate matrix elements of the quadrupole tensor between the four degenerate ground states and show that the acceptor has a nonzero quadrupole moment. As a result, the dominant contribution to the large-separation acceptor-acceptor interaction comes from direct (charge-density) terms rather than exchange terms. The quadrupole is the leading nonzero moment, so the electric quadrupole-quadrupole interaction dominates for large separation. We calculate the matrix elements of the quadrupole-quadrupole interaction Hamiltonian in a product-state basis and diagonalize, obtaining a closed-form expression for the energies and degeneracies of the sixteen-state energy spectrum. All dependence on material parameters enters via an overall prefactor, resulting in surprisingly simple and universal results. This simplicity is due, in part, to a mathematical happenstance, the nontrivial vanishing of a particular Wigner 6-$\mathcal{j}$ symbol, $^\{\frac{^2_3}{\small2} \frac{^2_3}{\small2} \frac{^2_3}{\small2}$$^\}$ = 0. Results are relevant to the control of two-qubit interactions in quantum computing implementations based on acceptor spins, as well as calculations of the thermodynamic properties of insulating $\mathcal{p}$-type semiconductors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1930

Experimental Investigation of Aircraft Propellers Exposed to Oblique Air Currents

Two screw propellers, a normal airplane propeller with a pitch/diameter ratio H/D = 0.5 and a helicopter propeller H/D = 0.2 were tested in the large wind tunnel of the Gottigen Aerodynamic Institute. With both propellers the angle between the propeller axis and the direction of the wind was varied from 0 to 90 degrees. In addition to the three force and the three moment components in a wind-fast coordinate system, the corresponding components in a propeller-fast coordinate system, a total of six force and six moment components, together with the propulsive efficiency, were measured or calculated from measurements. The results are given in the form of diagrams and briefly discussed. The propeller models and method of experimentation are described and the symbols are defined.

Flachsbart, O↗
NASA NTRS1992

Predictive Caching Using the TDAG Algorithm

We describe how the TDAG algorithm for learning to predict symbol sequences can be used to design a predictive cache store. A model of a two-level mass storage system is developed and used to calculate the performance of the cache under various conditions. Experimental simulations provide good confirmation of the model.

Laird, Philip↗
DOE OSTI2022

Vector boson pair production at one loop: analytic results for the process $q\bar{q}$$ℓ\bar{ℓ}$$ℓ'\bar{ℓ}'g$

We present compact analytic results for the one-loop amplitude for the process 0 → $q\bar{q}$$ℓ\bar{ℓ}$$ℓ'\bar{ℓ}'g$, relevant for both the production of a pair of Z and W-bosons in association with a jet. We focus on the gauge-invariant contribution mediated by a loop of quarks. We explicitly include all effects of the loop-quark mass m, appropriate for the production of a pair of Z-bosons. In the limit m → 0, our results are also applicable to the production of W-boson pairs, mediated by a loop of massless quarks. Implemented in a numerical code, the results are fast. The calculation uses novel advancements in spinor-helicity simplification techniques, for the first time applied beyond five-point massless kinematics. We make use of primary decompositions from algebraic-geometry, which now involve non-radical ideals, and p-adic numbers from number theory. We show how to infer whether numerator polynomials belong to symbolic powers of non-radical ideals through numerical evaluations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1992

Calculation of stress intensity factors in an isotropic multicracked plate: Part 2: Symbolic/numeric implementation

Analytical derivations of stress intensity factors (SIF's) of a multicracked plate can be complex and tedious. Recent advances, however, in intelligent application of symbolic computation can overcome these difficulties and provide the means to rigorously and efficiently analyze this class of problems. Here, the symbolic algorithm required to implement the methodology described in Part 1 is presented. The special problem-oriented symbolic functions to derive the fundamental kernels are described, and the associated automatically generated FORTRAN subroutines are given. As a result, a symbolic/FORTRAN package named SYMFRAC, capable of providing accurate SIF's at each crack tip, was developed and validated. Simple illustrative examples using SYMFRAC show the potential of the present approach for predicting the macrocrack propagation path due to existing microcracks in the vicinity of a macrocrack tip, when the influence of the microcrack's location, orientation, size, and interaction are taken into account.

Arnold, S. M.↗