Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “matrices”

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 1,333 records · Page 74
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Heterogeneous Morphologies and Hardness of Co-Sputtered Thin Films of Concentrated Cu-Mo-W Alloys

Heterogeneous microstructures in Cu-Mo-W alloy thin films formed by magnetron co-sputtering immiscible elements with concentrated compositions are characterized using scanning transmission electron microscopy (STEM) and nanoindentation. In this work, we modified the phase separated structure of a Cu-Mo immiscible system by adding W, which impedes surface diffusion during film growth. The heterogeneous microstructures in the Cu-Mo-W ternary system exhibited bicontinuous matrices and agglomerates composed of Mo(W)-rich phase. This is unique, as these are the slower-diffusing species, contrasting past reports of binary Cu-Mo thin films that exhibited Cu-rich agglomerates. The bicontinuous matrices comprised of Cu-rich and Mo(W)-rich phases exhibited bilayer thicknesses of less than 5 nm. The hardness of these thin films measured using nanoindentation is reported and compared to similar multilayers and nanocomposites in binary systems.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Filled Elastomers: Mechanistic and Physics-Driven Modeling and Applications as Smart Materials

Elastomers are made of chain-like molecules to form networks that can sustain large deformation. Rubbers are thermosetting elastomers that are obtained from irreversible curing reactions. Curing reactions create permanent bonds between the molecular chains. On the other hand, thermoplastic elastomers do not need curing reactions. Incorporation of appropriated filler particles, as has been practiced for decades, can significantly enhance mechanical properties of elastomers. However, there are fundamental questions about polymer matrix composites (PMCs) that still elude complete understanding. This is because the macroscopic properties of PMCs depend not only on the overall volume fraction (ϕ) of the filler particles, but also on their spatial distribution (i.e., primary, secondary, and tertiary structure). This work aims at reviewing how the mechanical properties of PMCs are related to the microstructure of filler particles and to the interaction between filler particles and polymer matrices. Overall, soft rubbery matrices dictate the elasticity/hyperelasticity of the PMCs while the reinforcement involves polymer–particle interactions that can significantly influence the mechanical properties of the polymer matrix interface. For ϕ values higher than a threshold, percolation of the filler particles can lead to significant reinforcement. While viscoelastic behavior may be attributed to the soft rubbery component, inelastic behaviors like the Mullins and Payne effects are highly correlated to the microstructures of the polymer matrix and the filler particles, as well as that of the polymer–particle interface. Additionally, the incorporation of specific filler particles within intelligently designed polymer systems has been shown to yield a variety of functional and responsive materials, commonly termed smart materials. We review three types of smart PMCs, i.e., magnetoelastic (M-), shape-memory (SM-), and self-healing (SH-) PMCs, and discuss the constitutive models for these smart materials.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Explicit Form for the Most General Lorentz Transformation Revisited

Explicit formulae for the 4×4 Lorentz transformation matrices corresponding to a pure boost and a pure three-dimensional rotation are very well known. Significantly less well known is the explicit formula for a general Lorentz transformation with arbitrary non-zero boost and rotation parameters. We revisit this more general formula by presenting two different derivations. The first derivation (which is somewhat simpler than previous ones appearing in the literature) evaluates the exponential of a 4×4 real matrix A, where A is a product of the diagonal matrix diag(+1,−1,−1,−1) and an arbitrary 4×4 real antisymmetric matrix. The formula for expA depends only on the eigenvalues of A and makes use of the Lagrange interpolating polynomial. The second derivation exploits the observation that the spinor product η†σ¯μχ transforms as a Lorentz four-vector, where χ and η are two-component spinors. The advantage of the latter derivation is that the corresponding formula for a general Lorentz transformation Λ reduces to the computation of the trace of a product of 2×2 matrices. Both computations are shown to yield equivalent expressions for Λ.

Science & Technology - Other Topics↗
DOE OSTI2017

Scattering Properties of Large Irregular Cosmic Dust Particles at Visible Wavelengths

The effect of internal inhomogeneities and surface roughness on the scattering behavior of large cosmic dust particles is studied by comparing model simulations with laboratory measurements. The present work shows the results of an attempt to model a dust sample measured in the laboratory with simulations performed by a ray-optics model code. We consider this dust sample as a good analogue for interplanetary and interstellar dust as it shares its refractive index with known materials in these media. Several sensitivity tests have been performed for both structural cases (internal inclusions and surface roughness). Three different samples have been selected to mimic inclusion/coating inhomogeneities: two measured scattering matrices of hematite and white clay, and a simulated matrix for water ice. These three matrices are selected to cover a wide range of imaginary refractive indices. The selection of these materials also seeks to study astrophysical environments of interest such as Mars, where hematite and clays have been detected, and comets. Based on the results of the sensitivity tests shown in this work, we perform calculations for a size distribution of a silicate-type host particle model with inclusions and surface roughness to reproduce the experimental measurements of a dust sample. The model fits the measurements quite well, proving that surface roughness and internal structure play a role in the scattering pattern of irregular cosmic dust particles.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

$\bar{\nu}_\mu$ charged-current $\pi^0$ data release

Data release for the NOvA muon antineutrino charged-current (CC) pi^0 cross section presented in arXiv:2511.05807. The signal for this analysis is defined as muon antineutrino CC interactions in the fiducial volume of the NOvA near detector (a 2.7 m × 2.7 m × 9.0 m region) that produce at least one pi^0 in the final state emerging from the nucleus, within the phase space of muon momentum [0.5, 2.5) GeV/c and muon angle [0, 60) degree, as described in arXiv:2511.05807. The released zip file contains two files: NOvA_NumubarCCPi0_DataRelease.root README.txt The ROOT file includes the cross-section results as well as the statistical and systematic covariance matrices for each variable used in this analysis. The README provides a detailed description of the contents of the data release. Official Flux: The flux used in this analysis is available from the NOvA Public Docs: https://publicdocs.fnal.gov/cgi-bin/ShowDocument?docid=8. File structure --- The ROOT file contains the following TDirectories: pi0p - pi^0 momentum distributions pi0dir - pi^0 angular distributions muonp - muon momentum distributions muondir - muon angular distributions Q2 - reconstructed Q^2 distributions Wmass - reconstructed W_mass distributions Each directory contains three histograms: xsec (TH1D): Cross section result cov_stat (TH2D): Statistical covariance matrix cov_syst (TH2D): Systematic covariance matrix Usage notes: - xsec gives the measured differential cross section w.r.t. the corresponding variable. - cov_stat and cov_syst provide the full covariance matrices. - The bin definitions and kinematic phase spaces follow those used in arXiv:2511.05807. Citation --- If you use these data, please cite: NOvA Collaboration, arXiv:2511.05807.

Wu, Wanwei [Pittsburgh U.] (ORCID:0000000326327215↗
DOE OSTI2023

FUN-BioCROP model with litter decomposition parameters derived from the LIDET dataset

This repository contains the code and data necessary to run the FUN-BioCROP (Fixation and Uptake of Nitrogen-Bioenergy Carbon, Rhizosphere, Organisms, and Protection) model with litter decomposition parameters derived from a modified Monte Carlo simulation that used the Long-term Intersite Decomposition Experiment Team dataset. Related publication:Juice, S.M., Ridgeway, J.R., Hartman, M.D., Parton, W.J., Berardi, D.M., Sulman, B.N., Allen, K.E., & Brzostek, E.R. Reparameterizing litter decomposition using a simplified Monte Carlo method improves litter decay simulated by a microbial model and alters bioenergy soil carbon estimates. Description of Files: FUNBioCROP_LIDET Study.Rmd R code with FUN-BioCROP model that can be run with 10 different sets of parameters for litter decomposition (Baseline, LIDET, or eight other best parameter sets identified in the modified Monte Carlo simulation. CORPSE Functions_Bioenergy_V2.R Code with CORPSE model functions, called by FUNBioCROP_LIDET Study.Rmd Model Input Data: bulk.csv, bulk_till.csv, rhizo.csv, rhizo_till.csv, litter.csv Initial C and N (kg C or N/m2) pool values for each soil compartment, final values from spin up. All five files have the same columns: (Column - Description - Units) uFastC - Unprotected fast decomposing carbon - kg carbon/m2 uSlowC - Unprotected slow decomposing carbon - kg carbon/m2 uNecroC - Unprotected necromass carbon - kg carbon/m2 pFastC - Protected fast decomposing carbon - kg carbon/m2 pSlowC - Protected slow decomposing carbon - kg carbon/m2 pNecroC - Protected necromass carbon - kg carbon/m2 livingMicrobeC - Carbon in living microbial biomass - kg carbon/m2 uFastN - Unprotected fast decomposing nitrogen - kg nitrogen/m2 uSlowN - Unprotected slow decomposing nitrogen - kg nitrogen/m2 uNecroN - Unprotected necromass nitrogen - kg nitrogen/m2 pFastN - Protected fast decomposing nitrogen - kg nitrogen/m2 pSlowN - Protected slow decomposing nitrogen - kg nitrogen/m2 pNecroN - Protected necromass nitrogen - kg nitrogen/m2 inorganicN - Inorganic nitrogen - kg nitrogen/m2 CO2 - Carbon in carbon dioxide - kg carbon/m2 livingMicrobeN - Nitrogen in living microbial biomass - kg nitrogen/m2 Model Input Data: FluxTower_AvgSoilT.csv: Average daily soil temperature (oC) at 10 cm depth at University of Illinois Urbana-Champaign (UIUC) Energy Farm flux tower from 7/2008-3/2016. (One year of averaged data) Model Input Data: FluxTower_AvgSoilVWC.csv: Average daily soil volumetric water content (VWC) at 10 cm depth at UIUC Energy Farm flux tower from 7/2008-3/2016. (One year of averaged data) Model Input Data: input_CCS_LIDET Study.csv: This file has daily data to run FUN-BioCROP (Column - Description - Units): yr - calendar year - year doy - day of year (1 to 365) (no leap year) - day anpp - aboveground NPP (DayCent) - kg C/m2/day bnpp - belowground NPP (DayCent) - kg C/m2/day aglivc - live aboveground biomass carbon (DayCent) - kg C/m2 bglivcj - live juvenile fine root biomass carbon (DayCent) - kg C/m2 bglivcm - live mature fine root biomass carbon (DayCent) - kg C/m2 aglivn - live aboveground biomass nitrogen (DayCent) - kg N/m2 bglivnj - live juvenile fine root biomass nitrogen (DayCent) - kg N/m2 bglivnm - live mature fine root biomass nitrogen (DayCent) - kg N/m2 nyr - simulation year - year cult - indicates a cultivation event (0 or 1) crop - indicates a new crop (0 or 1) fert - indicates a fertilizer event (0 or 1) frst - indicates the first day of the growing season (0 or 1) harv - indicates a harvest event (0 or 1) last - indicates the end of the growing season (0 or 1) croptype - crop type (0=none; 1=alfalfa; 2=corn; 3=grass clover pasture; 4=soybean; 5=wheat) cropsrl - crop specific root length - mm/g root cultrhizmix - fraction of rhizosphere mixed with bulk soil during cultivation (0.0-1.0) - fraction cultlitmix - fraction of litter mixed with bulk soil during cultivation (0.0-1.0) - fraction harvremov - fraction of above ground biomass removed during harvest (0.0-1.0) - fraction fertamt - fertilization amount - g N/m2 lifehist - plant life history (0 = annual, 1 = perennial) froot_turnover_c - amount of C in fine root turnover - kg C/m2 froot_turnover_n - amount of N in fine root turnover - kg N/m2 agrd_turnover_c - amount of C in aboveground biomass turnover - kg C/m2 agrd_turnover_n - amount of N in aboveground biomass turnover - kg N/m2 leaf_litter_fastfrac - Fast decomposing fraction of leaf litter (0.0-1.0) - fraction root_litter_fastfrac - Fast decomposing fraction of root litter (0.0-1.0) - fraction root_diameter - root diameter - mm root_length - root length - mm root/m2 rhizo_frac - fraction of total soil volume that is rhizosphere (0.0 - 1.0) - fraction date - date in format YYYY-MM-DD Instructions: Save the model code ("FUN-BioCROP_LIDET Study.Rmd") and accompanything files (data streams and CORPSE function code) in the same folder. In model code "Chunk 3: Load CORPSE Data Streams" set the working directory (setwd) to the folder with the files saved in step #1. In "Chunk 5: Define LIDET parameter sets" select the litter decomposition parameter set to be used in the run, and comment out all other sets. If changing any parameter values, edit them in "Chunk 6: Load parameters." Run all chunks up to and including "Chunk 10: Prepare Data for Export." In "Chunk 11: Export Output Data" edit data frames for export and filenames, as necessary. "Chunk 12: Graph Total Soil C" makes a figure of C remaining over the model run period. Description of each model chunk (in file FUN-BioCROP_LIDET Study.Rmd): Chunk 1: Remove all functions, clear memory. Removes all functions from R environment, clears the memory. Chunk 2: Load Packages. Loads packages necessary to run the code. Chunk 3: Load CORPSE Data Streams. Sets the working directory and loads the data files necessary to run CORPSE. Chunk 4: Load CORPSE Functions. Loads the R script with CORPSE functions from the working directory, "CORPSE Functions_Bioenergy_V2.R". Chunk 5: Define LIDET parameter sets. Has ten different parameter sets for litter decomposition tested in this study: Baseline parameters, LIDET parameters, and the other 8 best performing parameter sets identified in the modified Monte Carlo. To run the model, all but one parameter set must be commented out. Chunk 6: Load Parameters. Loads all fixed parameters to run the model. Data frame with definitions of parameters is in the CORPSE function script "CORPSE Functions_Bioenergy_V2.R" Chunk 7: Prepare Data Streams. Takes data streams loaded in Chunk 3 and puts them in the format necessary to run the model. The model is coded to run at least two sites at a time, so if only one site is being run it must be run in duplicate. Individual data tables of daily values are created in this chunk from the input data file. Chunk 8: Set Initial Conditions. Creates data tables of soil C and N pools for each soil compartment (rhizo_till, rhizo, bulk_till, bulk, litter) and loads initial values into the data tables. Creates lists for each soil compartment to hold model output. Chunk 9: Load FUN Data and Set Up Matrices. Uses DayCent data to calculate FUN input data: root and leaf N demand, total N demand, plant CN, leaf N available for retranslocation, and litter production. Creates matrices for FUN model outputs. Chunk 10: Run Model. Runs the model. Chunk 11: Prepare Data for Export. Combines data from each day saved as lists into data frames for each soil compartment. Adds values from all soil compartments together to calculate total soil values, creates separate data frames for each soil C and N pool (e.g., protected slow C) for the total soil value. Adds different C and N pools together to calculate total soil C and N for all layers. Creates data frame of ratio of protected to unprotected SOC. Organizes FUN data for export. Chunk 12: Export Results. Exports CSV files of model results to the working directory. Chunk 13: Graph Total Soil C. Makes figure of C remaining over time. Related Links: Original FUN-BioCROP model: https://github.com/BrzostekEcologyLab/FUN-BioCROP LIDET dataset: https://andlter.forestry.oregonstate.edu/data/abstract.aspx?dbcode=TD023

Juice, Stephanie↗
NASA NTRS1964

Codes with special correlation.

Uniform binary codes with special correlation including transorthogonality and simplex code, Hadamard matrices and difference sets uniform binary codes with special correlation including transorthogonality and simplex code, Hadamard matrices and difference sets

AUTOCORRELATION↗
NASA NTRS1971

Substructuring techniques

The substructure function generator program is discussed. Input to this program consists of a definition of a finite element model of a substructure, and specification of the type and number of displacement functions to be generated. Primary output is a substructure data file containing the substructure mass and stiffness matrices expressing kinetic and potential energies as quadratic forms in coefficients of the displacement functions, etc. The substructure synthesis program forms complete system mass, stiffness, and damping matrices, computes system modes and frequencies, and executes transient response calculations. Input to this program consists of the array of substructure data files generated by the function generator program for individual substructures, and data cards defining the position and interconnection of the substructures, damping data, forcing function details, and function control parameters.

Whetstone, W. D.↗
NASA NTRS1971

Navigation analysis for Viking 1979, option B

A parametric study performed for 48 trans-Mars reference missions in support of the Viking program is reported. The launch dates cover several months in the year 1979, and each launch date has multiple arrival dates in 1980. A plot of launch versus arrival dates with case numbers designated for reference purposes is included. The analysis consists of the computation of statistical covariance matrices based on certain assumptions about the ground-based tracking systems. The error model statistics are listed in tables. Tracking systems were assumed at three sites: Goldstone, California; Canberra, Australia; and Madrid, Spain. The tracking data consisted of range and Doppler measurements taken during the tracking intervals starting at E-30(d) and ending at E-10(d) for the control data and ending at E-18(h) for the knowledge data. The control and knowledge covariance matrices were delivered to the Planetary Mission Analysis Branch for inputs into a delta V dispersion analysis.

Mitchell, P. H.↗
NASA NTRS1970

Sorting and ordering sparse linear systems

Transformations of sparse linear systems by row-column permutations are considered and various algorithms are constructed to transform arbitrary symmetric positive definite sparse matrices, as well as matrices in band form, doubly bordered band form, and doubly bordered block diagonal form.

Tewarson, R. P.↗
NASA NTRS1972

Mars gravitational field estimation error

The error covariance matrices associated with a weighted least-squares differential correction process have been analyzed for accuracy in determining the gravitational coefficients through degree and order five in the Mars gravitational potential junction. The results are presented in terms of standard deviations for the assumed estimated parameters. The covariance matrices were calculated by assuming Doppler tracking data from a Mars orbiter, a priori statistics for the estimated parameters, and model error uncertainties for tracking-station locations, the Mars ephemeris, the astronomical unit, the Mars gravitational constant (G sub M), and the gravitational coefficients of degrees six and seven. Model errors were treated by using the concept of consider parameters.

Compton, H. R.↗
NASA NTRS1972

Complex eigenvalue analysis of rotating structures

A FORTRAN subroutine to NASTRAN which constructs coriolis and centripetal acceleration matrices, and a centrifugal load vector due to spin about a selected point or about the mass center of the structure is discussed. The rigid translational degrees of freedom can be removed by using a transformation matrix T and its explicitly given inverse. These matrices are generated in the subroutine and their explicit expressions are given.

Patel, J. S.↗
NASA NTRS1972

Level 12 NASTRAN experiences at General Dynamics, Convair Aerospace Division, Fort Worth Operations

The level 12 NASTRAN was used to support the NASA/LaRC advanced transport technology study, a predesign, short response time effort. Aeroelastic analyses were performed. NASTRAN calculated the vibration modes for the supported airfoil components and the entire unsupported vehicle. Other procedures were then used for the aeroelastic analysis, with procedure interfacing accomplished through use of the NASTRAN-produced restart tape. Stiffness matrices were used in static aeroelastic analyses; natural vibration modes were used for flutter and flight control system definition. Various level 12 NASTRAN characteristics were discovered and are discussed; e.g., the ability to solve singular matrices in rigid format 1, run times using multipoint constraints, restart tape problems, and the inaccurate stresses from the quad membrane when used with anisotropic materials.

Allen, M.↗
NASA NTRS1972

On the equinoctial orbit elements.

This paper investigates the equinoctial orbit elements for the two-body problem, showing that the associated matrices are free from singularities for zero eccentricities and zero and ninety degree inclinations. The matrix of the partial derivatives of the position and velocity vectors with respect to the orbit elements is given explicitly, together with the matrix of inverse partial derivatives, in order to facilitate construction of the matrizant (state transition matrix) corresponding to these elements. The Lagrange and Poisson bracket matrices are also given. The application of the equinoctial orbit elements to general and special perturbations is discussed.

Broucke, R. A.↗
NASA NTRS1972

A comparative study of tensile fracture mechanisms.

Identification of the failure mechanism characteristic for the more widely used carbon fibers in epoxy matrices under tensile loads as an aid toward improvements and more reliable predictions of the performance of these composites. The presented results pertain to high-strength, high-modulus, and low-modulus fibers in unmodified and modified epoxy novolac matrices.

Mullin, J. V.↗
NASA NTRS1972

N-burn optimal analytic trajectories.

Derivation of N-burn analytic solutions for propellant-optimal transfer trajectories of a vehicle in a vacuum between arbitrary boundary conditions. Variational changes in the desired boundary conditions are expressed, in general, in terms of variational changes in the control vector and in the initial state vector. All coefficient matrices are computed recursively in terms of the analytic matrices established from the subarcs of the N-burn solution. The solution is applicable to shuttle ascent (exoatmospheric), rendezvous, and deorbit problems. Consideration is also given to state-variable and control-variable inequality constraints.

Jezewski, D. J.↗
NASA NTRS1972

Closed-form solutions for atomspheric flight with applications to shuttle guidance

Closed-form solutions for the motion of a rocket-powered vehicle during atmospheric ascent and closed-form solutions for unpowered atmospheric reentry are developed. These closed-form solutions are then used to develop a simplified guidance scheme and to develop a variation-of-parameters integration of more accurate equations of motion with the closed-form solutions as base solutions. The variation-of-parameters integration of the more accurate equations of motion also allows the transition partial derivative matrices associated with these equations to be easily developed. Then the partial derivative transition matrices are used to develop a guidance scheme based on the more accurate equations of motion instead of the less accurate closed-form solutions.

Ingram, H. L.↗
NASA NTRS1972

Multivariable control theory applied to hierarchial attitude control for planetary spacecraft

Multivariable control theory is applied to the design of a hierarchial attitude control system for the CARD space vehicle. The system selected uses reaction control jets (RCJ) and control moment gyros (CMG). The RCJ system uses linear signal mixing and a no-fire region similar to that used on the Skylab program; the y-axis and z-axis systems which are coupled use a sum and difference feedback scheme. The CMG system uses the optimum steering law and the same feedback signals as the RCJ system. When both systems are active the design is such that the torques from each system are never in opposition. A state-space analysis was made of the CMG system to determine the general structure of the input matrices (steering law) and feedback matrices that will decouple the axes. It is shown that the optimum steering law and proportional-plus-rate feedback are special cases. A derivation of the disturbing torques on the space vehicle due to the motion of the on-board television camera is presented. A procedure for computing an upper bound on these torques (given the system parameters) is included.

Boland, J. S., III↗