Search NASA⌕ Search

SEARCH · Search NASA

Results for “Reference Model 3”

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 775 records · Page 43

SU-G-201-13: Investigation of Dose Variation Induced by HDR Ir-192 Source Global Shift Within the Varian Ring Applicator Using Monte Carlo Methods

Purpose: The Varian tandem and ring applicators are used to deliver HDR Ir-192 brachytherapy for cervical cancer. The source path within the ring is hard to predict due to the larger interior ring lumen. Some studies showed the source could be several millimeters different from planned positions, while other studies demonstrated minimal dosimetric impact. A global shift can be applied to limit the effect of positioning offsets. The purpose of this study was to assess the necessities of implementing a global source shift using Monte Carlo (MC) simulations. Methods: The MCNP5 radiation transport code was used for all MC simulations. To accommodate TG-186 guidelines and eliminate inter-source attenuation, a BrachyVision plan with 10 dwell positions (0.5cm step sizes) was simulated as the summation of 10 individual sources with equal dwell times for simplification. To simplify the study, the tandem was also excluded from the MC model. Global shifts of ±0.1, ±0.3, ±0.5 cm were then simulated as distal and proximal from the reference positions. Dose was scored in water for all MC simulations and was normalized to 100% at the normalization point 0.5 cm from the cap in the ring plane. For dose comparison, Point A was 2 cm caudal from the buildup cap and 2 cm lateral on either side of the ring axis. With seventy simulations, 108 photon histories gave a statistical uncertainties (k=1) <2% for (0.1 cm)3 voxels. Results: Compared to no global shift, average Point A doses were 0.0%, 0.4%, and 2.2% higher for distal global shifts, and 0.4%, 2.8%, and 5.1% higher for proximal global shifts, respectively. The MC Point A doses differed by < 1% when compared to BrachyVision. Conclusion: Dose variations were not substantial for ±0.3 cm global shifts, which is common in clinical practice.

60 APPLIED LIFE SCIENCES↗

Magnetospheric-field distortions observed by OGO 3 and 5.

The rubidium vapor magnetometer data of the scalar magnetic-field intensity obtained by the OGO 3 and 5 satellites are analyzed to study the magnetospheric-field distortions in terms of the observed field magnitude under quiet and slightly disturbed conditions minus the magnitude of the reference geomagnetic field (delta B). Average contours of equal delta Bs are shown in the geomagnetic noon-midnight and dawn-dusk meridian planes for magnetically quiet and slightly disturbed conditions. The equatorial distribution of observed delta Bs as a function of geocentric distance differs substantially from that expected from the well-known models of the quiet-time ring current. Other findings suggest that there must be a population of low-energy particles with substantial total energy near the equator at distances of 2 to 5 earth radii that has not been recognized as having sufficient energy to inflate the magnetic field.

Sugiura, M.↗

HEAO A-2 soft X-ray source catalog

The HEAO A-2 low energy X-ray detectors have surveyed over 95% of the sky in the spectral bands 0.18-0.44 and 0.44-2.8 keV, down to a typical limiting sensitivity of 1 x 10 to the -11th and 3 x 10 to the -11th ergs per sq cm per sec in each band, respectively. Using a significance criterion of 6 sigma for existence, 114 sources are cataloged, of which 54 were previously undiscovered and 32 remain unidentified. The catalog contains a listing of all counterpart identifications and a cross-reference to all HEAO 1 A-2 low energy detector team publications on the catalog sources complete through the end of 1981. Supplementary material allows the estimation of spectral parameters for the spectral models from the observed intensities. Simple graphs allow the extraction of energy fluxes at the earth, both with and without the effects of interstellar absorption. The angular distribution of the cataloged sources in the 0.44-2.8 keV band is concentrated toward the galactic plane and resembles that seen at higher energy. The distribution in the 0.18-0.44 keV band is more uniform and contains many more newly discovered and unidentified sources.

Nugent, J. J.↗

S-band multiple-access interference study for advanced tracking and data relay satellite systems

The results of a study on the effect of mutual interference among S-band multiple access (SMA) system users of advanced tracking and data relay satellite system (ATDRSS) are presented. In the ATDRSS era, the SMA system is required to support data rates ranging from 10 kb/s to 3 Mb/s. The system will consist of four advanced tracking and data relay satellites (ATDRS) each supporting up to five telemetry links. All users have 10 MHz bandwidth with their carrier frequency equal to 2.2875 GHz. A hybrid SDMA/CDMA scheme is used to mitigate the effect of the interference among system users. SMA system interference probability is evaluated with CLASS software. User link margin degradation due to mutual interference between two users is evaluated. System interference probability is evaluated for the projected 1996 mission model, a reference mission model, and a modified reference mission model.

Peng, Wei-Chung↗

Selected 3D Flash-X Checkpoints for the Long-Time Evolution of a 9.6 Solar-Mass Core-Collapse Supernova Model

This dataset contains selected 3D Flash-X checkpoint files from the long-time evolution of a low-energy core-collapse supernova explosion of a 9.6 Msun zero-metallicity, low-mass iron-core progenitor. The checkpoints span the shock-breakout phase through the young-remnant phase, ending at approximately 3 yr after core bounce. The dataset is intended for follow-up analysis and post-processing, especially radiation-transport calculations using the hydrodynamic and compositional structure of the ejecta. For a full description of the numerical setup, physical assumptions, limitations, and interpretation of the simulation, users should refer to the associated paper.

79 ASTRONOMY AND ASTROPHYSICS↗

Biomass supply chain equipment for renewable fuels production: A review

The production of renewable fuels is a critical component of global strategies to reduce greenhouse gas (GHG) emissions. Moreover, the collection of raw materials for its production can provide added benefits such as reduction of wildfire risk, additional income for farmers, and decreased disposal costs. Although there is substantial literature on design and modeling of supply chains, the authors were unable to find a single reference with the information needed for the selection and cost estimation of each type of equipment involved in the supply chain. Therefore, the goal of this research is to gather information necessary for the construction and utilization of models that might drive the identification of a feasible supply chain to produce renewable fuels at a commercial scale. The primary objectives are to 1) understand the supply chain of critical feedstocks for renewable fuels production; 2) identify the equipment commercially available for collection and adequation of feedstock; and 3) consolidate information regarding equipment cost, energy consumption, and efficiency, as well as feedstock storage and transportation systems. This paper provides a compilation for five feedstock types studied for sustainable aviation fuel production: 1) agricultural residues and grasses, 2) forest residues, 3) urban wood waste, 4) oilseeds, 5) fats, oils & greases. All the technologies involved from the field to the gate of the preprocessing or conversion unit were reviewed. The information on fats, oils & greases supply chains and equipment purposely designed for forest thinning and pruning was very limited.

: Feedstock, Collection and Adequation, Renewable ↗

Automated theoretical chemical kinetics: Predicting the kinetics for the initial stages of pyrolysis

Large scale implementation of high level computational theoretical chemical kinetics offers the prospect for dramatically improving the fidelity of combustion chemical modeling. To facilitate such efforts, we have developed a suite of codes, collectively referred to as AutoMech, that allow for the automatic prediction of the kinetics for large sets of reactions via ab initio transition-state-theory based master-equation calculations. The primary input is simply the mechanism, a dictionary relating chemically identifiable species descriptors (e.g., SMILES or InChIs) to species labels in the mechanism, and a specification of the electronic structure and transition state theory models to be implemented. Here we illustrate the current utility of AutoMech through a study of the initial stages of pyrolysis for 3 sets of fuels: sequences of alkanes, alcohols, and aldehydes. For simplicity, the analysis focuses on abstractions from the fuel by H, CH 3 , and OH, and the decomposition of the resulting radicals. Altogether, there are a total of 166 input channels in these sets (more than 363 forward reactions when expanded to the full set of elementary reactions). The code successfully produces high quality rate estimates (with apparent uncertainties less than a factor of two in limited comparisons with experiment) for > 95% of these. For the radical decomposition reactions, the analysis includes predictions for the pressure dependence of the kinetics. This wide-ranging exploration illustrates (i) the effect of different levels of prediction on the expected accuracy, (ii) the branching between abstractions at different sites for different abstractors, (iii) the dependence of the rates on the chemical structure, and (iv) the variation in radical stabilities across chemical families. These results, as well as the demonstrated feasibility of the methodology, should find further utility in the development of accurate rate expressions for arbitrary fuels. (c) 2020 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Elliott, Sarah N.↗

Validation of galvanomagnetic and thermomagnetic transport measurements using Standard Reference Material 3451

In the “method of four coefficients,” electrical resistivity (ρ), Seebeck coefficient (S), Hall coefficient (RH), and Nernst coefficient (Q) of a material are measured and typically fit or modeled with theoretical expressions based on Boltzmann transport theory to glean experimental insights into features of electronic structure and/or charge carrier scattering mechanisms in materials. Although well-defined and readily available reference materials exist for validating measurements of ρ and S, none currently exists for R H or Q. We show that measurements of all four transport coefficients—ρ, S, R H , and Q—can be validated using a single reference sample, namely, the low-temperature Seebeck coefficient Standard Reference Material® (SRM) 3451 (composition Bi 2 Te 3+x ) available from the National Institute for Standards and Technology (NIST) without the need for inter-laboratory sample exchange. Here, R H and Q data for NIST SRM 3451 reported here for the temperature range 80–400 K complement the data already available for ρ and S and will therefore be of interest to researchers desiring to validate new or existing galvanomagnetic and thermomagnetic transport properties measurement systems.

47 OTHER INSTRUMENTATION↗

Parametric Modeling and Economic Analysis of a 2MW th 3-Stream sCO 2 Heat Exchanger

Here, this paper presents the design and cost optimization of a novel 2MW th 3-stream sCO2 plate-fin heat exchanger. This heat exchanger design is unique in that it uses reduced metal oxide particle-to-sCO2 heat exchanger for cost-effective energy storage applications. The design uses low velocity, laminar air as the re-oxidizing reactant to transfer the heat of the re-oxidizing reaction to a sCO2 power loop. The design of the heat exchanger is based on a 2-D, 3-fluid plate/fin heat transfer model. The model parameterizes the size, shape, and number of passages of the heat exchanger to calculate the temperature profile, pressure drop, and fluid velocities of all three fluids. Global heat exchanger parameters such as the effectiveness and total heat transferred to the sCO2 are then calculated for overall performance. Due to the value and increased use of sCO2 heat exchangers in power cycles, a cost model of the system based on the unique high temperature/high pressure operating conditions was created using quotes from reference projects and market analysis. These quoted air-to-sCO2 heat exchangers are then processed using multiple weighting factors pertinent to heat exchanger design, including heat exchanger type, maximum temperature, differential pressures, fluids, duty, and more. These factors are then used in an exponential function in order to generate a parameterized cost curve. The design and cost of the heat exchanger are then optimized using the SMPSO genetic algorithm in Python. The optimization objectives for the system are to maximize the overall system effectiveness, including an air recuperator for preheating, and to minimize unit costs. Additional constraints are added to the system for the sCO2 and air pressure drops, air velocity to reduce particle entrainment, and the length and volume of the heat exchanger.

Cost Model↗

SU-E-T-750: Three Dimensional in Silico Study of Brachytherapy Application with In-Situ Dose-Painting Administered Via Gold-Nanoparticle Eluters

Purpose: Brachytherapy Application with in-situ Dose-painting Administered via Gold-Nanoparticle Eluters (BANDAGE) has been proposed as a new therapeutic strategy for radiation boosting of high-risk prostate tumor subvolume while minimizing dose to neighboring organs-at-risk. In a previous study the one-dimensional dose-painting with gold nanoparticles (GNP) released from GNP-loaded brachytherapy spacers was investigated. The current study investigates BANDAGE in three-dimensions. Methods: To simulate GNPs transport in prostrate tumors, a three dimensional, cylindrically symmetric transport model was generated using a finite element method (FEM). A mathematical model of Gold nanoparticle (GNPs) transport provides a useful strategy to optimize potential treatment planning for BANDAGE. Here, treatment of tumors with a radius of 2.5 cm was simulated in 3-D. This simulation phase considered one gold based cylindrical spacer (GBS of size 5mm × 0.8 mm) introduced at the center of the spherical tumor with initial concentration of 100 mg/g or 508 mol/m3 of GNP. Finite element mesh is used to stimulate the GNP transport. Gold concentrations within the tumor were obtained using a 3-D FEM solution implemented by COMSOL. Results: The analysis shows the spread of the GNPs through-out the tumor with the increase of concentration towards the periphery with time. The analysis also shows the concentration profiles and corresponding dose enhancement factors (dose boost factor) as a function of GNP size. Conclusion: This study demonstrates the use of computational modeling and optimal parameter estimation to predict local GNPs from central implant as a function of x, y and z axis . Such a study provides a useful reference for ongoing translational studies for the BANDAGE approach.

60 APPLIED LIFE SCIENCES↗

SU-F-T-01: Optimization of the Accelerated Partial Breast Brachytherapy Fractionation with Consideration of Physical Doses to Tumor and Organ at Risk

Purpose: The accelerated partial breast irradiation (APBI) with brachytherapy prescribes 34Gy to be delivered in 10 fractions over 5 consecutive working days without considering the physical dose to the target and organs at risk (OARs) for an individual patient. The purpose of this study is to optimize the fractionation scheme by evaluating the radiation effect on tumor and OARs with a modified linear-quadratic (LQ) model based on dose-volume histograms (DVHs). Methods: Five breast patients treated with multilumen balloon brachytherapy were selected. The minimum skin and rib spacing were ranged from 2.5mm to 14.3mm and from 1.0mm to 25.0mm, respectively. The LQ model parameters were set as: (1) breast: α=0.08, β=0.028, doubling time Tpot=14.4 days, and starting time Tk=21days; (2) skin: acute reaction α=0.101, β=0.009; late reaction α=0.064, β=0.029; (3) rib: α=0.3, β=0.12. Boundary dose Dt was 6 Gy for both target and OARs. The relation between radiation effects on the tumor (ET) and OARs (EOAR) were plotted for fraction number from 1 to 20. Results: The value of radiation effect from routine 3.4Gyx10 fractions was used as reference, ETref and EOARref. If set ET=ETref, the fractionation that results in minimum EOAR values correspond to the optimal fractionation. For these patients, the optimal numbers are 10 fractions for skin acute reaction, 18 fractions for skin and rib late reaction while the doses per fraction are 3.4Gy and 2.05–2.10Gy, respectively. If set EOAR=EOARref, the fractionation that results in a maximum ET value corresponds to the optimal fractionation. The optimal fractionation is 3.4Gyx10 fractions for skin acute reaction, and 2.10–2.25Gyx18 fractions for skin late reaction and rib. Conclusion: For APBI brachytherapy, the routine 3.4Gyx10 fractions is optimal fractionation for skin acute reaction, while 2.05–2.25Gyx18 fractions is optimal fractionation for late reaction of skin and rib.

60 APPLIED LIFE SCIENCES↗

Assessment of Pump Coastdown and Reactor Protection Scram Delays during Station Blackout Conditions

This report presents an assessment of the impact of pump coastdown time and reactor protection scram delays for the Versatile Test Reactor (VTR) during Protected Station Blackout (PSBO) conditions. While previous simulations for the VTR assumed centrifugal pumps in the primary system, the current pre-conceptual design uses electromagnetic (EM) pumps. Because there is uncertainty as to what the parameters of the EM pump design will be, this report focuses on the impact of the flow coastdown and the reactor protection scram delay, not on the needs of the pump design. PSBO transient simulations were performed using the SAS4A/SASSYS-1 fast reactor safety analysis code (version 5.2.3). The model used in the simulations is based on the FY18 SAS4A/SASSYS-1 model. A change to the model was made to replace the centrifugal pump model with an electromagnetic pump model with a motor generator as a coastdown mechanism. The results of the PSBO transient simulations were assessed against the criteria used in Reference 2 with an additional 50°C for conservatism to account for uncertainties. The results show that as the delay before scramming the rods increases, the moment of inertia of the coastdown mechanism must increase to satisfy the criteria. By increasing the moment of inertia to extend the flow coastdown, temperatures can be kept below the desired limits with reactor protection scram delays between 3 and 10 seconds.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Novel Gamma Attenuation Methods Utilized for Waste Characterization of UO{sub 2}F{sub 2}-Bearing Materials at the Paducah GDP - 17327

The Paducah Gaseous Diffusion Plant (PGDP) is currently under deactivation with demolition in the decades to follow. UO{sub 2}F{sub 2}-bearing waste is generated at PGDP by UF{sub 6} hydrolysing to materials such as pipes, valves, PPE, etc. when UF{sub 6} is exposed to humid air. In addition, Al{sub 2}O{sub 3} and NaF trap materials contain significant amounts of Uranium. The UO{sub 2}F{sub 2} deposits within the generated waste can be of sub-gram levels to several hundreds of localized grams and are much denser than the surrounding interfering matrix materials and may be of very complex geometric and chemical forms such as with the Al{sub 2}O{sub 3} and NaF trap materials. The main objective is to characterize the fissile (U-235) content of the UO{sub 2}F{sub 2}-bearing waste so as to meet the Data Quality Objectives (DQO) for proper disposal. If a waste container cannot meet the DQO then it must be subjected to costly remediation, repackaging and re-characterization processes. We have developed, at PGDP, several novel model-based methods and techniques that vastly improve the standard gamma attenuation correction methods and do not require Working Reference Materials (WRM) for calibration. These new methods involve rotating and non-rotating 18.9 liter (5 U.S. gallon) waste containers with and without a transmission modality. A new model-based variant of differential attenuation has been developed that provides a high-quality self-absorption correction that does not require knowledge of the Uranium enrichment or isotopic ratios. For more challenging waste containers, a method using multi-view (non-rotating) 18.9 liter waste containers has been considered using a recently developed Advanced ISOCS{sup C} Uncertainty Estimator (AIUE) package. The new methods suffice to significantly improve accuracy and precision and to lower the Total Measurement Uncertainty (TMU) leading to satisfactory DQO's that were not previously achievable using the standard gamma attenuation correction methods. In this paper we present real 18.9 liter waste container and Working Reference Material (WRM) data subjected to the new methods and compared to standard methods depicting the significant improvement in the DQO that is realized. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Floodplain Wetland Channel Planform, Cross-Sectional Morphology, and Sediment Characteristics Along an Estuarine to Tidal River Gradient

The formation of wetland channel networks on coastal river floodplains is affected by spatial transitions in tidal-fluvial processes. This study evaluated sedimentation patterns in tidal marshes on the 147-km tidal Columbia River and its 87-km estuary and characterized the cross-sectional geometry and planform morphometry of tidal wetlands along the estuarine to riverine gradient. Tidal marshes were predominantly depositional (median 0.7 cm yr-1, primarily silt), consistent with late-Holocene rates. Marsh sediment accretion rate increased with annual maximum 7-day average daily maximum water depth. Elevation was negatively correlated with accretion rate in the tidal river and positively correlated with total organic carbon (TOC%) in the tidal river and estuary. TOC% was greater in the estuary and, like percent fines, greater farther from the main-channel Columbia River. For four single-channel and six channel-network planforms of tidal marsh, shrub-dominated, and forested wetlands: (1) Spatial patterns of cross-sectional morphology conformed to typical coastal wetland morphology in estuarine reaches up to the tidal river. (2) Reach-based and common slope linear models for channel perimeter on wetland area were predictive in the estuary (R2 > 0.81) and differed between island (n = 144) and mainland (n = 164) wetlands. No planform linear models were predictive for the entire study area or the tidal river. No models for channel outlets were acceptable. (3) Channel perimeter, surface area, and outlets were all highly variable within and among estuarine–riverine reaches. Analyses of sediment, cross-section, and planform support the use of a “natural network paradigm” for wetland-restoration design on tidal river floodplains.

channel morphology↗

SU-F-T-643: Feasibility of Performing Patient Specific VMAT QA On Single Linac for Plans Treated in Beam-Matched Elekta Agility Linacs

Purpose: The increasing application of VMAT demands a more efficient workflow and QA solution. This study aims to investigate the feasibility of performing VMAT QA measurements on one linac for plans treated on other beam-matched Elekta Agility linacs. Methods: A single model was used to create 24 clinically approved VMAT plans (12 head-and-neck and 12 prostate using 6MV and 10MV respectively) on Pinnacle v9.10 (Philips, Einhoven, Netherlands). All head-and-neck plans were delivered on three beam-matched machines while all prostate cases were delivered on two beam-matched 10MV Agility machines. All plans were delivered onto PTW Octavius 4D phantom with 1500 detector array (PTW, Freiburg, Germany). Reconstructed volume doses were then compared with the Pinnacle reference plans in Verisoft 6.1 under 3%/3mm gamma criteria at local dose. Plans were considered clinically acceptable if >90% of the voxels passing the gamma criteria. Results: All measurements were passed (3D gamma passing rate >90%) and the result shows that the mean difference of 3D gamma of 12 head-and-neck cases is 1.2% with standard deviation of 0.6%. While for prostate cases, the mean difference of 3D gamma is 0.9% with standard deviation of 0.7%. Maximum difference of 3D gamma of all measurements between beam-matched machines is less than 2.5%. The differences of passing rates between different machines were statistically insignificant (p>0.05). Conclusion. The result suggests that ther Conclusion: The result suggests that there exists a 3D gamma threshold, in our case 92.5%, above which the VMAT QA performed in any one of beam-matched machine will also pass in another one. Therefore, VMAT QA efficiency may be increased and phantom set up time can be saved by implementing such method. A constant performance across all beam matched machines must be maintained to make this QA approach feasible.

60 APPLIED LIFE SCIENCES↗

Conductance distribution near the Anderson transition

Using a modification of the Shapiro approach, we introduce the two-parameter family of conductance distributions W(g), defined by simple differential equations, which are in the one-to-one correspondence with conductance distributions for quasi-one-dimensional systems of size L{sup d–1} × L{sub z}, characterizing by parameters L/ξ and L{sub z}/L (ξ is the correlation length, d is the dimension of space). This family contains the Gaussian and log-normal distributions, typical for the metallic and localized phases. For a certain choice of parameters, we reproduce the results for the cumulants of conductance in the space dimension d = 2 + ϵ obtained in the framework of the σ-model approach. The universal property of distributions is existence of two asymptotic regimes, log-normal for small g and exponential for large g. In the metallic phase they refer to remote tails, in the critical region they determine practically all distribution, in the localized phase the former asymptotics forces out the latter. A singularity at g = 1, discovered in numerical experiments, is admissible in the framework of their calculational scheme, but related with a deficient definition of conductance. Apart of this singularity, the critical distribution for d = 3 is well described by the present theory. One-parameter scaling for the whole distribution takes place under condition, that two independent parameters characterizing this distribution are functions of the ratio L/ξ.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Simultaneous mitigation of density and energy errors in approximate DFT for transition metal chemistry (Final Technical Report)

There were three major goals and objectives of this project: 1) Develop tools to understand density-driven errors in transition metal complexes, 2) Evaluate and minimize energy delocalization error and static correlation error through judicious functional choice, and 3) applying this workflow to machine-learning accelerated screening of redox couples. Over the reporting period, we developed a framework for eliminating flat plane errors. We introduced fully non-empirical coefficients. We demonstrated the approach on both molecules and solids. We investigated and eliminated density driven errors and demonstrated their impact on potential energy surfaces. We trained machine learning models both in a method-dependent fashion and to predict errors in method accuracy. We built large data sets of small molecule energetics and multi-reference character.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A review of some problems in global-local stress analysis

The various types of local-global finite-element problems point out the need to develop a new generation of software. First, this new software needs to have a complete analysis capability, encompassing linear and nonlinear analysis of 1-, 2-, and 3-dimensional finite-element models, as well as mixed dimensional models. The software must be capable of treating static and dynamic (vibration and transient response) problems, including the stability effects of initial stress, and the software should be able to treat both elastic and elasto-plastic materials. The software should carry a set of optional diagnostics to assist the program user during model generation in order to help avoid obvious structural modeling errors. In addition, the program software should be well documented so the user has a complete technical reference for each type of element contained in the program library, including information on such topics as the type of numerical integration, use of underintegration, and inclusion of incompatible modes, etc. Some packaged information should also be available to assist the user in building mixed-dimensional models. An important advancement in finite-element software should be in the development of program modularity, so that the user can select from a menu various basic operations in matrix structural analysis.

Nelson, Richard B.↗