Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Differential Experiments”

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 1,711 records · Page 95

Aviary: An Open-Source Multidisciplinary Design, Analysis, and Optimization Tool for Modeling Aircraft with Analytic Gradients

In recent years demands on aircraft design methods have begun to require higher degrees of coupling between disciplines and optimization in order to satisfy competing objectives involving large numbers of design parameters that define unconventional configurations. These expanding requirements have amplified a need for new and improved aircraft design, analysis, and optimization codes that are capable of performing coupled design and exploiting analytic gradients to perform gradient-based optimization where possible. To address this need, a new multidisciplinary design optimization and analysis tool called Aviary is presented. This tool, built on OpenMDAO, allows for tightly coupled, simultaneous aircraft and subsystem design using analytic gradients. Aviary includes methods from two NASA developed legacy aircraft analysis tools and provides native analytically differentiated calculations for five different disciplines (weights and sizing, aerodynamics, geometry, propulsion, and mission analysis), while also allowing external discipline analysis tools to be coupled, regardless of whether those tools can provide analytic gradients. Verification and preliminary examples and modeling efforts show Aviary’s ability to effectively model novel concepts and explore large and non-intuitive design spaces. Additionally, a multi-level user interface in Aviary creates an easy entry point for users with any level of multidisciplinary design, analysis, and optimization experience.

optimization↗

Photoproduction of Cascade Baryons Using the GlueX Detector at Jefferson Laboratory

Multi-strange baryons have played an important role in understanding the strong interaction. Despite their importance to advancing quantum chromodynamics (QCD), little is known about such hyperons due to the lack of a strange probe. Almost all knowledge of Cascade baryons today stems from kaon-nucleon interactions in bubble chamber experiments performed in the 1960s and 1970s. The 1980s saw advancement in electronics and computational resources allowing for higher statistic experiments such as the MultiParticle Spectrometer (MPS) at Brookhaven National Laboratory. From these previous experiments, the octet and decuplet ground states, Xi(1320) and Xi(1530) respectively, were well established with known properties and four excited states were well established. This research uses the GlueX experiment at Jefferson Laboratory to extend photoproduction cross section measurements for Xi(1320)- to higher beam energies to further understand the production mechanism, as well as to search for the first excited Cascade resonance observation in photoproduction through the decay Xi-* -> K-Lambda. The GlueX Spectrometer is a nearly hermetic detector used to study exclusive photoproduction reactions with photon beam energies up to 12 GeV. The first phase of GlueX running has recently been completed. Preliminary results for the total cross section and differential cross sections in terms of momentum transfer -t are shown within. Additionally, the first observation of an excited Cascade baryon, in particular Xi(1820)-, is shown.

Ernst, Ashley↗

Low Energy Sputtering Experiments for Ion Engine Lifetime Assessment

The sputtering yield of molybdenum under xenon ion bombardment was measured using a Quartz Crystal Microbalance. The measurements were made for ion kinetic energies in the range 100-1keV on molybdenum films deposited by magnetron sputtering in conditions optimized to reproduce or approach bulk-like properties. SEM micrographs for different anode bias voltages during the deposition are compared, and four different methods were implemented to estimate the density of the molybdenum films. A careful discussion of the Quartz Crystal Microbalance is proposed and it is shown that this method can be used to measure mass changes that are distributed unevenly on the crystal electrode surface, if an analytical expression is known for the differential mass-sensitivity of the crystal and the erosion profile. Finally, results are presented that are in good agreement with previously published data, and it is concluded that this method holds the promise of enabling sputtering yield measurements at energies closer to the threshold energy in the very short term.

Duchemin Olivier B.↗

DONUT: physics-aware machine learning for real-time X-ray nanodiffraction analysis

Coherent X-ray scattering techniques are critical for investigating the fundamental structural properties of materials at the nanoscale. While advancements have made these experiments more accessible, real-time analysis remains a significant bottleneck, often hindered by artifacts and computational demands. In scanning X-ray nanodiffraction microscopy, which is widely used to spatially resolve structural heterogeneities, this challenge is compounded by the convolution of the divergent beam with the sample’s local structure. To address this, we introduce DONUT (Diffraction with Optics for Nanobeam by Unsupervised Training), a physics-aware neural network designed for the rapid and automated analysis of nanobeam diffraction data. By incorporating a differentiable geometric diffraction model directly into its architecture, DONUT learns to predict crystal lattice strain and orientation in real-time. Crucially, this is achieved without reliance on labeled datasets or pre-training, overcoming a fundamental limitation for supervised machine learning in X-ray science. We demonstrate experimentally that DONUT accurately extracts all features within the data over 200 times more efficiently than conventional fitting methods.

Materials science↗

Microbial inoculum effects on the rumen epithelial transcriptome and rumen epimural metatranscriptome in calves

Manipulation of the rumen microbial ecosystem in early life may affect ruminal fermentation and enhance the productive performance of dairy cows. The objective of this experiment was to evaluate the effects of dosing three different types of microbial inoculum on the rumen epithelium tissue (RE) transcriptome and the rumen epimural metatranscriptome (REM) in dairy calves. For this objective, 15 Holstein bull calves were enrolled in the study at birth and assigned to three different intraruminal inoculum treatments dosed orally once weekly from three to six weeks of age. The inoculum treatments were prepared from rumen contents collected from rumen fistulated lactating cows and were either autoclaved (control; ARF), processed by differential centrifugation to create the bacterial-enriched inoculum (BE), or through gravimetric separation to create the protozoal-enriched inoculum (PE). Calves were fed 2.5 L/d pasteurized waste milk 3x/d from 0 to 7 weeks of age and texturized starter until euthanasia at 9 weeks of age, when the RE tissues were collected for transcriptome and microbial metatranscriptome analyses, from four randomly selected calves from each treatment. The different types of inoculum altered the RE transcriptome and REM. Compared to ARF, 9 genes were upregulated in the RE of BE and 92 in PE, whereas between BE and PE there were 13 genes upregulated in BE and 114 in PE. Gene ontology analysis identified enriched GO terms in biological process category between PE and ARF, with no enrichment between BE and ARF. The RE functional signature showed different KEGG pathways related to BE and ARF, and no specific KEGG pathway for PE. We observed a lower alpha diversity index for RE microbiome in ARF (observed genera and Chao1 (p < 0.05)). Five microbial genera showed a significant correlation with the changes in host gene expression: Roseburia (25 genes), Entamoeba (two genes); Anaerosinus, Lachnospira, and Succiniclasticum were each related to one gene. sPLS-DA analysis showed that RE microbial communities differ among the treatments, although the taxonomic and functional microbial profiles show different distributions. Co-expression Differential Network Analysis indicated that both BE and PE had an impact on the abundance of KEGG modules related to acyl-CoA synthesis, type VI secretion, and methanogenesis, while PE had a significant impact on KEGGs related to ectoine biosynthesis and D-xylose transport. Our study indicated that artificial dosing with different microbial inocula in early life alters not only the RE transcriptome, but also affects the REM and its functions.

59 BASIC BIOLOGICAL SCIENCES↗

DONUT: Physics-aware Machine Learning for Real-time X-ray Nanodiffraction Analysis

SF-25-088 Coherent X-ray scattering techniques are critical for investigating the fundamental structural properties of materials at the nanoscale. While advancements have made these experiments more accessible, real-time analysis remains a significant bottleneck, often hindered by artifacts and computational demands. In scanning X-ray nanodiffraction microscopy, which is widely used to spatially resolve structural heterogeneities, this challenge is compounded by the convolution of the divergent beam with the sample’s local structure. To address this, we introduce DONUT (Diffraction with Optics for Nanobeam by Unsupervised Training), a physics-aware neural network designed for the rapid and automated analysis of nanobeam diffraction data. By incorporating a differentiable geometric diffraction model directly into its architecture, DONUT learns to predict crystal lattice strain and orientation in real-time. Crucially, this is achieved without reliance on labeled datasets or pre-training, overcoming a fundamental limitation for supervised machine learning in X-ray science. We demonstrate experimentally that DONUT accurately extracts all features within the data over 200 times more efficiently than conventional fitting methods.

Zhou, Tao [Argonne National Laboratory (ANL), Argo↗

Goldstone intracomplex connected element interferometry

Interferometric observations of the radio source pair 3C 84 and OE 400 were made on the 21 km baseline between Deep Space Station (DSS) 13 and DSS 15 to explore the angular navigation potential of intracomplex connected element interferometry (CEI). The differential phase-delay observable formed from pairs of 3 minute scans exhibited a precision of 1 psec, while the actual scatter of the phase-delay residuals for eleven scans over the 90 minute observing session was about 10 psec, consistent with the expected few millimeter fluctuations in the wet tropospheric path delay. Fitting for the position of OE 400 relative to 3C 84 yielded an error ellipse with a semi-minor axis of 60 nrad. Given the short data arc in this experiment, the orthogonal direction in the plane of the sky is not well determined; however, a second baseline or a data arc spanning a larger fraction of the source mutual visibility window could provide simultaneous determination of both right ascension and declination. Examination of the phase-delay residuals supports the accuracy of the cycle ambiguity resolution. However, reliable phase ambiguity resolution will pose the most significant challenge to routine use of CEI for spacecraft tracking, particularly when the a priori spacecraft source position is not well known. Several approaches for ambiguity resolution are briefly outlined.

Edwards, C. D.↗

Computation of nonequilibrium radiating shock layers

A computational technique of coupling radiative transfer to fluid motion is developed for axisymmetric blunt body shock layer flows in a thermochemical nonequilibrium environment. The coupled formulation of radiation and flowfield leads to a governing set of integro-differential equations. This equation set is solved using a modified Gauss-Seidel line relaxation techniques which incorporates the inversion of full block matrix associated with radiative transfer using a block iteration method. The thermodynamic state of the gas is described by three temperatures: translational, rotational, and vibrational-electronic. Radiation phenomenon is assumed to be governed by the vibrational-electronic temperature. The radiative properties are described by a spectrally detailed model. The computations are presented for two cases, including the Fire II flight experiment. It is shown that the method converges and the calculated spectra qualitatively agree with the experimental data for the two test cases. The calculated total radiative flux underestimates the measured values owing to the low vibrational-electronic temperature predicted in the flowfield calculation.

Gokcen, Tahir↗

The Effect of Clouds Upon Limb Scattered Radiances and the Retrieval of Ozone Profiles Using These Radiances

The use of limb scattered radiance profiles to retrieve ozone profiles is currently being investigated. The goal is to produce ozone profiles with better vertical resolution than is available with the Backscattered Ultraviolet (BUV) technique and with much greater spatial and temporal coverage than with the solar occultation method (i.e. SAGE II). This method, which uses UV and visible light scattered from the earth's limb, has recently been proven to work for clear sky cases with data from the STS-87 flight of the Shuttle Ozone Sounding Limb Experiment/Limb Ozone Retrieval Experiment (SOLSE/LORE). As to be expected, clouds have a substantial impact upon the limb radiance (increasing the radiance as much as 80-100% is some cases). Here we use a variety of radiative transfer models and limited SOLSE/LORE data to investigate the effect of clouds upon the limb radiance at wavelengths used in the ozone retrieval (approximately 600 nm). Though the presence of clouds can greatly increase the limb radiance, they have a minimal effect upon the retrieved ozone profile, since the retrieval uses a differential absorption technique.

Flittner, D. E.↗

Performance of the NASA Digitizing Core-Loss Instrumentation

The standard method of magnetic core loss measurement was implemented on a high frequency digitizing oscilloscope in order to explore the limits to accuracy when characterizing high Q cores at frequencies up to 1 MHz. This method computes core loss from the cycle mean of the product of the exciting current in a primary winding and induced voltage in a separate flux sensing winding. It is pointed out that just 20 percent accuracy for a Q of 100 core material requires a phase angle accuracy of 0.1 between the voltage and current measurements. Experiment shows that at 1 MHz, even high quality, high frequency current sensing transformers can introduce phase errors of a degree or more. Due to the fact that the Q of some quasilinear core materials can exceed 300 at frequencies below 100 kHz, phase angle errors can be a problem even at 50 kHz. Hence great care is necessary with current sensing and ground loops when measuring high Q cores. Best high frequency current sensing accuracy was obtained from a fabricated 0.1-ohm coaxial resistor, differentially sensed. Sample high frequency core loss data taken with the setup for a permeability-14 MPP core is presented.

Schwarze, Gene E.↗

Measurement of Multi-Proton Zero Pion Final States with the NuMI Neutrino Beam at ICARUS

Evidence suggests that charge-parity (CP) symmetry, or the principle that matter and antimatter must obey the same physics, might be violated in neutrino flavor mixing. The next-generation long-baseline experiment DUNE is designed to confirm whether or not neutrinos oscillate differently from antineutrinos. The magnitude of systematic uncertainties contributing to current long-baseline oscillation measurements, if left unimproved, is enough to jeopardize DUNE's ability to measure CP violation. Neutrino cross section measurements on argon targets are an essential input for improving neutrino interaction modelling and reducing the systematic uncertainties before DUNE turns on. The ICARUS experiment at Fermilab is well suited perform such measurements due to the NuMI neutrino beam providing neutrinos at the same energy as DUNE's first oscillation maximum. This work presents a measurement of muon neutrino charged-current interactions with multiple energetic protons and zero final state mesons in ICARUS. Multi-proton topologies are sensitive to contributions from two-particle two hole effects as well as resonant pion production and subsequent absorption via final state interactions (FSI) within the argon nucleus. Single-differential cross sections are measured in lab-frame opening angles and transverse kinematic imbalance variables, characterizing the initial sate momentum sharing between correlated nucleons and strength of FSI in argon.

Smedley, John [Rochester U.] (ORCID:00000002848611↗

Choline chloride-formic acid mixture as a medium for the reduction of pertechnetates – electrochemical and spectroscopic studies

In this work, physicochemical properties of the choline chloride (ChCl) and formic acid (FA) mixture (1:2 molar ratio) have been studied over a broad range of temperatures (-140°C – 60 °C). Differential scanning calorimetry has shown that the examined system remains in liquid state at very low temperatures - a glass transition is observed in the range of -125 °C to - 90 °C. The kinematic viscosity, ionic conductivity and the width of the electrochemical window determined for this system revealed its beneficial electrochemical properties. This indicates suitability of ChCl:FA electrolytes in electrochemical measurements. In this non-aqueous electrolyte, the electrochemical reduction of Tc(VII) ions has been studied for the first time. Cyclic voltammetry and chronopotentiometry experiments revealed that the electroreduction of the pertechnetates is a multi-path process which leads to formation of a Tc(IV) ionic form. X-ray absorption spectroscopy of the latter revealed its structure as a TcCl 6 2- complex.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Testing effective field theory with the most general neutron decay correlations

Built on the seminal works by Jackson-Treiman-Wyld and Ebel-Feldman, we derive the most general free neutron differential decay rate where all massive particles (neutron, proton, and electron) are polarized. This introduces 33 new correlations in addition to the 18 existing ones, which overconstrain the coupling constants in the low-energy effective field theory of charged weak interactions, and thus provides stringent tests of the validity of the theory framework itself. We classify the correlation coefficients in terms of their Standard Model limit and discrete symmetries, and study their expansion with respect to the new physics coupling strengths, supplemented by the experiment-independent 𝒪⁡(𝛼) virtual electromagnetic radiative corrections.

Astronomy & Astrophysics↗

Coal-based Bricks & Blocks (CBBs): Process Development to Prototype Fabrication Coupled with Techno-Economic Analysis and Market Survey

The decline of coal use for energy production provides an abundance of local feedstock for new innovative uses and value-added products. Expanding the U.S. coal-value chain to manufacture high-value carbon products can strengthen the nation’s energy and mineral security, enhance the U.S. national defense security, increase the United States’ economic prosperity, while achieving U.S. environmental objectives. The primary project goal is a relatively light-weight composite product with superior (or comparable) compressive strength. Both virgin and, where available, post-consumer recycled thermoplastic versions are tested for each thermoplastic species. A useful attribute of thermoplastics as binders is that they can be heated to their melting point, cooled, and reheated again without significant degradation. A key advantage of thermoset CBBs is that they require only mixing and molding. CBB advantages include low cost, availability, binding ability and processability. Coal-based bricks and blocks (CBBs) weigh about 50% less than clay bricks and can be manufactured with an interlocking design to promote ease of use for the novice builder. CBB formulation is evaluated according to a design-of-experiments (DoE) approach. DoE variables are a) relative weight fractions of binder, b) relative proportions of large versus small (milled) anthracite size fractions, and c) additive percentage. Fabrication methods include hot-press molding and extrusion, the later being the most commercially viable. CBBs are tested for compressive strength, modulus of rupture (by flexure test) and water absorption per ASTM C67, with density determined by the Archimedes drainage method. Fractured interfaces are examined by SEM (Scanning Electron Microscopy) to resolve fracture dynamics and interior microstructure uniformity. Differential scanning calorimetry (DSC) is used to compare plastic transition temperatures i.e., glass and melting temperatures to contrast virgin with post-consumer recycled thermoplastics and optimize their usage. These results are used in the DoE analysis to identify the binder and relative weight percentages for optimum strength, density, and porosity. Overall, CBBs possess strength comparable to clay-based bricks but are non-permeable and hydrophobic, and hence resistant to degradation by freeze-fracturing, corrosion, and efflorescence. The strongest composites have been made with the following thermoplastic binders (in order of strength): thermoset, high-density polyethylene crosslink resin, high-density polyethylene, nylon 6/6, and polypropylene. Results from a techno-economic analysis TEA show economy of scale for CBBs by modularization and reveal the binder as the cost driver for material costs. Ideally, the incorporation of post-consumer recycled thermoplastic will decrease material acquisition costs and increase product sustainability. Notably, CBBs do not require the high temperature calcination needed to produce cement, nor do they require firing in the 1600-2400 °F range for three days using natural gas, as do clay brick equivalents. Instead, CBBs are heated to a modest <600 °F according to the melt flow index of the thermoplastic binder. Existing anthracite mines can be expanded to produce CBBs to reduce aggregate transportation costs and emissions that exist for clay bricks. TEA reflects this reduced energy cost while a comparative CO2 emission analysis quantifies the reduced environmental footprint. The market survey identifies several commercialization opportunities, dependent upon the brick classification.

01 COAL, LIGNITE, AND PEAT↗

Astrocyte FABP7 Modulates Seizure Activity-Dependent Protein Expression in Mouse Brain

Background/Objectives: Patients with epilepsy commonly experience patterns of seizures that change with sleep/wake behavior or diurnal rhythms. The cellular and molecular mechanisms that underlie these patterns in seizure activity are not well understood but may involve non-neuronal cells, such as astrocytes. Our previous studies show the critical importance of one specific astrocyte factor, the brain-type fatty acid binding protein Fabp7, in the regulation of time-of-day-dependent electroshock seizure threshold and neural activity-dependent gene expression in mice. Here, we examined whether Fabp7 influences differential seizure activity-dependent protein expression, by comparing Fabp7 knockout (KO) to wild-type (WT) mice under control conditions and after reaching the maximal electroshock seizure threshold (MEST). Methods: We analyzed the proteome in cortical–hippocampal extracts from MEST and SHAM groups of WT and KO mice using mass spectrometry (MS), followed by Gene Ontology (GO) and pathway analyses. GO and pathway analyses of all groups revealed a diverse set of up- and downregulated differentially expressed proteins (DEPs). Results: We identified 65 significant DEPs in the comparison of KO SHAM versus WT SHAM; 33 proteins were upregulated and 32 were downregulated. We found downregulation in mitochondrial-associated proteins in WT MEST compared to WT SHAM controls, including Slc1a4, Slc25a27, Cox7a2, Cox8a, Micos10, and Atp5mk. Several upregulated DEPs in the KO SHAM versus WT SHAM comparison were associated with the 20S proteasomal subunit, suggesting proteasomal activity is elevated in the absence of Fabp7 expression. We also observed 92 DEPs significantly altered in the KO MEST versus WT MEST, with 49 proteins upregulated and 43 downregulated. Conclusions: Together, these data suggest that the astrocyte Fabp7 regulation of time-of-day-mediated neural excitability is modulated by multiple cellular mechanisms, which include proteasomal pathways, independent of its role in activity-dependent gene expression.

Neural Excitability↗

Evaluating the feasibility of using downwind methods to quantify point source oil and gas emissions using continuously monitoring fence-line sensors

The dependable reporting of methane (CH 4 ) emissions from point sources, such as fugitive leaks from oil and gas infrastructure, is important for profit maximization (retaining more hydrocarbons), evaluating climate impacts, assessing CH 4 fees for regulatory programs, and validating CH 4 intensity in differentiated gas programs. Currently, there are disagreements between emissions reported by different quantification techniques for the same sources. It has been suggested that downwind CH 4 quantification methods using CH 4 measurements on the fence line of production facilities could be used to generate emission estimates from oil and gas operations at the site level, but it is currently unclear how accurate the quantified emissions are. To investigate the accuracy of downwind methods, this study uses fence-line simulated data collected during controlled-release experiments as input for a non-standard closed-path eddy covariance (EC), the Gaussian plume inverse model (GPIM), and the backward Lagrangian stochastic (bLs) model in a range of atmospheric conditions. This study's EC attempt was unsuccessful due to data collection and instrumentation issues, resulting in invalid results characterized by underestimated emissions, large negative fluxes, and cospectra/ogives that deviated from their ideal shapes. Consequently, the EC results could not be compared with the GPIM and bLS model. The bLs model demonstrated the highest accuracy for single-release single-point emissions, though it exhibited greater uncertainty than GPIM under multi-release conditions. Across the GPIM and bLs model, the most reliable quantification was achieved with 15 min averaging and a narrow 5° wind sector range. Although EC was limited in this context, future studies should consider employing a standard EC system and further optimizing GPIM and bLs approaches – particularly for complex multi-source scenarios – to enhance quantification accuracy and reduce uncertainty.

03 NATURAL GAS↗

Activity coefficients of siderophile elements in Fe-Si liquids at high pressure

Metallic core formation in differentiated bodies in the inner solar system can take place between low pressures (near 1 bar) to much higher pressures (up to 100 GPa). Most thermodynamic models of metal-silicate equilibria utilise activity coefficients for metallic tracers in Fe liquids, nearly all of which have been carried out at low pressures. This study focuses on the effect of pressure on activity coefficients for Au, P, V, Mn, Ga, Zn, Cd, Sn, W, Pb, and Nb in liquid Fe-Si alloys. From a series of experiments at 10 GPa, 2373 K containing variable Si content in a metallic liquid we have derived epsilon interaction parameters in Fe-Si liquids ($ε^{Si}_{M}$). Comparison of 1 GPa and 10 GPa data shows no difference except for Nb. Epsilon parameters derived from low pressure experiments can thus be used to calculate activity coefficients for application to higher pressure processes (at least to 10 GPa).

58 GEOSCIENCES↗

Early differentiation of the Moon: Experimental and modeling studies and experimental and modeling studies of massif anorthosites

NASA grant NAG9-329 was in effect from 3/1/89 to 8/31/94, the last 18 months being a no-cost extension. While the grant was in effect, the P.I., coworkers, and students gave 22 talks and poster sessions at professional meetings, published 12 articles in referred journals (one more is in press, and another is in review), and edited 2 workshop reports relevant to this project. Copies of all the publications are appended to this report. The major accomplishments during the grant period have derived from three quarters: 1) the application of quantitative models of fractional crystallization and partial melting to various problems in planetary science, such as the petrogenesis of picritic glasses and mare basalts and the implications of the SNC meteorites for martian evolution; 2) an experimental study of silicate liquid immiscibility relevant to early lunar differentiation and the petrogenesis of evolved highlands rocks; and 3) experimental studies of massif anorthosites and related rocks that provide terrestrial analogs for the proposed origin of lunar anorthosites by multistage processes. The low-pressure aspects of the quantitative models were developed by the P.I. in the 1980s with NASA support and culminated with a paper comparing the crystallization of terrestrial and lunar lavas. The basis for the high-pressure modifications to the quantitative models is a data set gleaned from high pressure melting experiments done at Lamont and is supplemented by published data from other labs that constrain the baric and compositional dependences of various liquidus phase boundaries such as olivine/orthopyroxene, relevant to the melting of the mantles of the terrestrial planets. With these models it is possible to predict not only the thermal and compositional evolution of magmatic liquids ranging in composition from lumar mare basalt to terrestrial calc-alkaline basalts, but also the small increments of fractional melting that are produced when mantle rises adiabatically. Copies of the crystallization/melting programs have been given to several colleagues in planetary science. Additionally, a series of computer graphics programs, based on the algorithms in the crystallization programs have been developed that display liquidus diagrams appropriate to input compositions.

Longhi, John↗