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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 217 records · Page 12

Computational Modeling of Heterogeneity of Stress, Charge, and Cyclic Damage in Composite Electrodes of Li-Ion Batteries

Charge heterogeneity is a prevalent feature in many electrochemical systems. In a commercial cathode of Li-ion batteries, the composite is hierarchically structured across multiple length scales including the sub-micron single-crystal primary-particle domains up to the macroscopic particle ensembles. The redox kinetics of charge transfer and mass transport strongly couples with mechanical stresses. This interplay catalyzes substantial heterogeneity in the charge (re)distribution, stresses, and mechanical damage in the composite electrode during charging and discharging. We assess the heterogeneous electrochemistry and mechanics in a LiNi x Mn y Co z O 2 (NMC) cathode using a fully coupled electro-chemo-mechanics model at the cell level. A microstructure-resolved model is constructed based on the synchrotron X-ray tomography data. We calculate the stress field in the composite and then quantitatively evaluate the kinetics of surface charge transfer and Li transport biased by mechanical stresses. We further model the cyclic behavior of the cell. The repetitive deformation of the active particles and the weakening of the interfacial strength cause gradual increase of the interfacial debonding. The mechanical damage impedes electron transfer, incurs more charge heterogeneity, and results in the capacity degradation in batteries over cycles.

25 ENERGY STORAGE↗

Improv Dynamic Workflows

A workflow is a series of dependent computations which are executed to yield an experimental result, much like sheet music describes a musical performance. Dynamic workflows are like improvisational jazz, in which the musicians create unique, situation-driven, collaborative variations on themes. Dynamic workflows can potentially yield better results, save computation, and/or save human decision-making effort versus pre-specified or manual workflows, as they need not run the exhaustive set of studies which might be required in a pre-specified set, and they make their own experimental design decisions at run time. If you have an existing Maestro study where you would like to save computation and/or human time, Improv is for you. Improv provides core capabilities for creating a simple, hierarchical structure over Maestro studies, allowing you to connect ``experimental'' Maestro strudies with decision-making code to select parameters and run corresponding studies.

Goforth, John↗

Microstructural characterization of phase-separated co-deposited Cu–Ta immiscible alloy thin films

Elevated temperature co-sputtering of immiscible elements ends in a variety of self-organized morphologies due to phase separation. Cu–Ta is used as a model system to understand the evolution of phase-separated microstructural morphologies by co-sputtering thin films with nominal 50–50 at.% composition at four temperatures: 25, 400, 600, and 800 °C. Scanning/transmission electron microscopy of the film cross sections showed the microstructure morphology varied from nanocrystalline Cu–Ta at 25 °C to a wavy ribbon-like structure at 400 °C, to Cu-rich agglomerates surrounded by Ta-rich veins at 600 and 800 °C. In the agglomerate-vein morphology, microstructural features were present on two length scales, from a few nanometers to a few tens of nanometers, thus making the structures hierarchical. On the nanoscale, the Cu-rich agglomerates contained Ta precipitates, whereas the Ta-rich veins had embedded Cu nanocrystals. The various microstructures can be attributed to the highly disparate constituent element interdiffusion at the deposition temperatures with the Cu having orders of magnitude higher mobility than Ta at the deposition temperatures. This research of processing–microstructure relationship will be useful in guiding the design of hierarchical multiphase microstructures in binary or multicomponent thin films with tailored mechanical properties.

36 MATERIALS SCIENCE↗

Biomineral mesostructure

Abstract Biominerals formed by animals are most frequently calcium carbonate or phosphate polycrystalline materials with complex hierarchical structures. This article will focus on the 10-nm–10-µm scale, termed “mesoscale,” at which the “mesostructure” differs greatly across biominerals, is relevant to their mechanical properties, and reveals formation mechanisms in sea urchin teeth, mollusk shell prisms and nacre, human enamel, and coral skeletons. This article will conclude by focusing on important unanswered questions to inspire future research. Graphical abstract

36 MATERIALS SCIENCE↗

Event Definition for the Automated Detection of Nuclear Proliferation Activities

In FY2020, Savannah River National Laboratory (SRNL) in collaboration with the Discovery Analytics Center (DAC) at Virginia Polytechnic Institute and State University (VT) began developing a demonstration prototype system that uses multiple machine learning and data analytic methods on largescale open data sources to identify new, developing, or undeclared nuclear programs. One of the most challenging aspects of applying machine learning techniques to such a problem is the high likelihood of extremely sparse data from disparate sources. To overcome this challenge, the current work will use a strategic combination of supervised, semi-supervised, and unsupervised learning techniques to ingest and fuse data streams to make a forecast of nuclear activities in a targeted geospatial location. Identifying potential data sources and training supervised learning algorithms is dependent upon the development of a robust foundation of targeted event domains that fundamentally define the nuclear activities of interest. This report documents the definition of a hierarchical structure for both nuclear activity and event domains that will be used to guide the research team in development or use of existing semantic dictionaries that are instrumental to searching, parsing, and categorizing events for the forecasting system’s use.

97 MATHEMATICS AND COMPUTING↗

Multi-scale Multi-physics Scientific Machine Learning for Water Cycle Extreme Events Identification, Labelling, Representation, and Characterization

Impacts of climate are usually felt through extreme events such as droughts, floods, thunderstorms, windstorms, wildfires, and so on, that are intimately tied to the water cycle. Predicting the frequency and severity of extreme events under climate change remains a significant challenge; meanwhile, the mechanisms and impacts of these extremes are far from well understood. There are several major science challenges: (1) Lack of labelled extreme events data and missing standards in defining extremes; (2) Computational demand of high-resolution ensemble climate modeling; (3) Modeling the multiscale multi-physics hierarchical structure of compound extremes; (4) Lack of understanding of mechanisms of extreme events; (5) Large uncertainty in extreme events impacts on infrastructure; (6) Subjective assessment of weather-related risk from seasonal to multi-decadal time scales and lack of metrics for risk assessment and mitigation control.

54 ENVIRONMENTAL SCIENCES↗

Highly Ordered Hierarchical Anodes for Extreme Fast Charging Batteries (Final Report)

The goal of this project is to enable extreme fast charging (XFC) of Li-ion batteries, which was accomplished through a combination of 1) rational design and manufacturing of hierarchically structured anode architectures; 2) blending graphite/hard carbon into a bulk hybrid anode; 3) engineering artificial solid-electrolyte interphase (SEI) coatings with reduced interphase impedance; 4) computational modeling of coupled transport, kinetic, and electrochemical phenomena; and 5) improved fundamental understanding of lithium plating through operando analysis. This work integrated structural, compositional, and surface modification of graphite anodes, multi-physics modeling of ion transport, electrochemical activity, and heat transfer, advanced strategies to detect Li plating, and semi-automated roll-to-roll cell assembly. The unique facilities at the University of Michigan (UM) and Sandia National Laboratories (SNL) were leveraged to manufacture, prototype, and characterize commercially relevant >2Ah and >180 Wh/kg cells with a target of <20% capacity fade over 500 XFC cycles.

25 ENERGY STORAGE↗

Understanding Event Trajectories Across Massive Temporal Datasets with Word Embeddings and Visualization

In collaboration with researchers from Virginia Tech, Savannah River National Laboratory has continued development of a natural language processing pipeline to identify and extract events of interest from massive open data sources in the domain of worldwide state-sponsored civil nuclear energy. The foundation of the pipeline is built on compass aligned temporal word embedding models, whereby contextual shifts are automatically identified by comparing keyword embedding vectors across successive time windows. Within the approach, a contextual shift indicates the occurrence of a potential event of interest. However, in such a broad topical domain that captures events at a global scale, across various life cycle stages, and across numerous different technology types, a user that is monitoring events may have broad interests in capturing many different event types with varying degrees of signal. As such, the quantity of information that may be returned from an automated event extraction pipeline can be substantial, requiring manual effort to sift through the information to identify any relevant bits of information. Therefore, a more streamlined workflow that aids in directing a user toward specific information at different points in time is necessary. The workflow presented here has been developed with this concept in mind, built on top of the initial prototype event extraction pipeline, whereby a user can analyze temporal text-based data sources at multiple different contextual levels to isolate key points in time and key subdomains captured within a data corpus. Using multiple corpuses that consist of approximately 7 million Tweets and 7 million news articles, the team has extended compass aligned temporal word embedding models to establish an interconnected and hierarchical structure that relates known key words of interest to documents, local topics (i.e., within a time window), and global topics across the corpuses. All of this information is packaged into a visual analytics system that is linked to the information extraction pipeline and enables a user to identify contextual information that describes the evolution of a high dimensional embedding space across time to isolate changes of interest and explore associated events. This report demonstrates the use of these analytics and a means to fuse information across multiple datasets.

97 MATHEMATICS AND COMPUTING↗

Manufacturing of Fabric Electrodes using a High-Throughput Screening Platform for Redox Flow Batteries

The objective of this project is to establish a new manufacturing methodology with machine learning- based high-throughput screening for the design and development of hierarchical structured, high-performance fabric electrodes for redox flow batteries (RFBs). The end goal of the project is to design and manufacture fabric electrodes for RFB applications that can provide 250 mA/cm2 current density operation for 100-cycles with 80% average energy efficiency. This was accomplished by first examining the structure-performance-property linkages of the electrodes provided by our partner, AvCarb. The electrodes’ microstructure was characterized by determining their pore size distribution, tortuosity, specific surface area, and porosity. The ohmic, charge transfer and mass transfer resistances were then calculated using electrochemical impedance spectroscopy. Carbon cloth electrodes showed the greatest resistance, which was dominated by charge transfer resistance, which we believe is related to the surface functionalization. Full cell cycling was used in order to determine the area specific resistance and energy efficiency of the cells. All of this experimental data and the results of the mathematical model (to increase the amount of inputs with parametric sweeping) were used to develop a machine learning-based model for the design of high-performance fabric electrodes. Using the results from the machine learning tool, optimized electrodes were fabricated by AvCarb. The ohmic, charge transfer and mass transfer resistances for these new electrodes were measured, and both performed better than any of the initial samples which had been provided by AvCarb.

25 ENERGY STORAGE↗

Improving ICARUS Track Reconstruction Algorithms

The ICARUS experiment is part of the Short-Baseline Neutrino (SBN) program at Fermilab. The main goal of the experiment is to investigate the possibility of sterile neutrinos in the O(1 eV) mass region and provide clarification of the anomaly detected from the Liquid Scintillator Neutrino Detector (LSND) and MiniBooNE experiments. The ICARUS-T600 detector is a Liquid Argon Time Projection Chamber (LAr-TPC), that can provide excellent 3D imaging and calorimetric reconstruction of any ionizing particles. This detection technique allows a detailed study of neutrino interactions, spanning a wide energy spectrum (from a few keV to several hundreds of GeV). The detector consists of two identical adjacent modules, filled with a total of 760 tons of ultra-pure liquid argon. Each module houses two LAr-TPCs separated by a common cathode with a maximum drift distance of 1.5 m, equivalent to about 1 ms drift time for the nominal $500$ V/m electric drift field. The anode is made of three parallel wire planes positioned 3 mm apart, where the stainless-steel wires are oriented on each plane at a different angle with respect to the horizontal direction ($+60^\degree$,$-60^\degree$,$0^\degree$). The first two planes (Induction 1 and Induction 2) provide a non-destructive charge measurement, whereas the ionization charge is fully collected by the last collection plane. In total, 53248 wires with a 3 mm pitch and length up to 9 m are installed in the detector. In the first stage of the reconstruction, segments of waveforms corresponding to physical signals (hits) are searched for in the deconvolved wire waveform with a threshold-based hit-finding algorithm. Each hit is then fitted with a Gaussian, whose area is proportional to the number of drift electrons generating the signal. In the second stage of the reconstruction, hits are passed as input to Pandora, a framework software composed of different pattern recognition algorithms, that performs a 3D reconstruction of the full image recorded in the collected event, including the identification of interaction vertices and tracks and showers inside the TPC. These are organized into a hierarchical structure (called slice) of particles generated starting from a primary interaction vertex. In some cases, related to the inefficiencies in the hit detection or excessive deflection of the particle trajectory, Pandora breaks the particle's track into two or more smaller pieces and considers each piece as an independent track. We studied this phenomenon focusing on primary muons from ν_μ CC interactions contained in a single module with a track at least 20 cm long, to exclude delta rays. The study determined that about $7-8\%$ of the muon tracks are broken. Approximately $80\%$ of the times, Pandora assigns all segments of the track to the same slice (intra-slice track split), while in the remaining $20\%$ of the cases, one of the segments is associated with another slice (extra-slice track split). To mitigate this phenomenon, we designed an algorithm that detects and stitches the tracks broken by Pandora for the intra-slice split. In Monte Carlo simulations, the algorithm showed an efficiency exceeding $80\%$ and a purity exceeding $93\%$.

Ricci, Alessandro Maria [Pisa U.; INFN, Pisa] (ORC↗

Thermal Reservoir Networks for Modularly Expandable Thermal Microgrids

The Department of Defense (DoD) faces the substantial challenge of cost-effectively retrofitting one to two installations per month, each comprising approximately 1,000 buildings, to improve resilience, reduce energy consumption, and enhance energy supply security. Achieving these objectives requires optimal system selection and effective risk mitigation during system integration. To address this need, we introduce Platform-Based Design (PBD), a structured, hierarchical methodology adapted from other industrial sectors to the domain of energy system retrofits. We demonstrate the effectiveness of PBD through a techno-economic feasibility study comparing geothermal-coupled thermal energy networks (TENs) with conventional energy systems for heating, cooling, and powering 17 buildings at Joint Base Andrews (JBA) in Maryland. Our analysis illustrates that the PBD approach enables rigorous, data-driven, sequential decision making, resulting in a family of Pareto-optimal systems, among which the TEN emerged as the most promising solution. The selected TEN design integrates geothermal borefields, heat recovery heat pumps, photovoltaic (PV) arrays, and battery storage. Compared to the baseline system – gas heating combined with air-source chillers – the proposed TEN reduces annual imported energy by 74% and peak electricity demand by 45%, achieves a levelized cost of energy of $\$0.210$/kWh, and substantially enhances resilience. Life-cycle costs increase by approximately 6%, and initial investment costs are about 2.5 times higher than the baseline. However, if central plant infrastructure, district loops, and utility-scale PV and battery systems are privately funded and operated, the initial investment would fall below the baseline system cost. Critical to achieving these significant performance improvements were detailed nonlinear dynamic simulations coupling geothermal heat transfer, energy system operation, and realistic feedback control logic. These simulations identified essential design modifications and control strategy refinements that substantially reduced energy use, peak demand, and compressor shortcycling, thereby improving durability and reliability—issues that would have been significantly more expensive to resolve during operation. Additionally, the verification step highlighted sensitivities to key design parameters that could reduce initial investment by approximately $\$2$ million and reduce annual life-cycle costs more than $\$300,000$. We recommend adopting the PBD methodology for future feasibility studies and TEN pilot projects to gain valuable operational experience. Furthermore, we recommend that DoD invest in transferring and scaling the PBD methodology to other installations. This entails developing standardized computational frameworks and component libraries as well as training industry in conducting PBD. Such investments would enable rapid, robust, reliable, and cost-effective retrofits, supporting DoD’s ambitious energy system modernization goals.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DataSet for Elucidating molecular level interfacial interactions between a de novo protein and nucleated calcite with solid-state NMR

Biomineralization is the process by which organisms use biomolecules to produce hierarchically structured organic-inorganic composites. Using biology as inspiration, a protein construct (FD31) was previously designed to accelerate formation of nano-calcite with an unconventional {110} face. To understand the molecular interactions essential for protein aided calcite nucleation, solid-state nuclear magnetic resonance (ssNMR) spectroscopy was used in this work to characterize the FD31-calcite interface at the atomic level. Glutamic acid side chains designed to interact directly with calcium ions on the surface were found to have dynamics on the sub-millisecond timescale, indicating possible interactions between the protein and surface waters that were not included in the original model. Dipolar ssNMR recoupling techniques also showed that the protein backbone is ~2 Å closer to the surface than in the original docking model. Refined molecular simulations were done in the presence of explicit waters, which resulted in the protein backbone closer to the surface than in the original docking structure, providing better agreement with experiment and highlighting the important role played by water in FD31-calcite interactions. These studies provide the first experimental evidence to confirm that FD31 interactions with calcite are localized to the surface of the protein designed to serve as a template. However, these studies do indicate a more dynamic binding and closer binding mode between FD31 and the nucleated surface than originally proposed. In all, this enhanced molecular insight into the FD31-calcite interface has advanced our fundamental understanding of the atomic interactions at the organic-inorganic interface and will aid in the design of biological templates for the nucleation of inorganic crystals.

Saccuzzo Close, Emily Grace [Pacific Northwest Nat↗

Deactivation of Cu/ZSM-5 Catalysts during the Conversion of 2,3-Butanediol to Butenes

This work determines the deactivation mechanisms of Cu/ZSM-5 catalysts used for the conversion of 2,3-butanediol to butene as part of an alcohol-to-jet route. The deactivation of the catalyst, reflected by a drop in the rate of the limiting hydrogenation step by over 90% in 24 h at a weight hourly space velocity of 5.92 h−1, proceeds via both the agglomeration of copper particles and the obstruction of copper surfaces due to carbonaceous deposits, although the former has less impact on the decrease in the hydrogenation rate. To reduce the detrimental effect of carbonaceous deposits on catalytic activity, ZMS-5 is modified through desilication of the HZSM-5 support with NaOH and CsOH solutions to generate a hierarchical structure with mesopores. The catalyst with the CsOH-treated support generates the highest overall yield of desired olefin products and experiences the slowest deactivation. This is a result of the lower Brønsted acidity and larger mesopores found in the CsOH-treated catalyst, leading to the slower formation of carbonaceous deposits and the faster diffusion of their precursors out of the pores.

Chemistry↗

TIC 168789840: A Sextuply Eclipsing Sextuple Star System

We report the discovery of a sextuply eclipsing sextuple star system from TESS data, TIC 168789840, also known as TYC 7037-89-1, the first known sextuple system consisting of three eclipsing binaries. The target was observed in Sectors 4 and 5 during Cycle 1, with lightcurves extracted from TESS Full Frame Image data. It was also previously observed by the WASP survey and ASAS-SN. The system consists of three gravitationally bound eclipsing binaries in a hierarchical structure of an inner quadruple system with an outer binary subsystem. Follow-up observations from several different observatories were conducted as a means of determining additional parameters. The system was resolved by speckle interferometry with a 0.″42 separation between the inner quadruple and outer binary, inferring an estimated outer period of ∼2 kyr. It was determined that the fainter of the two resolved components is an 8.217 day eclipsing binary, which orbits the inner quadruple that contains two eclipsing binaries with periods of 1.570 days and 1.306 days. Markov Chain Monte Carlo (MCMC) analysis of the stellar parameters has shown that the three binaries of TIC 168789840 are “triplets,” as each binary is quite similar to the others in terms of mass, radius, and T {sub eff}. As a consequence of its rare composition, structure, and orientation, this object can provide important new insight into the formation, dynamics, and evolution of multiple star systems. Future observations could reveal if the intermediate and outer orbital planes are all aligned with the planes of the three inner eclipsing binaries.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

On a Critical Acceleration Scale of Dark Matter in ΛCDM and Dynamical Dark Energy

Abstract Universal acceleration a 0 emerges in various empirical laws, yet its fundamental nature remains unclear. Using Illustris and Virgo N -body simulations, we focus on the velocity and acceleration fluctuations in collisionless dark matter involving long-range gravity. For comparison, in the kinetic theory of gases, molecules undergo random elastic collisions involving short-range interactions, where only velocity fluctuations are relevant. Hierarchical structure formation proceeds through the merging of smaller halos to form larger halos, which facilitates a continuous energy cascade from small to large halos at a constant rate ε u ≈ −10 −7 m 2 s −3 . Velocity fluctuations involve a critical velocity u c ∝ (1 + z ) −3/4 . Acceleration fluctuations involve a critical acceleration a c ∝ (1 + z ) 3/4 . Two critical quantities are related by the rate of energy cascade ε u ≈ − a c u c /[2(3 π ) 2 ], where factor 3 π is from the angle of incidence during merging. With critical velocity u c on the order of 300 km s −1 at z = 0, the critical acceleration is determined to be a c 0 ≡ a c ( z = 0) ≈ 10 −10 m s −2 , suggesting a c might explain the universal acceleration a 0 ≈ 10 −10 m s −2 in the empirical Tully–Fisher relation or modified Newtonian dynamics. The redshift evolution a c ∝ (1 + z ) 3/4 is in good agreement with Magneticum and EAGLE simulations and in reasonable agreement with limited observations. This suggests a larger a 0 at a higher redshift such that galaxies of fixed mass rotate faster at a higher redshift. Note that for dark energy (DE) density ρ DE 0 ≈ a c 0 2 / G = 1 0 − 10 J m −3 , we postulate an entropic origin of the DE from acceleration fluctuations of dark matter, analogous to the gas pressure from velocity fluctuations. This leads to a dynamical DE coupled to the structure evolution involving a relatively constant DE density followed by a slow weakening phase, suggesting possible deviations from the standard ΛCDM paradigm.

N-body simulations↗

ELVES-Dwarf. I. Satellite Systems of Eight Isolated Dwarf Galaxies in the Local Volume

The satellite populations of Milky Way (MW)–mass systems have been extensively studied, significantly advancing our understanding of galaxy formation and dark matter physics. In contrast, the satellites of lower-mass dwarf galaxies remain largely unexplored, despite hierarchical structure formation predicting that dwarf galaxies should host their own satellites. We present the first results of the ELVES-Dwarf survey, which aims to statistically characterize the satellite populations of isolated dwarf galaxies in the Local Volume (4 < D < 10 Mpc). We identify satellite candidates in integrated light using Legacy Surveys data and achieve completeness down to M g ≈ −9 mag. We then confirm the association of satellite candidates with host galaxies using surface-brightness fluctuation distances measured from Hyper Suprime-Cam data. We surveyed eight isolated dwarf galaxies with stellar masses ranging from sub-Small Magellanic Cloud to Large Magellanic Cloud scales $(10^{7.8} < M^{\textrm{host}}_{\star} < 10^{9.5} M_⊙)$, and confirmed six satellites with stellar masses between 10 5.6 and 10 8 M ⊙ . Most confirmed satellites are star-forming, in contrast to the primarily quiescent satellites observed around MW-mass hosts. By comparing observed satellite abundances and stellar mass functions with theoretical predictions, we find no evidence of a “missing satellite problem” in the dwarf galaxy regime.

Li, Jiaxuan 嘉轩李 [Princeton University, NJ (United ↗

Anisotropic Satellite Galaxy Quenching: A Unique Signature of Energetic Feedback by Supermassive Black Holes?

The quenched fraction of satellite galaxies is aligned with the orientation of the halo's central galaxy, such that on average, satellites form stars at a lower rate along the major axis of the central. This effect, called anisotropic satellite galaxy quenching (ASGQ), has been found in observational data and cosmological simulations. Analyzing the IllustrisTNG simulation, Martín-Navarro et al. recently argued that ASGQ is caused by anisotropic energetic feedback and constitutes "compelling observational evidence for the role of black holes in regulating galaxy evolution." In this Letter, we study the causes of ASGQ in state-of-the-art galaxy formation simulations to evaluate this claim. We show that cosmological simulations predict that on average, satellite galaxies along the major axis of the dark matter halo tend to have been accreted at earlier cosmic times and are hosted by subhalos of larger peak halo masses. As a result, a modulation of the quenched fraction with respect to the major axis of the central galaxy is a natural prediction of hierarchical structure formation. We show that ASGQ is predicted by the UniverseMachine galaxy formation model, a model without anisotropic feedback. Furthermore, we demonstrate that even in the IllustrisTNG simulation, anisotropic satellite accretion properties are the main cause of ASGQ. Ultimately, we argue that ASGQ is not a reliable indicator of supermassive black hole feedback in galaxy formation simulations and, thus, should not be interpreted as such in observational data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Utilization of a CRT display light pen in the design of feedback control systems

A hierarchical structure of the interlinked programs was developed to provide a flexible computer-aided design tool. A graphical input technique and a data structure are considered which provide the capability of entering the control system model description into the computer in block diagram form. An information storage and retrieval system was developed to keep track of the system description, and analysis and simulation results, and to provide them to the correct routines for further manipulation or display. Error analysis and diagnostic capabilities are discussed, and a technique was developed to reduce a transfer function to a set of nested integrals suitable for digital simulation. A general, automated block diagram reduction procedure was set up to prepare the system description for the analysis routines.

Thompson, J. G.↗