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At least 541 records · Page 30

Controlling Nanoscale Pore Size and Wall Composition in Polycarbonate Membranes via Atomic Layer Deposition and Sequential Infiltration Synthesis: Implications for High Water Permeance

Polymer membranes have a wide variety of applications, ranging from water treatment to energy storage. Many of these applications require precise control over the membrane porosity and surface chemistry. In this study, we explore the modification of isoporous polycarbonate (PC) track-etched membranes (PCTEs) by atomic layer deposition (ALD) and sequential infiltration synthesis (SIS) to tune the pore size and the pore wall surface chemistry. We first performed a detailed study of Al 2 O 3 ALD and SIS in PCTE using a variety of in situ and ex situ measurements. We discovered that short precursor exposure times are critical to achieve conformal Al 2 O 3 ALD in the PCTE nanopores, while longer precursor exposure times resulted in Al 2 O 3 SIS within the bulk of the PC leaving the membranes brittle. Next, we tuned the PCTE pore size via Al 2 O 3 ALD and studied its effect on the water contact angle and the water permeance. Here, we found that the membranes became more hydrophilic, and the permeance decreased with increasing ALD Al 2 O 3 cycles. Finally, we studied the effect of hydrophilic (SnO 2 )/hydrophobic (In 2 O 3 ) ALD metal oxide coatings on membrane properties. We found that the most hydrophilic SnO 2 showed the highest water flux and the least hydrophilic In 2 O 3 showed the lowest water flux through the PCTE membranes. Our results demonstrate that ALD is an effective method to tune the surface and transport properties of PCTE membranes, but care must be exercised to avoid SIS and bulk modification of the polymer.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NLML: A Deep Neural Network Emulator for the Exact Nonlinear Interactions in a Wind Wave Model

Nonlinear wave interactions describe the resonant energy transfer between wave components, playing a fundamental role in the evolution of ocean wave spectra. Nonlinear wave interactions significantly influence wave growth and development, making them essential for accurate wave modeling. However, resolving the full six-dimensional Boltzmann integral of the exact nonlinear wave interactions (Webb-Resio-Tracy method, WRT) is computationally expensive, limiting its application in real-time operational wave forecasting and for research purposes. Current approximations, such as the Discrete Interaction Approximation (DIA), prioritize computational speed over accuracy, resulting in significant errors in wave mean parameters. Here, we introduce NLML, a machine learning (ML) emulator designed to approximate the exact nonlinear wave interactions within WAVEWATCH III (WW3), with the goal of achieving the accuracy of WRT while maintaining the stability and computational speed of DIA. By leveraging GPU capabilities such as half precision inference, we achieved substantial speedups, up to 136x mathematical equation faster than the WRT and only a modest 1.04x mathematical equation slowdown relative to DIA, while achieving 2x mathematical equation the accuracy of DIA in global wave spectral energy and mean wave parameters, with up to 7x mathematical equation higher accuracy in some regions. Unlike previous ML approaches, NLML maintained inherent stability throughout model integration in a standalone, year-long WW3 simulation, without requiring additional constraints. Our new ML parameterization bridges the gap between accuracy and efficiency, offering a promising alternative for improving wave modeling in operational settings and research purposes.

16 TIDAL AND WAVE POWER↗

Improving noisy free-energy measurements by adding more noise

Estimating free-energy differences using nonequilibrium work relations, such as the Jarzynski equality, is hindered by poor convergence when work fluctuations are large. For systems governed by overdamped Langevin dynamics, we propose the counterintuitive approach of adding noise in order to increase the precision of such calculations. Here, by introducing additional stochastic fluctuations to the system and rescaling its potential energy accordingly, we leave the thermodynamics of the system unchanged while increasing its relaxation rate. For a given time-dependent protocol this modification reduces the dissipated reduced work, leading to more accurate free-energy estimates. The method is designed to be used in experiment, and we illustrate its operation using computer simulations applied to two model systems. However, the regime of applicability of this strategy is likely limited, because it requires control of the system's potential energy in a way that is feasible in only a few experimental settings.

Whitelam, Stephen [Lawrence Berkeley National Labo↗

Measurement of U 238 ( n , n ' γ ) cross section data and their impact on reaction models

A better knowledge of (n,xn) reaction cross sections is important for both reaction modeling and energy applications. This article focuses on inelastic scattering of neutrons off 238 U for which improvements are needed to better constrain evaluations and solve inconsistencies in nuclear power reactor calculations. A new precise measurement of (n,xnγ) reaction cross sections on 238 U has been performed at the GELINA (Geel Electron LINear Accelerator) neutron facility operated by EC-JRC-Geel (Belgium) with the GRAPhEME (GeRmanium array for Actinides PrEcise MEasurements) setup. The prompt γ-ray spectroscopy method coupled to time-of-flight measurements is used to extract (n,xnγ) cross section values which can be further combined to infer the total neutron inelastic scattering cross section. Cross section data for 18 γ transitions (five never measured before) are presented and compared to the data in the literature. Here, emphasis is especially given to the uncertainty determination to produce partial cross section data as accurate as possible. Due to intrinsic limitations of the experimental method, the use of additional nuclear structure information coupled with theoretical modeling is required to determine the total (n, n') cross section over the whole neutron energy range. We have investigated modeling aspects of the 238 U(n,n'γ) cross sections related to the description of compound nucleus and preequilibirum mechanisms as well as the discrete part of nuclear structure. Through comparison between experimental and calculated (n,n'γ) cross sections, we pinpoint inaccuracies in the description of specific reaction mechanisms and challenge recently implemented models. This helps improving the whole modeling of the (n, n') reaction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Precision Landing and Hazard Avoidance Doman

The Precision Landing and Hazard Avoidance (PL&HA) domain addresses the development, integration, testing, and spaceflight infusion of sensing, processing, and GN&C functions critical to the success and safety of future human and robotic exploration missions. PL&HA sensors also have applications to other mission events, such as rendezvous and docking. Autonomous PL&HA builds upon the core GN&C capabilities developed to enable soft, controlled landings on the Moon, Mars, and other solar system bodies. Through the addition of a Terrain Relative Navigation (TRN) function, precision landing within tens of meters of a map-based target is possible. The addition of a 3-D terrain mapping lidar sensor improves the probability of a safe landing via autonomous, real-time Hazard Detection and Avoidance (HDA). PL&HA significantly improves the probability of mission success and enhances access to sites of scientific interest located in challenging terrain. PL&HA can also utilize external navigation aids, such as navigation satellites and surface beacons. Advanced Lidar Sensors High precision ranging, velocimetry, and 3-D terrain mapping Terrain Relative Navigation (TRN) TRN compares onboard reconnaissance data with real-time terrain imaging data to update the S/C position estimate Hazard Detection and Avoidance (HDA) Generates a high-resolution, 3-D terrain map in real-time during the approach trajectory to identify safe landing targets Inertial Navigation During Terminal Descent High precision surface relative sensors enable accurate inertial navigation during terminal descent and a tightly controlled touchdown within meters of the selected safe landing target.

Robertson, Edward A.↗

Recent and future developments in pultrusion technology with consideration for curved geometries: A review

Herein this paper examined the current state and future developments in pultrusion with particular emphasis on its application in curved part manufacturing. The relationship between factors such as resin chemistry, fiber characteristics, and die geometry that influences the properties of pultruded product were highlighted. Moreover, the specific challenges associated with pultruding curved parts such as the complexities in achieving uniformity and structural integrity in such geometries were discussed. The review emphasized mold design, process improvement, adaptive control systems for precise resin impregnation and material selection to address these challenges. Additionally, the paper suggests the integration of real-time monitoring and data analytics as ways to enhance quality control during curved parts pultrusion. These advancements will help to overcome challenges specific to curved pultrusion and make the process more efficient. Other manufacturing techniques such as filament winding, thermoforming, pulforming were mentioned as alternatives to curved parts pultrusion. The review also explores pultruded variable curvature processes, highlighting some notable patents and article related to this subject matter. Production of pultruded variable curvature parts was seen as a key driver that can shape the future of pultrusion. Finally, the paper anticipates future trends, with sustainability, customization, integration of advanced materials, and development of techniques for pultrusion of composites parts.

42 ENGINEERING↗

Synthesis, Processing, and Use of Isotopically Enriched Epitaxial Oxide Thin Films

Isotopic engineering has emerged as a key approach to study the nucleation, diffusion, phase transitions, and reactions of materials at an atomic level. It aims to uncover mass transport pathways, kinetics, and operational and failure mechanisms of functional materials and devices. Understanding these phenomena leads to deeper insights into important physical processes, such as the transport of ions in energy conversion and storage devices and the role of active sites and supports during heterogeneous catalytic reactions. Likewise, isotopic engineering is being pursued as a means of modifying functionality to enable future technological applications. In this Account, we summarize our recent work employing isotope labeling (e.g., 18 O 2 and 57 Fe) during thin film synthesis and postgrowth processing to reveal growth mechanisms, defect chemistry, and elemental diffusion under working and extreme conditions. Isotope-resolved analysis techniques with nanometer-scale spatial resolution, such as time-of-flight secondary ion mass spectrometry and atom probe tomography, facilitate the accurate quantification of isotopic placement and concentration in our well-defined heterostructures with precisely positioned, isotope-enriched layers. By measuring the nanometer-scale redistribution between natural abundance and isotopically enriched oxygen layers during the deposition of Fe 2 O 3 and Cr 2 O 3 by molecular beam epitaxy, we identified intermixing processes driven by surface adatoms occurring both at the film growth surface and within the first few layers below the surface. Further insights into synthesis mechanisms were gained by studying the tungsten oxide thin films grown by evaporating WO 3 powder in the presence of background 18 O 2 , revealing minimal incorporation of background oxygen during the film formation process. Thermal and radiation-enhanced diffusion in epitaxial Fe and Cr oxides were precisely tracked using 18 O and 57 Fe tracer layers incorporated into model epitaxial oxide thin films. This approach has allowed us to access thermal diffusion behavior at lower temperatures than previously measured, revealing a potential changeover in diffusion mechanism. Understanding radiation-enhanced diffusion in model oxides that represent the surface layers on the structural components of nuclear reactors informs our understanding of their corrosion behavior under irradiation. Isotopic labeling can also provide unique insights into the surface exchange reactions and defect chemistry of electrocatalysts. For instance, tracking the change in 18 O concentration at the surface of an epitaxial LaNiO 3 thin film after the electrocatalytic oxygen evolution reaction revealed the participation of lattice oxygen, confirming a hypothesis that had been proposed previously. Lastly, we highlight a new direction wherein we perform in situ processing studies utilizing isotopic tracers in conjunction with model epitaxial thin films within the atom probe tomography instrument. Additionally, this Account illustrates the great potential of isotopic engineering to enable fundamental mechanistic insights into physical processes and engineer functional properties in epitaxial films, heterostructures, and superlattices.

36 MATERIALS SCIENCE↗

Mid-IR UAV-based sensing platform with deep learning to Identify and Quantify Gaseous Emission in Gas Flares

This report details the development and evaluation of a Mid-Infrared (Mid-IR) Unmanned Aerial Vehicle (UAV)-based sensing platform integrated with deep learning algorithms for the identification and quantification of gaseous emissions in gas flares. The project, spearheaded by Omega Optics, Inc., aimed to address environmental monitoring challenges by leveraging advanced photonic technologies and autonomous UAV operations. The research focused on designing, optimizing, and fabricating photonic crystal waveguides and grating couplers to enhance the sensitivity and accuracy of gas detection. A comprehensive drone-based system was developed, featuring a miniaturized sensor, GPS module, and microcontroller communication network for real-time gas concentration monitoring. The system's adaptive sampling algorithm, implemented using the Robot Operating System (ROS), enables autonomous detection and localization of gas emission sources. Preliminary results demonstrate the platform's capability to detect and monitor gas emissions with high precision, cost-effectiveness, and scalability. Future work will expand upon this foundation by introducing 3D wind model-based learning for dynamic environmental conditions and further enhancing the user interface and data processing algorithms to support broader environmental monitoring applications. Overall, this project represents a significant step forward in UAV-based environmental sensing technologies, offering robust solutions for detecting and mitigating the impacts of gaseous emissions on public health and safety.

47 OTHER INSTRUMENTATION↗

A Novel Technique of Extracting UCN Decay Lifetime from Storage Chamber Measurements Dominated by Scattering Losses

The neutron’s lifetime is a critical parameter in the standard model. Its measurements, particularly measurements using both beamline and ultracold neutron storage techniques, have revealed significant tension. In this work, we review the status of the tension between various measurements, especially in light of the insights provided by the β-decay correlation measurements. We revisit the lifetime measurement in a material storage chamber, dominated by losses from scattering off the walls of the storage chamber. The neutron energy spectra and associated uncertainties were, for the first time, well-characterized using storage data alone. Such models have applications in the extraction of the mean time between wall bounces, which is a key parameter for neutron storage disappearance experiments in search of neutron oscillation. A comparison between the loss model and the number of neutrons stored in a single chamber allowed us to extract a neutron lifetime of τn*=880(+158/−78)stat.(+230/−114)sys.s (68.3% C.I.). Though the uncertainty of this lifetime is not competitive with currently available measurements, the highlight of this work is that we precisely identified the systematic sources of uncertainty that contribute to the neutron lifetime measurements in material storage bottles, namely from the uncertainty in the energy spectra, as well as from the storage chamber surface parameters of the Fermi potential and loss per bounce. In doing so, we highlight the underestimation of the uncertainties in the previous Monte Carlo simulations of experiments using the technique of ultracold neutron storage in material bottles.

Mohanmurthy, Prajwal (ORCID:0000000275737010)↗

Solid state neutron dosimeter for space applications

Personnel engaged in space flight are exposed to significant flux of high energy neutrons arising from both primary and secondary sources of ionizing radiation. Presently, there exist no compact neutron sensor capable of being integrated in a flight instrument to provide real time measurement of this radiation flux. A proposal was made to construct such an instrument using special PIN silicon diode which has the property of being insensitive to the other forms of ionizing radiation. Studies were performed to determine the design and construction of a better reading system to allow the PIN diode to be read with high precision. The physics of the device was studied, especially with respect to those factors which affect the sensitivity and reproducibility of the neutron response. This information was then used to develop methods to achieve high sensitivity at low neutron doses. The feasibility was shown of enhancing the PIN diode sensitivity to make possible the measurement of the low doses of neutrons encountered in space flights. The new PIN diode will make possible the development of a very compact, accurate, personal neutron dosimeter.

Entine, Gerald↗

Transient Numerical Modeling of Catalytic Channels

This paper presents a transient model of catalytic combustion suitable for isolated channels and monolith reactors. The model is a lumped two-phase (gas and solid) model where the gas phase is quasi-steady relative to the transient solid. Axial diffusion is neglected in the gas phase; lateral diffusion, however, is accounted for using transfer coefficients. The solid phase includes axial heat conduction and external heat loss due to convection and radiation. The combustion process utilizes detailed gas and surface reaction models. The gas-phase model becomes a system of stiff ordinary differential equations while the solid phase reduces, after discretization, into a system of stiff ordinary differential-algebraic equations. The time evolution of the system came from alternating integrations of the quasi-steady gas and transient solid. This work outlines the numerical model and presents some sensitivity studies on important parameters including internal transfer coefficients, catalytic surface site density, and external heat-loss (if applicable). The model is compared to two experiments using CO fuel: (1) steady-state conversion through an isothermal platinum (Pt) tube and (2) transient propagation of a catalytic reaction inside a small Pt tube. The model requires internal mass-transfer resistance to match the experiments at lower residence times. Under mass-transport limited conditions, the model reasonably predicted exit conversion using global mass-transfer coefficients. Near light-off, the model results did not match the experiment precisely even after adjustment of mass-transfer coefficients. Agreement improved for the first case after adjusting the surface kinetics such that the net rate of CO adsorption increased compared to O2. The CO / O2 surface mechanism came from a sub-set of reactions in a popular CH4 / O2 mechanism. For the second case, predictions improved for lean conditions with increased external heat loss or adjustment of the kinetics as in the first case. Finally, the results show that different initial surface-species distribution leads to different steady-states under certain conditions. These results demonstrate the utility of a lumped two-phase model of a transient catalytic combustor with detailed chemistry.

Struk, Peter M.↗

Use of Global Navigation Satellite Systems in Space

Products that rely on Global Navigation Satellite Systems (GNSS) have become an essential part of daily life for millions of people around the world. In addition to enabling navigation, these constellations of satellites and the signals they transmit provide a global, precise timing source, used in everything from electrical power grid phasing to synchronization of financial networks. This colloquium introduces the concept of radio navigation, describes the features of GNSS signals that make navigation possible, and explains how these signals are processed by GNSS receivers. The resulting measurements and error sources, such as atmospheric effects and multipath, are discussed. Special consideration is given to the challenges of using GNSS in space, and the innovations that make it possible. A survey of space applications and recent flight experiences is provided. Active areas of research are discussed, including the use of GNSS for missions to the Moon.

Space service volume↗

Global Navigation Satellite Systems and How They Work

Products that rely on Global Navigation Satellite Systems (GNSS) have become an essential part of daily life for millions of people around the world. In addition to enabling navigation, these constellations of satellites and the signals they transmit provide a global, precise timing source, used in everything from electrical power grid phasing to synchronization of financial networks. This colloquium introduces the concept of radio navigation, describes the features of GNSS signals that make navigation possible, and explains how these signals are processed by GNSS receivers. The resulting measurements and error sources, such as atmospheric effects and multipath, are discussed. Special consideration is given to the challenges of using GNSS in space, and the innovations that make it possible. A survey of space applications and recent flight experiences is provided. Active areas of research are discussed, including the use of GNSS for missions to the Moon.

Ashman, Ben↗

An Introduction to Global Navigation Satellite Systems

Products that rely on Global Navigation Satellite Systems (GNSS) have become an essential part of daily life for millions of people around the world. In addition to enabling navigation, these constellations of satellites and the signals they transmit provide a global, precise timing source, used in everything from electrical power grid phasing to synchronization of financial networks. This lecture introduces the concept of radio navigation, describes the features of GNSS signals that make navigation possible, and explains how these signals are processed by GNSS receivers. The resulting measurements and error sources, such as atmospheric effects and multipath, are discussed. Special consideration is given to the challenges of using GNSS in space, and the innovations that make it possible. A survey of space applications and recent flight experiences is provided. Active areas of research are discussed, including the use of GNSS for missions to the Moon.

Ashman, Ben↗

Microwave Structure Construction Capability Year One Accomplishments

The Microwave Structure Construction Capability (MSCC) element, part of the Moon to Mars Planetary Autonomous Construction Project (MMPACT) was initiated in 2020. MSCC is responsible for creating horizontal and vertical infrastructure on the moon using microwave energy. Microwave energy was selected since it is the only method to volumetrically heat the regolith. All other sintering/melting methods rely on thermal conduction through the very low conductivity surface, resulting in an inefficient process. Advances were achieved in materials characterization and understanding, microwave sintering in vacuum, and microwave design and analyses. Two dielectric property testing systems have been developed at Radiance Technologies and JPL. These will examine dielectric properties at cryogenic temperatures and over a broad frequency range. Permittivity and permeability testing at -60 ̊C in vacuum from 0.05 to 3 GHz has been generated at JPL. Additional modifications will be made to go to -190 ̊C (LN2). Radiance Technologies created a test system to measure dielectric properties at greater than 10 GHz and initiated work on developing a vacuum capable, portable test system to measure dielectric properties of Apollo regolith and simulants from 100 MHz to 18 GHz. These tests are to identify optimal heating frequencies and protocols. During microwave sintering at about 1100 ̊C, volatiles were creating difficulty in achieving a reasonably dense specimen. Due to processing in vacuum and the nature of the lunar regolith, some volatiles and porosity are expected. However, the Earth produced simulants have non-lunar materials in them that create volatiles that aren’t representative of lunar regolith. Therefore, a five month effort was conducted to establish a heat treat method to remove these non-lunar materials. Tests were conducted using TGA mass spectrometry, heating in vacuum and conducting mass spectrometry, dielectric and DTA, Raman, BET, particle size analysis, morphological analysis, carbon and sulfur chemical content determination and microscopy. The process has been scaled-up to 6 kg batch size and undergoing evaluation. A 36 kg batch size is the target for JSC-1A and other limited availability simulants. These calcining protocols will be standard for NASA and beyond. MSCC has also created scalable processes for fabricating synthetic lunar materials. Processes to fabricate Anorthite (plagioclase CaAl2Si2O8), Diopside (pyroxene CaMgSi₂O₆), and Enstatite (pyroxene Mg2Si2O6) have been generated. These materials will enable generation of microwave sintering models to bound various composition ranges anticipated on the Moon, therefore mitigating the need for a precise simulant with respect to location on the Moon. Successful microwave sintering in air using a horn applicator was demonstrated. All previous microwave vacuum sintering in the literature was at small scale and in a contained enclosure thus taking advantage of reflections. This is the first to use a lunar like microwave applicator to sinter ceramic in a bed as it would be done on the Moon. Small scale and inert sintering were conducted to assist in developing protocols with quicker turnaround times than larger scale testing. Testing has anchored thermal analysis predicting heat flow in vacuum during microwave sintering. Thermal conductivity testing was also initiated. Microwave coupling to the regolith has been modeled by multiple organizations and with different software packages. At least six horn designs and applicator configurations for both magnetron and solid state sources are being examined. Optimal simulant container designs for microwaves have also been generated. The power and electronics design for the solid state microwave system has been initiated. Concept designs for a lander based microwave sintering have been evaluated.

microwave↗

Online thermal profile prediction for large format additive manufacturing: A hybrid CNN-LSTM based approach

Large format additive manufacturing (LFAM) is an advanced 3D printing technique that efficiently fabricates large-scale components through a layer-by-layer extrusion and deposition process. Accurate surface layer temperature monitoring is essential to prevent manufacturing failures and ensure final product quality. Traditional physics-based offline approaches for simulating thermal behavior are often inefficient and complex, posing challenges on real-time, in-situ monitoring. Here, to address this, we propose a data-driven hybrid CNN-LSTM model to predict sequential thermal images of arbitrary length using real-time infrared thermal imaging. In this approach, a Convolutional Neural Networks (CNN) is trained offline to capture spatial features, reduce dimensional complexity, and enhance time efficiency, while a stacked Long Short-Term Memory (LSTM) is applied online to capture temporal information for improved prediction of future thermal behavior in subsequent printing layers. Model performance is evaluated using MSE, SSIM, and PSNR metrics and is benchmarked against stacked LSTM and convolutional LSTM models, demonstrating superior accuracy and applicability. Additionally, to mitigate noise from moving extruders and gantry backgrounds in thermal images, a fine-tuned semantic segmentation model is implemented offline to extract printing geometry, enabling precise temperature tracking along the tool path for further thermal analysis. The frameworks developed in this study significantly advance temperature monitoring, thermal analysis, and in-situ manufacturing control for LFAM, bridging the gap between theoretical modeling and practical application.

Geometry extraction↗

A numerical comparison of discrete Kalman filtering algorithms - An orbit determination case study

An improved Kalman filter algorithm based on a modified Givens matrix triangularization technique is proposed for solving a nonstationary discrete-time linear filtering problem. The proposed U-D covariance factorization filter uses orthogonal transformation technique; measurement and time updating of the U-D factors involve separate application of Gentleman's fast square-root-free Givens rotations. Numerical stability and accuracy of the algorithm are compared with those of the conventional and stabilized Kalman filters and the Potter-Schmidt square-root filter, by applying these techniques to a realistic planetary navigation problem (orbit determination for the Saturn approach phase of the Mariner Jupiter-Saturn Mission, 1977). The new algorithm is shown to combine the numerical precision of square root filtering with the efficiency of the original Kalman algorithm.

Thornton, C. L.↗

Reliable and Efficient Parallel Processing Algorithms and Architectures for Modern Signal Processing

Least-squares (LS) estimations and spectral decomposition algorithms constitute the heart of modern signal processing and communication problems. Implementations of recursive LS and spectral decomposition algorithms onto parallel processing architectures such as systolic arrays with efficient fault-tolerant schemes are the major concerns of this dissertation. There are four major results in this dissertation. First, we propose the systolic block Householder transformation with application to the recursive least-squares minimization. It is successfully implemented on a systolic array with a two-level pipelined implementation at the vector level as well as at the word level. Second, a real-time algorithm-based concurrent error detection scheme based on the residual method is proposed for the QRD RLS systolic array. The fault diagnosis, order degraded reconfiguration, and performance analysis are also considered. Third, the dynamic range, stability, error detection capability under finite-precision implementation, order degraded performance, and residual estimation under faulty situations for the QRD RLS systolic array are studied in details. Finally, we propose the use of multi-phase systolic algorithms for spectral decomposition based on the QR algorithm. Two systolic architectures, one based on triangular array and another based on rectangular array, are presented for the multiphase operations with fault-tolerant considerations. Eigenvectors and singular vectors can be easily obtained by using the multi-pase operations. Performance issues are also considered.

Liu, Kuojuey Ray↗