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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 271 records · Page 15

3D Scanning System to Assess Gravity-Dependent Body Shape Changes

The human body shows unique physiological and morphological changes when exposed to different gravity conditions, including muscle atrophy, fluid shift, spinal elongation, and body posture adjustments. Such changes need to be incorporated for human-system integration in the vehicle habitat, garment, and spacesuit designs, as inaccurate body measurements can result in suboptimal crew protection that can potentially decrease injury tolerance. However, the traditional linear measurements, such as stature, segment lengths or circumferences measured using a caliper or tape measure, often show limited consistency and are unable to capture the nonlinear characteristics of the human body. While 3D body scanning can provide significant advantages over linear measurements, the technologies have not been fully developed or customized for in-flight scanning. For ground laboratory use, several different scanner types are commercially available. However, in-flight scanning requires additional technical considerations, such as minimal scan time, simplified calibration, and sufficient capture volume. This work aims to develop a prototype 3-D body scanning system that is customized for in-flight use to scan crewmembers, with the configuration and performance optimized for detecting known gravity-dependent body shape and posture changes. A hardware system will be custom built using a network of commercial off-the-shelf 3D sensors. The sensor parameters and settings will be optimized to detect the targeted body shape changes, specifically using body manikins of which the shape and size are iteratively permuted to simulate the known changes by fluid shift and spinal elongation. The capture volume will be also matched for a range of body sizes from a 1st percentile female to 99th percentile male. Unintentional body motions or floating in microgravity will be also simulated and incorporated. A data acquisition software will be developed for efficient in-flight operations with minimal overhead and easy-to-use user interface. A simplified calibration procedure will be designed for robust scanning against frequent vibration or unexpected sensor position shifts. The system will be tested in the ground laboratory for accuracy and reliability against a reference scanning system. New anthropometry measurements will be also identified to sensitively capture the gravity dependent body shape changes, in addition to the traditional anthropometry measurements. A novel landmark-based technique will be tested for consistent anthropometry measurements across posture variations. If successfully developed and deployed, the new system is expected to provide previously unavailable body shape and size data from different gravitational environments, including 0-g, 1/6-g, and 1-g. Such data can improve suit fit, habitat design, exercise efficacy quantification and sizing of orthostatic intolerance garments.

K H Kim↗

3D Scanning System to Assess Gravity-Dependent Body Shape Changes

The human body shows unique physiological and morphological changes when exposed to different gravity conditions, including muscle atrophy, fluid shift, spinal elongation, and body posture adjustments. Such changes need to be incorporated for human-system integration in the vehicle habitat, garment, and spacesuit designs, as inaccurate body measurements can result in suboptimal crew protection that can potentially decrease injury tolerance. However, the traditional linear measurements, such as stature, segment lengths or circumferences measured using a caliper or tape measure, often show limited consistency and are unable to capture the nonlinear characteristics of the human body. While 3D body scanning can provide significant advantages over linear measurements, the technologies have not been fully developed or customized for in-flight scanning. For ground laboratory use, several different scanner types are commercially available. However, in-flight scanning requires additional technical considerations, such as minimal scan time, simplified calibration, and sufficient capture volume. This work aims to develop a prototype 3-D body scanning system that is customized for in-flight use to scan crewmembers, with the configuration and performance optimized for detecting known gravity-dependent body shape and posture changes. A hardware system will be custom built using a network of commercial off-the-shelf 3D sensors. The sensor parameters and settings will be optimized to detect the targeted body shape changes, specifically using body manikins of which the shape and size are iteratively permuted to simulate the known changes by fluid shift and spinal elongation. The capture volume will be also matched for a range of body sizes from a 1st percentile female to 99th percentile male. Unintentional body motions or floating in microgravity will be also simulated and incorporated. A data acquisition software will be developed for efficient in-flight operations with minimal overhead and easy-to-use user interface. A simplified calibration procedure will be designed for robust scanning against frequent vibration or unexpected sensor position shifts. The system will be tested in the ground laboratory for accuracy and reliability against a reference scanning system. New anthropometry measurements will be also identified to sensitively capture the gravity dependent body shape changes, in addition to the traditional anthropometry measurements. A novel landmark-based technique will be tested for consistent anthropometry measurements across posture variations. If successfully developed and deployed, the new system is expected to provide previously unavailable body shape and size data from different gravitational environments, including 0-g, 1/6-g, and 1-g. Such data can improve suit fit, habitat design, exercise efficacy quantification and sizing of orthostatic intolerance garments.

K H Kim↗

SINDA - Systems Improved Numerical Differencing Analyzer

Capability to model fluid flow added. SINDA is software system developed to solve physical problems governed by diffusion-type equations mathematically modeled by lumped-parameter representations. Used as general thermal analyzer with resistor-and-capacitor-network representations. Adapted to wide range of problems represented by Fourier, Possion, Laplace, or other differential equations. Written in FORTRAN and Assembler.

Damico, Steve J.↗

High temperature superconductors applications in telecommunications

The purpose of this paper is twofold: (1) to discuss high temperature superconductors with specific reference to their employment in telecommunications applications; and (2) to discuss a few of the limitations of the normally employed two-fluid model. While the debate on the actual usage of high temperature superconductors in the design of electronic and telecommunications devices - obvious advantages versus practical difficulties - needs to be settled in the near future, it is of great interest to investigate the parameters and the assumptions that will be employed in such designs. This paper deals with the issue of providing the microwave design engineer with performance data for such superconducting waveguides. The values of conductivity and surface resistance, which are the primary determining factors of a waveguide performance, are computed based on the two-fluid model. A comparison between two models - a theoretical one in terms of microscopic parameters (termed Model A) and an experimental fit in terms of macroscopic parameters (termed Model B) - shows the limitations and the resulting ambiguities of the two-fluid model at high frequencies and at temperatures close to the transition temperature. The validity of the two-fluid model is then discussed. Our preliminary results show that the electrical transport description in the normal and superconducting phases as they are formulated in the two-fluid model needs to be modified to incorporate the new and special features of high temperature superconductors. Parameters describing the waveguide performance - conductivity, surface resistance and attenuation constant - will be computed. Potential applications in communications networks and large scale integrated circuits will be discussed. Some of the ongoing work will be reported. In particular, a brief proposal is made to investigate of the effects of electromagnetic interference and the concomitant notion of electromagnetic compatibility (EMI/EMC) of high T(sub c) superconductors.

Kumar, A. Anil↗

Permeability Prediction Using Vision Transformers

Accurate permeability predictions remain pivotal for understanding fluid flow in porous media, influencing crucial operations across petroleum engineering, hydrogeology, and related fields. Traditional approaches, while robust, often grapple with the inherent heterogeneity of reservoir rocks. With the advent of deep learning, convolutional neural networks (CNNs) have emerged as potent tools in image-based permeability estimation, capitalizing on micro-CT scans and digital rock imagery. This paper introduces a novel paradigm, employing vision transformers (ViTs)—a recent advancement in computer vision—for this crucial task. ViTs, which segment images into fixed-sized patches and process them through transformer architectures, present a promising alternative to CNNs. We present a methodology for implementing ViTs for permeability prediction, its results on diverse rock samples, and a comparison against conventional CNNs. The prediction results suggest that, with adequate training data, ViTs can match or surpass the predictive accuracy of CNNs, especially in rocks exhibiting significant heterogeneity. This study underscores the potential of ViTs as an innovative tool in permeability prediction, paving the way for further research and integration into mainstream reservoir characterization workflows.

58 GEOSCIENCES↗

Fluvial Volumes, Timescales, and Intermittency in Milna Crater, Mars

Ancient lake deposits and valley networks on Mars provide strong evidence that its surface was once modified by liquid water, but the extent of that modification is still debated. Ancient lacustrine deposits in Milna Crater provide insight into the timescale and fluid volume required to construct fluvially derived sedimentary deposits near the Noachian-Hesperian boundary. Placing the lacustrine deposits their regional context in Paraná Valles provides a quantitative measurement of the intermittency of large, water-mediated sediment transport events in that region.

Buhler, P.↗

3-D Flow Field Diagnostics and Validation Studies using Stereoscopic Tracking Velocimetry

The measurement of 3-D three-component velocity fields is of great importance in both ground and space experiments for understanding materials processing and fluid physics. Here, we present the investigation results of stereoscopic tracking velocimetry (STV) for measuring 3-D velocity fields. The effort includes diagnostic technology development, experimental velocity measurement, and comparison with analytical and numerical computation. The advantages of STV stems from the system simplicity for building compact hardware and in software efficiency for continual near-real-time process monitoring. It also has illumination flexibility for observing volumetric flow fields from arbitrary directions. STV is based on stereoscopic CCD observations of particles seeded in a flow. Neural networks are used for data analysis. The developed diagnostic tool is tested with a simple directional solidification apparatus using Succinonitrile. The 3-D velocity field in the liquid phase is measured and compared with results from detailed numerical computations. Our theoretical, numerical, and experimental effort has shown STV to be a viable candidate for reliably quantifying the 3-D flow field in materials processing and fluids experiments.

Cha, Soyoung Stephen↗

NeMO-Net The Neural Multi-Modal Observation Training Network for Global Coral Reef Assessment

In the past decade, coral reefs worldwide have experienced unprecedented stresses due to climate change, ocean acidification, and anthropomorphic pressures, instigating massive bleaching and die-off of these fragile and diverse ecosystems. Furthermore, remote sensing of these shallow marine habitats is hindered by ocean wave distortion, refraction and optical attenuation, leading invariably to data products that are often of low resolution and signal-to-noise (SNR) ratio. However, recent advances in UAV and Fluid Lensing technology have allowed us to capture multispectral 3D imagery of these systems at sub-cm scales from above the water surface, giving us an unprecedented view of their growth and decay. Exploiting the fine-scaled features of these datasets, machine learning methods such as MAP, PCA, and SVM can not only accurately classify the living cover and morphology of these reef systems (below 8 error), but are also able to map the spectral space between airborne and satellite imagery, augmenting and improving the classification accuracy of previously low-resolution datasets.We are currently implementing NeMO-Net, the first open-source deep convolutional neural network (CNN) and interactive active learning and training software to accurately assess the present and past dynamics of coral reef ecosystems through determination of percent living cover and morphology. NeMO-Net will be built upon the QGIS platform to ingest UAV, airborne and satellite datasets from various sources and sensor capabilities, and through data-fusion determine the coral reef ecosystem makeup globally at unprecedented spatial and temporal scales. To achieve this, we will exploit virtual data augmentation, the use of semi-supervised learning, and active learning through a tablet platform allowing for users to manually train uncertain or difficult to classify datasets. The project will make use of Pythons extensive libraries for machine learning, as well as extending integration to GPU and High-End Computing Capability (HECC) on the Pleiades supercomputing cluster, located at NASA Ames. The project is being supported by NASAs Earth Science Technology Office (ESTO) Advanced Information Systems Technology (AIST-16) Program.

Remote Sensin↗

NeMO-Net: The Neural Multi-Modal Observation and Training Network for Global Coral Reef Assessment

In the past decade, coral reefs worldwide have experienced unprecedented stresses due to climate change, ocean acidification, and anthropomorphic pressures, instigating massive bleaching and die-off of these fragile and diverse ecosystems. Furthermore, remote sensing of these shallow marine habitats is hindered by ocean wave distortion, refraction and optical attenuation, leading invariably to data products that are often of low resolution and signal-to-noise (SNR) ratio. However, recent advances in UAV and Fluid Lensing technology have allowed us to capture multispectral 3D imagery of these systems at sub-cm scales from above the water surface, giving us an unprecedented view of their growth and decay. Exploiting the fine-scaled features of these datasets, machine learning methods such as MAP, PCA, and SVM can not only accurately classify the living cover and morphology of these reef systems (below 8 percent error), but are also able to map the spectral space between airborne and satellite imagery, augmenting and improving the classification accuracy of previously low-resolution datasets. We are currently implementing NeMO-Net, the first open-source deep convolutional neural network (CNN) and interactive active learning and training software to accurately assess the present and past dynamics of coral reef ecosystems through determination of percent living cover and morphology. NeMO-Net will be built upon the QGIS platform to ingest UAV, airborne and satellite datasets from various sources and sensor capabilities, and through data-fusion determine the coral reef ecosystem makeup globally at unprecedented spatial and temporal scales. To achieve this, we will exploit virtual data augmentation, the use of semi-supervised learning, and active learning through a tablet platform allowing for users to manually train uncertain or difficult to classify datasets. The project will make use of Pythons extensive libraries for machine learning, as well as extending integration to GPU and High-End Computing Capability (HECC) on the Pleiades supercomputing cluster, located at NASA Ames. The project is being supported by NASAs Earth Science Technology Office (ESTO) Advanced Information Systems Technology (AIST-16) Program.

NeMO-Net↗

The Neuroendocrinology of Thirst and Salt Appetite: Visceral Sensory Signals and Mechanisms of Central Integration

This review examines recent advances in the study of the behavioral responses to deficits of body water and body sodium that in humans are accompanied by the sensations of thirst and salt appetite. Thirst and salt appetite are satisfied by ingesting water and salty substances. These behavioral responses to losses of body fluids, together with reflex endocrine and neural responses, are critical for reestablishing homeostasis. Like their endocrine and neural counterparts, these behaviors are under the control of both excitatory and inhibitory influences arising from changes in osmolality, endocrine factors such as angiotensin and aldosterone, and neural signals from low and high pressure baroreceptors. The excitatory and inhibitory influences reaching the brain require the integrative capacity of a neural network which includes the structures of the lamina terminalis, the amygdala, the perifornical area, and the paraventricular nucleus in the forebrain, and the lateral parabrachial nucleus (LPBN), the nucleus tractus solitarius (NTS), and the area postrema in the hindbrain. These regions are discussed in terms of their roles in receiving afferent sensory input and in processing information related to hydromineral balance. Osmoreceptors controlling thirst are located in systemic Viscera and in central structures that lack the blood-brain barrier. Angiotensin and aldosterone act on and through structures of the lamina terminalis and the amygdala to stimulate thirst and sodium appetite under conditions of hypovolemia. The NTS and LPBN receive neural signals from baroreceptors and are responsible for inhibiting the ingestion of fluids under conditions of increased volume and pressure and for stimulating thirst under conditions of bypovolemia and hypotension. The interplay of multiple facilitory influences within the brain may take the form of interactions between descending angiotensinergic systems originating in the forebrain and ascending adrenergic systems emanating from the hindbrain. Oxytocin and serotonin are additional candidate neuro- chemicals with postulated inhibitory central actions and with essential roles in the overall integration of sensory input within the neural network devoted to maintaining hydromineral balance.

Johnson, Alan Kim↗

Geophysical Imaging of Flow and Transport (GIFT): FY24 Status Report

The GIFT (Geophysical Imaging of Flow and Transport) system will improve predictive capabilities as a platform for collecting multi-physical (MP) time-lapse datasets from well-controlled laboratory experiments. This will enable more accurate prediction of multi-phase fluid flow during delivery and transport of insitu remedial amendments as important components of the overall Hanford Site cleanup mission. Design and construction of the GIFT system, which consists of a meter-scale test cell and a network of custom gas circulation and analysis systems, was accomplished in fiscal year (FY) 2024, with plans to add liquid circulation to the system and use this new capability for multi-phase deep vadose experiments starting in FY25.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Performance study of a data flow architecture

Teams of scientists studied data flow concepts, static data flow machine architecture, and the VAL language. Each team mapped its application onto the machine and coded it in VAL. The principal findings of the study were: (1) Five of the seven applications used the full power of the target machine. The galactic simulation and multigrid fluid flow teams found that a significantly smaller version of the machine (16 processing elements) would suffice. (2) A number of machine design parameters including processing element (PE) function unit numbers, array memory size and bandwidth, and routing network capability were found to be crucial for optimal machine performance. (3) The study participants readily acquired VAL programming skills. (4) Participants learned that application-based performance evaluation is a sound method of evaluating new computer architectures, even those that are not fully specified. During the course of the study, participants developed models for using computers to solve numerical problems and for evaluating new architectures. These models form the bases for future evaluation studies.

Adams, George↗

EGS Reservoir Modeling for Developing Geothermal District Heating at Cornell University: Preprint

Cornell University is pursuing development of an enhanced geothermal system (EGS) for providing heating to its main campus in Upstate New York. A ~10,000 ft (~3 km) deep vertical observation well ("CUBO") was drilled in 2022 to characterize the subsurface using wellbore logging, borehole imaging, fluid sampling, mini-frac tests, coring and drill cutting analysis. Down-hole temperatures measured at 3 km depth are about 80 degrees C, sufficiently high for direct-use heating. The well drilled through generally low porosity and low permeability Paleozoic sedimentary formations and into metamorphic basement rock, encountered at about 9,400 ft depth. Leveraging subsurface data obtained through CUBO, we investigated technical feasibility and design requirements of a doublet well system with horizontal laterals connected to a fracture network created through hydraulic fracturing. The EGS reservoir is sized to provide a nominal heat output in the range 5 to 10 MWth of continuous heating over a 15 year-lifetime with limited thermal drawdown. We applied the Gringarten Multiple parallel fracture model, the Cornell Discrete Fracture Simulator FOXFEM and the commercial simulator ResFrac to estimate required heat transfer area and design a potential hydraulic stimulation treatment. Reservoir simulations indicate that, depending on fluid flow rate and injection temperature, 2 to 3 km2 of effective fracture heat transfer area is required to supply the target heat output of 5 to 10 MWth over 15 years.

district heating↗

EGS Reservoir Modeling for Developing Geothermal District Heating at Cornell University

Cornell University is pursuing development of an enhanced geothermal system (EGS) for providing heating to its main campus in Upstate New York. A ~10,000 ft (~3 km) deep vertical observation well ('CUBO') was drilled in 2022 to characterize the subsurface using wellbore logging, borehole imaging, fluid sampling, mini-frac tests, coring and drill cutting analysis. Down-hole temperatures measured at 3 km depth are about 80 degrees C, sufficiently high for direct-use heating. The well drilled through generally low porosity and low permeability Paleozoic sedimentary formations and into metamorphic basement rock, encountered at about 9,400 ft depth. Leveraging subsurface data obtained through CUBO, we investigated technical feasibility and design requirements of a doublet well system with horizontal laterals connected to a fracture network created through hydraulic fracturing. The EGS reservoir is sized to provide a nominal heat output in the range 5 to 10 MWth of continuous heating over a 15 year-lifetime with limited thermal drawdown. We applied the Gringarten Multiple parallel fracture model, the Cornell Discrete Fracture Simulator FOXFEM and the commercial simulator ResFrac to estimate required heat transfer area and design a potential hydraulic stimulation treatment. Reservoir simulations indicate that, depending on fluid flow rate and injection temperature, 2 to 3 km2 of effective fracture heat transfer area is required to supply the target heat output of 5 to 10 MWth over 15 years.

district heating↗

Overview of Global/Regional Models Used to Evaluate Tropospheric Ozone in North America

Ozone (O3) is an important greenhouse gas, toxic pollutant, and plays a major role in atmospheric chemistry. Tropospheric O3 which resides in the planetary boundary layer (PBL) is highly reactive and has a lifetime on the order of days, however, O3 in the free troposphere and stratosphere has a lifetime on the order of weeks or months. Modeling O3 mixing ratios at and above the surface is difficult due to the multiple formation/destruction processes and transport pathways that cause large spatio-temporal variability in O3 mixing ratios. This talk will summarize in detail the global/regional models that are commonly used to simulate/predict O3 mixing ratios in the United States. The major models which will be focused on are the: 1) Community Multi-scale Air Quality Model (CMAQ), 2) Comprehensive Air Quality Model with Extensions (CAMx), 3) Goddard Earth Observing System with Chemistry (GEOS-Chem), 4) Real Time Air Quality Modeling System (RAQMS), 5) Weather Research and Forecasting/Chemistry (WRF-Chem) model, National Center for Atmospheric Research (NCAR)'s Model for OZone And Related chemical Tracers (MOZART), and 7) Geophysical Fluid Dynamics Laboratory (GFDL) AM3 model. I will discuss the major modeling components which impact O3 mixing ratio calculations in each model and the similarities/differences between these models. This presentation is vital to the 2nd Annual Tropospheric Ozone Lidar Network (TOLNet) Conference as it will provide an overview of tools, which can be used in conjunction with TOLNet data, to evaluate the complex chemistry and transport pathways controlling tropospheric O3 mixing ratios.

Mixing Ratios↗

NeMO-Net – The Neural Multi-Modal Observation & Training Network for Global Coral Reef Assessment

We present NeMO-Net, the Srst open-source deep convolutional neural network (CNN) and interactive learning and training software aimed at assessing the present and past dynamics of coral reef ecosystems through habitat mapping into 10 biological and physical classes. Shallow marine systems, particularly coral reefs, are under significant pressures due to climate change, ocean acidification, and other anthropogenic pressures, leading to rapid, often devastating changes, in these fragile and diverse ecosystems. Historically, remote sensing of shallow marine habitats has been limited to meter-scale imagery due to the optical effects of ocean wave distortion, refraction, and optical attenuation. NeMO-Net combines 3D cm-scale distortion-free imagery captured using NASA FluidCam and Fluid lensing remote sensing technology with low resolution airborne and spaceborne datasets of varying spatial resolutions, spectral spaces, calibrations, and temporal cadence in a supercomputer-based machine learning framework. NeMO-Net augments and improves the benthic habitat classification accuracy of low-resolution datasets across large geographic ad temporal scales using high-resolution training data from FluidCam.NeMO-Net uses fully convolutional networks based upon ResNet and ReSneNet to perform semantic segmentation of remote sensing imagery of shallow marine systems captured by drones, aircraft, and satellites, including WorldView and Sentinel. Deep Laplacian Pyramid Super-Resolution Networks (LapSRN) alongside Domain Adversarial Neural Networks (DANNs) are used to reconstruct high resolution information from low resolution imagery, and to recognize domain-invariant features across datasets from multiple platforms to achieve high classification accuracies, overcoming inter-sensor spatial, spectral and temporal variations.Finally, we share our online active learning and citizen science platform, which allows users to provide interactive training data for NeMO-Net in 2D and 3D, integrated within a deep learning framework. We present results from the PaciSc Islands including Fiji, Guam and Peros Banhos 1 1 2 1 3 1 where 24-class classification accuracy exceeds 91%.

Chirayath, Ved↗

NeuroSEM: A hybrid framework for simulating multiphysics problems by coupling PINNs and spectral elements

Multiphysics problems that are characterized by complex interactions among fluid dynamics, heat transfer, structural mechanics, and electromagnetics, are inherently challenging due to their coupled nature. While experimental data on certain state variables may be available, integrating these data with numerical solvers remains a significant challenge. Physics-informed neural networks (PINNs) have shown promising results in various engineering disciplines, particularly in handling noisy data and solving inverse problems in partial differential equations (PDEs). However, their effectiveness in forecasting nonlinear phenomena in multiphysics regimes, particularly involving turbulence, is yet to be fully established. Here, this study introduces NeuroSEM, a hybrid framework integrating PINNs with the highfidelity Spectral Element Method (SEM) solver, Nektar++. NeuroSEM leverages the strengths of both PINNs and SEM, providing robust solutions for multiphysics problems. PINNs are trained to assimilate data and model physical phenomena in specific subdomains, which are then integrated into the Nektar++ solver. We demonstrate the efficiency and accuracy of NeuroSEM for thermal convection in cavity flow and flow past a cylinder. The framework effectively handles data assimilation by addressing those subdomains and state variables where the data is available. We applied NeuroSEM to the Rayleigh-B´enard convection system, including cases with missing thermal boundary conditions and noisy datasets. Finally, we applied the proposed NeuroSEM framework to real particle image velocimetry (PIV) data to capture flow patterns characterized by horseshoe vortical structures. Our results indicate that NeuroSEM accurately models the physical phenomena and assimilates the data within the specified subdomains. The framework’s plug-and-play nature facilitates its extension to other multiphysics or multiscale problems. Furthermore, NeuroSEM is optimized for efficient execution on emerging integrated GPU-CPU architectures. This hybrid approach enhances the accuracy and efficiency of simulations, making it a powerful tool for tackling complex engineering challenges in various scientific domains.

42 ENGINEERING↗

A higher order panel method for general analysis and design applications in subsonic flow

A higher-order panel method is described for numerical solution of boundary-value problems relating to steady inviscid irrotational incompressible subsonic fluid flow in a domain. Both Neumann and Dirichlet boundary conditions are treated; two types of auxiliary conditions are used to remove the degrees of freedom that arise from specifying only the derivative of the perturbation velocity potential. Four general network types and two expansions of the induced potential kernel are employed in the numerical solution. Some results are presented which illustrate the modeling options and numerical characteristics of the method.

Johnson, F. T.↗