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At least 1,315 records · Page 73

Energization and transport of ions of ionospheric origin in the terrestrial magnetosphere

The work of this grant has been predominantly focused on ion outflows from two data sets: Prognoz 7 and Dynamics Explorer. The Prognoz analysis studied ion densities, temperatures, and flow velocities in the magnetotail. The work performed under this contract consisted of developing a program to load the raw data, computing the background subtraction of a strong sun pulse, and using the net count to calculate the low order moments of the distribution function. The study confirms the results of ISEE with regard to the supply of plasma from the cusp as a major source of plasmasheet plasma and goes beyond this to discuss the use of ion velocities as a way to examine the motions of the magnetotail. The abstract of the work to be reported is included as an appendix. The work on the DE/Retarding Ion Mass Spectrometer is separated into two categories: (1) classification of low-energy ion flows from high-latitudes, and (2) studies of the polar wind. Major publications resulting from this work are also included as an appendix to this report. The polar wind is in a category by itself as a result of the thermal escape of hydrogen and helium because of ambipolar diffusion through the heavier, oxygen-dominated topside ionosphere. The analysis of the polar wind reports the flux variability as a function of season, magnetic activity, etc. Much effort has been expended under this grant to complete a follow on study of the thermal structure of the polar wind. Extensive display tools and analysis software have been developed and used in an attempt to carry out this thermal analysis. The present work uses a constrained fit scheme that combines the ion densities and flow velocities derived from Chandler et al. and a spacecraft potential derived from an empirical relation to the total ion density to determine the remaining fit parameter, the ion temperature, via a least squares fit to the RIMS data.

Waite, J. Hunter JR.↗

An IEEE 1451.1 Architecture for ISHM Applications

The IEEE 1451.1 Standard for a Smart Transducer Interface defines a common network information model for connecting and managing smart elements in control and data acquisition networks using network-capable application processors (NCAPs). The Standard is a network-neutral design model that is easily ported across operating systems and physical networks for implementing complex acquisition and control applications by simply plugging in the appropriate network level drivers. To simplify configuration and tracking of transducer and actuator details, the family of 1451 standards defines a Transducer Electronic Data Sheet (TEDS) that is associated with each physical element. The TEDS contains all of the pertinent information about the physical operations of a transducer (such as operating regions, calibration tables, and manufacturer information), which the NCAP uses to configure the system to support a specific transducer. The Integrated Systems Health Management (ISHM) group at NASA's John C. Stennis Space Center (SSC) has been developing an ISHM architecture that utilizes IEEE 1451.1 as the primary configuration and data acquisition mechanism for managing and collecting information from a network of distributed intelligent sensing elements. This work has involved collaboration with other NASA centers, universities and aerospace industries to develop IEEE 1451.1 compliant sensors and interfaces tailored to support health assessment of complex systems. This paper and presentation describe the development and implementation of an interface for the configuration, management and communication of data, information and knowledge generated by a distributed system of IEEE 1451.1 intelligent elements monitoring a rocket engine test system. In this context, an intelligent element is defined as one incorporating support for the IEEE 1451.x standards and additional ISHM functions. Our implementation supports real-time collection of both measurement data (raw ADC counts and converted engineering units) and health statistics produced by each intelligent element. The handling of configuration, calibration and health information is automated by using the TEDS in combination with other electronic data sheets extensions to convey health parameters. By integrating the IEEE 1451.1 Standard for a Smart Transducer Interface with ISHM technologies, each element within a complex system becomes a highly flexible computation engine capable of self-validation and performing other measures of the quality of information it is producing.

Morris, Jon A.↗

DS-GL: Advancing Graph Learning via Harnessing the Power of Nature within Dynamic Systems

With the rapid digitization of the world, an increasing number of real-world applications are turning to nonEuclidean data, modeled as graphs. Due to their intrinsic high complexity and irregularity, learning from graph data demands tremendous computational power. Recently, CMOS-compatible Ising machines, i.e., dynamic systems composed of CMOS components, have emerged as a new approach that harnesses the inherent power of natural annealing within dynamic systems to efficiently resolve binary optimization problems and have been adopted for traditional graph computation, such as max-cut. However, when performing complex Graph Learning (GL) tasks, Ising machines face significant hurdles: (i) they are inherently binary and thus ill-suited for real-valued problems; (ii) their expensive all-to-all coupling network that guarantees effective natural annealing poses daunting scalability concerns. To address these challenges, this paper proposes a nature-powered graph learning framework dubbed DS-GL, which is the first effort to transform the process of solving graph learning problems into the natural annealing process within a parameterized dynamic system embodied as a CMOS chip. To tackle the two major hurdles, DS-GL first augments the Ising machine architecture to modify the self-reaction term of its Hamiltonian function from linear to quadratic, effectively serving as an energy regulator. This adjustment maintains the system’s original physical interpretation while enabling it to process continuous, real-valued data. Second, to address the scaling issue, DS-GL further upgrades the real-valued dense Ising machine by decomposing it into a mesh-based multi-PE dynamic system that supports efficient distributed spatial-temporal co-annealing across different PEs through sparse interconnects. By exploiting the inherent sparsity and component structures in real-world graphs, DS-GL is able to map complex graph learning tasks onto the scalable dynamic system while maintaining high accuracy. Evaluations with three diverse GL applications across six real-world datasets, including traffic flow and COVID-19 prediction, show that DS-GL can deliver from 102× to 106× speedups and 500× energy reduction over Graph Neural Networks on GPUs, with 5% - 20% accuracy enhancement.

Song, Ruibing↗

Sparse-grid, reduced-basis Bayesian inversion: Nonaffine-parametric nonlinear equations

We extend the reduced basis (RB) accelerated Bayesian inversion methods for affine-parametric, linear operator equations which are considered in [16,17] to non-affine, nonlinear parametric operator equations. We generalize the analysis of sparsity of parametric forward solution maps in [20] and of Bayesian inversion in [48,49] to the fully discrete setting, including Petrov–Galerkin high-fidelity (“HiFi”) discretization of the forward maps. We develop adaptive, stochastic collocation based reduction methods for the efficient computation of reduced bases on the parametric solution manifold. The nonaffinity and nonlinearity with respect to (w.r.t.) the distributed, uncertain parameters and the unknown solution is collocated; specifically, by the so-called Empirical Interpolation Method (EIM). For the corresponding Bayesian inversion problems, computational efficiency is enhanced in two ways: first, expectations w.r.t. the posterior are computed by adaptive quadratures with dimension-independent convergence rates proposed in [49]; the present work generalizes [49] to account for the impact of the PG discretization in the forward maps on the convergence rates of the Quantities of Interest (QoI for short). Second, we propose to perform the Bayesian estimation only w.r.t. a parsimonious, RB approximation of the posterior density. Based on the approximation results in [49], the infinite-dimensional parametric, deterministic forward map and operator admit N-term RB and EIM approximations which converge at rates which depend only on the sparsity of the parametric forward map. In several numerical experiments, the proposed algorithms exhibit dimension-independent convergence rates which equal, at least, the currently known rate estimates for N-term approximation. We propose to accelerate Bayesian estimation by first offline construction of reduced basis surrogates of the Bayesian posterior density. The parsimonious surrogates can then be employed for online data assimilation and for Bayesian estimation. They also open a perspective for optimal experimental design.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Benefit-cost methodology study with example application of the use of wind generators

An example application for cost-benefit methodology is presented for the use of wind generators. The approach adopted for the example application consisted of the following activities: (1) surveying of the available wind data and wind power system information, (2) developing models which quantitatively described wind distributions, wind power systems, and cost-benefit differences between conventional systems and wind power systems, and (3) applying the cost-benefit methodology to compare a conventional electrical energy generation system with systems which included wind power generators. Wind speed distribution data were obtained from sites throughout the contiguous United States and were used to compute plant factor contours shown on an annual and seasonal basis. Plant factor values (ratio of average output power to rated power) are found to be as high as 0.6 (on an annual average basis) in portions of the central U. S. and in sections of the New England coastal area. Two types of wind power systems were selected for the application of the cost-benefit methodology. A cost-benefit model was designed and implemented on a computer to establish a practical tool for studying the relative costs and benefits of wind power systems under a variety of conditions and to efficiently and effectively perform associated sensitivity analyses.

Zimmer, R. P.↗

Impact of Time-Dependent Reactor and Sensor Physics on Core Power Synthesis (Rev.1)

Online synthesis of power distribution is critical in the operation and control of nuclear power reactors to ensure that the core is operating within safety margins and to provide essential knowledge associated with the burnup of the fuel. In light-water reactors, power synthesis is achieved by using some a priori knowledge of the state of the reactor core and updating based on the signals coming from in-core sensors—namely, self-powered neutron detectors (SPNDs). This report examines the effects of fuel burnup and sensor degradation on the ability to accurately synthesize the power distribution in a pressurized water reactor (PWR), considering the typical low-enriched uranium (LEU, 3%-5% enrichment) fuel cycle as well as the higher enrichment LEU+ (5%-8% enrichment) fuel cycle. Several modeling tools were used to simulate power synthesis based on the responses of SPNDs, with emitters made out of Rh or V. A representative PWR LEU core was modeled using the Polaris/Purdue Advanced Reactor Core Simulator (PARCS) approach. The Monte Carlo N-Particle Transport 6 (MCNP6) code was used as well to calculate response functions between different segments of fuel to individual SPNDs; this is a crucial parameter for power synthesis. The Oak Ridge Isotope GENeration (ORIGEN) package in the Standardized Computer Analyses for Licensing Evaluation (SCALE) code was used to model the time-dependent isotopic transmutation in the SPND emitters. All these data were fed into a custom code that enacted the point-based iterative method to simulate power synthesis. Developmental work was also performed on high-fidelity SPND models in the GEometry ANd Tracking 4 (Geant4) code, which enables higher-accuracy modeling of the current responses from SPNDs. In this work, five sets of time-dependent power synthesis test cases were conducted. In these test cases, systematic changes in the input conditions enabled an analysis of the effect of (1) slightly inaccurate a priori power distribution assumptions with respect to fuel burnup, (2) highly inaccurate a priori power distribution assumptions with respect to fuel burnup (such that burnup is not included in the a priori assumed distribution), and (3) differences between Rh and V SPNDs in terms of downstream consequences of the transmutation in the emitters and the extended nature of the LEU+ fuel cycle in comparison with LEU. The authors discovered that one may permissibly have slightly inaccurate a priori assumptions of the fuel burnup (such that the level of burnup may be slightly underapproximated or overapproximated by the accumulated burnup in approximately 9.3 full power days), but to not account for burnup at all in the a priori assumptions leads to severe levels of error, approaching 25% at maximum (for LEU). The authors also discovered that V SPNDs are extraordinarily robust in both the LEU and LEU+ fuel cycles considered in this modeling work, whereas Rh SPNDs undergo significant transmutation that can result in large errors in the synthesized power distribution.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Multi-Scale Modeling Framework for Mercury Biogeochemistry

Multi-Scale modeling of mercury (Hg) geochemical speciation and reactions has been performed by integrating atomistic quantum chemical calculations with continuum scale speciation models. Major progress has been made in the improvement of quantum chemical models to calculate critical thermodynamic data for Hg complexes in aquatic environments. Rapid and reliable quantum chemical approaches have been developed for calculating acid dissociation constants (pK a ) and stability constants (log K), with calculated mean unsigned errors of 0.5 and 1.5 log units, respectively for ligand molecules and Hg complexes. At the continuum scale, systematic analysis of uncertainty propagation in mercury (Hg) speciation modeling has been conducted and was used to identify environmental conditions under which thermodynamic constant uncertainties are significant and recommended to be accounted for. The integrated framework for multi-scale modeling of mercury geochemistry is open to the research community through the web-based multiscale modeling aqueous speciation resource, AQUA-MER. The improved quantum chemical approaches for thermodynamic constant calculations are accessible through AQUA-MER and can be used to provide the missing constants in the continuum scale speciation calculations. In addition to low molecular mass Hg complex speciation, modeling natural aquatic environments also involve the transport of high molecular weight dissolved organic matter (DOM) in reactive flows simultaneously with equilibrium and kinetic reactions. To this end, atomistic MD simulations were performed to capture the details of aggregation, mechanisms and distribution of functional groups in DOM at the molecular level. The elemental composition and calculated bulk properties of the DOM models are in close agreement with experimental measurements. A travel-time based reactive transport model in the hyporheic zone of stream corridors was established for the multicomponent Hg-DOM-S system and implemented through PFLOTRAN.

54 ENVIRONMENTAL SCIENCES↗

Impacts of high resolution data on traveler compliance levels in emergency evacuation simulations

In this article, we conducted a comparison study of evacuation assignment based on Traffic Analysis Zones (TAZ) and high resolution LandScan USA Population Cells (LPC) with detailed real world roads network. A platform for evacuation modeling built on high resolution population distribution data and activity-based microscopic traffic simulation was proposed. This platform can be extended to any cities in the world. The results indicated that evacuee compliance behavior affects evacuation efficiency with traditional TAZ assignment, but it did not significantly compromise the performance with high resolution LPC assignment. The TAZ assignment also underestimated the real travel time during evacuation. This suggests that high data resolution can improve the accuracy of traffic modeling and simulation. The evacuation manager should consider more diverse assignment during emergency evacuation to avoid congestions.

97 MATHEMATICS AND COMPUTING↗

Fuel cycle depletion validation and code-to-code verification studies for High Flux Isotope Reactor highly and low-enriched uranium fuel designs

Here, this paper documents fuel cycle depletion validation and code-to-code verification studies for the High Flux Isotope Reactor (HFIR) highly enriched uranium (HEU) and proposed low-enriched uranium (LEU) fuel designs. In support of HFIR’s world-leading performance, transport and depletion simulations are performed to ensure safe operations, design and qualify irradiation experiments, enhance core components and irradiation facilities, and design and characterize LEU fuel designs. Identifying well-validated, computationally efficient codes is required for the success of these efforts. The HFIR Controller, Shift, and VESTA codes were deployed to simulate HEU uranium–oxide dispersion fuel cycles at 85, 95, and 100 MW operations, as well as LEU fuel cycles operating at 95 MW with uranium–silicide dispersion and uranium–molybdenum monolithic alloy fuel forms. Excellent agreement between the codes and with experimentally obtained 235 U enrichment distributions provides increased confidence in the ability of these codes to model and simulate HFIR’s unique core design.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Cooperative fault management for resilient integration of renewable energy

Cooperative fault management (CFM) is designed herein to control different types of renewable energy resources cooperatively during electrical faults. This paper studies systems with a high penetration of photovoltaic (PV) energy and wind energy. First, CFM leverages power converters of PV farms to boost the ride-through capability of nearby doubly-fed induction generators (DFIGs). By controlling PV farms’ output voltages to change smoothly during both fault initiation and fault clearance, the widely used crowbar in DFIGs is less likely to be activated. Crowbar activation adversely makes DFIGs lose controllability and absorb reactive power. The second contribution is the development of a software-defined CFM controller and a controller in-the-loop demonstration of the real-time performance of this optimization-based CFM. CFM capitalizes on distributed optimization formulation to enable flexibility, plug-and-play, and privacy-preserving. Computation time, however, is a major concern for optimization-based dynamics control. Here, real-time controller-in-the-loop simulation results show optimization-based CFM can output reference values around 60 ms and is quick enough for dynamic control.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

FitCache: A Transparent Drop-In Framework for Multi-Tier Caching to Accelerate Distributed Deep Learning Workloads

Training in Deep learning (DL) remains highly compute- and data-intensive, with I/O becoming a critical bottleneck as models and datasets scale. Recent studies report that data loading can dominate training time, especially on large-scale HPC systems with shared parallel file systems (PFS). Existing caching approaches either rely on single-tier designs or require intrusive modifications to training pipelines, limiting their portability and effectiveness. In this work, we present FitCache, a transparent drop-in framework for multi-tier caching to accelerate distributed DL training by coordinating fast local memory (e.g., DRAM, Persistent Memory (PMem)) and NVMe as hierarchical caches atop PFS. Our design adapts to hardware diversity, i.e., if NVMe is missing, memory transparently acts as a caching tier, ensuring stable performance. FitCache transparently intercepts I/O requests and issues concurrent fetches across all tiers, returning data from the fastest responder without centralized metadata or static redirection paths. FitCache adapts to dynamic workloads and heterogeneous clusters while maintaining POSIX compatibility. Experiments on Frontier (2048 GPUs) and smaller research clusters show that FitCache reduces training time by up to 40% and per-batch I/O latency by up to 71.6% compared to Lustre Orion PFS, offering a drop-in solution for scalable DL training.

Hu, Guangxing [ORNL] (ORCID:0009000283203614)↗

Nuclear Physics Network Requirements Review Report

The Energy Sciences Network (ESnet) is the Office of Science’s high-performance network user facility, delivering highly reliable data transport capabilities optimized for the requirements of data-intensive science. In essence, ESnet is the circulatory system that enables the U.S. Department of Energy (DOE) science mission by connecting each and every DOE lab and its user facilities. ESnet is funded and stewarded by the Advanced Scientific Computing Research (ASCR) Program and managed and operated by the Scientific Networking Division at Lawrence Berkeley National Laboratory (LBNL). ESnet is widely regarded as a global leader in the research and education networking community. ESnet connects DOE national laboratories, user facilities, and major experiments so scientists can use remote instruments and computing resources as well as share data with collaborators, transfer large data sets, and access distributed data repositories. While ESnet provides network connectivity, it cannot be characterized as an internet service provider as it is specifically built to provide a range of network services that are tailored to meet the unique requirements of DOE’s data-intensive science.

97 MATHEMATICS AND COMPUTING↗

Nuclear Physics Network Requirements Review Report

The Energy Sciences Network (ESnet) is the Office of Science’s high-performance network user facility, delivering highly reliable data transport capabilities optimized for the requirements of data-intensive science. In essence, ESnet is the circulatory system that enables the U.S. Department of Energy (DOE) science mission by connecting each and every DOE lab and its user facilities. ESnet is funded and stewarded by the Advanced Scientific Computing Research (ASCR) Program, and managed and operated by the Scientific Networking Division at Lawrence Berkeley National Laboratory (LBNL). ESnet is widely regarded as a global leader in the research and education networking community. ESnet connects DOE national laboratories, user facilities, and major experiments so scientists can use remote instruments and computing resources as well as share data with collaborators, transfer large data sets, and access distributed data repositories. While ESnet provides network connectivity, it cannot be characterized as an internet service provider as it is specifically built to provide a range of network services that are tailored to meet the unique requirements of DOE’s data-intensive science. In short, ESnet’s mission is to enable and accelerate scientific discovery by delivering unparalleled network infrastructure, capabilities, and tools. ESnet’s vision is summarized by these three points. 1. Scientific progress will be completely unconstrained by the physical location of instruments, people, computational resources, or data. 2. Collaborations at every scale, in every domain, will have the information and tools they need to achieve maximum benefit from scientific facilities, global networks, and emerging network capabilities. 3. ESnet will foster the partnerships and pioneer the technologies necessary to ensure that these transformations occur. In May 2019, ESnet and the Office of Nuclear Physics (NP) of the DOE Office of Science organized an ESnet requirements review of NP-supported activities. Preparation for this event included identification of key stakeholders to the process: program and facility management, research groups, technology providers, and a number of external observers. These individuals were asked to prepare formal case study documents about their relationship to the NP program to build a complete understanding of the current, near-term, and long-term status, expectations, and processes that will support the science going forward. A series of pre-planning meetings better prepared case study authors for this task and facilitated a smooth transition to the in-person review.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Computation of supersonic jet mixing noise for an axisymmetric CD nozzle using k-epsilon turbulence model

The turbulent mixing noise of a supersonic jet is calculated for a round convergent-divergent nozzle at the design pressure ratio. Aerodynamic computations are performed using the PARC code with a k-epsilon turbulence model. Lighthill's acoustic analogy combined with Ribner's assumption is adopted. The acoustics solution is based upon the methodology followed by GE in the MGB code. The source correlation function is expressed as a linear combination of second-order tensors. Assuming separable second-order correlations and incorporating Batchelor's isotropic turbulence model, the source term was calculated from the kinetic energy of turbulence. A Gaussian distribution for the time-delay of correlation was introduced. The computational fluid dynamics (CFD) solution was used to obtain the source strength as well as the characteristic time-delay of correlation. The effect of sound/flow interaction was incorporated using the high frequency asymptotic solution to Lilley's equation for axisymmetric geometries. Acoustic results include sound pressure level directivity and spectra at different polar angles. The aerodynamic and acoustic results demonstrate favorable agreement with experimental data.

Khavaran, Abbas↗

Computation of supersonic jet mixing noise for an axisymmetric CD nozzle using k-epsilon turbulence model

The turbulent mixing noise of a supersonic jet is calculated for a round convergent-divergent nozzle at the design pressure ratio. Aerodynamic computations are performed using the PARC code with a k-epsilon turbulence model. Lighthill's acoustic analogy combined with Ribner's assumption is adopted. The acoustics solution is based upon the methodology followed by GE in the MGB code. The source correlation function is expressed as a linear combination of second-order tensors. Assuming separable second-order correlations and incorporating Batchelor's isotropic turbulence model, the source term was calculated from the kinetic energy of turbulence. A Gaussian distribution for the time-delay of correlation was introduced. The computational fluid dynamics (CFD) solution was used to obtain the source strength as well as the characteristic time-delay of correlation. The effect of sound/flow interaction was incorporated using the high frequency asymptotic solution to Lilley's equation for axisymmetric geometries. Acoustic results include sound pressure level directivity and spectra at different polar angles. The aerodynamic and acoustic results demonstrate favorable agreement with experimental data.

Khavaran, A.↗

CFD Study of NACA 0018 Airfoil with Flow Control

The abilities of two different Reynolds-Averaged Navier-Stokes codes to predict the effects of an active flow control device are evaluated. The flow control device consists of a blowing slot located on the upper surface of an NACA 0018 airfoil, near the leading edge. A second blowing slot present on the airfoil near mid-chord is not evaluated here. Experimental results from a wind tunnel test show that a slot blowing with high momentum coefficient will increase the lift of the airfoil (compared to no blowing) and delay flow separation. A slot with low momentum coefficient will decrease the lift and induce separation even at low angles of attack. Two codes, CFL3D and FUN3D, are used in two-dimensional computations along with several different turbulence models. Two of these produced reasonable results for this flow, when run fully turbulent. A more advanced transition model failed to predict reasonable results, but warrants further study using different inputs. Including inviscid upper and lower tunnel walls in the simulations was found to be important in obtaining pressure distributions and lift coefficients that best matched experimental data. A limited number of three-dimensional computations were also performed.

Eggert, Christopher A.↗

BigPanDA: PanDA Workload Management System and its Applications beyond ATLAS

Modern experiments collect peta-scale volumes of data and utilize vast, geographically distributed computing infrastructure that serves thousands of scientists around the world. Requirements for rapid, near real-time data processing, fast analysis cycles and need to run massive detector simulations to support data analysis pose special premium on efficient use of available computational resources. A sophisticated Workload Management System (WMS) is needed to coordinate the distribution and processing of data and jobs in such environment. The ATLAS experiment at CERN uses PanDA (Production and Data Analysis) Workload Management System for managing the workflow for all data processing on over 150 data centers. While PanDAcurrently uses more than 250,000 cores with a peak performance of 0.3 petaFLOPS, it runs around 2 million jobs per day on hundreds of Grid sites and serving thousands of ATLAS users. In 2017 about 1.5 exabytes of data were processed with PanDA.In 2012 BigPanDA project project was started with aim to introduce new types of computing resources into ATLAS computing infrastructure, but also to offering PanDA features to different data-intensive applications for projects and experiments outside of ATLAS and High-Energy and Nuclear Physics. In this article we will present accomplishments and discuss possible directions for future work.

Svirin, Pavlo↗

Sheared wing-tip aerodynamics - Wind-tunnel and computational investigation

Computational and experimental performance benefits are presented for a high-aspect-ratio unswept wing configuration with sheared tips. The sheared tip is a highly swept and highly tapered surface located in the same plane as the inboard wing panel to which it is attached. The compuational results were obtained with an inviscid surface panel method that models the nonlinear influence of the trailing wake. Both wind-tunnel and calculated results were obtained for a 12-ft span wing model with various wing-tip configurations. The computational and experimental data are in fair agreement and demonstrate that sheared wing tips can reduce induced drag at cruise and climb lift coefficients. The drag reduction is the result of wake deformation effects and changes in spanwise load distribution. Wind-tunnel measured longitudinal and lateral directional stability characteristics are also presented for the various wing-tip layouts.

Vijgen, P. M. H. W.↗