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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 145 records · Page 8

3D analysis of TRISO fuel compacts via X-ray computed tomography

In this study, low-enriched uranium oxycarbide (LEUCO) and surrogate tristructural isotropic (TRISO)- coated-particle compacts with particle volumetric packing fractions of 25%, 40%, and 48% were imaged utilizing X-ray-computed tomography. Subsequent 3D image analysis identified and further quantified kernel size, sphericity, and observed porosity. In addition, the spatial distribution, coordination number, and kernel-nearest neighbors were analyzed and compared for the different packing fractions. Metrics such as observed porosity and sphericity enabled quantification and screening for abnormal kernels within TRISO compacts. Assessment of TRISO particle location confirmed and further quantified a non-uniform distribution of TRISO particles with the spatial distribution in the radial direction being roughly described as a dampened sinusoidal function. The amplitude and frequency of this non-uniform distribution increased with increasing packing fraction. Measured kernel-nearest neighbor distances indicated two regions along the radial surfaces of compacts where TRISO particles are more likely to be in intimate contact with one another. These regions were found: (1) at upper and lower faces of compacts (i.e., corners); (2) offset ~10% of a compact's length from the axial center near the exterior surface. Within these regions, small quantities of defective TRISO surrogate particles (48% packing fraction) and defective LEUCO TRISO particles (40% packing fraction) were found. No defective particles were found within 25% packing fraction LEUCO TRISO compacts.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

The Application of New Software Technology to the Architecture of the National Cycle Program

As part of the Numerical Propulsion System Simulation (NPSS) effort of NASA Lewis in conjunction with the United States aeropropulsion industry, a new system simulation framework, the National Cycle Program (NCP), capable of combining existing empirical engine models with new detailed component-based computational models is being developed. The software architecture of the NCP program involves a generalized object- oriented framework and a base-set of engine component models along with supporting tool kits which will support engine simulation in a distributed environment. As the models are extended to contain two and three dimensions the computing load increases rapidly and it is intended that this load be distributed across multiple work stations executing concurrently in order to get acceptably fast results. The research carried out was directed toward performance analysis of the distributed object system. More specifically, the performance of the actor-based distributed object design I created earlier was desired. To this end, the research was directed toward the design and implementation of suitable performance-analysis techniques and software to demonstrate those techniques. There were three specific results which are reported in two separate reports submitted separately as NASA Technical Memoranda. The results are: (1) Design, implementation, and testing of a performance analysis program for a set of active objects (actor based objects) which allowed the individual actors to be assigned to arbitrary processes on an arbitrary set of machines. (2) The global-balance-equation approach has the fundamental limitation that the number of equations increases exponentially with the number of actors. Hence, unlike many approximate approaches to this problem, the nearest-neighbor approach allows checking of the solution and an estimate of the error. The technique was demonstrated in a prototype analysis program as part of this research. The results of the program were checked against the global-balance solution discussed above. Late during the grant, a much better approximation was developed and this is discussed in result below. As a consequence, a proposal was submitted to continue the research by developing the new approximation including development of a complete program from the prototype. (3) The source of approximation in the nearest-neighbor algorithm is the requirement for estimating some joint probabilities from some marginal distributions. A completely ad hoc estimate was used in the prototype.

Schoeffler, James D.↗

Medium-range atomic correlation in simple liquids. II. Theory of temperature dependence

The spatial atomic correlations in liquids and glasses extend often significantly beyond the nearest neighbors. Such correlations, called the medium-range order (MRO), affect many physical properties, but their nature is not well understood. In this article the variation of the MRO with temperature is calculated based upon the concept of the atomic-level pressure, focusing on simple liquids, such as metallic liquids. It is shown that the structural coherence length that characterizes MRO follows the Curie-Weiss law with a negative Curie temperature as observed by experiment and simulation. It is also shown that the glass transition is induced by freezing of the MRO, rather than the freezing of the nearest-neighbor shell. The implications of these results are discussed.

74 ATOMIC AND MOLECULAR PHYSICS↗

ArborX

ArborX library tackles a problem of efficiently finding geometric objects that are close in space. Variations of this problem, such as finding the nearest neighbors of a point, or finding all objects within a certain distance, are inherent components of applications in many fields. The data may be large so that solving the problem efficiently may require significant computational resources, such as multiple processors or accelerators such as general purpose GPUs. ArborX' main advantage in its ability to solve large problems efficiently utilizing a combination of distributed and on-node parallelism. ArborX can be run efficiently on a wide variety of hardware, including GPUs from different vendors, which distinguishes it from other available libraries which typically choose only few of these. The other advantage is that it supports both types of user problems: spatial problems (useful for intersections and finding objects within certain distance), and nearest neighbor problems. ArborX also supports flexible interface in its interaction with a user. Particularly, it allows a user to call user's own function on a positive match, a functionality not rarely available in other libraries. ArborX implements construction and traversal algorithms using efficient tree structures, such as bounding volume hierarchy (BVH). At its core, it uses linear BVH for its low construction cost and sufficient quality. ArborX is written using C++, and is parallelized using the message passing interface (MPI) for the distributed communication, and the Kokkos library for on-node parallelism. This approach allows ArborX to be run on a wide variety of hardware, from common laptops and desktops to supercomputers while using the same codebase. ArborX also implements several advanced algorithms using geometric search, such as density-based clustering algorithm DBSCAN.

ECP↗

Ferrimagnetic spin waves in honeycomb and triangular layers of Mn{sub 3}Si{sub 2}Te{sub 6}.

A detailed analysis of the ferrimagnetic ground state of Mn 3 Si 2 Te 6 has been performed using inelastic neutron scattering. Although the proposed valence of the nominal Mn 2+ ions would have quenched orbital angular momentum, a significant exchange anisotropy exists in Mn 3 Si 2 Te 6 . This apparent exchange anisotropy is a manifestation of a weak spin-orbit coupling in the layered material. We employ a detailed simulation of the spin-wave spectrum coupling traditional refinement of dispersion parameters to image analysis techniques, while including Monte Carlo simulations of the instrumental resolution to accurately identify the exchange couplings to the third nearest neighbor. An independent validation of our results is made by comparing our final Hamiltonian to heat capacity measurements.

Sala, G.↗

Isolated galaxies, pairs, and groups of galaxies

The authors searched for isolated galaxies, pairs and groups of galaxies in the CfA survey (Huchra et al. 1983). It was assumed that the distances to galaxies are given by R = V/H sub o, where H sub o = 100 km s(exp -1) Mpc(exp -1) and R greater than 6 Mpc. The searching procedure is close to those, applied to find superclusters of galaxies (Kalinkov and Kuneva 1985, 1986). A sphere with fixed radius r (asterisk) is described around each galaxy. The mean spatial density in the sphere is m. Let G (sup 1) be any galaxy and G (sup 2) be its nearest neighbor at a distance R sub 2. If R sub 2 exceeds the 95 percent quintile in the distribution of the distances of the second neighbors, then G (sup 1) is an isolated galaxy. Let the midpoint of G (sup 1) and G (sup 2) be O sub 2 and r sub 2=R sub 2/2. For the volume V sub 2, defined with the radius r sub 2, the density D sub 2 less than k mu, the galaxy G (sup 2) is a single one and the procedure for searching for pairs and groups, beginning with this object is over and we have to pass to another object. Here the authors present the groups - isolated and nonisolated - with n greater than 3, found in the CfA survey in the Northern galactic hemisphere. The parameters used are k = 10 and r (asterisk) = 5 Mpc. Table 1 contains: (1) the group number, (2) the galaxy, nearest to the multiplet center, (3) multiplicity n, (4) the brightest galaxy if it is not listed in (2); (5) and (6) are R.A. and Dec. (1950), (7) - mean distance D in Mpc. Further there are the mean density rho (8) of the multiplet (galaxies Mpc (exp -3), (9) the density rho (asterisk) for r (asterisk) = 5 Mpc and (10) the density rho sub g for the group with its nearest neighbor. The parenthesized digits for densities in the last three columns are powers of ten.

Kuneva, I.↗

Beyond the universal Dyson singularity for 1-D chains with hopping disorder

We study a simple non-interacting nearest neighbor tight-binding model in one dimension with disorder, where the hopping terms are chosen randomly. This model exhibits a well-known singularity at the band center both in the density of states and localization length. If the probability distribution of the hopping terms is well-behaved, then the singularities exhibit universal behavior, the functional form of which was first discovered by Freeman Dyson in the context of a chain of classical harmonic oscillators. We show here that this universal form can be violated in a tunable manner if the hopping elements are chosen from a divergent probability distribution. We also demonstrate a connection between a breakdown of universality in this quantum problem and an analogous scenario in the classical domain — that of random walks and diffusion with anomalous exponents.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Predicting nepheline precipitation in waste glasses using ternary submixture model and machine learning

Nepheline precipitation in nuclear waste glasses during vitrification can be detrimental due to its negative effect on chemical durability. Developing models to accurately predict nepheline precipitation from compositions is important to increase waste loading since existing models can be overly conservative. In this study, an expanded dataset containing 955 glasses was compiled from literature data, where 355 glasses are for high-level waste (HLW). Previously developed submixture models were refitted using the new dataset, where a misclassification rate of 7.8% was achieved. Nine machine learning (ML) algorithms (e.g., k-nearest neighbor, Gaussian process regression, artificial neural network, support vector machine, decision tree, etc.) were applied to evaluate their ability of predicting nepheline precipitation from compositions. Model accuracy, precision, recall/sensitivity, and F1 score were systemically compared between different ML algorithms and modeling protocols. Good model prediction with an accuracy ~0.9 (misclassification rate of ~10%) was observed with different algorithms under certain protocol. This study evaluated various ML models to predict nepheline precipitations in waste glasses, highlighting the importance of data preparation, modeling protocol, and their effect on model stability and reproducibility. The results provide insights into applying ML to predict glass properties and suggest areas for future research on modeling nepheline precipitations.

Lu, Xiaonan↗

Automatic Classification of Biological Targets in a Tidal Channel Using a Multibeam Sonar

Multibeam sonars are widely used for environmental monitoring of fauna at marine renewable energy sites. However, they can rapidly accrue vast volumes of data, which poses a challenge for data processing. Here, using data from a deployment in a tidal channel with peak currents of 1–2 m s –1 , we demonstrate the data-reduction benefits of real-time automatic classification of targets detected and tracked in multibeam sonar data. First, we evaluate classification capabilities for three machine learning algorithms: random forests, support vector machines, and k-nearest neighbors. For each algorithm, a hill-climbing search optimizes a set of hand-engineered attributes that describe tracked targets. Here, the random forest algorithm is found to be most effective—in postprocessing, discriminating between biological and nonbiological targets with a recall rate of 0.97 and a precision of 0.60. In addition, 89% of biological targets are correctly classified as either seals, diving birds, fish schools, or small targets. Model dependence on the volume of training data is evaluated. Second, a real-time implementation of the model is shown to distinguish between biological targets and nonbiological targets with nearly the same performance as in postprocessing. From this, we make general recommendations for implementing real-time classification of biological targets in multibeam sonar data and the transferability of trained models.

16 TIDAL AND WAVE POWER↗

Data for Spatial Analysis of Cell Patterning to Aid Genetic and Phenotypic Understanding of Grass Stomatal Density: A Case Study in Maize

Biological processes involve complex hierarchies where composite traits result from multiple component traits. However, holistically understanding of how sets of component traits interact to underpin genotype-to-phenotype relationships is generally lacking. Stomatal density (SD) is a tractable model system for exploring how high-throughput phenotyping (HTP) data could be exploited by a new spatial analysis approach to better understand a developmentally and functionally important trait. SD is a composite trait, resulting from various components related to cell identity and size, which are themselves governed by a series of spatio-developmental processes. Data from 192 recombinant inbred lines of maize [Zea mays (L.)] were analyzed by a new stomatal patterning phenotype (SPP) to (1) describe the average spatial probability distribution of the nearest neighboring stomata; (2) derive a core set of component traits related to cell size, cell packing, and positional probabilities; (3) build a structural equation model of component traits underlying SD; and (4) identify stomatal patterning quantitative trait loci (QTL). The core set of SPP-derived traits explained 74% of the variation in SD. Analyzing SPP component traits allowed some loci previously identified as generic SD QTL to be recognized as specific to lateral versus longitudinal elements of stomatal patterning. Therefore, this study highlights how novel insights can be gained by decomposing a composite trait (e.g., SD) into a set of component traits that were present in HTP data but not previously exploited.

AI/ML↗

Fast Query-Optimized Kernel-Machine Classification

A recently developed algorithm performs kernel-machine classification via incremental approximate nearest support vectors. The algorithm implements support-vector machines (SVMs) at speeds 10 to 100 times those attainable by use of conventional SVM algorithms. The algorithm offers potential benefits for classification of images, recognition of speech, recognition of handwriting, and diverse other applications in which there are requirements to discern patterns in large sets of data. SVMs constitute a subset of kernel machines (KMs), which have become popular as models for machine learning and, more specifically, for automated classification of input data on the basis of labeled training data. While similar in many ways to k-nearest-neighbors (k-NN) models and artificial neural networks (ANNs), SVMs tend to be more accurate. Using representations that scale only linearly in the numbers of training examples, while exploring nonlinear (kernelized) feature spaces that are exponentially larger than the original input dimensionality, KMs elegantly and practically overcome the classic curse of dimensionality. However, the price that one must pay for the power of KMs is that query-time complexity scales linearly with the number of training examples, making KMs often orders of magnitude more computationally expensive than are ANNs, decision trees, and other popular machine learning alternatives. The present algorithm treats an SVM classifier as a special form of a k-NN. The algorithm is based partly on an empirical observation that one can often achieve the same classification as that of an exact KM by using only small fraction of the nearest support vectors (SVs) of a query. The exact KM output is a weighted sum over the kernel values between the query and the SVs. In this algorithm, the KM output is approximated with a k-NN classifier, the output of which is a weighted sum only over the kernel values involving k selected SVs. Before query time, there are gathered statistics about how misleading the output of the k-NN model can be, relative to the outputs of the exact KM for a representative set of examples, for each possible k from 1 to the total number of SVs. From these statistics, there are derived upper and lower thresholds for each step k. These thresholds identify output levels for which the particular variant of the k-NN model already leans so strongly positively or negatively that a reversal in sign is unlikely, given the weaker SV neighbors still remaining. At query time, the partial output of each query is incrementally updated, stopping as soon as it exceeds the predetermined statistical thresholds of the current step. For an easy query, stopping can occur as early as step k = 1. For more difficult queries, stopping might not occur until nearly all SVs are touched. A key empirical observation is that this approach can tolerate very approximate nearest-neighbor orderings. In experiments, SVs and queries were projected to a subspace comprising the top few principal- component dimensions and neighbor orderings were computed in that subspace. This approach ensured that the overhead of the nearest-neighbor computations was insignificant, relative to that of the exact KM computation.

Mazzoni, Dominic↗

Dependence of the Element Patterns of HYDROSTAR on Mutual Coupling

HYDROSTAR is a hybrid synthesis radiometer, intended for spaceborne applications, which employs a real aperture (waveguide stick antenna) for resolution along track and employs aperture synthesis to obtain resolution across track. This L-band system is an extension of the successful aircraft prototype, the Electronically Steered Thinned Array Radiometer (ESTAR). A proof-of-concept, full size system was constructed (45 wavelength in the synthesis direction) and subjected to extensive antenna pattern and associated microwave component measurements in an outdoor antenna test facility. HYDROSTAR employs a thinned array of 16 elements each 5.8 inches long in the along track dimension and spanning 9.5 inches across track. Each element is a narrow-wall shunt slot array with 36 slots. The polarization is linear (along-track). In the across track dimension, the antennas are deployed in a minimum redundancy array which has 90 independent baselines spaced in integer multiples of half a wavelength. The closest spacings used are for the first three elements at each end, which are spaced by only one-half wavelength. This study was intended to assess how closely each of 16 stick element patterns compare with their nominal values (as an individual, isolated radiator), when installed in their intended composite thinned array configuration. Extensive pattern measurements of the 16 elements that constitute the HYDROSTAR antenna subsystem were conducted to observe their relative features along the synthesis plane. Data was also collected for the mutual coupling between pairs of selected antennas. All antenna patterns had features different from that of an isolated element indicating some level of interaction among neighboring radiators. Those elements which had nearest neighbors at least five wavelengths away were located near the middle of the array. Their radiation patterns displayed sonic small, symmetric ripple across their full azimuth range. The patterns of elements that lie within 2.5 wavelengths of their neighbors showed stronger and asymmetric features. These are believed to be caused by mutual coupling among these structures. Evidence for this was seen when an antenna position was displaced by 0.05 wavelengths, Its pattern and those of its near neighbors were seen to change. Displacement within the plane of the array were observed to have different effects than displacements out-of-plane. A program of data analysis and theoretical development is in progress to provide a physical interpretation of the properties of these antenna patterns and to develop methods which can optimize the performance of this synthetic aperture imaging system. This includes compensation for pattern asymmetries and element position perturbation.

Weissman, David E.↗

Nonlinear elasticity and short-range mechanical coupling govern the rate and symmetry of mouth opening in Hydra

Hydra has a tubular bilayered epithelial body column with a dome-shaped head on one end and a foot on the other. Hydra lacks a permanent mouth: its head epithelium is sealed. Upon neuronal activation, a mouth opens at the apex of the head which can exceed the body column diameter in seconds, allowing Hydra to ingest prey larger than itself. While the kinematics of mouth opening are well characterized, the underlying mechanism is unknown. We show that Hydra mouth opening is generated by independent local contractions that require tissue-level coordination. We model the head epithelium as an active viscoelastic nonlinear spring network. The model reproduces the size, timescale and symmetry of mouth opening. It shows that radial contractions, travelling inwards from the outer boundary of the head, pull the mouth open. Nonlinear elasticity makes mouth opening larger and faster, contrary to expectations. Here, the model correctly predicts changes in mouth shape in response to external forces. By generating innervated : nerve-free chimera in experiments and simulations, we show that nearest-neighbor mechanical signaling suffices to coordinate mouth opening. Hydra mouth opening shows that in the absence of long-range chemical or neuronal signals, short-range mechanical coupling is sufficient to produce long-range order in tissue deformations.

59 BASIC BIOLOGICAL SCIENCES↗

Sizing ramping reserve using probabilistic solar forecasts: A data-driven method

Ramping products have been introduced or proposed in several U.S. power markets to mitigate the impact of load and renewable uncertainties on market efficiency and reliability. Current methods often rely on historical data to estimate the requirements of ramping products and fail to take into account the effects of the latest weather conditions and their uncertainties, which could lead to overly conservative or insufficient requirements. This study proposes a k-nearest-neighbor-based method to give weather-informed estimates of ramping needs based on short-term probabilistic solar irradiance forecasts. Forecasts from multiple sites are employed in conjunction with principal component analysis to derive numerical classifiers to characterize system-level weather conditions. In addition, we develop a data-driven method to optimize the model parameters in a rolling-forward manner. By using real-world data from the California Independent System Operator, we design two metrics to evaluate method performance: 1) frequency of shortage and 2) oversupply of ramping product. Our proposed method presents advantages in comparison with the baseline and a set of benchmark methods: without compromising system reliability, it reduces system ramping requirements by up to 25%, therefore improving both system reliability and economics.

14 SOLAR ENERGY↗

A GPU accelerated mixed-precision Smoothed Particle Hydrodynamics framework with cell-based relative coordinates

Smoothed Particle Hydrodynamics (SPH) is essential for modeling complex large-deformation problems across various applications, requiring significant computational power. A major portion of SPH computation time is dedicated to the Nearest Neighboring Particle Search (NNPS) process. While advanced NNPS algorithms have been developed to enhance SPH efficiency, the potential efficiency gains from modern computation hardware remain underexplored. Here, this study investigates the impact of GPU parallel architecture, low-precision computing on GPUs, and GPU memory management on NNPS efficiency. Our approach employs a GPU-accelerated mixed-precision SPH framework, utilizing low precision float-point 16 (FP16) for NNPS while maintaining high precision for other components. To ensure FP16 accuracy in NNPS, we introduce a Relative Coordinated-based Link List (RCLL) algorithm, storing FP16 relative coordinates of particles within background cells. Our testing results show three significant speedup rounds for CPU-based NNPS algorithms. The first comes from parallel GPU computations, with up to a 1000x efficiency gain. The second is achieved through low-precision GPU computing, where the proposed FP16-based RCLL algorithm offers a 1.5x efficiency improvement over the FP64-based approach on GPUs. By optimizing GPU memory bandwidth utilization, the efficiency of the FP16 RCLL algorithm can be further boosted by 2.7x, as demonstrated in an example with 1 million particles. Our code is released at https://github.com/pnnl/lpNNPS4SPH.

97 MATHEMATICS AND COMPUTING↗

Weak trimerization in the frustrated two-dimensional triangular Heisenberg antiferromagnet Lu y Y 1-y MnO 3

To understand the 2D triangular Heisenberg antiferromagnetic system, we investigated the magnetic structures and the dynamics of Lu y Y 1-y MnO 3 in detail. The substitutions are adjusted to the Mn atomic position close to x Mn =$\frac{1}{3}$. The neutron powder diffraction data claims that the magnetic structure of Lu y Y 1-y MnO 3 is described as a mixture of Γ 3 (P6' 3 cm') and Γ 4 (P6' 3 c'm) at the x Mn position for y=0.15, 0.30, and 0.45. The ratio of Γ 3 and Γ 4 depends on temperature and composition and the fraction of Γ 3 increases upon cooling, while no clear trimerization was observed at the xMn position. We estimated exchange parameters from the analysis of the low-energy part of the spin waves. The results showed a weak trimerization effect on cooling because the nearest-neighbor exchange interaction is slightly enhanced. The temperature dependence of the spin-wave dispersion around the Γ point shows that the spin gap closes with increasing temperature because the exchange interactions in the nearest Mn-Mn neighbor become smaller. Gapless diffusive magnetic excitation from a Mn triangular lattice has been observed in a wide range in Q and E space of Lu y Y 1-y MnO 3 . We found that Lu 0.3 Y 0.7 MnO 3 could be an ideal case to investigate the trimerization, frustrated magnetism, and magnetoelastic coupling often observed in two-dimensional triangular lattice Heisenberg antiferromagnet systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

High-count-rate effects in event processing for the XRISM/Resolve X-ray microcalorimeter. II. Energy scale and resolution in orbit

The Resolve instrument on the X-ray Imaging and Spectroscopy Mission (XRISM) uses a 36 pixel microcalorimeter designed to deliver high-resolution, non-dispersive X-ray spectroscopy. Although it is optimized for extended sources with low count rates, Resolve observations of bright point sources are still able to provide unique insights into the physics of these objects, as long as high-count-rate effects are addressed in the analysis. These effects include the loss of exposure time for each pixel, changes in the energy scale, and changes in the energy resolution. To investigate these effects under realistic observational conditions, we observed the bright X-ray source, the Crab Nebula, with XRISM at several offset positions with respect to the Resolve field of view and with continuous illumination from 55 Fe sources on the filter wheel. For the spectral analysis, we excluded data where exposure-time loss was too significant to ensure reliable spectral statistics. The energy scale at 6 keV shows a slight negative shift in the high-count-rate regime. The energy resolution at 6 keV worsens as the count rate in electrically neighboring pixels increases, but can be restored by applying a nearest-neighbor coincidence cut (“cross-talk cut”). We examined how these effects influence the observation of bright point sources, using GX 13+1 as a test case, and identified an eV-scale energy offset at 6 keV between the inner (brighter) and outer (fainter) pixels. Users who seek to analyze velocity structures on the order of tens of km s–1 should account for such high-count-rate effects. These findings will aid in the interpretation of Resolve data from bright sources and provide valuable considerations for designing and planning for future microcalorimeter missions.

X-rays: general↗

The Monotonic Lagrangian Grid for Fast Air-Traffic Evaluation

This paper describes the continued development of a dynamic air-traffic model, ATMLG, intended for rapid evaluation of rules and methods to control and optimize transport systems. The underlying data structure is based on the Monotonic Lagrangian Grid (MLG), which is used for sorting and ordering positions and other data needed to describe N moving bodies, and their interactions. In ATMLG, the MLG is combined with algorithms for collision avoidance and updating aircraft trajectories. Aircraft that are close to each other in physical space are always near neighbors in the MLG data arrays, resulting in a fast nearest-neighbor interaction algorithm that scales as N. In this paper, we use ATMLG to examine how the ability to maintain a required separation between aircraft decreases as the number of aircraft in the volume increases. This requires keeping track of the primary and subsequent collision avoidance maneuvers necessary to maintain a five mile separation distance between all aircraft. Simulation results show that the number of collision avoidance moves increases exponentially with the number of aircraft in the volume.

Alexandrov, Natalia↗