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At least 973 records · Page 54

Small-Sample Estimator Decisions – Certainly Uncertain in Human Spaceflight at NASA

Within statistics when estimating means, we rely heavily on the Central Limit Theorem (CLT) to aid in our inference, however in cases where the CLT does not apply we begin to be strongly limited in our choices. If a violation to the CLT comes in the form of small samples and unknown population variance, yet we maintain the assumption of normality, the use of t-distributions is perfectly valid. We explore cases where population normality is not assumed, where sample sizes are small, and where some actionable estimate of the central tendency of a distribution is needed such as for spaceflight operational decisions. Here we identify different scenarios based on measures taken from spaceflight, characterizing performance of estimators of central tendency within our set of simulations. We examine bias and variability of standard estimators of central tendency as they apply to varying small sample sizes and varying population distributions. Further work in this area is needed to develop a framework or set of guidelines for individuals set in these situations. Even with limited information, decisions need to be made.

Central Tendency↗

Normalization Method and Application for MODIS TEB Assessments using Earth Scene Measurements

Selected Earth targets are commonly used for satellite sensor calibration assessments (e.g. sensor stability and inter-comparisons). Moreover, typical scenes used for the calibration assessment of the thermal emissive bands (TEBs) includeDome Concordia (Dome-C), ocean, desert, and deep convective clouds (DCC). Reference data used for these calibration assessments can come from another band, another instrument, or ground measurements. The Dome-C site, covered with uniformly-distributed permanent snow, is normally used for the assessment of the TEBsat cold temperatures. Furthermore, ocean and desert measurements prove useful for scenes with higher temperatures. The DCC, one of the most consistent and coldest targets, can be used for the TEBs calibration and product stability assessments. MODIS band 31 (~ 11 m) can be used as a reference for these scenes. However, measurements over these scenes have seasonal variations, and the DCC brightness temperatures (BTs) have asymmetrical distributions. These features can introduce additional uncertainty to the stability assessments. A normalization method is applied by using an empirical model to derive reference-dependent BTs. Using the developed empirical model, measurements can be normalized to a reference BT in order to enhance the calibration assessment’s accuracy. This method is evaluated using all four scene types (i.e. ocean, desert, snow (Dome-C), and DCC) and applied to all the Terra and Aqua MODIS TEBs. Stability assessments over the instruments’ entire data records are presented and discussed. The technique can be applied in future efforts to support MODIS TEBs calibration assessments.

MODIS TEB↗

Characteristics of Multi-scale Current Sheets in the Solar Wind at 1 au Associated with Magnetic Reconnection and the Case for a Heliospheric Current Sheet Avalanche

Wind spacecraft measurements are analyzed to obtain a current sheet (CS) normal width dcs-distribution of 3374 confirmed magnetic reconnection exhausts in the ecliptic plane of the solar wind at 1 AU. The dcs-distribution displays a nearly exponential decay from a peak at dcs=25 di to a median at dcs=85 di and a 95th percentile at dcs=905 di with a maximum exhaust width at dcs=8077 di. A magnetic field ϴ-rotation angle distribution increases linearly from a relatively few high-shear events toward a broad peak at 35o<ϴ<65o. The azimuthal φ-angles of the CS normal directions of 430 thick dcs≥500 di exhausts are consistent with a dominant Parker-spiral magnetic field and a CS normal along the ortho-Parker direction. The CS normal orientations of 370 kinetic-scale dcs<25 di exhausts are isotropic in contrast, and likely associated with Alfvénic solar wind turbulence. We propose that the alignment of exhaust normal directions from narrow dcs~15-25 di widths to well beyond dcs~500 di with an ortho-Parker azimuthal direction of a large-scale HCS is a consequence of CS bifurcation and turbulence within the HCS exhaust that may trigger reconnection of the adjacent pair of bifurcated CSs. The proposed HCS-31 avalanche scenario suggests that the underlying large-scale parent HCS closer to the Sun evolves with heliocentric distance to fracture into many, more or less aligned, secondary current sheets due to reconnection. A few wide exhaust-associated HCS-like CSs could represent a population of HCSs that failed to reconnect as frequently between the Sun and 1 AU as other HCSs.

Stefan Eriksson↗

Ejected Particle Size Distributions from Shocked Metal Surfaces

Here, we present size distributions for particles ejected from features machined onto the surface of shocked Sn targets. The functional form of the size distributions is assumed to be log-normal, and the characteristic parameters of the distribution are extracted from the measured angular distribution of light scattered from a laser beam incident on the ejected particles. We also found strong evidence for a bimodal distribution of particle sizes with smaller particles evolved from features machined into the target surface and larger particles being produced at the edges of these features.

36 MATERIALS SCIENCE↗

Modal representations in control/structure interaction

When control/structure interaction problems are examined, a standard method for representing the structure is to choose a truncated set of normal modes calculated from either a finite-element or a distributed-parameter model. However, the normal modes can neglect important static information about the structure. Using a set of fixed interface modes results in a much more accurate closed-loop model, even when relatively low-bandwidth controllers are used. The fixed interface modes are calculated with control input degrees of freedom held fixed, and standard finite-element software can be used. Illustrative examples include a simple hinged beam and a complex model of the phase-I Space Station configuration.

Blelloch, Paul A.↗

Current distributions by moving vortices in superconductors

We take account of normal currents that emerge when vortices move. Abrikosov vortices in the bulk and Pearl vortices in thin films are considered. Velocity dependent distributions of both normal and persistent currents are studied in the frame of time-dependent London equations. In thin films near the Pearl vortex core, these distributions are intriguing in particular.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Pressure dependence of Kapitza resistance at gold/water and silicon/water interfaces

We conducted non-equilibrium molecular dynamics simulations to investigate Kapitza length at solid/liquid interfaces under the effects of bulk liquid pressures. Gold and silicon were utilized as hydrophilic and hydrophobic solid walls with different wetting surface behaviors, while the number of confined liquid water molecules was adjusted to obtain different pressures inside the channels. The interactions of solid/liquid couples were reparameterized accurately by measuring the water contact angle of solid substrates. In this paper, we present a thorough analysis of the structure, normal stress, and temperature distribution of liquid water to elucidate thermal energy transport across interfaces. Our results demonstrate excellent agreement between the pressures of liquid water in nano-channels and published thermodynamics data. The pressures measured as normal stress components were characterized using a long cut-off distance reinforced by a long-range van der Waals tail correction term. To clarify the effects of bulk liquid pressures on water structure at hydrophilic and hydrophobic solid surfaces, we defined solid/liquid interface spacing as the distance between the surface and the peak value of the first water density layer. Near the gold surface, we found that interface spacing and peak value of first water density layer were constant and did not depend on bulk liquid pressure; near the silicon surface, those values depended directly upon bulk liquid. Our results reveal that the pressure dependence of Kapitza length strongly depends on the wettability of the solid surface. In the case of the hydrophilic gold surface, Kapitza length was stable despite increasing bulk liquid pressure, while it varied significantly at the hydrophobic silicon surface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Differential distributions for t-channel single top-quark production and decay at next-to-next-to-leading order in QCD

We present a detailed phenomenological study of the next-to-next-to-leading order (NNLO) QCD corrections for t-channel single top (anti-)quark production and its semi-leptonic decay at the CERN Large Hadron Collider (LHC). We find the NNLO corrections for the total inclusive rates at the LHC with different center of mass energies are generally smaller than the NLO corrections, indicative of improved convergence. However, they can be large for differential distributions, reaching a level of 10% or more in certain regions of the transverse momentum distributions of the top (anti-)quark and the pseudo-rapidity distributions of the leading jet in the event. In all cases the perturbative hard-scale uncertainties are greatly reduced after the NNLO corrections are included. We also show a comparison of the normalized parton-level distributions to recent data from the 8 TeV measurement of the ATLAS collaboration. The NNLO corrections tend to shift the theoretical predictions closer to the measured transverse momentum distribution of the top (anti)-quark. Importantly, for the LHC at 13 TeV, we present NNLO cross sections in a fiducial volume with decays of the top quark included.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

The pressure distribution over a standard and a modified Navy elliptical wing tip on a biplane in flight

This note presents the results of flight pressure distribution tests on the right upper wing panel of a Douglas M-3 airplane equipped in turn with a standard Navy elliptical tip and a tip having the same plan form but modified in its front elevation from the swept-up aspect of the standard tip to a symmetrical aspect. The results are given in such form that the load distribution for any normal-force coefficient within the usual range encountered in flight may easily be determined. The results indicate that the modification in front elevation of the tip had no appreciable effect on the load distribution.

Rhode, Richard V↗

Preliminary Results on Applying Nonparametric Clustering and Bayesian Consensus Clustering Methods to Multimodal Data

In this report, we present preliminary research into nonparametric clustering methods for multi-source imagery data and quantifying the performance of these models. In many domain areas, data sets do not necessarily follow well-defined and well-known probability distributions, such as the normal, gamma, and exponential. This is especially true when combining data from multiple sources describing a common set of objects (which we call multimodal analysis), where the data in each source can follow different distributions and need to be analyzed in conjunction with one another. This necessitates nonparametric density estimation methods, which allow the data to better dictate the distribution of the data. One prominent example of multimodal analysis is multimodal image analysis, when we analyze multiple images taken using different radar systems of the same scene of interest. We develop uncertainty analysis methods, which are inherent in the use of probabilistic models but often not taken advance of, to assess the performance of probabilistic clustering methods used for analyzing multimodal images. This added information helps assess model performance and how much trust decision-makers should have in the obtained analysis results. The developed methods illustrate some ways in which uncertainty can inform decisions that arise when designing and using machine learning models.

42 ENGINEERING↗

Jet radius dependence of dijet momentum balance and suppression in Pb + Pb collisions at 5.02 TeV with the ATLAS detector

This paper describes a measurement of the jet radius dependence of the dijet momentum balance between leading back-to-back jets in 1.72 nb -1 of Pb + Pb collisions collected in 2018 and 255 pb -1 of pp collisions collected in 2017 by the ATLAS detector at the LHC. Both datasets were collected at $\sqrt{s_{NN}}$ = 5.02 TeV. Jets are reconstructed using the anti-k t algorithm with jet radius parameters R = 0.2, 0.3, 0.4, 0.5, and 0.6. The dijet momentum balance distributions are constructed for leading jets with transverse momentum p T from 100 to 562 GeV for R = 0.2, 0.3, and 0.4 jets, and from 158 to 562 GeV for R = 0.5 and 0.6 jets. The absolutely normalized dijet momentum balance distributions are constructed to compare measurements of the dijet yields in Pb + Pb collisions directly to the dijet cross sections in pp collisions. For all jet radii considered here, there is a suppression of more balanced dijets in Pb + Pb collisions compared with pp collisions, while for more imbalanced dijets there is an enhancement. There is a jet radius dependence to the dijet yields, being stronger for more imbalanced dijets than for more balanced dijets. Additionally, jet pair nuclear modification factors are measured. The subleading jet yields are found to be more suppressed than leading jet yields in dijets. A jet radius dependence of the pair nuclear modification factors is observed, with the suppression decreasing with increasing jet radius. These measurements provide new constraints on jet quenching scenarios in the quark-gluon plasma.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

SIMULATED HUMAN ERROR PROBABILITY AND ITS APPLICATION TO DYNAMIC HUMAN FAILURE EVENTS

Abstract Objectives: Human reliability analysis (HRA) methods typically analyze human failure events (HFEs) at the overall task level. For dynamic HRA, it is important to model human activities at the subtask level. There exists a disconnect between dynamic subtask level and static task level that presents issues when modeling dynamic scenarios. For example, the SPAR-H method is typically used to calculate the human error probability (HEP) at the task level. As demonstrated in this paper, quantification in SPAR-H does not translate to the subtask level. Methods: Two different discrete distributions were generated for each SPAR-H Performance Shaping Factor (PSF) to define the frequency of PSF levels. The first distribution was a uniform, or uninformed distribution that assumed the frequency of each PSF level was equally likely. The second non-continuous distribution took the frequency of PSF level as identified from an assessment of the HERA database. These two different approaches were created to identify the resulting distribution of the HEP. The resulting HEP that appears closer to the known distribution, a log-normal centered on 1E-3, is the more desirable. Each approach then has median, average and maximum HFE calculations applied. To calculate these three values, three events, A, B and C are generated from the PSF level frequencies comprised of subtasks. The median HFE selects the median PSF level from each PSF and calculates HEP. The average HFE takes the mean PSF level, and the maximum takes the maximum PSF level. The same data set of subtask HEPs yields starkly different HEPs when aggregated to the HFE level in SPAR-H. Results: Assuming that each PSF level in each HFE is equally likely creates an unrealistic distribution of the HEP that is centered at 1. Next the observed frequency of PSF levels was applied with the resulting HEP behaving log-normally with a majority of the values under 2.5% HEP. The median, average and maximum HFE calculations did yield different answers for the HFE. The HFE maximum grossly over estimates the HFE, while the HFE distribution occurs less than HFE median, and greater than HFE average. Conclusions: Dynamic task modeling can be perused through the framework of SPAR-H. Identification of distributions associated with each PSF needs to be defined, and may change depending upon the scenario. However it is very unlikely that each PSF level is equally likely as the resulting HEP distribution is strongly centered at 100%, which is unrealistic. Other distributions may need to be identified for PSFs, to facilitate the transition to dynamic task modeling. Additionally discrete distributions need to be exchanged for continuous so that simulations for the HFE can further advance. This paper provides a method to explore dynamic subtask to task translation and provides examples of the process using the SPAR-H method.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Monitoring Airspace Complexity and Determining Contributing Factors

The national airspace has evolved over many years to accommodate increased traffic demand [1] while simultaneously maintaining one of the safest forms of transportation [2], [3]. One of the reasons for this success is the ability of the system and the operators to adapt and accommodate to situations that routinely disrupt optimal operations. These situations may include: adverse weather, delays, early arrivals, equipment outages, and other factors that are outside the operators ability to control. These factors can lead to states where automation is unable to properly handle these issues and therefore air traffic controllers and pilots have to intervene, ultimately increasing communication between operators resulting in higher workload. As controller workload increases to handle sub-optimal operating conditions this can be viewed as an increase in complexity. The reasoning for this is because humans are now required to make tactical decisions in response to external factors, resulting in a departure from the strategic plan where operations would be more efficiently managed. Human operators control airspace complexity under rigid regulations that are constantly changing. The airspace is divided into sectors and the number of aircraft assigned to each controller is limited for safe handling. There has been past work that devised airspace complexity metrics in commercial aviation and related these metrics to controller workload (e.g., [4],[5]). The upper bounds on the system load are pre-determined. Such bounds on complexity make for a safe system, but the system cannot scale and adapt to autonomous, dense, and heterogeneous traffic, including the many types of Unmanned Aerial Vehicles (UAVs) envisioned to be added to the operations. We hypothesize that, as traffic density and heterogeneity grow, and other key metrics change, there will be phase transitions at which the way traffic should be managed changes significantly [6]. We offer a method for in-time detection of contributing factors that lead to phase transitions, characterized by increased complexity. To the best of our knowledge, there is no tool similar to our proposed effort that identifies such contributing factors or precursor patterns. To define the scope we are proposing to measure complexity from the viewpoint of the Terminal Radar Approach Control Facilities (TRACON) controller’s perspective. In particular we are analyzing arrivals into KSFO. With safety as the top concern for airspace operators, it is important to recognize that as density and heterogeneity grow, the focus of the system will change. Times of the day when the airspace has low density and heterogeneity, the flights will follow more efficient paths where the aircraft move on established routes that are more or less directly to the destination. However, when density and heterogeneity increases, the system will begin changing focus to avoiding conflicts and collisions and route the flights in a more flexible way. Higher flexibility requires more communication and coordination between controllers and pilots which the current automation is unable to handle. This paper proposes a novel approach that monitors airspace complexity at multiple scales, uses a Machine Learning-based tool that predicts when operations will transition to a regime of greater complexity, and identifies actions that can reduce the complexity while still maintaining efficient and safe operations. We demonstrate our proposed approach using data from multiple complementary sources. This includes, but is not limited to: historical aircraft surveillance data from NASA’s Sherlock Data Warehouse [7], METAR weather data, and airport configuration data from Aviation System Performance Metrics (ASPM). The surveillance data flight paths are sampled at a variable sample rate — increasing as the aircraft approaches the airport. This is due to how Sherlock manages flight track stitching between different radar facilities which have different sampling rates. The weather and performance data are logged at defined intervals throughout the day at a courser refresh rate. In addition to the logged data and metrics, we leverage pre-defined Standard Terminal Arrival Routes (STARs) procedures to characterize the path of each flight. Each flight files for one of these routes in the flight plan well before entering the terminal airspace, and approximately follows the route until it leaves the STAR, typically on the final fix of a runway transition. However, most flights do not always fly the full STAR procedure to completion [8], but the majority do adhere to the fixes within the common route of the procedure. Our approach leverages fixes in the common route of each of the STARs to build a reference path to the airport. This allows us to characterize the flight paths in what we are defining as the “maneuvering area” (the airspace between the STAR and before the flight is lined up on the runway’s final approach) to determine how off nominal the flights are to calculate its complexity score. Determining airspace complexity is a concept that does not have a concrete answer. In designing this metric, we consider what increases the workload for the air traffic controllers. Consequently more specialized vectoring maneuvers results in higher workload. Accordingly, we start with a theory: each flight has a direct path it takes from the STAR’s common route to the final approach’s outer marker fix for the flight’s landing runway. It is important to note that the direct path is only used as a reference. If the majority of the flights have a large consistent offset as compared to other routes it does not necessarily mean that those flights have higher complexity. We are merely building a distribution based on this direct path for that particular STAR and runway pair to determine the normal mode of operations for that route. Flights that are in the upper tail of these distributions will result in higher complexity scores and flights that fly in the median will represent the normal mode of operations and therefore will have lower complexity scores. Since flights following each STAR route take different paths to the airport, we have a different distribution for each STAR route and therefore can model these distributions to compute a complexity score from their respective normalized distributions. To evaluate the effectiveness of our proposed airspace complexity metric we will compare against an established approach based on trajectory clustering [9]. This unsupervised learning technique consists of the following steps: (1) identify the general maneuvering areas (waypoints) by performing $\kappa$-means or DBSCAN clustering on locations where aircraft frequently turn based on the surveillance radar track data, (2) map flight trajectories onto sequences of waypoints, and (3) cluster the sequences based on their common subsequences. From a high-level perspective, this baseline model learns nominal operations in the airspace through the sequence of waypoints that are representative of where aircraft change direction and defines deviations from the nominal operations as “complex.” Therefore, more deviations from the nominal operations correspond to higher complexity values. For our validation, we re-implemented this technique and tune model hyper-parameters to correctly detect waypoints for the arrival traffic into the San Francisco bay area. We will compute the complexity measure over a one-year period using our proposed technique as well as the baseline. Our validation will be based on each technique’s ability to detect a set of undesirable outcomes (e.g., go-arounds, holding patterns, average time in the airspace, etc.). Since our current complexity metric is derived from the offset from the direct reference path, it’s important to understand what causes these offsets. In many of the flights with high offset distance, flights performing holding patterns and S turns can be observed. These maneuvering tactics are utilized to add distance between the aircraft and the destination runway to prevent multiple flights from having conflicting arrival times. In order to predict a rise in complexity (or the precursor to complexity), it’s necessary to be able to identify these potential conflicts (which in turn, result in higher offsets). To do this, we define a “representative flight” for each STAR route and runway pair. This flight is approximately the path the flight would take if there was a clear path with no other flights in the airspace — including the time remaining to the airport. We first identify the flights for a given STAR runway pair using the offset to the reference path distributions that fall between the 44-55 percentiles. This yields the flights that conform to the most normal mode of operation. Each of these flights is partitioned based on the percent complete from the entry point into the maneuvering areas from 0\% – 100\% complete. Then for each percent “bin”, we take the median value of the flight’s latitude/longitude coordinates, airspeed, and (non causal) time remaining to the airport to construct a lookup table for each percent complete bin on a given route. As a flight enters the maneuvering area, we can find the estimated arrival time of a flight to the airport by finding the closest point to the representative path’s percent complete bin (relative to the flight’s current position at any snapshot in the airspace) and therefore retrieve the corresponding remaining time left on the “representative path”. We assume that the flight will follow the representative path to completion when deriving these estimates. We can then compare these estimated arrival times against other flights for the same snapshot in time to identify potential conflicts. If more flights are estimated to arrive within a tolerance window than there are runways available, then we have a potential conflict. We can use this derived measure along with other factors expected to add disruption to the operation such as weather and runway configuration changes as an input to machine learning tools to detect precursors that increases in our complexity measure. This novel method will assist in uncovering insights into the contributing factors that lead to increased complexity that may allow for in-time responses to avoid reaching a high complexity state in the airspace.

complexity↗

Combustion Instabilities Modeled

NASA Lewis Research Center's Advanced Controls and Dynamics Technology Branch is investigating active control strategies to mitigate or eliminate the combustion instabilities prevalent in lean-burning, low-emission combustors. These instabilities result from coupling between the heat-release mechanisms of the burning process and the acoustic flow field of the combustor. Control design and implementation require a simulation capability that is both fast and accurate. It must capture the essential physics of the system, yet be as simple as possible. A quasi-one-dimensional, computational fluid dynamics (CFD) based simulation has been developed which may meet these requirements. The Euler equations of mass, momentum, and energy have been used, along with a single reactive species transport equation to simulate coupled thermoacoustic oscillations. A very simple numerical integration scheme was chosen to reduce computing time. Robust boundary condition procedures were incorporated to simulate various flow conditions (e.g., valves, open ends, and choked inflow) as well as to accommodate flow reversals that may arise during large flow-field oscillations. The accompanying figure shows a sample simulation result. A combustor with an open inlet, a choked outlet, and a large constriction approximately two thirds of the way down the length is shown. The middle plot shows normalized, time-averaged distributions of the relevant flow quantities, and the bottom plot illustrates the acoustic mode shape of the resulting thermoacoustic oscillation. For this simulation, the limit cycle peak-to-peak pressure fluctuations were 13 percent of the mean. The simulation used 100 numerical cells. The total normalized simulation time was 50 units (approximately 15 oscillations), which took 26 sec on a Sun Ultra2.

Paxson, Daniel E.↗

An Experimental and Computational Study on Soot Formation in a Coflow Jet Flame Under Microgravity and Normal Gravity

Upon the completion of the Structure and Liftoff in Combustion Experiment (SLICE) in March 2012, a comprehensive and unique set of microgravity coflow diffusion flame data was obtained. This data covers a range of conditions from weak flames near extinction to strong, highly sooting flames, and enabled the study of gravitational effects on phenomena such as liftoff, blowout and soot formation. The microgravity experiment was carried out in the Microgravity Science Glovebox (MSG) on board the International Space Station (ISS), while the normal gravity experiment was performed at Yale utilizing a copy of the flight hardware. Computational simulations of microgravity and normal gravity flames were also carried out to facilitate understanding of the experimental observations. This paper focuses on the different sooting behaviors of CH4 coflow jet flames in microgravity and normal gravity. The unique set of data serves as an excellent test case for developing more accurate computational models.Experimentally, the flame shape and size, lift-off height, and soot temperature were determined from line-of-sight flame emission images taken with a color digital camera. Soot volume fraction was determined by performing an absolute light calibration using the incandescence from a flame-heated thermocouple. Computationally, the MC-Smooth vorticity-velocity formulation was employed to describe the chemically reacting flow, and the soot evolution was modeled by the sectional aerosol equations. The governing equations and boundary conditions were discretized on an axisymmetric computational domain by finite differences, and the resulting system of fully coupled, highly nonlinear equations was solved by a damped, modified Newtons method. The microgravity sooting flames were found to have lower soot temperatures and higher volume fraction than their normal gravity counterparts. The soot distribution tends to shift from the centerline of the flame to the wings from normal gravity to microgravity.

microgravity↗

The zonal distribution of hydrogen in the Jovian atmosphere

The Lyman-alpha intensities measured by Voyagers 1 and 2 and by the IUE are used as the bases of deductions for the distribution of atomic hydrogen in the Jovian atmosphere, under the assumption that the sources of the dayside Lyman alpha include resonance scattering of solar Lyman alpha, resonance scattering of the interplanetary Lyman-alpha radiation, and direct excitation by charged particles. The daytime equation of radiative transfer is solved to determine the longitudinal distribution of freely scattering atomic hydrogen that would account for the observed flux. This solution indicates that if the hydrogen bulge is due to localized heating and a consequent increase in scale height, the perturbed region temperature must be about 100 K warmer than that in the normal region. The H distribution derived from the dayside solution is used with the nightside flux to estimate the longitude variation of particle precipitation on the nightside.

Killen, R. M.↗