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DOE OSTI2015

Electronic structures of [001]- and [111]-oriented InSb and GaSb free-standing nanowires

We report on a theoretical study of the electronic structures of InSb and GaSb nanowires oriented along the [001] and [111] crystallographic directions. The nanowires are described by atomistic, tight-binding models, including spin-orbit interaction. The band structures and the wave functions of the nanowires are calculated by means of a Lanczos iteration algorithm. For the [001]-oriented InSb and GaSb nanowires, the systems with both square and rectangular cross sections are considered. Here, it is found that all the energy bands are doubly degenerate. Although the lowest conduction bands in these nanowires show good parabolic dispersions, the top valence bands show rich and complex structures. In particular, the topmost valence bands of the nanowires with a square cross section show a double maximum structure. In the nanowires with a rectangular cross section, this double maximum structure is suppressed, and the top valence bands gradually develop into parabolic bands as the aspect ratio of the cross section is increased. For the [111]-oriented InSb and GaSb nanowires, the systems with hexagonal cross sections are considered. It is found that all the bands at the Γ-point are again doubly degenerate. However, some of them will split into non-degenerate bands when the wave vector moves away from the Γ-point. Although the lowest conduction bands again show good parabolic dispersions, the topmost valence bands do not show the double maximum structure. Instead, they show a single maximum structure with its maximum at a wave vector slightly away from the Γ-point. The wave functions of the band states near the band gaps of the [001]- and [111]-oriented InSb and GaSb nanowires are also calculated and are presented in terms of probability distributions in the cross sections. It is found that although the probability distributions of the band states in the [001]-oriented nanowires with a rectangular cross section could be qualitatively described by one-band effective mass theory, the probability distributions of the band states in the [001]-oriented nanowires with a square cross section and the [111]-oriented nanowires with a hexagonal cross section show characteristic patterns with symmetries closely related to the irreducible representations of the relevant double point groups and, in general, go beyond the prediction of a simple one-band effective mass theory. We also investigate the effects of quantum confinement on the band structures of the [001]- and [111]-oriented InSb and GaSb nanowires and present an empirical formula for the description of quantization energies of the band edge states in the nanowires, which could be used to estimate the enhancement of the band gaps of the nanowires as a result of quantum confinement. The size dependencies of the electron and hole effective masses in these nanowires are also investigated and discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2016

California Reservoir Inflow Projections Using a Hybrid EMD-Matalas Method

Inflow projections provide scenarios for future water availability and are integral to operational reservoir management. They can aid water practitioners in decision-making for conservation efforts, multiyear storage retention, managing flood risk, downstream water releases, and regional growth planning. However, conventional methods are often limited in terms of their ability to incorporate non-stationarity, long run persistence, and the cross-correlation of multiple series in a region. This research aims to address these issues with a hybrid approach that integrates Empirical Mode Decomposition (EMD) with the Matalas multisite generation method. Multiple long-run inflows were examined for the Shasta/Trinity Reservoirs and Oroville Reservoir of California. EMD is used to decompose each inflow series into a set of independent intrinsic mode functions (IMFs) that have different timescales and frequencies. These IMFs were grouped into intradecadal (less-than- 10-year average periodicity) and interdecadal (greater-than-10-year average periodicity) series for each site. The IMF projections at each site were then combined to produce replicates of the historical data. This preserves the correlation structure of the intra- and interdecadal components of the series. The hybrid EMD-Matalas method was compared to a traditional autoregressive lag-one model. Both methods were found to retain the statistical characteristics of the historical data. However, the EMD-Matalas method retained the multiyear wet and dry periods to a greater degree. This was examined by comparing the 5-year and 10-year sums from the traditional model with the hybrid EMD-Matalas model. An advantage of the EMD-Matalas method is the ability to explicitly incorporate modes of non-stationary long-run persistence often associated with large-scale climate drivers such as the El Nino Southern Oscillation (ENSO) or the Pacific Decadal Oscillation (PDO). This contributes to scenario planning that may be particularly important for managing multiyear low flow periods.

inflow projections↗

NASA NTRS2011

Computational Validation of a Two-Dimensional Semi-Empirical Model for Inductive Coupling in a Conical Pulsed Inductive Plasma Thruster

A two-dimensional semi-empirical model of pulsed inductive thrust efficiency is developed to predict the effect of such a geometry on thrust efficiency. The model includes electromagnetic and gas-dynamic forces but excludes energy conversion from radial motion to axial motion, with the intention of characterizing thrust efficiency loss mechanisms that result from a conical versus a at inductive coil geometry. The range of conical pulsed inductive thruster geometries to which this model can be applied is explored with the use of finite element analysis. A semi-empirical relation for inductance as a function of current sheet radial and axial position is the limiting feature of the model, restricting the applicability as a function of half cone angle to a range from ten degrees to about 60 degrees. The model is nondimensionalized, yielding a set of dimensionless performance scaling parameters. Results of the model indicate that radial current sheet motion changes the axial dynamic impedance parameter at which thrust efficiency is maximized. This shift indicates that when radial current sheet motion is permitted in the model longer characteristic circuit timescales are more efficient, which can be attributed to a lower current sheet axial velocity as the plasma more rapidly decouples from the coil through radial motion. Thrust efficiency is shown to increase monotonically for decreasing values of the radial dynamic impedance parameter. This trend indicates that to maximize the radial decoupling timescale should be long compared to the characteristic circuit timescale.

Hallock, Ashley K.↗

NASA NTRS2004

An Effective Initial Mass Function for Galactic Disks

We derive a semi-empirical effective galactic initial mass function (IMF), which represents the IMF averaged over the age of the galactic disk, from observational constraints. We assume that the star formation rate in a galaxy can be expressed as the product of the IMF,psi(m), which is a smooth function of mass m (in units of solar mass), and a time and space dependent rate zeta(sub *1). The mass dependence of the proposed IMF is determined by four parameters: the low-mass slope gamma, the high-mass slope -Gamma, the characteristic mass m(sub ch) at which the IMF turns over, and the upper limit on the mass, m(sub u).

Hollenbach, David↗

NASA NTRS1984

The Influence of Synoptic Scales on Low-frequency Modes of Variability

Model analysis and predictablity studies using an equivalent barotropic empirical orthogonal function (EOF) model described in Schubert (1984b) are dicussed. An extensive set of 10-day forecasts was produced for the 12 component version of the model. Comparisons with observed data show apparently useful forecasts for individual winters. However, when averaged over 10 winters, the improvement over persistence was marginal and only one of the EOF's (resembling North Atlantic blocking) showed a statistically significant improvement. These results suggest the need for a more realistic model which includes shorter time scale baroclinic processes and spatial modes capable of efficiently representing the characteristic structures associated with baroclinic instability.

Schubert, S. D.↗

NASA NTRS2014

Developing an Empirical Model for Jet-Surface Interaction Noise

The process of developing an empirical model for jet-surface interaction noise is described and the resulting model evaluated. Jet-surface interaction noise is generated when the high-speed engine exhaust from modern tightly integrated or conventional high-bypass ratio engine aircraft strikes or flows over the airframe surfaces. An empirical model based on an existing experimental database is developed for use in preliminary design system level studies where computation speed and range of configurations is valued over absolute accuracy to select the most promising (or eliminate the worst) possible designs. The model developed assumes that the jet-surface interaction noise spectra can be separated from the jet mixing noise and described as a parabolic function with three coefficients: peak amplitude, spectral width, and peak frequency. These coefficients are fit to functions of surface length and distance from the jet lipline to form a characteristic spectra which is then adjusted for changes in jet velocity and/or observer angle using scaling laws from published theoretical and experimental work. The resulting model is then evaluated for its ability to reproduce the characteristic spectra and then for reproducing spectra measured at other jet velocities and observer angles; successes and limitations are discussed considering the complexity of the jet-surface interaction noise versus the desire for a model that is simple to implement and quick to execute.

Brown, Clifford A.↗

NASA NTRS2014

Developing an Empirical Model for Jet-Surface Interaction Noise

The process of developing an empirical model for jet-surface interaction noise is described and the resulting model evaluated. Jet-surface interaction noise is generated when the high-speed engine exhaust from modern tightly integrated or conventional high-bypass ratio engine aircraft strikes or flows over the airframe surfaces. An empirical model based on an existing experimental database is developed for use in preliminary design system level studies where computation speed and range of configurations is valued over absolute accuracy to select the most promising (or eliminate the worst) possible designs. The model developed assumes that the jet-surface interaction noise spectra can be separated from the jet mixing noise and described as a parabolic function with three coefficients: peak amplitude, spectral width, and peak frequency. These coefficients are t to functions of surface length and distance from the jet lipline to form a characteristic spectra which is then adjusted for changes in jet velocity and/or observer angle using scaling laws from published theoretical and experimental work. The resulting model is then evaluated for its ability to reproduce the characteristic spectra and then for reproducing spectra measured at other jet velocities and observer angles; successes and limitations are discussed considering the complexity of the jet-surface interaction noise versus the desire for a model that is simple to implement and quick to execute.

Brown, Clif↗

NASA NTRS1984

Arc-driven rail gun research

The equations describing the performance of an inductively-driven rail gun are analyzed numerically. Friction between the projectile and rails is included through an empirical formulation. The equations are applied to the experiment of Rashleigh and Marshall to obtain an estimate of energy distribution in rail guns as a function of time. The effect of frictional heat dissipation on the bore of the gun is calculated. The mechanism of plasma and projectile acceleration in a dc rail gun is described from a microscopic point of view through the establishment of the Hall field. The plasma conductivity is shown to be a tensor indicating that there is a small component of current parallel to the direction of acceleration. The plasma characteristics are evaluated as a function of plasma mass through a simple fluid mechanical analysis of the plasma. By equating the energy dissipated in the plasma with the radiation heat loss, the properties of the plasma are determined.

Ray, P. K.↗

NASA NTRS1994

The discrete and localized nature of the variable emission from active regions

Using data from the Extreme Ultraviolet (EUV) Spectroheliometer on Skylab, we study the empirical characteristics of the variable emission in active regions. These simultaneous multi-wavelength observations clearly confirm that active regions consist of a complex of loops at different temperatures. The variable emission from this complex has very well-defined properties that can be quantitatively summarized as follows: (1) It is localized predominantly around the footpoints where it occurs at discrete locations. (2) The strongest variability does not necessarily coincide with the most intense emission. (3) The fraction of the area of the footpoints, (delta n)/N, that exhibits variable emission, varies by +/- 15% as a function of time, at any of the wavelengths measured. It also varies very little from footpoint to footpoint. (4) This fractional variation is temperature dependent with a maximum around 10(exp 5) K. (5) The ratio of the intensity of the variable to the average background emission, (delta I)/(bar-I), also changes with temperature. In addition, we find that these distinctive characteristics persist even when flares occur within the active region.

Arndt, Martina Belz↗

NASA NTRS2007

Ignition Characterization Test Results for the LO2/Ethanol Propellant Combination

A series of contracts were issued by the Marshall Space Flight Center (MSFC) of the National Aeronautics and Space Administration (NASA) un der the auspices of the Exploration Systems Mission Directorate to de velop and expand the maturity of candidate technologies considered to be important for future space exploration. One such technology was to determine the viability of incorporating non-toxic propellants for R eaction Control Subsystems (RCS). Contract NAS8-01109 was issued to A erojet to develop a dual thrust Reaction Control Engine (RCE) that ut ilized liquid oxygen and ethanol as the propellants. The dual thrust RCE incorporated a primary thrust level of 870 lbf, and a vernier thru st level of 10 - 30 lbf. The preferred RCS approach for the dual thru st RCE was to utilize pressure-fed liquid oxygen (LOX) and ethanol pr opellants; however, previous dual thrust feasibility testing incorporated GOX/Ethanol igniters as opposed to LOX/Ethanol igniters in the de sign. GOX/Ethanol was easier to ignite, but this combination had syst em design implications of providing GOX for the igniters. A LOX/Ethan ol igniter was desired; however, extensive LOX/Ethanol ignition data over the anticipated operating range for the dual thrust RCE did not e xist. Therefore, Aerojet designed and tested a workhorse LOX igniter to determine LOX/Ethanol ignition characteristics as part of a risk m itigation effort for the dual thrust RCE design. The objective of the ignition testing was to demonstrate successful ignition from GOX to LOX, encompassing potential two-phase flow conditions anticipated being present in real mission applications. A workhorse igniter was desig ned to accommodate the full LOX design flowrate, as well as a reduced GOX flowrate. It was reasoned that the initial LOX flow through the igniter would flash to GOX due to the latent heat stored in the hardwa re, causing a reduced oxygen flowrate because of a choked, or sonic, flow condition through the injection elements. As LOX flow continued, the hardware would chill-in, with the injected oxygen flow transitioning from cold GOX through two'phase flow to subcooled LOX. The Workh orse igniter was well instrumented: Pressure and temperature instrumentation permitted oxygen state points to be determined in the igniter oxidizer manifold, and gas-side igniter chamber thermocouples provide d chamber thermal profile characteristics. The cold flow chamber pres sure (Pc) for each test was determined and coupled with the igniter chamber diameter (De) to calculate the characteristic quench parameter (Pc x Dc), which was plotted as a function of core mixture ratio, MRc . Ignition limits were determined over a broad range of valve inlet conditions, and ignition was demonstrated with oxygen inlet conditions that ranged from subcooled 210 deg R LOX to 486 deg R GOX. Once ign ited at cold GOX conditions, combustion was continuous as the hardwar e chilled in and the core mixture ratio transitioned from values near 1.0 to over 12.5. Pulsing is required in typical RCS engines; therefore, the workhorse igniter was pulse tested to verify the ability to pr ovide the required ignition for a pulsing RCE. The minimum electrical pulse width (EPW) of the dual thrust RCE was 0.080 seconds. Igniter pulse tests were performed at three conditions: (1) an EPW of 0.080 se conds at 25% duty cycle for 400 pulses; (2) an EPW of 0.160 seconds a nd a 5% duty cycle for 124 pulses; (3) an EPW of 0.160 seconds and a 50% duty cycle for 380 pulses. Successful ignition of LOX/Ethanol was demonstrated over a broad range of valve inlet conditions, with the empirically determined LOX/Ethanol ignition limits extending the previous database established for GOX/Ethanol ignition limits. Although th e observed chill-in characteristics of the hardware varied significan tly with flowrate, ignition was readily achieved. Combustion was marg inal at extremely fuel-rich conditions, and it fluctuated as the oxygen passed rough the twophase flow regime during the period of hardware chill-in. Pulse testing showed good repeatability with 100 percent r e-ignition for all pulses. Certain pulse-to-pulse repeatability requirements for actual RCS operation may necessitate establishment of mini mum oxygen flow rates and engine thrust levels for satisfactory engin e performance.

Robinson, Philip J.↗

DOE OSTI2020

Reynolds-Averaged Turbulence Modeling Using Deep Learning with Local Flow Features: An Empirical Approach

Reynolds-Averaged Navier-Stoke (RANS) models offer an alternative avenue in predicting flow characteristics when the corresponding experiments are difficult to achieve due to geometry complexity, limited budget, or knowledge. RANS models require the knowledge of subgrid scale physics to solve conservation equations for mass, energy, and momentum. Mechanistic turbulence models, such as k-epsilon, are generally evaluated and calibrated for specific flow conditions with various degrees of uncertainty. These models have limited capability to assimilate a substantial amount of data due to model form constraints. Meanwhile, deep learning (DL) has been proven to be universal approximators with the potential to assimilate available, relevant, and adequately evaluated data. Moreover, deep neural networks (DNNs) can create surrogate models without knowing function forms. Such a data-driven approach can be used in updating fluid models based on observations as opposed to hard-wiring models with precalibrated correlations. The paper presents progress in applying DNNs to model Reynolds stress using two machine learning (ML) frameworks. A novel flow feature coverage mapping is proposed to quantify the physics coverage of DL-based closures. It can be used to examine the sufficiency of training data and input flow features for data-driven turbulence models. The case of a backward-facing step is formulated to demonstrate that not only can DNNs discover underlying correlation behind fluid data but also they can be implemented in RANS to predict flow characteristics without numerical stability issues. Finally, the presented research is a crucial stepping-stone toward the data-driven turbulence modeling, which potentially benefits the design of data-driven experiments that can be used to validate fluid models with ML-based fluid closures.

42 ENGINEERING↗

DOE OSTI2022

Anomalies in the topology of the temperature fluctuations in the cosmic microwave background: An analysis of the NPIPE and FFP10 data releases

We present a topological analysis of the temperature fluctuation maps from the Planck 2020 Data Release 4 NPIPE dataset and the Planck 2018 Data Release 3 FFP10 dataset. We performed a multiscale analysis in terms of the homology characteristics of the maps, invoking relative homology to account for the analysis in the presence of masks. We performed our analysis for a range of smoothing scales spanning sub- and super-horizon scales corresponding to a full width at half maximum (FWHM) of 5',10',20',40',80',160',320', and 640', and employed simulations based on the standard model for comparison, which assumes the initial fluctuation field to be an isotropic and homogeneous Gaussian random field. Examining the behavior of topological components, represented by the 0D homology group, we find the observations to be approximately 2σ or less deviant from the simulations for all resolutions and scales for the NPIPE dataset. For the FFP10 dataset, we detect a 2.96σ deviation between the observations and simulations at N = 128, FWHM = 80'. For the topological loops, represented by the first homology group, the simulations and observations are consistent within 2σ for most resolutions and scales for both the datasets. However, for the NPIPE dataset, we observe a high deviation between the observation and simulations in the number of loops at FWHM = 320', but at a low dimensionless threshold ν = –2.5. Under a Gaussian assumption, this would amount to a deviation of ~4σ. However, the distribution in this bin is manifestly non-Gaussian and does not obey Poisson statistics either. In the absence of a true theoretical understanding, we simply note that the significance is higher than what may be resolved by 600 simulations, yielding an empirical p-value of at most 0.0016. Specifically in this case, our tests indicate that the numbers arise from a statistically stable regime, despite being based on small numbers. For the FFP10 dataset, the differences are not as strong as for the NPIPE dataset, indicating a 2.77σ deviation at this resolution and threshold. The Euler characteristic, which is the alternating sum of the ranks of relative homology groups, reflects the deviations in the components and loops. To assess the significance of combined levels for a given scale, we employed the empirical and theoretical versions of the χ 2 test as well as the nonparametric Tukey depth test. Although all statistics exhibit a stable distribution, we favor the empirical version of the χ 2 test in the final interpretation, as it indicates the most conservative differences. For the NPIPE dataset, we find that the components and loops differ at more than 95%, but agree within the 99% confidence level with respect to the base model at N = 32, FWHM = 320'. The Euler characteristic at this resolution displays a per mil deviation. In contrast, the FFP10 dataset shows that the observations are consistent with the base model within the 95% confidence level, at this and smaller scales. This is consistent with the observations of the Planck analysis pipeline via Minkowski functionals. For the largest smoothing scale, N = 16, FWHM = 640', both datasets exhibit an anomalous behavior of the loops, where FFP10 data exhibit a deviation that is larger by an order of magnitude than that of the NPIPE dataset. In contrast, the values for the topological components and the Euler characteristic agree between observations and model to within a confidence level of 99%. However, for the largest scales, the statistics are based on low numbers and may have to be regarded with caution. Even though both datasets exhibit mild to significant discrepancies, they also exhibit contrasting behaviors at various instances. Therefore, we do not find it feasible to convincingly accept or reject the null hypothesis. Disregarding the large-scale anomalies that persist at similar scales in WMAP and Planck, observations of the cosmic microwave background are largely consistent with the standard cosmological model within 2σ.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1990

LB 1800 - A bright eclipsing cataclysmic variable and a transient X-ray source

The star LB 1800 has been discovered to be a 13th mag high-excitation cataclysmic variable exhibiting novalike characteristics and partial eclipses in its light curve. It has subsequently been identified as the optical counterpart of the transient hard X-ray source 4U 0608-49 following analysis of HEAO 1 data. Both the radial velocity and photometric variations have a period of 5.56 hr, while the K-velocity of the relatively uncomplicated radial velocity curves is 134 + or - 9 km/s, leading to a mass function of 0.058 + or - 0.003 solar mass. The dynamical and eclipse solutions point to an orbital inclination of 87 deg + or - 3 deg and a mass ratio of 0.46 + or - 0.04 for the empirical secondary mass 0.55 solar mass. The implied white dwarf mass is therefore quite high at about 1.2 solar mass. The disk size, from timings of first and last contact, was estimated to be very close to that of the secondary star. Phase-dependent, double-peak emission lines are sometimes observed. It is argued that the orbital variations in the relative strengths of the red and blue peaks arise from changing hot-spot visibility.

Buckley, D. A. H.↗

NASA NTRS2013

Analyzing Tropical Waves Using the Parallel Ensemble Empirical Model Decomposition Method: Preliminary Results from Hurricane Sandy

In this study, we discuss the performance of the parallel ensemble empirical mode decomposition (EMD) in the analysis of tropical waves that are associated with tropical cyclone (TC) formation. To efficiently analyze high-resolution, global, multiple-dimensional data sets, we first implement multilevel parallelism into the ensemble EMD (EEMD) and obtain a parallel speedup of 720 using 200 eight-core processors. We then apply the parallel EEMD (PEEMD) to extract the intrinsic mode functions (IMFs) from preselected data sets that represent (1) idealized tropical waves and (2) large-scale environmental flows associated with Hurricane Sandy (2012). Results indicate that the PEEMD is efficient and effective in revealing the major wave characteristics of the data, such as wavelengths and periods, by sifting out the dominant (wave) components. This approach has a potential for hurricane climate study by examining the statistical relationship between tropical waves and TC formation.

PEEMD↗

DOE OSTI2015

Online residence time distribution measurement of thermochemical biomass pretreatment reactors

Residence time is a critical parameter that strongly affects the product profile and overall yield achieved from thermochemical pretreatment of lignocellulosic biomass during production of liquid transportation fuels. The residence time distribution (RTD) is one important measure of reactor performance and provides a metric to use when evaluating changes in reactor design and operating parameters. An inexpensive and rapid RTD measurement technique was developed to measure the residence time characteristics in biomass pretreatment reactors and similar equipment processing wet-granular slurries. Sodium chloride was pulsed into the feed entering a 600 kg/d pilot-scale reactor operated at various conditions, and aqueous salt concentration was measured in the discharge using specially fabricated electrical conductivity instrumentation. This online conductivity method was superior in both measurement accuracy and resource requirements compared to offline analysis. Experimentally measured mean residence time values were longer than estimated by simple calculation and screw speed and throughput rate were investigated as contributing factors. In conclusion, a semi-empirical model was developed to predict the mean residence time as a function of operating parameters and enabled improved agreement.

09 BIOMASS FUELS↗

NASA NTRS1989

A detailed model of electrothermal propulsion systems

A semi-empirical model is presented which describes the operating characteristics of resistojet and arcjet engines. Propellants considered include hydrogen, ammonia and hydrazine. Specific engine design and performance correlations are derived from previously published contractor reports, conference and journal papers of the past three decades. Fundamental performance relationships are identified and correlating parameters derived to describe engine operation over a wide range of input powers and propellant mass flow rates. Outputs are presented from a computer program formulated using these modeling relationships. Comparisons are made with present electrothermal engine designs and examples are presented to illustrate the usefulness of the models in predicting engine operation as a function of changes in engine geometry and operating modes.

Aston, Graeme↗

NASA NTRS2009

Tin Whisker Electrical Short Circuit Characteristics

Existing risk simulations make the assumption that when a free tin whisker has bridged two adjacent exposed electrical conductors, the result is an electrical short circuit. This conservative assumption is made because shorting is a random event that has an unknown probability associated with it. Note however that due to contact resistance electrical shorts may not occur at lower voltage levels. In our first article we developed an empirical probability model for tin whisker shorting. In this paper, we develop a more comprehensive empirical model using a refined experiment with a larger sample size, in which we studied the effect of varying voltage on the breakdown of the contact resistance which leads to a short circuit. From the resulting data we estimated the probability distribution of an electrical short, as a function of voltage. In addition, the unexpected polycrystalline structure seen in the focused ion beam (FIB) cross section in the first experiment was confirmed in this experiment using transmission electron microscopy (TEM). The FIB was also used to cross section two card guides to facilitate the measurement of the grain size of each card guide's tin plating to determine its finish.

Courey, Karim J.↗

NASA NTRS1978

Effect of the Mott cross section on the determination of the charge of ultraheavy cosmic rays from emulsion tracks

Energy deposition due to secondary electrons is calculated as a function of distance from the axis of the track of a heavy ion. The calculation incorporates the empirical formulas of Kobetich and Katz (1968) for delta-ray energy dissipation. Both the Mott and Born-approximation expressions for the delta-ray energy distributions are used, and the results are compared. The energy deposition projected along a line perpendicular to the track is also calculated. These results are used to estimate the effect that the use of the Mott cross section would have in the interpretation of photometric measurements on emulsion tracks of trans-iron cosmic-ray particles. It is shown that the use of 50 keV as a characteristic track-formation electron energy to estimate the effect of the Mott cross section systematically overestimates charge as derived from emulsions for Z greater than 20.

Eby, P. B.↗