Prediction of electron density and collision cross section. Volume 2 - Equilibrium electron density prediction, a mathematical model Final report
Mathematical model for prediction of electron density at equilibrium
Mc Dermit, J. H.↗
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Semi-Automated Creation of Density Functional Tight Binding Models through Leveraging Chebyshev Polynomial-Based Force Fields
Density functional tight binding (DFTB) is an attractive method for accelerated quantum simulations of condensed matter due to its enhanced computational efficiency over standard density functional theory (DFT) approaches. However, DFTB models can be challenging to determine for individual systems of interest, especially for metallic and interfacial systems where different bonding arrangements can lead to significant changes in electronic states. In this regard, we have created a rapid-screening approach for determining systematically improvable DFTB interaction potentials that can yield transferable models for a variety of conditions. Our method leverages a recent reactive molecular dynamics force field where many-body interactions are represented by linear combinations of Chebyshev polynomials. This allows for the efficient creation of multi-center representations with relative ease, requiring only a small investment in initial DFT calculations. Here, we have focused our workflow on TiH 2 as a model system and show that a relatively small training set based on unit-cell-sized calculations yields a model accurate for both bulk and surface properties. Our approach is easy to implement and can yield reliable DFTB models over a broad range of thermodynamic conditions, where physical and chemical properties can be difficult to interrogate directly and there is historically a significant reliance on theoretical approaches for interpretation and validation of experimental results.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Electron Density and Two-Channel Neutron Emission Measurements in Steady-State Spherical Inertial-Electrostatically Confined Plasmas, with Review of the 1-D Kinetic Model
Electron density measurements have been made in steady-state plasmas in a spherical inertial electrostatic confinement (IEC) discharge using microwave interferometry. Plasma cores interior to two cathodes, having diameters of 15 and 23 cm, respectively, were probed over a transverse range of 10 cm with a spatial resolution of about 1.4 cm for buffer gas pressures from 0.2 to 6 Pa in argon and deuterium. The transverse profiles are generally flat, in some cases with eccentric symmetric minima, and give mean densities of from approx. = 0.4 to 7x 10(exp 10)/cu cm, the density generally increasing with the neutral gas pressure. Numerical solutions of the 1-D Poisson equation for EC plasmas are reviewed and energy distribution functions are identified which give flat transverse profiles. These functions are used with the plasma approximation to obtain solutions which also give densities consistent with the measurements, and a double potential well solution is obtained which has minima qualitatively similar to those observed. Explicit consideration is given to the compatibility of the solutions interior and exterior to the cathode, and to grid transparency. Deuterium fusion neutron emission rates were also measured and found to be isotropic, to within the measurement error, over two simultaneous directions. Anisotropy was observed in residual emissions during operation with non-fusing hydrogen-1. The deuterium rates are consistent with predictions from the model.
Dobson, Chris C.↗
Automated Processing of ISIS Topside Ionograms into Electron Density Profiles
Modeling of the topside ionosphere has for the most part relied on just a few years of data from topside sounder satellites. The widely used Bent et al. (1972) model, for example, is based on only 50,000 Alouette 1 profiles. The International Reference Ionosphere (IRI) (Bilitza, 1990, 2001) uses an analytical description of the graphs and tables provided by Bent et al. (1972). The Alouette 1, 2 and ISIS 1, 2 topside sounder satellites of the sixties and seventies were ahead of their times in terms of the sheer volume of data obtained and in terms of the computer and software requirements for data analysis. As a result, only a small percentage of the collected topside ionograms was converted into electron density profiles. Recently, a NASA-funded data restoration project has undertaken and is continuing the process of digitizing the Alouette/ISIS ionograms from the analog 7-track tapes. Our project involves the automated processing of these digital ionograms into electron density profiles. The project accomplished a set of important goals that will have a major impact on understanding and modeling of the topside ionosphere: (1) The TOPside Ionogram Scaling and True height inversion (TOPIST) software was developed for the automated scaling and inversion of topside ionograms. (2) The TOPIST software was applied to the over 300,000 ISIS-2 topside ionograms that had been digitized in the fkamework of a separate AISRP project (PI: R.F. Benson). (3) The new TOPIST-produced database of global electron density profiles for the topside ionosphere were made publicly available through NASA s National Space Science Data Center (NSSDC) ftp archive at . (4) Earlier Alouette 1,2 and ISIS 1, 2 data sets of electron density profiles from manual scaling of selected sets of ionograms were converted fiom a highly-compressed binary format into a user-friendly ASCII format and made publicly available through nssdcftp.gsfc.nasa.gov. The new database for the topside ionosphere established as a result of this project, has stimulated a multitude of new studies directed towards a better description and prediction of the topside ionosphere. Marinov et al. (2004) developed a new model for the upper ion transition height (Oxygen to Hydrogen and Helium) and Bilitza (2004) deduced a correction term for the I N topside electron density model. Kutiev et al. (2005) used this data to develop a new model for the topside ionosphere scale height (TISH) as a function of month, local time, latitude, longitude and solar flux F10.7. Comparisons by Belehaki et al. (2005) show that TISH is in general agreement with scale heights deduced from ground ionosondes but the model predicts post-midnight and afternoon maxima whereas the ionosonde data show a noon maximum. Webb and Benson (2005) reported on their effort to deduce changes in the plasma temperature and ion composition from changes in the topside electron density profile as recorded by topside sounders. Limitations and possible improvements of the IRI topside model were discussed by Coisson et al. (2005) including also the possible use of the NeQuick model, Our project progressed in close collaboration and coordination with the GSFC team involved in the ISIS digitization effort. The digitization project was highly successful producing a large amount of digital topside ionograms. Several no-cost extensions of the TOPIST project were necessary to keep up with the pace and volume of the digitization effort.
Reinisch, bodo W.↗
Electron Density and Two-Channel Neutron Emission Measurements in Steady-State Spherical Inertial-Electrostatically Confined Plasmas, with Review of the One-Dimensional Kinetic Model
Electron density measurements have been made in steady-state plasmas in a spherical inertial electrostatic confinement (IEC) discharge using microwave interferometry. Plasma cores interior to two cathodes, having diameters of 15 and 23 cm, respectively, were probed over a transverse range of 10 cm with a spatial resolution of about 1.4 cm for buffer gas pressures from 0.2 to 6 Pa in argon and deuterium. The transverse profiles are generally flat, in some cases with eccentric symmetric minima, and give mean densities of from approx. = 0.4 to 7 x 10(exp 10)/cu cm, the density generally increasing with the neutral gas pressure. Numerical solutions of the one-dimensional Poisson equation for IEC plasmas are reviewed and energy distribution functions are identified which give flat transverse profiles. These functions are used with the plasma approximation to obtain solutions which also give densities consistent with the measurements, and a double potential well solution is obtained which has minima qualitatively similar to those observed. Explicit consideration is given to the compatibility of the solutions interior and exterior to the cathode, and to grid transparency. Deuterium fusion neutron emission rates were also measured and found to be isotropic, to within the measurement error, over two simultaneous directions. Anisotropy was observed in residual emissions during operation with nonfusing hydrogen- 1. The deuterium rates are consistent with predictions from the model.
Dobson, Chris C.↗
A model of F2 peak electron densities in the main trough region of the ionosphere
An empirical model of the peak electron densities in the region of the northerly main trough in the ionospheric F region is presented. The model was derived from measurements made by the satellites Alouette I and II and is in the form of a multiplicative modification factor to the CCIR peak electron density model. The model is a computer program which, when provided with the location, universal time, day number, sunspot number, and Kp index, provides the modification factor, the CCIR model prediction of Nm F2, and the new prediction including the effect of the trough. The model is expected to be of considerable use for propagation calculations in the affected region.
Halcrow, B. W.↗
On the theoretical model for vertical ozone density distributions in the mesosphere and upper stratosphere.
Calculations based on an improved, time-dependent theoretical model for the vertical ozone density distribution in the upper atmosphere are shown to clarify the cause and determine the appearance precondition for the depression at the 70-85 km altitude region in the ozone density distribution suggested by several theoretical models and only sometimes experimentally observed. It is concluded that the depression develops at night through the effects of hydrogen-oxygen and nitrogen-oxygen reactions, as well as those of eddy diffusion transports.
Shimazaki, T.↗
The problem of using Mariner IV ionospheric densities to deduce a model of the Martian atmospheric structure.
Mariner 4 ionospheric densities to deduce Martian atmospheric modes, discussing validity of using ionospheric properties to discriminate between models
Donahue, T. M.↗
All Recent Mars Landers Have Landed Downrange - Are Mars Atmosphere Models Mis-Predicting Density?
All recent Mars landers (Mars Pathfinder, the two Mars Exploration Rovers Spirit and Opportunity, and the Mars Phoenix Lander) have landed further downrange than their pre-entry predictions. Mars Pathfinder landed 27 km downrange of its prediction [1], Spirit and Opportunity landed 13.4 km and 14.9 km, respectively, downrange from their predictions [2], and Phoenix landed 21 km downrange from its prediction [3]. Reconstruction of their entries revealed a lower density profile than the best a priori atmospheric model predictions. Do these results suggest that there is a systemic issue in present Mars atmosphere models that predict a higher density than observed on landing day? Spirit Landing: The landing location for Spirit was 13.4 km downrange of the prediction as shown in Fig. 1. The navigation errors upon Mars arrival were very small [2]. As such, the entry interface conditions were not responsible for this downrange landing. Consequently, experiencing a lower density during the entry was the underlying cause. The reconstructed density profile that Spirit experienced is shown in Fig. 2, which is plotted as a fraction of the pre-entry baseline prediction that was used for all the entry, descent, and landing (EDL) design analyses. The reconstructed density is observed to be less dense throughout the descent reaching a maximum reduction of 15% at 21 km. This lower density corresponded to approximately a 1- low profile relative to the dispersions predicted. Nearly all the deceleration during the entry occurs within 10- 50 km. As such, prediction of density within this altitude band is most critical for entry flight dynamics analyses and design (e.g., aerodynamic and aerothermodynamic predictions, landing location, etc.).
Desai, Prasun N.↗
Investigating 3,4-bis(3-nitrofurazan-4-yl)furoxan detonation with a rapidly tuned density functional tight binding model
In this work, we describe a machine learning approach to rapidly tune density functional tight binding models for the description of detonation chemistry in organic molecular materials. Resulting models enable simulations on the several 10s of ps scales characteristic to these processes, with “quantum-accuracy.” We use this approach to investigate early shock chemistry in 3,4-bis(3-nitrofurazan-4-yl)furoxan, a hydrogen-free energetic material known to form onion-like nanocarbon particulates following detonation. We find that the ensuing chemistry is significantly characterized by the formation of large C x N y O z species, which are likely precursors to the experimentally observed carbon condensates. Beyond utility as a means of investigating detonation chemistry, the present approach can be used to generate quantum-based reference data for the development of full machine-learned interatomic potentials capable of simulation on even greater time and length scales, i.e., for applications where characteristic time scales exceed the reach of methods including Kohn–Sham density functional theory, which are commonly used for reference data generation.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
The problem of using Mariner IV IONOSPHERIC densities to deduce a model of the Martian atmospheric structure
Martian atmosphere model deduced from Mariner IV IONOSPHERE electron density measurements
MARINER IV SPACE PROBE↗
A kinematic eddy viscosity model including the influence of density variations and preturbulence
A model for the kinematic eddy viscosity was developed which accounts for the turbulence produced as a result of jet interactions between adjacent streams as well as the turbulence initially present in the streams. In order to describe the turbulence contribution from jet interaction, the eddy viscosity suggested by Prandtl was adopted, and a modification was introduced to account for the effect of density variation through the mixing layer. The form of the modification was ascertained from a study of the compressible turbulent boundary layer on a flat plate. A kinematic eddy viscosity relation which corresponds to the initial turbulence contribution was derived by employing arguments used by Prandtl in his mixing length hypothesis. The resulting expression for self-preserving flow is similar to that which describes the mixing of a submerged jet. Application of the model has led to analytical predictions which are in good agreement with available turbulent mixing experimental data.
Cohen, L. S.↗
Aerodynamic Models for the Low Density Supersonic Declerator (LDSD) Supersonic Flight Dynamics Test (SFDT)
An overview of pre-flight aerodynamic models for the Low Density Supersonic Decelerator (LDSD) Supersonic Flight Dynamics Test (SFDT) campaign is presented, with comparisons to reconstructed flight data and discussion of model updates. The SFDT campaign objective is to test Supersonic Inflatable Aerodynamic Decelerator (SIAD) and large supersonic parachute technologies at high altitude Earth conditions relevant to entry, descent, and landing (EDL) at Mars. Nominal SIAD test conditions are attained by lifting a test vehicle (TV) to 36 km altitude with a large helium balloon, then accelerating the TV to Mach 4 and and 53 km altitude with a solid rocket motor. The first flight test (SFDT-1) delivered a 6 meter diameter robotic mission class decelerator (SIAD-R) to several seconds of flight on June 28, 2014, and was successful in demonstrating the SFDT flight system concept and SIAD-R. The trajectory was off-nominal, however, lofting to over 8 km higher than predicted in flight simulations. Comparisons between reconstructed flight data and aerodynamic models show that SIAD-R aerodynamic performance was in good agreement with pre-flight predictions. Similar comparisons of powered ascent phase aerodynamics show that the pre-flight model overpredicted TV pitch stability, leading to underprediction of trajectory peak altitude. Comparisons between pre-flight aerodynamic models and reconstructed flight data are shown, and changes to aerodynamic models using improved fidelity and knowledge gained from SFDT-1 are discussed.
Van Norman, John W.↗
Experimental validation of thermodynamic mixture rules at extreme pressures and densities
Accurate modeling of a mixed material Equation of State (EOS) at high pressures (~1 to 100 Mbar) is critical for simulating inertial confinement fusion and high energy density systems. Here, this paper presents a comparison of two mixing rule models to the experiment to assess their applicability in this regime. The shock velocities of polystyrene, aluminum, and nickel aluminide (NiAl) were measured at a shock pressure of ~3 TPa (~30 Mbar) on the Omega EP laser facility (Laboratory for Laser Energetics, University of Rochester, New York). The resultant shock velocities were compared to those derived from the RAGE (Eulerian) hydrodynamics code to validate various mixing rules used to construct an EOS for NiAl. The simulated shock transit time through the sample (Al or NiAl) matched the measurements to within the ±45ps measurement uncertainty. The law of partial volume (Amagat) and the law of partial pressure (Dalton) mixture rules provided equally good matches to the NiAl shock data. Other studies showed that the Amagat mixing rule is superior, and we recommend it since our results also show a satisfactory match. In conclusion, the comparable quality of the simulation to data for the Al and NiAl samples implies that a mixture rule can supply an EOS for plasma mixtures with adequate fidelity for simulations where mixing takes place, such as advective mix in an Eulerian code or when two materials are mixed together via diffusion, turbulence, or other physical processes.
36 MATERIALS SCIENCE↗
Comprehensive uncertainty quantification (UQ) for full engineering models by solving probability density function (PDF) equation
This report details a new method for propagating parameter uncertainty (forward uncertainty quantification) in partial differential equations (PDE) based computational mechanics applications. The method provides full-field quantities of interest by solving for the joint probability density function (PDF) equations which are implied by the PDEs with uncertain parameters. Full-field uncertainty quantification enables the design of complex systems where quantities of interest, such as failure points, are not known apriori. The method, motivated by the well-known probability density function (PDF) propagation method of turbulence modeling, uses an ensemble of solutions to provide the joint PDF of desired quantities at every point in the domain. A small subset of the ensemble is computed exactly, and the remainder of the samples are computed with approximation of the driving (dynamics) term of the PDEs based on those exact solutions. Although the proposed method has commonalities with traditional interpolatory stochastic collocation methods applied directly to quantities of interest, it is distinct and exploits the parameter dependence and smoothness of the dynamics term of the governing PDEs. The efficacy of the method is demonstrated by applying it to two target problems: solid mechanics explicit dynamics with uncertain material model parameters, and reacting hypersonic fluid mechanics with uncertain chemical kinetic rate parameters. A minimally invasive implementation of the method for representative codes SPARC (reacting hypersonics) and NimbleSM (finite- element solid mechanics) and associated software details are described. For solid mechanics demonstration problems the method shows order of magnitudes improvement in accuracy over traditional stochastic collocation. For the reacting hypersonics problem, the method is implemented as a streamline integration and results show very good accuracy for the approximate sample solutions of re-entry flow past the Apollo capsule geometry at Mach 30.
42 ENGINEERING↗
Mathematical model predictions and optimization study of the gamma ray atmospheric density sensor
Mathematical model predictions and optimization study of gamma ray atmospheric density sensor
Gardner, R. P.↗
What is the source of observed annual variations in plasmaspheric density?
Plasmaspheric densities have been observed previously to be higher in December than in June, with the ratio varying between 1.5 and 3.0 and with larger variations at lower L shells. In order to search for the cause of the observed annual variations, we have modeled plasmaspheric density, using a time-dependent hydrodynamic model. On an L = 2 field line with geomagnetic longitude equal to 300 deg, the modeled plasmaspheric densities were a factor of 1.5 times higher in December than in June. The modeled December to June density ratio was found to increase slightly with L shell, in contrast to observations; this discrepancy may be due to the fact that outer plasmaspheric flux tubes are never completely full. In addition, for an L = 2 field line with geomagnetic longitude equal to 120 deg, the modeled plasmaspheric density was higher in June than in December by a factor of about 1.2. Various numerical tests were also performed in order to examine the sensitivity of plasmaspheric density to various parameters. In particular, a large vertical neutral wind was applied in order to raise the O(+) profile which had the effect of raising plasmaspheric density by a factor of 6. This in conjunction with a theoretical analysis suggests that plasmaspheric density levels are very sensitive to O(+) levels in the upper ionosphere. We conclude that annual variations in plasmaspheric density are due to similar variations in ionospheric O(+).
Guiter, S. M.↗
Electrochemical CO2 Reduction over Metal-/Nitrogen-Doped Graphene Single-Atom Catalysts Modeled Using the Grand-Canonical Density Functional Theory
Renewably driven, electrochemical conversion of carbon dioxide into value-added products is expected to be a critical tool in global decarbonization. However, theoretical studies based on the computational hydrogen electrode largely ignore the nonlinear effects of the applied potential on the calculated results, leading to inaccurate predictions of catalytic behavior or mechanistic pathways. Here, we use grand canonical density functional theory (GC-DFT) to model electrochemical CO2 reduction (CO2R) over metal- and nitrogen-doped graphene catalysts (MNCs) and explicitly include the effects of the applied potential. We used GC-DFT to compute the CO2 to CO reaction intermediate energies at -0.3, -0.7, and -1.2 VSHE catalyzed by MNCs each doped with 1 of the 10 3d block metals coordinated by four pyridinic nitrogen atoms. Our results predict that Sc-, Ti-, Co-, Cu-, and Zn-N4Cs effectively catalyze CO2R at moderate to large reducing potentials (-0.7 to -1.2 VSHE). ZnN4C is a particularly promising electrocatalyst for CO2R to CO both at low and moderate applied potentials based on our thermodynamic analysis. Our findings also explain the observed pH independence of CO production over FeN4C and predict that the rate-determining step of CO2R over FeN4C is not *CO2- formation but rather *CO desorption. Additionally, the GC-DFT-computed density of states analysis illustrates how the electronic states of MNCs and adsorbates change non-uniformly with applied potential, resulting in a significantly increased *CO2- stability relative to other intermediates and demonstrating that the formation of the adsorbed *CO2- anion is critical to CO2R activation. This work demonstrates how GC-DFT paves the way for physically realistic and accurate theoretical simulations of reacting electrochemical systems.
CO2 reduction↗