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Tutorial: Langevin Dynamics methods for aerosol particle trajectory simulations and collision rate constant modeling

The Langevin Dynamics (LD) method (also known in the literature as Brownian Dynamics) is routinely used to simulate aerosol particle trajectories for transport rate constant calculations as well as to understand aerosol particle transport in internal and external fluid flows. This tutorial intends to explain the methodological details of setting up a LD simulation of a population of aerosol particles and to deduce rate constants from an ensemble of classical trajectories. We discuss the applicability and limitations of the translational Langevin equation to model the combined stochastic and deterministic motion of particles in fields of force or fluid flow. The drag force and stochastic “diffusion” force terms that appear in the Langevin equation are discussed elaborately, along with a summary of common forces relevant to aerosol systems (electrostatic, gravity, van der Waals, …); a commonly used first order and a fourth order Runge-Kutta time stepping schemes for linear stochastic ordinary differential equations are presented. A MATLAB® implementation of a LD code for simulating particle settling under gravity using the first order scheme is included for illustration. Scaling analysis of aerosol transport processes and the selection of timestep and domain size for trajectory simulations are demonstrated through two specific aerosol processes: particle diffusion charging and coagulation. Fortran® implementations of the first order and fourth order time-stepping schemes are included for simulating the 3D motion of a particle in a periodic domain. Lastly, potential applications and caveats to the usage of LD are included as a summary.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Radio Occultation Studies of Venus' Atmosphere with Magellan

We have been conducting a systematic study of the middle and lower atmosphere of Venus through analysis of 20 radio occultation experiments conducted with the Magellan spacecraft between October, 1991, and August, 1994. These studies have revealed a rich but sparsely sampled trove of information regarding the structure, composition and dynamics of the Venus atmosphere. The five sets of experiments sampled a variety of latitudes. Basic results include vertical profiles of: (1) electron density in the ionosphere, (2) pressure, temperature, density, and static stability in the neutral atmosphere (from 33 km to 98 km), and (3) sulfuric acid vapor (H2SO4) abundance below the main cloud deck. Further analysis of the temperature profiles led to the discovery of small vertical-scale gravity waves in the neutral atmosphere. The retrieved profiles show intriguing zonal variations that might be due to planetary- scale waves. During the performance period of this grant, we have concentrated on reanalyzing the 15 experiments conducted in 1994 using improved trajectory files for Magellan provided by JPL, obtaining more reliable results, and on conducting an error analysis of the derived profiles. In addition, we have begun an analysis of microwave emission maps of Venus obtained at the Very Large Array (VLA) in April, 1996. This report is organized as follows: A summary of results is presented, giving representative examples of the various physical profiles retrieved from all the Magellan radio occultation studies, emphasizing latitudinal variations evident in the data. Next, a preliminary analysis of the VLA maps is given. A summary of activities follows the scientific results, detailing papers published and presented at various conferences. This report concludes with a "Conclusions and Suggestions for Future Work" section.

Jenkins, Jon M.↗

Regression Analysis of Top of Descent Location for Idle-thrust Descents

In this paper, multiple regression analysis is used to model the top of descent (TOD) location of user-preferred descent trajectories computed by the flight management system (FMS) on over 1000 commercial flights into Melbourne, Australia. The independent variables cruise altitude, final altitude, cruise Mach, descent speed, wind, and engine type were also recorded or computed post-operations. Both first-order and second-order models are considered, where cross-validation, hypothesis testing, and additional analysis are used to compare models. This identifies the models that should give the smallest errors if used to predict TOD location for new data in the future. A model that is linear in TOD altitude, final altitude, descent speed, and wind gives an estimated standard deviation of 3.9 nmi for TOD location given the trajec- tory parameters, which means about 80% of predictions would have error less than 5 nmi in absolute value. This accuracy is better than demonstrated by other ground automation predictions using kinetic models. Furthermore, this approach would enable online learning of the model. Additional data or further knowl- edge of algorithms is necessary to conclude definitively that no second-order terms are appropriate. Possible applications of the linear model are described, including enabling arriving aircraft to fly optimized descents computed by the FMS even in congested airspace. In particular, a model for TOD location that is linear in the independent variables would enable decision support tool human-machine interfaces for which a kinetic approach would be computationally too slow.

trajectory prediction↗

Center of mass estimation in closed vortices - A verification in principle and practice

The problem of tracking closed mesoscale vortices using center of mass estimation techniques is studied. Three estimators are evaluated using data from a warm core Gulf Stream ring. The comparisons show that a method based on the intersection of perpendicular bisectors and one using a least-squares fit of a conic section perform comparably. The perpendicular bisector algorithm is used in conjunction with a Gaussian ring model and a star-shaped survey pattern to produce an expected error curve as a function of vortex translation, survey speed and vortex size. For typical ring parameters, center estimation is usually possible to within + or - 5 km. The feasibility of using differing data sets to construct a history of ring motion based on a coordinate system moving with the ring is also investigated. In this way, the validity of using satellite-derived data and drifter trajectories to estimate the center of mass of a mesoscale feature is assessed. The results of the analysis demonstrate that the location of the deeper structure of the ring and the surface expression are sufficiently well correlated to permit dynamically relevant calculations based on surface measurements. It is shown that satellite-derived data can be used to approximate the center of mass trajectory to within the error in the individual center estimates for the period analyzed. The Lagrangian-drifter-derived centers are offset from the center of mass trajectory in a manner consistent with kinematic arguments.

Hooker, S. B.↗

Aerodynamics for the Mars Phoenix Entry Capsule

Pre-flight aerodynamics data for the Mars Phoenix entry capsule are presented. The aerodynamic coefficients were generated as a function of total angle-of-attack and either Knudsen number, velocity, or Mach number, depending on the flight regime. The database was constructed using continuum flowfield computations and data from the Mars Exploration Rover and Viking programs. Hypersonic and supersonic static coefficients were derived from Navier-Stokes solutions on a pre-flight design trajectory. High-altitude data (free-molecular and transitional regimes) and dynamic pitch damping characteristics were taken from Mars Exploration Rover analysis and testing. Transonic static coefficients from Viking wind tunnel tests were used for capsule aerodynamics under the parachute. Static instabilities were predicted at two points along the reference trajectory and were verified by reconstructed flight data. During the hypersonic instability, the capsule was predicted to trim at angles as high as 2.5 deg with an on-axis center-of-gravity. Trim angles were predicted for off-nominal pitching moment (4.2 deg peak) and a 5 mm off-axis center-ofgravity (4.8 deg peak). Finally, hypersonic static coefficient sensitivities to atmospheric density were predicted to be within uncertainty bounds.

Edquist, Karl T.↗

Passive Thermal Control for the Low Density Supersonic Decelerator (LDSD) Test Vehicle Spin Motors Sub-System

Future missions to Mars will require improved entry, descent, and landing (EDL) technology over the Viking-heritage systems which recently landed the largest payload to date, the 900 kg Mars Science Laboratory. As a result, NASA's Low Density Supersonic Decelerator (LDSD) project is working to advance the state of the art in Mars EDL systems by developing and testing three key technologies which will enable heavier payloads and higher altitude landing sites on the red planet. These technologies consist of a large 33.5 m diameter Supersonic Disk Sail (SSDS) parachute and two different Supersonic Inflatable Aerodynamic Decelerator (SIAD) devices - a robotic class that inflates to a 6 m diameter torus (SIAD-R), and an exploration class that inflates to an 8 m diameter isotensoid (SIADE). All three technologies will be demonstrated on test vehicles at high earth altitudes in order to simulate the Mars EDL environment. Each vehicle will be carried to altitude by a large helium balloon, released, spun up using spin motors to stabilize the vehicle's trajectory, and accelerated to supersonic speeds using a large solid rocket motor. The vehicle will then be spun down using another set of spin motors, and will deploy either the SIAD-R or SIAD-E, followed by the SSDS parachute until the vehicle lands in the ocean. Component level testing and bounding analysis are used to ensure the survival of system components in extreme thermal environments and predict temperatures throughout the flight. This paper presents a general description of the thermal testing, model correlation, and analysis of the spin motor passive thermal control sub-system to maintain spin motor performance, prescribed vehicle trajectory, and structural integrity of the test vehicle. The spin motor subsystem is predicted to meet its requirements with margin.

thermal analysis↗

Aerothermal Analysis of the Project Fire II Afterbody Flow

Computational fluid dynamics (CFD) is used to simulate the wake flow and afterbody heating of the Project Fire II ballistic reentry to Earth at 11.4 km/sec. Laminar results are obtained over a portion of the trajectory between the initial heat pulse and peak afterbody heating. Although non-catalytic forebody convective heating results are in excellent agreement with previous computations, initial predictions of afterbody heating were about a factor of two below the experimental values. Further analysis suggests that significant catalysis may be occurring on the afterbody heat shield. Computations including finite-rate catalysis on the afterbody surface are in good agreement with the data over the early portion of the trajectory, but are conservative near the peak afterbody heating point, especially on the rear portion of the conical frustum. Further analysis of the flight data from Fire II shows that peak afterbody heating occurs before peak forebody heating, a result that contradicts computations and flight data from other entry vehicles. This result suggests that another mechanism, possibly pyrolysis, may be occurring during the later portion of the trajectory, resulting in less total heat transfer than the current predictions.

Wright, Michael J.↗

Impact of Saturn's rings on mission analysis for MJS 77

Mariner Jupiter-Saturn '77 mission objectives for Saturn are considered which affect the trajectory design and in particular the aim point at Saturn. These objectives include the following: (1) earth, sun occulation of Saturn, rings, and satellites; (2) close as possible to surface; (3) close as possible to rings; (4) close encounter with Titan (approximately 20,000 km); (5) close encounter with lapetus; (6) multiple satellite encounters; (7) post-Saturn trajectory to Uranus; and (8) post-Saturn trajectory toward solar apex.

Penzo, P. A.↗

Development of a method for optimal maneuver analysis of complex space missions

A system that allows mission planners to find optimal multiple-burn space trajectories easily is described. Previously developed methods with different gravity assumptions perform the optimization function. The power of these programs is extended by a method of costate estimation. A penalty function method of constraining coast arc times to be positive is included. The capability of the method is demonstrated by finding the optimal control for three different space missions. These include a shuttle abort-once-around mission and two- and three-burn geosynchronous satellite-placement missions.

Mcadoo, S. F., Jr.↗

The effects of spaceflight on open-loop and closed-loop postural control mechanisms: human neurovestibular studies on SLS-2

Stabilogram-diffusion analysis was used to examine how prolonged periods in microgravity affect the open-loop and closed-loop postural control mechanisms. It was hypothesized that following spaceflight: (1) the effective stochastic activity of the open-loop postural control schemes in astronauts is increased; (2) the effective stochastic activity and uncorrelated behavior, respectively, of the closed-loop postural control mechanisms in astronauts are increased; and (3) astronauts utilized open-loop postural controls schemes for shorter time intervals and smaller displacements. Four crew members and two alternates from the 14-day Spacelab Life Sciences 2 Mission were included in the study. Each subject was tested under eyes-open, quiet-standing conditions on multiple preflight and postflight days. The subjects' center-of-pressure trajectories were measured with a force platform and analyzed according to stabilogram-diffusion analysis. It was found that the effective stochastic activity of the open-loop postural control schemes in three of the four crew members was increased following spaceflight. This result is interpreted as an indication that there may be in-flight adaptations to higher-level descending postural control pathways, e.g., a postflight increase in the tonic activation of postural muscles. This change may also be the consequence of a compensatory (e.g., "stiffening") postural control strategy that is adopted by astronauts to account for general feeling of postflight unsteadiness. The crew members, as a group, did not exhibit any consistent preflight/postflight differences in the steady-state behavior of their closed-loop postural control mechanisms or in the functional interaction of their open-loop and closed-loop postural control mechanisms. These results are interpreted as indications that although there may be in-flight adaptations to the vestibular system and/or proprioceptive system, input from the visual system can compensate for such changes during undisturbed stance.

NASA Program Flight↗

Bringing Molecular Dynamics Simulation Data into View

Molecular Dynamics (MD) simulations monitor time-resolved motions of macromolecules. While visualization of MD trajectories allows an instant and intuitive understanding of dynamics and function, so far mainly static representations are provided in published literature. Recent advances in browser technology may allow for the sharing of trajectories through interactive visualization on the web. We believe that by providing intuitive and interactive visualization along with related protocols and analysis data promotes understanding, reliability, and re-usability of MD simulations. Existing barriers for sharing MD simulations are discussed and emerging solutions are highlighted. We predict that interactive visualization of MD trajectories will quickly be adopted by researchers, research consortiums, journals, and funding agencies to gather and distribute results from MD simulations via the web.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Scalable Analysis Methods and In Situ Infrastructure for Extreme Scale Knowledge Discovery

High performance computers have for many years been on a trajectory that gives them extraordinary compute power with the addition of more and more compute cores. At the same time, other system parameters such as the amount of memory per core and bandwidth to storage have remained constant or have barely increased. This creates an imbalance in the computer, giving it the ability to compute a lot of data that it cannot reasonably save out due to time and storage constraints. While technologies have been invented to mitigate this problem (burst buffers, etc.), software has been adapting to employ in situ libraries which perform data analysis and visualization on simulation data while it is still resident in memory. This avoids the need to ever have to pay the costs of writing many terabytes of data files. Instead, in situ enables the creation of more concentrated data products such as statistics, plots, and data extracts, which are all far smaller than the full-sized volume data. With the increasing popularity of in situ, multiple in situ infrastructures have been created, each with its own mechanism for integrating with a simulation. To make it easier to instrument a simulation with multiple in situ infrastructures and include custom analysis algorithms, this project created the SENSEI framework.

97 MATHEMATICS AND COMPUTING↗

The single-cell transcriptome program of nodule development cellular lineages in Medicago truncatula

Legumes establish a symbiotic relationship with nitrogen-fixing rhizobia by developing nodules. Nodules are modified lateral roots that undergo changes in their cellular development in response to bacteria, but the transcriptional reprogramming that occurs in these root cells remains largely uncharacterized. Here, we describe the cell-type-specific transcriptome response of Medicago truncatula roots to rhizobia during early nodule development in the wild-type genotype Jemalong A17, complemented with a hypernodulating mutant (sunn-4) to expand the cell population responding to infection and subsequent biological inferences. The analysis identifies epidermal root hair and stele sub-cell types associated with a symbiotic response to infection and regulation of nodule proliferation. Trajectory inference shows cortex-derived cell lineages differentiating to form the nodule primordia and, posteriorly, its meristem, while modulating the regulation of phytohormone-related genes. Gene regulatory analysis of the cell transcriptomes identifies new regulators of nodulation, including STYLISH 4, for which the function is validated.

Cell Biology↗

Thermal protection optimization for the space shuttle.

This paper discusses optimal entry trajectories for the space shuttle that minimize the weight of an entry thermal protection system. The analysis was made using mathematical models of two types of thermal protection systems that were under consideration for the space shuttle: a metallic thermal protection system, and a reusable surface insulation thermal protection system. Optimal entries were generated using maximum orbiter nose temperature as a parameter. Thermal protection system weights were computed for both fixed and variable angles of attack using three-dimensional entry trajectories. Results indicated that variable angle-of-attack entries require less thermal protection system weight than entries at a constant angle of attack (35 deg) for both systems considered. Results also showed that 95 to 99 per cent of the thermal protection system weight requirement resulted from flight regimes in which the flow was still laminar.

Garcia, F., Jr.↗

Photoproduction of η mesons off the proton for 1.2 < E γ < 4.7GeV using CLAS at Jefferson Laboratory

Photoproduction cross sections are reported for the reaction $\gamma p\to p\eta$ using energy-tagged photons and the CLAS spectrometer at Jefferson Laboratory. The $\eta$ mesons are detected in their dominant charged decay mode, $\eta\to \pi^+\pi^-\pi^0$, and results on differential cross sections are presented for incident photon energies between 1.2 and 4.7 GeV. These new $\eta$ photoproduction data are consistent with earlier CLAS results but extend the energy range beyond the nucleon resonance region into the Regge regime. The normalized angular distributions are also compared with the experimental results from several other experiments, and with predictions of $\eta$ MAID\,2018 and the latest solution of the Bonn-Gatchina coupled-channel analysis. Differential cross sections $d\sigma/dt$ are presented for incident photon energies $E_\gamma > 2.9$ GeV ($W > 2.5$ GeV), and compared with predictions which are based on Regge trajectories exchange in the $t$-channel (Regge models). Overall, the data confirm the expected dominance of $\rho$, $\omega$ vector-meson exchange in an analysis by the Joint Physics Analysis Center.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Assessment of thermochemical nonequilibrium and slip effects for Orbital Reentry Experiment (OREX)

Results are provided from a viscous shock layer (VSL) analysis of the reentry flowfield around the forebody of the Japanese Orbital Reentry Experiment (OREX) vehicle. This vehicle is a 50 deg. spherically blunted cone with a nose radius of 1.35 m and a base diameter of 3.4 m. Calculations are done for the OREX trajectory from 105 to 48.4 km altitude range. A 7-species chemical model is found adequate for the flowfield analysis. However, for altitudes greater than 84 km, the low density effects (such as thermal nonequilibrium and slip) are to be implemented for good agreement between the predictions and flight inferred heat-transfer rate data. Further, at altitudes lower than 84 km, a finite surface recombination probability is to be employed in place of a non-catalytic surface for better comparison between the calculations and data. VSL results are also compared with the direct simulation Monte Carlo (DSMC) predictions at high altitudes (greater than 80 km) and the electron number density data for three altitudes in the OREX trajectory. Overall, there is a good comparison between the flight data and calculated results. With the ongoing refinements in data extraction procedures, the OREX data should prove valuable for validating theoretical models employed in flowfield codes for calculation of reacting-gas flowfields.

Gupta, Roop N.↗

Integrating Learning and Physics based Computation for Fast Online Transient Analysis

In this work, a novel method that integrates learning and physics based computation is developed for greatly accelerating the simulation of full power system transient trajectories. To solve the dynamic algebraic equations, the method replaces the time-consuming dynamic computation for generator dynamics with trained predictors, while retaining the time-efficient algebraic computation of solving AC-power flow (PF) for power systems. In particular, a predictor is trained for each generator, and the system trajectories are computed by alternating steps of calling the predictors and solving AC-PF. The proposed method also allows fully parallelizable training strategies and a flexible trade-off between training time and testing accuracy. Comprehensive evaluations of the proposed method for transient/dynamic contingency analysis of the New York/New England 16-machine 68-bus power systems demonstrate excellent performance and significant acceleration of computation.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Simulation and analysis of a geopotential research mission

Computer simulations were performed for a Geopotential Research Mission (GRM) to enable the study of the gravitational sensitivity of the range rate measurements between the two satellites and to provide a set of simulated measurements to assist in the evaluation of techniques developed for the determination of the gravity field. The simulations were conducted with two satellites in near circular, frozen orbits at 160 km altitudes separated by 300 km. High precision numerical integration of the polar orbits were used with a gravitational field complete to degree and order 360. The set of simulated data for a mission duration of about 32 days was generated on a Cray X-MP computer. The results presented cover the most recent simulation, S8703, and includes a summary of the numerical integration of the simulated trajectories, a summary of the requirements to compute nominal reference trajectories to meet the initial orbit determination requirements for the recovery of the geopotential, an analysis of the nature of the one way integrated Doppler measurements associated with the simulation, and a discussion of the data set to be made available.

Schutz, B. E.↗