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At least 235 records · Page 13

Advanced Thin Ionization Calorimeter (ATIC) Balloon Experiment

During grant NAG5-5064, Louisiana State University (LSU) led the ATIC team in the development, construction, testing, accelerator validation, pre-deployment integration and flight operations of the Advanced Thin Ionization Calorimeter (ATIC) Balloon Experiment. This involved interfacing among the ATIC collaborators (UMD, NRL/MSFC, SU, MSU, WI, SNU) to develop a new balloon payload based upon a fully active calorimeter, a carbon target, a scintillator strip hodoscope and a pixilated silicon solid state detector for a detailed investigation of the very high energy cosmic rays to energies beyond 10(exp 14) eV/nucleus. It is in this very high energy region that theory predicts changes in composition and energy spectra related to the Supernova Remnant Acceleration model for cosmic rays below the "knee" in the all-particle spectrum. This report provides a documentation list, details the anticipated ATIC science return, describes the particle detection principles on which the experiment is based, summarizes the simulation results for the system, describes the validation work at the CERN SPS accelerator and details the balloon flight configuration. The ATIC experiment had a very successful LDB flight from McMurdo, Antarctica in 12/00 - 1/01. The instrument performed well for the entire 15 days. Preliminary data analysis shows acceptable charge resolution and an all-particle power law energy deposition distribution not inconsistent with previous measurements. Detailed analysis is underway and will result in new data on the cosmic ray charge and energy spectra in the GeV - TeV energy range. ATIC is currently being refurbished in anticipation of another LDB flight in the 2002-03 period.

Wefel, John P.↗

An Analytical Comparison of the Fidelity of "Large Motion" Versus "Small Motion" Flight Simulators in a Rotorcraft Side-Step Task

This paper presents an analytical and experimental methodology for studying flight simulator fidelity. The task was a rotorcraft bob-up/down maneuver in which vertical acceleration constituted the motion cue. The task considered here is aside-step maneuver that differs from the bob-up one important way: both roll and lateral acceleration cues are available to the pilot. It has been communicated to the author that in some Verticle Motion Simulator (VMS) studies, the lateral acceleration cue has been found to be the most important. It is of some interest to hypothesize how this motion cue associated with "outer-loop" lateral translation fits into the modeling procedure where only "inner-loop " motion cues were considered. This Note is an attempt at formulating such an hypothesis and analytically comparing a large-motion simulator, e.g., the VMS, with a small-motion simulator, e.g., a hexapod.

Hess, Ronald A.↗

Orion MPCV Touchdown Detection Threshold Development and Testing

A robust method of detecting Orion Multi ]Purpose Crew Vehicle (MPCV) splashdown is necessary to ensure crew and hardware safety during descent and after touchdown. The proposed method uses a triple redundant system to inhibit Reaction Control System (RCS) thruster firings, detach parachute risers from the vehicle, and transition to the post ]landing segment of the Flight Software (FSW). The vehicle crew is the prime input for touchdown detection, followed by an autonomous FSW algorithm, and finally a strictly time based backup timer. RCS thrusters must be inhibited before submersion in water to protect against possible damage due to firing these jets under water. In addition, neglecting to declare touchdown will not allow the vehicle to transition to post ]landing activities such as activating the Crew Module Up ]righting System (CMUS), resulting in possible loss of communication and difficult recovery. A previous AIAA paper gAssessment of an Automated Touchdown Detection Algorithm for the Orion Crew Module h concluded that a strictly Inertial Measurement Unit (IMU) based detection method using an acceleration spike algorithm had the highest safety margins and shortest detection times of other methods considered. That study utilized finite element simulations of vehicle splashdown, generated by LS ]DYNA, which were expanded to a larger set of results using a Kriging surface fit. The study also used the Decelerator Systems Simulation (DSS) to generate flight dynamics during vehicle descent under parachutes. Proto ]type IMU and FSW MATLAB models provided the basis for initial algorithm development and testing. This paper documents an in ]depth trade study, using the same dynamics data and MATLAB simulations as the earlier work, to further develop the acceleration detection method. By studying the combined effects of data rate, filtering on the rotational acceleration correction, data persistence limits and values of acceleration thresholds, an optimal configuration was determined. The lever arm calculation, which removes the centripetal acceleration caused by vehicle rotation, requires that the vehicle angular acceleration be derived from vehicle body rates, necessitating the addition of a 2nd order filter to smooth the data. It was determined that using 200 Hz data directly from the vehicle IMU outperforms the 40 Hz FSW data rate. Data persistence counter values and acceleration thresholds were balanced in order to meet desired safety and performance. The algorithm proved to exhibit ample safety margin against early detection while under parachutes, and adequate performance upon vehicle splashdown. Fall times from algorithm initiation were also studied, and a backup timer length was chosen to provide a large safety margin, yet still trigger detection before CMUS inflation. This timer serves as a backup to the primary acceleration detection method. Additionally, these parameters were tested for safety on actual flight test data, demonstrating expected safety margins.

Daum, Jared↗

Spectral Single and Double Power-law Formation by Sequential Particle Acceleration in Flare Magnetic Islands

Spectral single and double power laws are common in high-energy phenomena, such as solar flares and solar energetic particles, including ground level enhancement events. It is not clear what determines the energy breaks and spectral indexes of these power laws. Here, we will describe a first-principles model of pitch-angle and energy distribution function evolution, which produces power laws and provides physical interpretation for such spectral features (Guidoni et al. 2022, ApJ). In this model, a prescribed fraction of particles sequentially “hops” between shrinking magnetic islands (accelerators) formed by flare reconnection. Each accelerator increases particles’ energies by a modest amount, but particles must visit only a few accelerators to increase their energies by orders of magnitude. Data from global magnetohydrodynamic simulations of an eruptive flare/coronal mass ejection provide ambient conditions for the evolving particle distributions. We will also describe the fully analytic method for forming and interpreting power laws, which requires only a few constrained physical parameters of the acceleration region and is independent of the acceleration model, as well as preliminary results extending the analytical model to the formation of double power laws.

S E Guidoni↗

Wind-tunnel simulation of store jettison with the aid of magnetic artificial gravity

A method employed in the simulation of jettison of stores from aircraft involving small scale wind-tunnel drop tests from a model of the parent aircraft is described. Proper scaling of such experiments generally dictates that the gravitational acceleration should ideally be a test variable. A method of introducing a controllable artificial component of gravity by magnetic means has been proposed. The use of a magnetic artificial gravity facility based upon this idea, in conjunction with small scale wind-tunnel drop tests, would improve the accuracy of simulation. A review of the scaling laws as they apply to the design of such a facility is presented. The design constraints involved in the integration of such a facility with a wind tunnel are defined. A detailed performance analysis procedure applicable to such a facility is developed. A practical magnet configuration is defined which is capable of controlling the strength and orientation of the magnetic artificial gravity field in the vertical plane, thereby allowing simulation of store jettison from a diving or climbing aircraft. The factors involved in the choice between continuous or intermittent operation of the facility, and the use of normal or superconducting magnets, are defined.

Stephens, T.↗

Primate translational vestibuloocular reflexes. III. Effects of bilateral labyrinthine electrical stimulation

The effects of functional, reversible ablation and potential recruitment of the most irregular otolith afferents on the dynamics and sensitivity of the translational vestibuloocular reflexes (trVORs) were investigated in rhesus monkeys trained to fixate near and far targets. Translational motion stimuli consisted of either steady-state lateral and fore-aft sinusoidal oscillations or short-lasting transient lateral head displacements. Short-duration (usually <2 s) anodal (inhibitory) and cathodal (excitatory) currents (50-100 microA) were delivered bilaterally during motion. In the presence of anodal labyrinthine stimulation, trVOR sensitivity and its dependence on viewing distance were significantly decreased. In addition, anodal currents significantly increased phase lags. During transient motion, anodal stimulation resulted in significantly lower initial eye acceleration and more sluggish responses. Cathodal currents tended to have opposite effects. The main characteristics of these results were simulated by a simple model where both regularly and irregularly discharging afferents contribute to the trVORs. Anodal labyrinthine currents also were found to decrease eye velocity during long-duration, constant velocity rotations, although results were generally more variable compared with those during translational motion.

NASA Program Biomedical Research and Countermeasur↗

Evaluation of a Seat Attenuation System for the Orion Crew Module

The function of the crew seat attenuation system for the Orion Crew Module (CM) is to provide the crew with a low injury-risk landing environment under a range of crew configurations and landing conditions. The current design for the seat attenuation system provides the crew with a low risk of injury environment based on the Brinkley criteria for most of the landing conditions considered. Furthermore, the stroking of the seat attenuation system is within limits, and the clearance between the seat support platform and vehicle is not exceeded. For the limited number of landing conditions where a low injury risk is exceeded, the risk is never beyond a moderate level. The results presented in this study are based on a CM structural model that is rigid except for the pallet struts, which attenuate landing loads and reduce the accelerations transferred to the astronauts. The CM simulations include a soft soil landing. Several different crew configurations are evaluated in this study. It is expected that situations where the risk is above low can be eliminated in future design iterations.

Lawrence, Charles↗

Role of Oxidative Damage in Radiation-Induced Bone Loss

During prolonged spaceflight, astronauts are exposed to both microgravity and space radiation, and are at risk for increased skeletal fragility due to bone loss. Evidence from rodent experiments demonstrates that both microgravity and ionizing radiation can cause bone loss due to increased bone-resorbing osteoclasts and decreased bone-forming osteoblasts, although the underlying molecular mechanisms for these changes are not fully understood. We hypothesized that excess reactive oxidative species (ROS), produced by conditions that simulate spaceflight, alter the tight balance between osteoclast and osteoblast activities, leading to accelerated skeletal remodeling and culminating in bone loss. To test this, we used the MCAT mouse model; these transgenic mice over-express the human catalase gene targeted to mitochondria, the major organelle contributing free radicals. Catalase is an anti-oxidant that converts reactive species, hydrogen peroxide into water and oxygen. This animal model was selected as it displays extended lifespan, reduced cardiovascular disease and reduced central nervous system radio-sensitivity, consistent with elevated anti-oxidant activity conferred by the transgene. We reasoned that mice overexpressing catalase in mitochondria of osteoblast and osteoclast lineage cells would be protected from the bone loss caused by simulated spaceflight. Over-expression of human catalase localized to mitochondria caused various skeletal phenotypic changes compared to WT mice; this includes greater bone length, decreased cortical bone area and moment of inertia, and indications of altered microarchitecture. These findings indicate mitochondrial ROS are important for normal bone-remodeling and skeletal integrity. Catalase over-expression did not fully protect skeletal tissue from structural decrements caused by simulated spaceflight; however there was significant protection in terms of cellular oxidative damage (MDA levels) to the skeletal tissue. Furthermore, we used an array of countermeasures (Antioxidant diets and injections) to prevent the radiation-induced bone loss, although these did not prevent bone loss, analysis is ongoing to determine if these countermeasure protected radiation-induced damage to other tissues.

oxidative damage↗

Ordering Unstructured Meshes for Sparse Matrix Computations on Leading Parallel Systems

The ability of computers to solve hitherto intractable problems and simulate complex processes using mathematical models makes them an indispensable part of modern science and engineering. Computer simulations of large-scale realistic applications usually require solving a set of non-linear partial differential equations (PDES) over a finite region. For example, one thrust area in the DOE Grand Challenge projects is to design future accelerators such as the SpaHation Neutron Source (SNS). Our colleagues at SLAC need to model complex RFQ cavities with large aspect ratios. Unstructured grids are currently used to resolve the small features in a large computational domain; dynamic mesh adaptation will be added in the future for additional efficiency. The PDEs for electromagnetics are discretized by the FEM method, which leads to a generalized eigenvalue problem Kx = AMx, where K and M are the stiffness and mass matrices, and are very sparse. In a typical cavity model, the number of degrees of freedom is about one million. For such large eigenproblems, direct solution techniques quickly reach the memory limits. Instead, the most widely-used methods are Krylov subspace methods, such as Lanczos or Jacobi-Davidson. In all the Krylov-based algorithms, sparse matrix-vector multiplication (SPMV) must be performed repeatedly. Therefore, the efficiency of SPMV usually determines the eigensolver speed. SPMV is also one of the most heavily used kernels in large-scale numerical simulations.

Oliker, Leonid↗

High-Performance Computing Optimization for Aladyn – Adaptive Neural Network Molecular Dynamics Mini-Application

This report provides a description and performance evaluation of the optimization techniques for high performance computing (HPC) implementation of the open source Computational Materials mini-application Aladyn (https://github.com/nasa/aladyn). Aladyn is a basic molecular dynamics code written in FORTRAN 2003, which is designed to demonstrate the use of adaptive neural networks (ANNs) in atomistic simulations. The role of ANNs is to efficiently reproduce the very complex energy landscape resulting from the atomic interactions in materials with the accuracy of the more expensive quantum mechanics-based calculations. The ANN is trained on a large set of atomic structures calculated using the density functional theory (DFT) method. While achieving orders of magnitude faster computational performance than DFT, the ANN-based approach was still very computationally demanding compared to the conventional approach of using empirically fitted energy functions. After its initial development, Aladyn was evaluated and optimized by experts at the NASA Advanced Supercomputing (NAS) division to exploit modern supercomputer architectures. The code has been optimized for execution on multicore central processing units (CPUs), including Intel® Skylake microarchitecture, and on graphic accelerators, such as Nvidia® V100 graphic processing units (GPUs), using Open Multi-Processing (OpenMP) and Open Accelerators (OpenACC) programming interfaces. The optimization achieved a speedup of 4.7 times the baseline version on CPU performance and an additional 2.4 times on CPU+GPU performance. Atomistic computer simulations are a fundamental tool in materials research to model material properties form physics-based first principles. Atomic interaction, governed by Quantum Mechanics (QM) require sophisticated and highly computationally demanding mathematical models to calculate [1]. Classical methods use approximate functional forms, empirically fitted through a set of variable parameters to emulate atomic energies as direct functions of atomic coordinates [2]. While empirical potentials are computationally much simpler, allowing simulations of large-scale systems of up to a trillion (1012) atoms [3], they are substantially less accurate compared to quantum calculations and applicable only to very specific atomic configurations or predefined crystallographic phases. A recently suggested approach is to use heuristic machine learning methods [4], such as those based on Adaptive Neural Networks (ANNs) to predict atomic energies, after being trained on a sufficiently large database of QM-calculated structures [5,6]. This approach reduces significantly the computational complexity, allowing for simulations of orders of magnitude larger systems compared to QM-based methods without compromising accuracy. Still, compared to classical methods using empirical energy functions, ANN methods remain two- to three orders of magnitude more computationally demanding. Hence, the computational cost of simulations, together with the need for extensive training of ANNs, still makes the practical implementation of ANN-based methods quite challenging. The purpose of the Aladyn mini-application software [7], available as open source at https://github.com/nasa/aladyn, is to be a testbed for exploring possible optimization strategies to develop highly scalable parallel algorithms for ANN-based atomistic simulations. Aladyn is aimed at utilizing the architecture of the high-end modern highperformance computing (HPC) hardware based on multicore central processing units (CPUs) equipped with graphic processing unit (GPU) accelerators. Specifically, the goal is to optimize the performance on a single HPC compute node, before implementing scaling to multi-node parallelization using message passing interface (MPI). At the same time, the open source code of Aladyn can serve as a training model for students and professors in academia.

Yamakov, Vesselin I.↗

Accelerated Test Methods

Neural network systems were evaluated for use in predicting wear of mechanical systems. Three different neural network software simulation packages were utilized in order to create models of tribological wear tests. Representative simple, medium, and high complexity simulation packages were selected. Pin-on-disk, rub shoe, and four-ball tribological test data was used for training, testing, and verification of the neural network models. Results showed mixed success. The neural networks were able to predict results with some accuracy if the number of input variables was low or the amount of training data was high. Increased neural network complexity resulted in more accurate results, however there was a point of diminishing return. Medium complexity models were the best trade off between accuracy and computing time requirements. A NASA Technical Memorandum and a Society of Tribologists and Lubrication Engineers paper are being published which detail the work.

Jansen, Ralph↗

Simulation and Optimization of Vacuum Swing Adsorption Units for Spacesuit Carbon Dioxide and Humidity Control

Controlling carbon dioxide (CO2) and humidity levels in a spacesuit is critical to ensuring both the safety and comfort of an astronaut during extra-vehicular activity (EVA). Traditionally, this has been accomplished utilizing non-regenerative lithium hydroxide (LiOH) or regenerative metal oxide (MetOx) canisters which pose a significant weight burden. Although such technology enables air revitalization, the volume requirements to store the waste canisters as well as the mass to transport multiple units become prohibitive as mission durations increase. Consequently, motivation exists toward developing a fully regenerative technology for environmental control. The application of solid amine materials with vacuum swing adsorption technology has shown the capacity to control CO2 and concomitantly manage humidity levels through a fully regenerative cycle eliminating mission constraints imposed with non-regenerative technologies. Experimental results for full-size and sub-scale test articles have been collected and are described herein. In order to accelerate the developmental efforts, an axially-dispersed plug ow model with an accompanying energy balance has been established and correlated with the experimental data. The experimental and simulation results display good agreement for a variety of ow rates (110-170 SLM), replicated metabolic challenges (100-590 Watts), and atmosphere pressures under consideration for the spacesuit (248 and 760 mm Hg). The relationship between swing adsorption cycles for an outlet criterion of 6.0 mm Hg of CO2 partial pressure has been established for each metabolic challenge. In addition, variable metabolic profiles were imposed on the test articles in order to assess the ability of the technology to transition to new operational constraints. The advent of the model provides the capacity to apply computer-aided engineering practices to support the ongoing efforts to optimize and mature this technology for future application to space exploration.

Swickrath, Michael J.↗

ST7 Disturbance Reduction System (DRS) Colloid Micronewton Thruster Performance and Control Algorithm Model Simulation Validation in Flight

Colloid Micronewton Thrusters (CMNT) were flight demonstrated for the first time on the ST7Disturbance Reduction System (DRS) payload on the European Space Agency (ESA) Laser Interferometer Space Antenna (LISA) Pathfinder spacecraft for attitude and drag-free spacecraft control. LISA Pathfinder was a technology demonstration mission for ESA’s LISA gravitational wave observatory, currently in Phase A with a launch date of 2034. The DRS included the Integrated Avionics Unit (IAU), eight Colloid Micronewton Thrusters (CMNT), Dynamic Control Software (DCS) and Flight Software (FSW). The CMNT technology met performance requirements operating at 5-30 µN of thrust with ≤0.1 µN resolution and ≤0.1 µN/Hz thrust noise to deliver the required nanometer-level precision spacecraft control measured by the gravitational reference sensor (GRS) in the ESA LISA Technology Package (LTP). The performance of seven of the CMNT in flight was consistent with ground test results. The colloid thruster performance model of thrust and thrust noise as a function of operational parameters (i.e. beam current, voltage, temperature, etc.) was validated in flight over a wide range of conditions. A model and simulation of the thruster control algorithm was developed and validated with flight data to predict thrust noise. This capability is important because it is considered to be a significant source of position noise on the spacecraft and, therefore, the acceleration noise on the test masses, which provide the gravity wave measurements. The CMNT thruster model data and validation with LISA Pathfinder/ST7-DRS flight experiments are discussed in this paper.

Hruby, Vlad↗

Ditching Tests of a 1/20-Scale Model of the Northrop B-35 Airplane

Tests of a 1/20-scale dynamically similar model of the Northrop B-35 airplane were made to study its ditching characteristics. The model was ditched in calm water at the Langley tank no. 2 monorail. Various landing attitudes, speeds,and conditions of damage were simulated during the investigation. The ditching characteristics were determined by visual observation and from motion-picture records and time-history acceleration records. Both longitudinal and lateral accelerations were measured. Results are given in tabular form and time-history acceleration curves and sequence photographs are presented. Conclusions based on the model investigation are as follows: 1. The best ditching of the B-35 airplane probably can be made by contacting the water in a near normal landing attitude of about 9 deg with the landing flaps full down so as to have a low horizontal speed. 2. The airplane usually will turn or yaw but the motion will not be violent. The maximum lateral acceleration will be about 2g. 3. If the airplane does not turn or yaw immediately after landing, it probably will trim up and then make a smooth run or porpoise slightly. The maximum longitudinal decelerations that will be encountered are about 6g or 7g. 4. Although the decelerations are not indicated to be especially large, the construction of the airplane is such that extensive damage is to be expected, and it probably will be difficult to find ditching stations where crew members can adequately brace themselves and be reasonably sure of avoiding a large inrush of water.

Fisher, Lloyd J.↗

Simulation and Optimization of Vacuum Swing Adsorption Units for Spacesuit Carbon Dioxide and Humidity Control

Controlling carbon dioxide (CO2) and humidity levels in a spacesuit is critical to ensuring both the safety and comfort of an astronaut during extra-vehicular activity (EVA). Traditionally, this has been accomplished utilizing either non-regenerative lithium hydroxide (LiOH) or regenerative but heavy metal oxide (MetOx) canisters which pose a significant weight burden. Although such technology enables air revitalization, the volume requirements to store the waste canisters as well as the mass to transport multiple units become prohibitive as mission durations increase. Consequently, motivation exists toward developing a fully regenerative technology for spacesuit environmental control. The application of solid amine materials with vacuum swing adsorption technology has shown the capacity to control CO2 while concomitantly managing humidity levels through a fully regenerative cycle eliminating constraints imposed with the traditional technologies. Prototype air revitalization units employing this technology have been fabricated in both a rectangular and cylindrical geometry. Experimental results for these test articles have been collected and are described herein. In order to accelerate the developmental efforts, an axially-dispersed plug flow model with an accompanying energy balance has been established and correlated with the experimental data. The experimental and simulation results display good agreement for a variety of flow rates (110-170 ALM), replicated metabolic challenges (100-590 Watts), and atmosphere pressures under consideration for the spacesuit (248 and 760 mm Hg). The testing and model results lend insight into the operational capabilities of these devices as well as the influence the geometry of the device has on performance. In addition, variable metabolic profiles were imposed on the test articles in order to assess the ability of the technology to transition to new metabolic conditions. The advent of the model provides the capacity to apply computer-aided engineering practices to support the ongoing efforts to optimize and mature this technology for future application to space exploration.

Swickrath, Michael J.↗

Computer simulation of astrophysical plasmas

The role of sophisticated numerical models and simulations in the field of plasma astrophysics is discussed. The need for an iteration between microphysics and macrophysics in order for astrophysical plasma physics to produce quantitative results that can be related to astronomical data is stressed. A discussion on computational requirements for simulations of astrophysical plasmas contrasts microscopic plasma simulations with macroscopic system models. An overview of particle-in-cell simulations (PICS) is given and two examples of PICS of astrophysical plasma are discussed including particle acceleration by collisionless shocks in relativistic plasmas and magnetic field reconnection in astrophysical plasmas.

Max, Claire E.↗

Modeling radiation forces acting on TOPEX/Poseidon for precision orbit determination

Geodetic satellites such as GEOSAT, SPOT, ERS-1, and TOPEX/Poseidon require accurate orbital computations to support the scientific data they collect. Until recently, gravity field mismodeling was the major source of error in precise orbit definition. However, albedo and infrared re-radiation, and spacecraft thermal imbalances produce in combination no more than a 6-cm radial root-mean-square (RMS) error over a 10-day period. This requires the development of nonconservative force models that take the satellite's complex geometry, attitude, and surface properties into account. For TOPEX/Poseidon, a 'box-wing' satellite form was investigated that models the satellite as a combination of flat plates arranged in a box shape with a connected solar array. The nonconservative forces acting on each of the eight surfaces are computed independently, yielding vector accelerations which are summed to compute the total aggregate effect on the satellite center-of-mass. In order to test the validity of this concept, 'micro-models' based on finite element analysis of TOPEX/Poseidon were used to generate acceleration histories in a wide variety of orbit orientations. These profiles are then compared to the box-wing model. The results of these simulations and their implication on the ability to precisely model the TOPEX/Poseidon orbit are discussed.

Marshall, J. A.↗

Interstellar clouds in high-speed, supersonic flows: Two-dimensional simulations

We present a series of gasdynamical simulations of the interaction of a dense, cool interstellar cloud with a high-speed, supersonic wind that confines and accelerates the embedded cloud. Our goal is to attempt to determine if such clouds can survive various potentially disruptive instabilities, that occur at their peripheries, long enough to be accelerated to speeds which are comparable to the wind velocity. These simulations are performed using two-dimensional, Eulerian gas dynamics on both an axisymmetric (about the cloud axis) and 'slab' geometric grid. The spatial and temporal resolutions of the simulations are varied over a wide range to investigate the effects of small-scale instabilities on the overall acceleration of clouds and the development of large-scale, disruptive instabilities. Also, we study the effects of wind/cloud Mach number variations by changing the wind speed constant at about 12 km/s (which corresponds to a cloud temperature of 10,000 K). The current simulations track the evolution of clouds as they are accelerated to speeds approximately 4-5 times greater than their internal sound speeds. Furthermore, the models with the highest resolution were extended far beyond quasi-linear Rayleigh-Taylor growth times reaching 6-7 Rayleigh-Taylor growth times for the largest scale instabilities before being terminated because of the accumulation of errors at the rear grid boundary.

Schiano, A. V. R.↗