Search NASA⌕ Search

SEARCH · Search NASA

Results for “RANDOM NUMBER”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 397 records · Page 22

Suppression of biodynamic interference in head-tracked teleoperation

The utility of helmet-tracked sights to provide pointing commands for teleoperation of cameras, lasers, or antennas in aircraft is degraded by the presence of uncommanded, involuntary heat motion, referred to as biodynamic interference. This interference limits the achievable precision required in pointing tasks. The noise contributions due to biodynamic interference consists of an additive component which is correlated with aircraft vibration and an uncorrelated, nonadditive component, referred to as remnant. An experimental simulation study is described which investigated the improvements achievable in pointing and tracking precision using dynamic display shifting in the helmet-mounted display. The experiment was conducted in a six degree of freedom motion base simulator with an emulated helmet-mounted display. Highly experienced pilot subjects performed precision head-pointing tasks while manually flying a visual flight-path tracking task. Four schemes using adaptive and low-pass filtering of the head motion were evaluated to determine their effects on task performance and pilot workload in the presence of whole-body vibration characteristic of helicopter flight. The results indicate that, for tracking tasks involving continuously moving targets, improvements of up to 70 percent can be achieved in percent on-target dwelling time and of up to 35 percent in rms tracking error, with the adaptive plus low-pass filter configuration. The results with the same filter configuration for the task of capturing randomly-positioned, stationary targets show an increase of up to 340 percent in the number of targets captured and an improvement of up to 24 percent in the average capture time. The adaptive plus low-pass filter combination was considered to exhibit the best overall display dynamics by each of the subjects.

Lifshitz, S.↗

Quantification of uncertainties in coupled material degradation processes - High temperature, fatigue and creep

This paper describes the development of methodology that provides for quantification of uncertainties in lifetime strength of aerospace materials subjected to a number of diverse effects. A probabilistic material degradation model, in the form of a randomized multifactor interaction equation, has been postulated for lifetime strength degradation of structural components of aerospace propulsion systems. The model includes effects that typically reduce lifetime strength and may include temperature, mechanical fatigue, creep and others. The paper also includes the analysis of experimental data from the open literature for Inconel 718. These data are used to provide an initial check for model validity, as well as for calibration of the model's empirical material constants. The model validity check and calibration is carried out for three effects, namely, high temperature, mechanical fatigue and creep.

Boyce, L.↗

Three-dimensional simulations of large eddies in the compressible mixing layer

Consideration is given to the effect of compressibility on a plane mixing layer that is a prototype free shear layer, amenable to study by numerical simulation and experiment. The full time-dependent compressible Navier-Stokes equations are solved numerically for a temporally evolving mixing layer employing a mixed spectral and high-order finite difference method. Simulations with random initial conditions confirm the prediction of linear stability theory that at high Mach numbers oblique waves grow faster than two-dimensional waves. Simulations are presented of the nonlinear temporal evolution of the most rapidly amplified linear instability waves.

Sandham, N. D.↗

Sparse distributed memory and related models

Described here is sparse distributed memory (SDM) as a neural-net associative memory. It is characterized by two weight matrices and by a large internal dimension - the number of hidden units is much larger than the number of input or output units. The first matrix, A, is fixed and possibly random, and the second matrix, C, is modifiable. The SDM is compared and contrasted to (1) computer memory, (2) correlation-matrix memory, (3) feet-forward artificial neural network, (4) cortex of the cerebellum, (5) Marr and Albus models of the cerebellum, and (6) Albus' cerebellar model arithmetic computer (CMAC). Several variations of the basic SDM design are discussed: the selected-coordinate and hyperplane designs of Jaeckel, the pseudorandom associative neural memory of Hassoun, and SDM with real-valued input variables by Prager and Fallside. SDM research conducted mainly at the Research Institute for Advanced Computer Science (RIACS) in 1986-1991 is highlighted.

Kanerva, Pentti↗

Numerical modeling for dilute and dense sprays

We have successfully implemented a numerical model for spray-combustion calculations. In this model, the governing gas-phase equations in Eulerian coordinate are solved by a time-marching multiple pressure correction procedure based on the operator-splitting technique. The droplet-phase equations in Lagrangian coordinate are solved by a stochastic discrete particle technique. In order to simplify the calculation procedure for the circulating droplets, the effective conductivity model is utilized. The k-epsilon models are utilized to characterize the time and length scales of the gas phase in conjunction with turbulent modulation by droplets and droplet dispersion by turbulence. This method entails random sampling of instantaneous gas flow properties and the stochastic process requires a large number of computational parcels to produce the satisfactory dispersion distributions even for rather dilute sprays. Two major improvements in spray combustion modelings were made. Firstly, we have developed a probability density function approach in multidimensional space to represent a specific computational particle. Secondly, we incorporate the Taylor Analogy Breakup (TAB) model for handling the dense spray effects. This breakup model is based on the reasonable assumption that atomization and drop breakup are indistinguishable processes within a dense spray near the nozzle exit. Accordingly, atomization is prescribed by injecting drops which have a characteristic size equal to the nozzle exit diameter. Example problems include the nearly homogeneous and inhomogeneous turbulent particle dispersion, and the non-evaporating, evaporating, and burning dense sprays. Comparison with experimental data will be discussed in detail.

Chen, C. P.↗

Suppression of biodynamic interference in head-tracked teleoperation

Results are reported from an experimental simulation study examining improvements achievable in pointing and tracking precision using dynamic display shifting in helmet-mounted displays. The experiment was conducted in a 6-deg-of-freedom motion base simulator with an emulated helmet-mounted sight. It is shown that, for tracking tasks involving continuously moving targets, improvements of up to 70 percent can be achieved in percent on-target dwelling time and of up to 35 percent in rms tracking error, with the adaptive plus low-pass filter configuration. The results with the same filter configuration for the task of capturing randomly positioned, stationary targets show an increase of up to 340 percent in the number of targets captured and an improvement of up to 24 percent in the average capture time. The adaptive plus low-pass filter combination is considered to exhibit the best overall display dynamics by each of the subjects.

Lifshitz, S.↗

Relationship of attenuation in a vegetation canopy to physical parameters of the canopy

A discrete scatter model is employed to compute the radiometric response (i.e. emissivity) of a layer of vegetation over a homogeneous ground. This was done to gain insight into empirical formulas for the emissivity which have recently appeared in the literature and which indicate that the attenuation through the canopy is proportional to the water content of the vegetation and inversely proportional to wavelength raised to a power around unity. The analytical result assumes that the vegetation can be modeled by a sparse layer of discrete, randomly oriented particles (leaves, stalks, etc.). The attenuation is given by the effective wave number of the layer obtained from the solution for the mean wave using the effective field approximation. By using the Ulaby-El Rayes formula to relate the dielectric constant of the vegetation to its water content, it can be shown that the attenuation is proportional to water content. The analytical form offers insight into the dependence of the empirical parameters on other variables of the canopy, including plant geometry (i.e. shape and orientation of the leaves and stalks of which the vegetation is comprised), frequency of the measurement and even the physical temperature of the vegetation. Solutions are presented for some special cases including layers consisting of cylinders (stalks) and disks (leaves).

Karam, M. A.↗

An Overdetermined System for Improved Autocorrelation Based Spectral Moment Estimator Performance

Autocorrelation based spectral moment estimators are typically derived using the Fourier transform relationship between the power spectrum and the autocorrelation function along with using either an assumed form of the autocorrelation function, e.g., Gaussian, or a generic complex form and applying properties of the characteristic function. Passarelli has used a series expansion of the general complex autocorrelation function and has expressed the coefficients in terms of central moments of the power spectrum. A truncation of this series will produce a closed system of equations which can be solved for the central moments of interest. The autocorrelation function at various lags is estimated from samples of the random process under observation. These estimates themselves are random variables and exhibit a bias and variance that is a function of the number of samples used in the estimates and the operational signal-to-noise ratio. This contributes to a degradation in performance of the moment estimators. This dissertation investigates the use autocorrelation function estimates at higher order lags to reduce the bias and standard deviation in spectral moment estimates. In particular, Passarelli's series expansion is cast in terms of an overdetermined system to form a framework under which the application of additional autocorrelation function estimates at higher order lags can be defined and assessed. The solution of the overdetermined system is the least squares solution. Furthermore, an overdetermined system can be solved for any moment or moments of interest and is not tied to a particular form of the power spectrum or corresponding autocorrelation function. As an application of this approach, autocorrelation based variance estimators are defined by a truncation of Passarelli's series expansion and applied to simulated Doppler weather radar returns which are characterized by a Gaussian shaped power spectrum. The performance of the variance estimators determined from a closed system is shown to improve through the application of additional autocorrelation lags in an overdetermined system. This improvement is greater in the narrowband spectrum region where the information is spread over more lags of the autocorrelation function. The number of lags needed in the overdetermined system is a function of the spectral width, the number of terms in the series expansion, the number of samples used in estimating the autocorrelation function, and the signal-to-noise ratio. The overdetermined system provides a robustness to the chosen variance estimator by expanding the region of spectral widths and signal-to-noise ratios over which the estimator can perform as compared to the closed system.

Keel, Byron M.↗

Effects of vibration and shock on the performance of gas-bearing space-power Brayton cycle turbomachinery. Part 4: Suppression of rotor-bearing system vibrations through flexible bearing support damping

A bearing damper, operating on the support flexure of a pivoted pad in a tilting-pad type gas-lubricated journal bearing, has been designed, built, and tested under externally-applied random vibrations. The NASA Brayton Rotating Unit (BRU), a 36,000 rpm, 10-Kwe turbogenerator had previously been subjected in the MTI Vibration Test Laboratory to external random vibrations, and vibration response data had been recorded and analyzed for amplitude distribution and frequency content at a number of locations in the machine. Based on data from that evaluation, a piston-type damper was designed and developed for each of the two flexibly-supported journal bearing pads (one in each of the two three-pad bearings). A modified BRU, with dampers installed, has been re-tested under random vibration conditions. Root-mean-square vibration amplitudes were determined from the test data, and displacement power spectral density analyses have been performed. Results of these data reduction efforts have been compared with vibration tolerance limits. Results of the tests indicate significant reductions in vibration levels in the bearing gas-lubricant films, particularly in the rigidly-mounted pads. The utility of the gas-lubricated damper for limiting rotor-bearing system vibrations in high-speed turbomachinery has thus been demonstrated.

Tessarzik, J. M.↗

Concepts for a theoretical and experimental study of lifting rotor random loads and vibrations. Phase 5B: Analysis of gust alleviation methods and rotor dynamic stability

The effects of various gust alleviation methods on the random blade response in flapping were studied analytically, assuming a rigid rotor support. The analytical model assumes rigid flapping blades with elastic root restraints. Linearized equations which are approximately valid at low lift conditions were used. Because of the interblade coupling from the feedback devices, the method of multiblade generalized coordinates was most convenient and was extended to include coning, differential coning, and warping of the rotor. The numerical examples cover the dynamic stability characteristics as affected by feedback gains of three- to six-bladed rotors. The number of blades had large effects on stability limits and modal time functions at these limits. The random flapping response of the blades to atmospheric turbulence was determined at 1.6 rotor advance ratio using feedback gains below the stability limit. The most effective reduction of the flapping response per unit gain was achieved with a rotor coning angle feedback.

Hohenemser, K. H.↗

Quasiprobabilistic Readout Correction of Midcircuit Measurements for Adaptive Feedback via Measurement Randomized Compiling

Quantum measurements are a fundamental component of quantum computing. However, on present-day quantum computers, measurements can be more error prone than quantum gates and are susceptible to nonunital errors as well as nonlocal correlations due to measurement crosstalk. While readout errors can be mitigated in postprocessing, this is inefficient in the number of qubits due to a combinatorially large number of possible states that need to be characterized. In this work, we show that measurement errors can be tailored into a simple stochastic error model using randomized compiling, enabling the efficient mitigation of readout errors via quasiprobability distributions reconstructed from the measurement of a single preparation state in an exponentially large confusion matrix. We demonstrate the scalability and power of this approach by correcting readout errors without matrix inversion on a large number of different preparation states applied to a register of eight superconducting transmon qubits. Moreover, we show that this method can be extended to midcircuit measurements used for active feedback via quasiprobabilistic error cancellation, and we demonstrate the correction of measurement errors on an ancilla qubit used to detect and actively correct bit-flip errors on an entangled memory qubit. Our approach enables the correction of readout errors on large numbers of qubits and offers a strategy for correcting readout errors in adaptive circuits in which the results of midcircuit measurements are used to perform conditional operations on nonlocal qubits in real time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

On the first-excursion probability in stationary narrow-band random vibration. II.

The first-excursion probability of a stationary narrow-band Gaussian process with mean zero has been studied. Within the framework of point process approach, series approximations derived from the theory of random points and approximations based on the maximum entropy principle have been developed. With the aid of numerical examples, merits of the approximations proposed previously as well as of those developed in this paper have been compared. The results indicate that the maximum entropy principle has not produced satisfactory approximations but the approximation based on nonapproaching random points is found to be the best among all the approximations proposed herein. A conclusion drawn from the present and the previous studies is that the point process approach produces a number of useful approximations for the first-excursion probability, particularly those based on the concepts of the Markov process, the clump-size, and the nonapproaching random points.

Yang, J.-N.↗

HfZr_BCC_SolidSolution_128atoms_VASP6

We performed density functional theory (DFT) calculations for body-centered-cubic (BCC) structures with 128 lattices sites of solid solution binary alloys hafnium-zirconium (Hf-Zr). The electronic structures of alloys have been calculated using Vienna Ab initio Simulation Package (VASP). Within this package the DFT approach is used to reduce many-body Schrodinger equation to set of single particle Kohn-Sham (KS) equations. The generalized electronic exchange-correlation functional is described by generalized gradient approximation with the Perdew-Burke-Ernzerhof parametrization. The electron-ion interactions is described by pseudopotentials developed within the plane-wave basis projector augmented-wave (PAW) approach. These pseudopotentials are available at the VASP portal (http://cms.mpi.univie.ac.at/vasp/). Our calculations have been run with the pseudopotentials treating s and p semi-core states as valence in case for the elements Hf and Zr. The electronic densities and potentials are expanded over plane-waves with energy cutoff of 350 eV. 2x2x2 k-mesh and normal precision were used. The alloys were modeled by supercell containing 128 randomly distributed atoms. At initial step the atoms occupy perfect bcc lattice cites. This initial structure was optimized until energy changes less than 1e-6 eV, while forces acting on atoms don't exceed 1e-2 eV/angstrom. The electron-ion interaction is described by PAW pseudopotentials. The calculations have been collected by sampling chemical compositions across the entire compositional range. The chemical compositions have been sampled by progressively changing the number of atoms per constituent by 4. For each chemical composition of binaries and ternaries, the first-principle calculations have been run for 100 randomized arrangements of the constituents on the BCC lattice sites. We collected data for a total of 3,100 randomized atomic structures over 31 chemical compositions.

36 MATERIALS SCIENCE↗

NbTi_BCC_SolidSolution_128atoms_VASP6

We performed density functional theory (DFT) calculations for body-centered-cubic (BCC) structures with 128 lattices sites of solid solution binary alloys niobium-titanium (Nb-Ti). The electronic structures of alloys have been calculated using Vienna Ab initio Simulation Package (VASP), https://github.com/ORNL/ScalableWorkflow_VASP_Calculations. Within this package the DFT approach is used to reduce many-body Schrodinger equation to set of single particle Kohn-Sham (KS) equations. The generalized electronic exchange-correlation functional is described by generalized gradient approximation with the Perdew-Burke-Ernzerhof parametrization. The electron-ion interactions is described by pseudopotentials developed within the plane-wave basis projector augmented-wave (PAW) approach. These pseudopotentials are available at the VASP portal (http://cms.mpi.univie.ac.at/vasp/). Our calculations have been run with the pseudopotentials treating s and p semi-core states as valence in case for the elements Nb and Ti. The electronic densities and potentials are expanded over plane-waves with energy cutoff of 350 eV. 2x2x2 k-mesh and normal precision were used. The alloys were modeled by supercell containing 128 randomly distributed atoms. At initial step the atoms occupy perfect bcc lattice cites. This initial structure was optimized until energy changes less than 1e-6 eV, while forces acting on atoms don't exceed 1e-2 eV/angstrom. The electron-ion interaction is described by PAW pseudopotentials. The calculations have been collected by sampling chemical compositions across the entire compositional range. The chemical compositions have been sampled by progressively changing the number of atoms per constituent by 4. For each chemical composition of binaries and ternaries, the first-principle calculations have been run for 100 randomized arrangements of the constituents on the BCC lattice sites. We collected data for a total of 3,100 randomized atomic structures over 31 chemical compositions. The calculations have been collected on Air Force HPC11 cluster using the VASP 6.5.1. Additional methodology and file structure information is available in the dataset README.txt file.

36 MATERIALS SCIENCE↗

HfTi_BCC_SolidSolution_128atoms_VASP6

We performed density functional theory (DFT) calculations for body-centered-cubic (BCC) structures with 128 lattices sites of solid solution binary alloys hafnium-titanium (Hf-Ti). The electronic structures of alloys have been calculated using Vienna Ab initio Simulation Package (VASP). Within this package the DFT approach is used to reduce many-body Schrodinger equation to set of single particle Kohn-Sham (KS) equations. The generalized electronic exchange-correlation functional is described by generalized gradient approximation with the Perdew-Burke-Ernzerhof parametrization. The electron-ion interactions is described by pseudopotentials developed within the plane-wave basis projector augmented-wave (PAW) approach. These pseudopotentials are available at the VASP portal (http://cms.mpi.univie.ac.at/vasp/). Our calculations have been run with the pseudopotentials treating s and p semi-core states as valence in case for the elements Hf and Ti. The electronic densities and potentials are expanded over plane-waves with energy cutoff of 350 eV. 2x2x2 k-mesh and normal precision were used. The alloys were modeled by supercell containing 128 randomly distributed atoms. At initial step the atoms occupy perfect bcc lattice cites. This initial structure was optimized until energy changes less than 1e-6 eV, while forces acting on atoms don't exceed 1e-2 eV/angstrom. The electron-ion interaction is described by PAW pseudopotentials. The calculations have been collected by sampling chemical compositions across the entire compositional range. The chemical compositions have been sampled by progressively changing the number of atoms per constituent by 4. For each chemical composition of binaries and ternaries, the first-principle calculations have been run for 100 randomized arrangements of the constituents on the BCC lattice sites. We collected data for a total of 3,100 randomized atomic structures over 31 chemical compositions. The calculations have been collected on Air Force HPC11 cluster using the VASP 6.5.1. Additional methodology and file structure information is available in the dataset README.txt file.

36 MATERIALS SCIENCE↗

TiV_BCC_SolidSolution_128atoms_VASP6

We performed density functional theory (DFT) calculations for body-centered-cubic (BCC) structures with 128 lattices sites of solid solution binary alloys titanium-vanadium (Ti-V). The electronic structures of alloys have been calculated using Vienna Ab initio Simulation Package (VASP). Within this package the DFT approach is used to reduce many-body Schrodinger equation to set of single particle Kohn-Sham (KS) equations. The generalized electronic exchange-correlation functional is described by generalized gradient approximation with the Perdew-Burke-Ernzerhof parametrization. The electron-ion interactions is described by pseudopotentials developed within the plane-wave basis projector augmented-wave (PAW) approach. These pseudopotentials are available at the VASP portal (http://cms.mpi.univie.ac.at/vasp/). Our calculations have been run with the pseudopotentials treating s and p semi-core states as valence in case for the elements Ti and V. The electronic densities and potentials are expanded over plane-waves with energy cutoff of 350 eV. 2x2x2 k-mesh and normal precision were used. The alloys were modeled by supercell containing 128 randomly distributed atoms. At initial step the atoms occupy perfect bcc lattice cites. This initial structure was optimized until energy changes less than 1e-6 eV, while forces acting on atoms don't exceed 1e-2 eV/angstrom. The electron-ion interaction is described by PAW pseudopotentials. The calculations have been collected by sampling chemical compositions across the entire compositional range. The chemical compositions have been sampled by progressively changing the number of atoms per constituent by 4. For each chemical composition of binaries and ternaries, the first-principle calculations have been run for 100 randomized arrangements of the constituents on the BCC lattice sites. We collected data for a total of 3,100 randomized atomic structures over 31 chemical compositions. The calculations have been collected on Air Force HPC11 cluster using the VASP 6.5.1. Additional methodology and file structure information is available in the dataset README.txt file.

36 MATERIALS SCIENCE↗

HfTa_BCC_SolidSolution_128atoms_VASP6

We performed density functional theory (DFT) calculations for body-centered-cubic (BCC) structures with 128 lattices sites of solid solution binary alloys hafnium-tantalum (Hf-Ta). The electronic structures of alloys have been calculated using Vienna Ab initio Simulation Package (VASP). Within this package the DFT approach is used to reduce many-body Schrodinger equation to set of single particle Kohn-Sham (KS) equations. The generalized electronic exchange-correlation functional is described by generalized gradient approximation with the Perdew-Burke-Ernzerhof parametrization. The electron-ion interactions is described by pseudopotentials developed within the plane-wave basis projector augmented-wave (PAW) approach. These pseudopotentials are available at the VASP portal (http://cms.mpi.univie.ac.at/vasp/). Our calculations have been run with the pseudopotentials treating s and p semi-core states as valence in case for the elements Hf and Ta. The electronic densities and potentials are expanded over plane-waves with energy cutoff of 350 eV. 2x2x2 k-mesh and normal precision were used. The alloys were modeled by supercell containing 128 randomly distributed atoms. At initial step the atoms occupy perfect BCC lattice sites. This initial structure was optimized until energy changes less than 1e-6 eV, while forces acting on atoms don't exceed 1e-2 eV/angstrom. The electron-ion interaction is described by PAW pseudopotentials. The calculations have been collected by sampling chemical compositions across the entire compositional range. The chemical compositions have been sampled by progressively changing the number of atoms per constituent by 4. For each chemical composition of binaries and ternaries, the first-principle calculations have been run for 100 randomized arrangements of the constituents on the BCC lattice sites. We collected data for a total of 3,040 randomized atomic structures over 31 chemical compositions. Further methodological and structural information is contained in the dataset README.txt file.

36 MATERIALS SCIENCE↗

Computer Modeling of Electrostatic Aggregation of Granular Materials in Planetary and Astrophysical Settings

Electrostatic forces strongly influence the behavior of granular materials in both dispersed (cloud) systems and semi-packed systems. These forces can cause aggregation or dispersion of particles and are important in a variety of astrophysical and planetary settings. There are also many industrial and commercial settings where granular matter and electrostatics become partners for both good and bad. This partnership is important for human exploration on Mars where dust adheres to suits, machines, and habitats. Long-range Coulombic (electrostatic) forces, as opposed to contact-induced dipoles and van der Waals attractions, are generally regarded as resulting from net charge. We have proposed that in addition to net charge interactions, randomly distributed charge carriers on grains will result in a dipole moment regardless of any net charge. If grains are unconfined, or fluidized, they will rotate so that the dipole always induces attraction between grains. Aggregates are readily formed, and Coulombic polarity resulting from the dipole produces end-to-end stacking of grains to form filamentary aggregates. This has been demonstrated in USML experiments on Space Shuttle where microgravity facilitated the unmasking of static forces. It has also been demonstrated in a computer model using grains with charge carriers of both sign. Model results very closely resembled micro-g results with actual sand grains. Further computer modeling of the aggregation process has been conducted to improve our understanding of the aggregation process, and to provide a predictive tool for microgravity experiments slated for Space Station. These experiments will attempt to prove the dipole concept as outlined above. We have considerably enhanced the original computer model: refinements to the algorithm have improved the fidelity of grain behavior during grain contact, special attention has been paid to simulation time steps to enable establishment of a meaningful, quantitative time axis, and calibration of rounding accuracies have been conducted to test cumulative numerical influences in the model. The model has been run for larger grain populations, variable initial cloud densities, and we have introduced random net charging to individual grains, as well as a net charge to the cloud as a whole. The model uses 3 positive and 3 negative charges randomly distributed on each grain, with up to 160 grains contained within various size "boxes" that define the initial number densities in the clouds. Each charge represents localized charged region on a grain, but does not necessarily imply single quantized charge carriers. The Coulomb equations are then allowed to interact for each monopole: dipoles and any higher order charge coupling is a natural product of these "free" interactions over which the modeler exerts no influence. The charges are placed on surfaces of grains at random locations. A series of runs was conducted for neutral grains that had a perfect balance of negative and positive char carriers. Runs were also conducted with grains having additional fractional charges ranging between 0 and 1. By adding fractional charges of one sign, the model created grain populations in which all grains had excess charges the same sign, giving the cloud an overall net charge. This simulates clouds subjected to ionizing radiation (e. protoplanetary debris disk around a protosun), or any other process of charge biasing in a grain population (e.g., volcanic plumes). In another run series, random fractional charges of either sign were added to the grains so th some grains had a slight net positive charge while others had a slight net negative charge. This simulates triboelectrically-charged grain populations in which acquisition of an electron by one surface is at the expense creating a hole elsewhere. This dual sign charging was applied in two ways: in one case the cloud remained neutral by ensuring that all grain excess charges added to zero; in the other case, the cloud was permitted slight net char by not imposing a charge-balance condition. Additional information is contained in the original.

Marshall, J.↗