Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Exponential distribution”

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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Evolution of the age-included nearest pair distribution in disperse multiphase flows

The age of the nearest particle pair is introduced as the difference between the current time and the most recent time when the nearest particle pair was formed. The evolution equation for the age-included nearest pair distribution function is derived. With the assumption of random destruction of the nearest particle pairs, the evolution equation predicts the exponential probability distribution of the ages of the nearest particle pairs. Particle-resolved numerical simulations with moving particles are performed to verify this prediction. The equation is then used to derive the evolution equation for the particle–fluid–particle (PFP) stress, which is known to be related to hyperbolicity of the two-fluid equations. It is found that the relaxation time of the age probability distribution is also the relaxation time for the PFP stress. Guided by the closure terms in the PFP stress evolution equation, we study kinematics of the nearest particle pairs in the particle-resolved simulations for flows caused by sedimentation of the particles with initially isotropic and homogeneous particle distributions. At the steady states, the particle Reynolds numbers are around 20. Anisotropy and inhomogeneity of particle distributions are seen to develop in these flows. The mean distances to the nearest particles and evolution of the distribution of the Voronoi cell volumes are studied. We also found the PFP stress is closely related to the changes in these inter-particle scale quantities.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1990

A scaling law of radial gas distribution in disk galaxies

Based on the idea that local conditions within a galactic disk largely determine the region's evolution time scale, researchers built a theoretical model to take into account molecular cloud and star formations in the disk evolution process. Despite some variations that may be caused by spiral arms and central bulge masses, they found that many late-type galaxies show consistency with the model in their radial atomic and molecular gas profiles. In particular, researchers propose that a scaling law be used to generalize the gas distribution characteristics. This scaling law may be useful in helping to understand the observed gas contents in many galaxies. Their model assumes an exponential mass distribution with disk radius. Most of the mass are in atomic gas state at the beginning of the evolution. Molecular clouds form through a modified Schmidt Law which takes into account gravitational instabilities in a possible three-phase structure of diffuse interstellar medium (McKee and Ostriker, 1977; Balbus and Cowie, 1985); whereas star formation proceeds presumably unaffected by the environmental conditions outside of molecular clouds (Young, 1987). In such a model both atomic and molecular gas profiles in a typical galactic disk (as a result of the evolution) can be fitted simultaneously by adjusting the efficiency constants. Galaxies of different sizes and masses, on the other hand, can be compared with the model by simply scaling their characteristic length scales and shifting their radial ranges to match the assumed disk total mass profile sigma tot(r).

Wang, Zhong↗
NASA NTRS1984

Linear distributed parameter systems - Closed-loop exponential stability with a finite-dimensional controller

Theoretical results are presented which characterize the linear distributed parameter system (DPS) which can be (exponentially) stabilized by a finite-dimensional controller. This characterization relies on stabilizing subspaces and the solvability of the nonlinear asymmetric Riccati equation. Also considered are connections with the usual model reduction approaches to finite-dimensional DPS controller design.

Balas, M. J.↗
NASA NTRS1974

The effect of Be/+/ ion implanted exponential and uniform impurity profiles on the electrical characteristics of GaAs solar cells

The high surface recombination velocity is the major deterrent to obtaining efficient GaAs solar cells. If, however, an electric field is built in at the surface, the carriers will be swept away from the surface thus minimizing the surface recombination velocity problem. It has been previously shown theoretically that an exponential impurity distribution in the doped region of the cell results in a built-in electric field. Ion implantation was used to produce solar cells with an exponential impurity profile and cells with uniform profiles. It is shown that cells with an exponential impurity profile have higher open-circuit voltage, fill factors, and spectral response than those with a uniform impurity profile.

Vaidyanathan, K. V.↗
NASA NTRS1977

Sampling errors in the measurement of rain and hail parameters

Attention is given to a general derivation of the fractional standard deviation (FSD) of any integrated property X such that X(D) = cD to the n. This work extends that of Joss and Waldvogel (1969). The equation is applicable to measuring integrated properties of cloud, rain or hail populations (such as water content, precipitation rate, kinetic energy, or radar reflectivity) which are subject to statistical sampling errors due to the Poisson distributed fluctuations of particles sampled in each particle size interval and the weighted sum of the associated variances in proportion to their contribution to the integral parameter to be measured. Universal curves are presented which are applicable to the exponential size distribution permitting FSD estimation of any parameters from n = 0 to n = 6. The equations and curves also permit corrections for finite upper limits in the size spectrum and a realistic fall speed law.

Gertzman, H. S.↗
NASA NTRS1999

Rain Fallspeeds and Rates Derived from Airborne Nadir-Pointing Doppler Radar Measurements

The use of vertical-incidence Doppler velocity in addition to radar reflectivity may yield information on drop size distribution and therefore result in better rainrate estimates. Doppler velocity can provide useful information on the raindrop size distribution. Doppler velocities from a zenith-pointing radar represent the sum of the mean reflectivity-weighted hydrometeor fallspeed and the vertical air motion. Dual-parameter rain estimation methods using the Doppler velocity, require that the latter can be removed, or is negligible. Atlas et al. (1972) derived relations between Doppler velocity, reflectivity, and rain rate assuming an exponential size distribution for rain. Ulbrich (1994) expanded on this work by deriving the relation between the Doppler velocity and the reflectivity assuming a Gamma size distribution. This distribution provides a more realistic representation of the small rain drops. To get accurate information on raindrop size distributions with the above method, the air motions must be removed from the observed Doppler velocities

Heymsfield, Gerald M.↗
NASA NTRS1982

Light ion concentrations in Jupiter's inner magnetosphere

The light ion distribution in the inner Jovian magnetosphere is investigated using whistler dispersion measurements from the Voyager 1 plasma wave instrument and heavy ion plasma concentrations from the plasma instrument. Two models are developed for the light ion concentration over 14 L shells between L = 5.2 and 6.2, one giving a constant concentration along the field line and the other corresponding to an exponential density distribution. Due to heavy ion concentrations near the equator that are typically an order of magnitude larger than the light ion concentration, results obtained are mainly relevant to the light ion concentration outside of the torus. Light ion concentration near the equator ranges from about 1-10% of the heavy ion concentration, while outside the torus the light ions are the dominant species.

Tokar, R. L.↗
DOE OSTI2022

Sizes of pure and doped helium droplets from single shot x-ray imaging

Advancements in x-ray free-electron lasers on producing ultrashort, ultrabright, and coherent x-ray pulses enable single-shot imaging of fragile nanostructures, such as superfluid helium droplets. Furthermore, this imaging technique gives unique access to the sizes and shapes of individual droplets. In the past, such droplet characteristics have only been indirectly inferred by ensemble averaging techniques. Here, we report on the size distributions of both pure and doped droplets collected from single-shot x-ray imaging and produced from the free-jet expansion of helium through a 5 μm diameter nozzle at 20 bars and nozzle temperatures ranging from 4.2 to 9 K. This work extends the measurement of large helium nanodroplets containing 10 9 –10 11 atoms, which are shown to follow an exponential size distribution. Additionally, we demonstrate that the size distributions of the doped droplets follow those of the pure droplets at the same stagnation condition but with smaller average sizes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Biophotonic rogue waves in red blood cell suspensions

Rogue waves are ubiquitous in nature, appearing in a variety of physical systems ranging from acoustics, microwave cavities, optical fibers, and resonators to plasmas, superfluids, and Bose–Einstein condensates. Unlike nonlinear solitary waves, rogue waves are extreme events that can occur even without nonlinearity by, for example, spontaneous synchronization of waves with different spatial frequencies in a linear system. Here, we report the observation of rogue-wave-like events in human red blood cell (RBC) suspensions under weak light illumination, characterized by an abnormal L-shaped probability distribution. Such biophotonic extreme events arise mostly due to the constructive interference of Mie-scattered waves from the suspended RBCs, whose biconcave shape and mutable orientation give rise to a time-dependent random phase modulation to an incident laser beam. We numerically simulate the beam propagation through the colloidal suspensions with added disorder in both spatial and temporal domains to mimic random scattering due to Brownian motion. In addition, at high power levels, nonlinear beam self-focusing is also observed, leading to a dual-exponential probability distribution associated with the formation of multiple soliton-like spots. Such rogue wave events should also exist in environments with cells of other species such as swimming bacteria, and understanding of their underlying physics may lead to unexpected biophotonic applications.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Perturbative readout-error mitigation for near-term quantum computers

Readout errors on near-term quantum computers can introduce significant error to the empirical probability distribution sampled from the output of a quantum circuit. These errors can be mitigated by classical postprocessing given the access of an experimental response matrix that describes the error associated with the measurement of each computational basis state. However, the resources required to characterize a complete response matrix and to compute the corrected probability distribution scale exponentially with the number of qubits, n . In this work, we modify standard matrix inversion techniques using perturbative approximations with significantly reduced complexity and bounded error when the likelihood of high-order bit-flip events is strongly suppressed. Given a characteristic error rate q , we discuss a method to recover the probability of the all-zeros bit string p 0 by sampling only a small subspace of the response matrix before inverting readout error, resulting in a relative speedup of poly [ 2 n / ( n w ) ] , which we motivate using a simplified error model for which the approximation incurs only O ( q w ) error for some integer w . We then provide a generalized technique to efficiently recover full output distributions with O ( q w ) error in the perturbative limit. These approximate techniques for readout-error correction may greatly accelerate near-term quantum computing applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Counting generations in birth and death processes with competing Erlang and exponential waiting times

Lymphocyte populations, stimulated in vitro or in vivo, grow as cells divide. Stochastic models are appropriate because some cells undergo multiple rounds of division, some die, and others of the same type in the same conditions do not divide at all. If individual cells behave independently, then each cell can be imagined as sampling from a probability density of times to division and death. The exponential density is the most mathematically and computationally convenient choice. It has the advantage of satisfying the memoryless property, consistent with a Markov process, but it overestimates the probability of short division times. With the aim of preserving the advantages of a Markovian framework while improving the representation of experimentally-observed division times, we consider a multi-stage model of cellular division and death. We use Erlang-distributed (or, more generally, phase-type distributed) times to division, and exponentially distributed times to death. We classify cells into generations, using the rule that the daughters of cells in generation n are in generation n + 1. In some circumstances, our representation is equivalent to established models of lymphocyte dynamics. We find the growth rate of the cell population by calculating the proportions of cells by stage and generation. The exponent describing the late-time cell population growth, and the criterion for extinction of the population, differs from what would be expected if N steps with rate λ were equivalent to a single step of rate λ/N. We link with a published experimental dataset, where cell counts were reported after T cells were transferred to lymphopenic mice, using Approximate Bayesian Computation. In the comparison, the death rate is assumed to be proportional to the generation and the Erlang time to division for generation 0 is allowed to differ from that of subsequent generations. The multi-stage representation is preferred to a simple exponential in posterior distributions, and the mean time to first division is estimated to be longer than the mean time to subsequent divisions.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

High Resolution Data Analysis: Plans and Prospects [Book Chapter]

Herein, a report on the progress on the high resolution data analysis of the ADMX experimental results is presented. In this paper, tools are developed and tested on a blind injection mimicking a Maxwellian like signal in the frequency domain. This blind injection will be used as a test bed which can be later implemented on all the high resolution data. The high resolution data is stored in the Fermilab server. In this analysis a PostgreSQL query was made to ensure the blind injection is in the middle of the frequency spectrum and 19 such files were found. The time series data is read using a c++ program. An apodization function is applied on the time series data and zero filled to reduce the frequency spacing in order to achieve a better interpolation. A FFTW header is used to compute the Fourier transform of the time series data. A Savitzky–Golay filter is applied on the unnormalized power which then can be used to remove the spectral shape. Each frequency spectrum has a bandwidth of 50 kHz.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Reducing dielectric loss and enhancing electrical insulation for multilayer polymer films by nanoconfined ion transport under high poling electric fields

High temperature polar polymers have demonstrated potential for good thermal stability and high dielectric constant at the same time. However, polarization of contaminated impurity ions in polar polymers, even at the ppm level, can significantly increase the dielectric loss at high temperature and low frequencies. One effective strategy to mitigate this problem is to multilayer them with a high temperature nonpolar dielectric polymer to confine impurity ion transport at the nanometer scale. In this study, confined ion transport in high temperature polycarbonate (HTPC)/poly(vinylidene fluoride) (PVDF) multilayer films under high AC electric fields was studied using a direct analytical simulation method. Different from the ion transport under low fields, the ion diffusion model failed to describe the ion transport under high electric fields. An exponential ion distribution profile, which was observed for the DC poling situation, was employed to implement the direct analytical simulation. Confined impurity ion transport under high AC fields was quantitatively understood. As the AC field increased, the mobile ion concentration decreased whereas the diffusion coefficient increased. The decrease of mobile ion concentration was explained by the blockage of impurity ions by the HTPC layers. This knowledge helped in the determination of optimal conditions to polarize impurity ions from the PVDF layers into the HTPC layers. After cooling below the glass transition temperature of HTPC, polarized impurity ions were locked inside the HTPC layers. As a result, increased discharge efficiency and enhanced electrical insulation (i.e., increased dielectric breakdown strength) were achieved for the polarized multilayer films.

36 MATERIALS SCIENCE↗
DOE OSTI2020

A quantum algorithm to efficiently sample from interfering binary trees

Quantum computers provide an opportunity to efficiently sample from probability distributions that include non-trivial interference effects between amplitudes. Using a simple process wherein all possible state histories can be specified by a binary tree, we construct an explicit quantum algorithm that runs in polynomial time to sample from the process once. The corresponding naive Markov Chain algorithm does not produce the correct probability distribution and an explicit classical calculation of the full distribution requires exponentially many operations. Finally, the problem can be reduced to a system of two qubits with repeated measurements, shedding light on a quantum-inspired efficient classical algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

The Cosmic Evolution of C IV Absorbers at 1.4 < z < 4.5: Insights from 100,000 Systems in DESI Quasars

We present the largest catalog to date of triply ionized carbon (C IV ) absorbers detected in quasar spectra from the Dark Energy Spectroscopic Instrument. Using an automated matched-kernel convolution method with adaptive signal-to-noise thresholds, we identify 101,487 C IV systems in the redshift range 1.4 < z < 4.5 from 300,637 quasar spectra. Completeness is estimated via Monte Carlo simulations, and the catalog is 50% complete at EW C IV ≥ 0.4 Å. The differential equivalent width frequency distribution declines exponentially and shows weak redshift evolution. The absorber incidence per unit comoving path increases by a factor of 2–5 from z ≈ 4.5 to z ≈ 1.4, with stronger redshift evolution for strong systems. Using column densities derived from the apparent optical depth method, we constrain the cosmic mass density of C IV , Ω C IV , which increases by a factor of ∼3.8 from (0.82 ± 0.05) × 10 −8 at z ≈ 4.5 to (3.16 ± 0.2) × 10 −8 at z ≈ 1.4. From Ω C IV , we estimate a lower limit on intergalactic medium metallicity ${\mathrm{log}}({Z}_{{\rm{IGM}}}/{Z}_{\odot })\gtrsim -3.25$ at z ∼ 2.3, with a smooth decline at higher redshifts. These trends trace the cosmic star formation history and He II photoheating rate, suggesting a link between C IV enrichment, star formation, and UV background over ∼3 Gyr. The catalog also provides a critical resource for future studies connecting circumgalactic metals to galaxy evolution, especially near cosmic noon.

79 ASTRONOMY AND ASTROPHYSICS↗