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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.

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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Tempered fractional calculus

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

A NUMERICAL STUDY OF DIFFUSIVE COSMIC-RAY TRANSPORT WITH ADIABATIC FOCUSING

Focused particle transport in a nonuniform large-scale magnetic field is investigated numerically in the case of isotropic pitch-angle scattering. Evolving particle density profiles and distribution moments are computed from solutions of a system of stochastic differential equations, equivalent to the original Fokker-Planck equation for the particle distribution. Conflicting analytical predictions for the transport coefficients in the diffusion limit, independently calculated by Beeck and Wibberenz and Shalchi, are compared with the numerical results. The reasons for the discrepancies among the analytical and numerical treatments, as well as the general limitations of the diffusion model, are discussed. The telegraph equation, derived in a higher-order expansion of the particle distribution function, is shown to describe the particle transport much more accurately than the diffusion model, especially ahead of a moving density pulse.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Stranski-Krastanow islanding initiated on the stochastic rough surfaces of the epitaxially strained thin films

Quantum dots (QD) have discrete energy spectrum, which can be adjusted over a wide range by tuning composition, density, size, lattice strain, and morphology. These features make quantum dots attractive for the design and fabrication of novel electronic, magnetic and photonic devices and other functional materials used in cutting-edge applications. The formation of QD on epitaxially strained thin film surfaces, known as Stranski-Krastanow (SK) islands, has attracted great attention due to their unique electronic properties. Here, we present a systematic dynamical simulation study for the spontaneous evolution of the SK islands on the stochastically rough surfaces (nucleationless growth). During the development of SK islands through the mass accumulation at randomly selected regions of the film via surface drift-diffusion (induced by the capillary and mismatch stresses) with and/or without growth, one also observes the formation of an extremely thin wetting layer having a thickness of a few Angstroms. Above a certain threshold level of the mismatch strain and/or the size of the patch, the formation of multiple islands separated by shallow wetting layers is also observed as metastable states such as doublets even multiplets. These islands are converted into a distinct SK islands after long annealing times by coalescence through the long range surface diffusion. Extensive computer simulation studies demonstrated that after an initial transient regime, there is a strong quadratic relationship between the height of the SK singlet and the intensity of the lattice mismatch strain (in a wide range of stresses up to 8.5 GPa for germanium thin crystalline films), with the exception at those critical points where the morphological (shape change with necking) transition takes place.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

A NUMERICAL SIMULATION OF COSMIC RAY MODULATION NEAR THE HELIOPAUSE. II. SOME PHYSICAL INSIGHTS

Cosmic ray (CR) transport near the heliopause (HP) is studied using a hybrid transport model, with the parameters constrained by observations from the Voyager 1 spacecraft. We simulate the CR radial flux along different directions in the heliosphere. There is no well-defined thin layer between the solar wind region and the interstellar region along the tail and polar directions of the heliosphere. By analyzing the radial flux curve along the direction of Voyager 2 , together with its trajectory information, the crossing time of the HP by Voyager 2 is predicted to be in 2017.14. We simulate the CR radial flux for different energy values along the direction of Voyager 1 . We find that there is only a modest modulation region of about 10 au wide beyond the HP, so that Voyager 1 observing the Local Interstellar Spectra is justified in numerical modeling. We analyze the heliospheric exit information of pseudo-particles in our stochastic numerical (time-backward) method, conjecturing that they represent the behavior of CR particles, and we find that pseudo-particles that have been traced from the nose region exit in the tail region. This implies that many CR particles diffuse directly from the heliospheric tail region to the nose region near the HP. In addition, when pseudo-particles were traced from the Local Interstellar Medium (LISM), it is found that their exit location (entrance for real particles) from the simulation domain is along the prescribed Interstellar Magnetic Field direction. This indicates that parallel diffusion dominates CR particle transport in the LISM.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Fractional Modeling in Action: A Survey of Nonlocal Models for Subsurface Transport, Turbulent Flows, and Anomalous Materials

Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior with greater efficiency than fully-resolved classical models. In this review article, we first provide a broad overview of fractional-order derivatives with a clear emphasis on the stochastic processes that underlie their use. We then survey three exemplary application areas – subsurface transport, turbulence, and anomalous materials – in which fractional-order differential equations provide accurate and predictive models. For each area, we report on the evidence of anomalous behavior that justifies the use of fractional-order models, and survey both foundational models as well as more expressive state-of-the-art models. We also propose avenues for future research, including more advanced and physically sound models, as well as tools for calibration and discovery of fractional-order models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

The theory of stochastic cosmological lensing

On the scale of the light beams subtended by small sources, e.g. supernovae, matter cannot be accurately described as a fluid, which questions the applicability of standard cosmic lensing to those cases. In this article, we propose a new formalism to deal with small-scale lensing as a diffusion process: the Sachs and Jacobi equations governing the propagation of narrow light beams are treated as Langevin equations. We derive the associated Fokker-Planck-Kolmogorov equations, and use them to deduce general analytical results on the mean and dispersion of the angular distance. This formalism is applied to random Einstein-Straus Swiss-cheese models, allowing us to: (1) show an explicit example of the involved calculations; (2) check the validity of the method against both ray-tracing simulations and direct numerical integration of the Langevin equation. As a byproduct, we obtain a post-Kantowski-Dyer-Roeder approximation, accounting for the effect of tidal distortions on the angular distance, in excellent agreement with numerical results. Besides, the dispersion of the angular distance is correctly reproduced in some regimes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Simulating the mechanisms of serrated flow in interstitial alloys with atomic resolution over diffusive timescales

Abstract The Portevin-Le Chatelier (PLC) effect is a phenomenon by which plastic slip in metallic materials becomes unstable, resulting in jerky flow and the onset of inhomogeneous deformation. The PLC effect is thought to be fundamentally caused by the dynamic interplay between dislocations and solute atoms. However, this interplay is almost always inaccessible experimentally due to the extremely fine length and time scales over which it occurs. In this paper, simulations of jerky flow in W-O interstitial solid solutions reveal three dynamic regimes emerging from the simulated strain rate-temperature space: one resembling standard solid solution strengthening, another one mimicking solute cloud formation, and a third one where dislocation/solute coevolution leads to jerky flow as a precursor of dynamic strain aging. The simulations are carried out in a stochastic framework that naturally captures rare events in a rigorous manner, providing atomistic resolution over diffusive time scales using no adjustable parameters.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Enabling probabilistic learning on manifolds through double diffusion maps

Here, we present a generative learning framework for probabilistic sampling that extends Probabilistic Learning on Manifolds (PLoM), which is designed to generate statistically consistent realizations of a random vector in a finite-dimensional Euclidean space, informed by a (representative) set of observations. In its original form, PLoM constructs a reduced-order probabilistic model by combining three main components: (a) kernel density estimation to approximate the underlying probability measure, (b) Diffusion Maps to characterize the manifold of the data, and (c) a reduced-order Itô Stochastic Differential Equation (ISDE) to sample from the learned distribution. However, its sampling dynamics are posed in the ambient space and the retained number of reduced coordinates is chosen by projection-reconstruction error. In practice, this often (i) requires more coordinates than the data’s intrinsic dimension to achieve stable sampling and (ii) lacks a smooth, basis-independent lifting back to the data domain; moreover, standard Diffusion Maps emphasize harmonic eigenfunctions and can miss non-harmonic latent structure. We address these limitations by decoupling geometry learning from sampling: a first Diffusion Maps pass identifies non-harmonic coordinates on which we formulate a full-order ISDE directly in the latent space, while Double Diffusion Maps captures multiscale geometric features and Geometric Harmonics (GH) learns a smooth lifting map to the ambient variables that is independent of the particular diffusion basis. This hybrid design preserves the system’s dynamical richness with a compact geometric representation and enables principled out-of-sample inference. The effectiveness and robustness of the proposed method are illustrated through two numerical studies: one based on data generated from two-dimensional Hermite polynomial functions and another based on high-fidelity simulations of a detonation wave in a reactive flow.

Double diffusion maps↗
DOE OSTI2025

Generative learning of densities on manifolds

A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent) spaces in the high-dimensional data (ambient) space. Two approaches for sampling from the latent data density are described. The first is a score-based diffusion model, which is trained to map a standard normal distribution to the latent data distribution using a neural network. The second one involves solving an Itô stochastic differential equation in the latent space. Additional realizations of the data are generated by lifting the samples back to the ambient space using Double Diffusion Maps , a recently introduced technique typically employed in studying dynamical system reduction; here the focus lies in sampling densities rather than system dynamics. The proposed approaches enable sampling high dimensional data densities restricted to low-dimensional, a priori unknown manifolds. The efficacy of the proposed framework is demonstrated through a benchmark problem and a material with multiscale structure.

Double diffusion maps↗
DOE OSTI2015

Energy in density gradient

Inhomogeneous plasmas and fluids contain energy stored in inhomogeneity and they naturally tend to relax into lower energy states by developing instabilities or by diffusion. But the actual amount of energy in such inhomogeneities has remained unknown. In the present work, the amount of energy stored in a density gradient is calculated for several specific density profiles in a cylindrical configuration. This is of practical importance for drift wave instability in various plasmas, and, in particular, in its application in models dealing with the heating of solar corona because the instability is accompanied with stochastic heating, so the energy contained in inhomogeneity is effectively transformed into heat. It is shown that even for a rather moderate increase of the density at the axis in magnetic structures in the corona by a factor 1.5 or 3, the amount of excess energy per unit volume stored in such a density gradient becomes several orders of magnitude greater than the amount of total energy losses per unit volume (per second) in quiet regions in the corona. Consequently, within the life-time of a magnetic structure such energy losses can easily be compensated by the stochastic drift wave heating.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Spatial dependence of the growth of polycyclic aromatic compounds in an ethylene counterflow flame

The complex environments that characterize combustion systems can influence the distribution of gas-phase species, the relative importance of various growth mechanisms and the chemical and physical characteristics of the soot precursors generated. In order to provide molecular insights on the effect of combustion environments on the formation of gas-phase species, in this paper, we study the temporal and spatial dependence of soot precursors growth mechanisms in an ethylene/oxygen/argon counterflow diffusion flame. As computational tools of investigation, we included fluid dynamics simulations and stochastic discrete modeling. Results show the relative importance of various reaction pathways in flame, with the hydrogen-abstraction-acetylene-addition mechanism contributing to the formation of pure hydrocarbons near the stagnation plane, and oxygen chemistry prevailing near the maximum temperature region, where the concentration of atomic oxygen reaches its peak and phenols, ethers and furan-embedded species are formed. The computational results show excellent agreement with measurements obtained using aerosol mass spectrometry coupled with vacuum-ultraviolet photoionization. Knowledge acquired in this study can be used to predict the type of compounds formed in various locations of the flame and eventually provide insights on the environmental parameters that influence the growth of soot precursors. In addition, the results reported in this paper highlight the importance of modeling counterflow flames in two or three dimensions to capture the spatial dependence of growth mechanisms of soot precursors.

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

Effect of particle size on the capture of uranium oxide colloidal particles from aqueous suspensions via high-gradient magnetic filtration

The effectiveness of High Gradient Magnetic Filtration (HGMF) in capturing uranium oxide particles from suspensions was investigated in this study. Two sets of experiments were performed to evaluate the importance of size on the capture of uranium oxide particles. The first considered two batches sieved into size bins of< 5, 5–10, 10–15, and 15–20 µm, while the second was performed using two suspensions with diameters smaller than 1.0 µm and between 1.0 and 1.5 µm. Iron oxide experiments, with particles between 0.3 and 0.8 µm, were performed for calibration purposes. In all experiments, a surfactant (Triton-X100 or sodium dodecyl sulfate) was used to prevent particle aggregation and limit the influence of non-magnetic capture mechanisms. A magnetic field of approximately 1.1 Tesla was generated using a water cooled electromagnet. HGMF was performed using tubular filters packed with ferromagnetic stainless-steel wool. Of the initial four uranium oxide particle sizes, magnetic capture was only observed for particles with a diameter of less than 5 µm, while larger particles experienced no magnetic and minimal total capture. For particles with diameters smaller than 1.0 µm and between 1.0 and 1.5 µm, capture efficiencies increased by 39 ± 9% and 34 ± 6% respectively, solely due to the magnetic field. Although the magnetic force is proportional to particle diameter, the capture efficiency decreased as diameter increased. So these results suggest that Brownian diffusion, which is influential for micron sized particles and increases with decreasing particle size, is acting in conjunction with the magnetic force to influence the efficacy of HGMF for uranium oxide. This important finding underscores the effectiveness of Brownian diffusion in increasing the rate of collision between particles and collector fibers. A stochastic trajectory model was developed to incorporate the influence of Brownian motion on particle behavior and filter removal efficiency. Modeling results are discussed and compared for uranium and iron oxide particles.

42 ENGINEERING↗
DOE OSTI2019

A Fokker–Planck approach to a moment closure for mixing in variable-density turbulence

We develop a theory for the cascade mixing terms in a moment closure approach to binary active scalar mixing in variable-density turbulence. To address the variable-density complications we apply, as a principle and constraint, the conservation of the probability density function (PDF) through a Fokker–Planck equation with bounded sample space whose attractor is the beta PDF with skewness. Mixing is related to a single-point PDF as a realisability principle to provide mathematically rigorous expressions for the small scale statistics in terms of largescale moments. The problem of the unknown small-scale mixing is replaced with the determination of the drift and diffusion terms of a Fokker–Planck equation in a beta-PDF-convergent stochastic process. We find that realisability of a beta-convergent process requires the mixing time-scale ratio, taken as a constant in passive scalar mixing, to be a function of the mean mass fraction, mean fluid density, the Atwood number, the density-volume correlation and moments of the density field. We develop and compare the new model with direct numerical simulations data of non-stationary homogeneous variable-density turbulence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1984

Chaotic ion motion in magnetosonic plasma waves

The motion of test ions in a magnetosonic plasma wave is considered, and the 'stochasticity threshold' of the wave's amplitude for the onset of chaotic motion is estimated. It is shown that for wave amplitudes above the stochasticity threshold, the evolution of an ion distribution can be described by a diffusion equation with a diffusion coefficient D approximately equal to 1/v. Possible applications of this process to ion acceleration in flares and ion beam thermalization are discussed.

Varvoglis, H.↗
NASA NTRS1987

Simulation of charged particle transport on the MPP

Computations of cosmic ray transport based upon finite difference methods are afflicted by instabilities, inaccuracies, and artifacts. To avoid these problems, a Monte Carlo formulation was developed which is closely related not only to the finite difference formulation, but also to the underlying physics of transport phenomena. Implementations of this approach are currently running on the Massively Parallel Processor at Goddard, whose enormous computing power overwhelms the poor statistical accuracy that usually limits the use of stochastic methods. In a Monte Carlo simulation of rectilinear transport, the coherent and diffusive effects that appeared are in good quantitative agreement with both finite difference and analytical calculations.

Earl, James A.↗
DOE OSTI2017

Precipitation and Release of Solar Energetic Particles from the Solar Coronal Magnetic Field

Most solar energetic particles (SEPs) are produced in the corona. They propagate through complex coronal magnetic fields subject to scattering and diffusion across the averaged field lines by turbulence. We examine the behaviors of particle transport using a stochastic 3D focused transport simulation in a potential field source surface model of coronal magnetic field. The model is applied to an SEP event on 2010 February 7. We study three scenarios of particle injection at (i) the compact solar flare site, (ii) the coronal mass ejection (CME) shock, and (iii) the EUV wave near the surface. The majority of particles injected on open field lines are able to escape the corona. We found that none of our models can explain the observations of wide longitudinal SEP spread without perpendicular diffusion. If the perpendicular diffusion is about 10% of what is derived from the random walk of field lines at the rate of supergranular diffusion, particles injected at the compact solar flare site can spread to a wide range of longitude and latitude, very similar to the behavior of particles injected at a large CME shock. Stronger pitch-angle scattering results in a little more lateral spread by holding the particles in the corona for longer periods of time. Some injected particles eventually end up precipitating onto the solar surface. Even with a very small perpendicular diffusion, the pattern of the particle precipitation can be quite complicated depending on the detailed small-scale coronal magnetic field structures, which could be seen with future sensitive gamma-ray telescopes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Combined effects of gas pressure and exciting frequency on electron energy distribution functions in hydrogen capacitively coupled plasmas

The combined effects of the variation of hydrogen pressure (40-400 mTorr) and exciting frequency (13.56-50 MHz) on the electron energy probability function (EEPF) and other plasma parameters in capacitively coupled hydrogen H{sub 2} discharge at fixed discharge voltage were investigated using rf-compensated Langmuir probe. At a fixed exciting frequency of 13.56 MHz, the EEPF evolved from Maxwellian-like distribution to a bi-Maxwellian distribution when the H{sub 2} pressure increased, possibly due to efficient vibrational excitation. The electron density largely increased to a peak value and then decreased with the increase of H{sub 2} pressure. Meanwhile, the electron temperature and plasma potential significantly decrease and reaching a minimum at 120 mTorr beyond, which saturated or slightly increases. On the other hand, the dissipated power and electron density markedly increased with increasing the exciting frequency at fixed H{sub 2} pressure and voltage. The electron temperatures negligibly dependent on the driving frequency. The EEPFs at low pressure 60 mTorr resemble Maxwellian-like distribution and evolve into a bi-Maxwellian type as frequency increased, due to a collisonless (stochastic) sheath-heating in the very high frequency regime, while the EEPF at hydrogen pressure {>=}120 mTorr retained a bi-Maxwellian-type distribution irrespective of the driving frequency. Such evolution of the EEPFs shape with the driving frequency and hydrogen pressure has been discussed on the basis of electron diffusion processes and low threshold-energy inelastic collision processes taking place in the discharge. The ratio of stochastic power to bulk power heating ratio is dependent on the hydrogen pressure while it is independent on the driving frequency.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Quantifying Resolution Implications for Agent-based Distributed Energy Resource Customer Adoption Models

In this report we explore tradeoffs of top-down and bottom-up methods in their precision and computational burden using NREL's dGen model, an agent-based model of residential and non-residential distributed PV adoption. In particular, we assess the role of agent resolution in instantiating statistically-representative populations in the model--and the resulting variance of model projections at the state, sector and county levels. Running the model for a single state with fixed macroeconomic assumptions, we vary both the number of agents instantiated and the number of unique simulations. Notably, in each run we introduce sources of uncertainty in cumulative DPV adoption results during agent instantiation as we stochastically sample agent attributes from localized building characteristic and solar resource distributions. We find three key trends which guide what can be expected of results. First, precision of the model projections, as measured by the variance of the unique simulations increased as a function of the number of agents sampled, though with diminishing returns to scale. The result is expected given the Law of Large Numbers. Second, the mean or expected value of projections decreased as the number of agents instantiated increased. Empirically, aggregate DPV capacities projected by dGen are 7% lower on average at a 10-agent resolution compared to 1-agent resolutions, and up to 10% lower in the non-residential sector. We attribute this outcome to a system sizing scheme that biases lower cumulative installed capacity as agent resolution increases when roof size and load are not positively correlated. Finally, the variance of model projections differed by sector, where variance was substantially larger in the commercial sector, largely due to differences in parameterization by sector. We explain the larger variance in the non-residential sector as an outcome of the greater variance in building uses and load shapes as compared to the residential sector, and we find that a resolution on the order of 100-agents per county would be necessary to bring non-residential variance in line with residential variance at a 2-agent resolution. We propose that further research explore increasing precision and agent resolution in the non-residential sector. Moreover, given that days of intensive computing may be required to resolve a suitable estimate even at the extent of a single state within acceptable levels of precision, to promote computational efficiency we also suggest more clearly quantifying sources of variability at the county level such that resolution can by dynamically increased where county level results are least precise.

14 SOLAR ENERGY↗