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At least 937 records · Page 52
All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

Stochastic partial differential equations in turbulence related problems

The theory of stochastic partial differential equations (PDEs) and problems relating to turbulence are discussed by employing the theories of Brownian motion and diffusion in infinite dimensions, functional differential equations, and functional integration. Relevant results in probablistic analysis, especially Gaussian measures in function spaces and the theory of stochastic PDEs of Ito type, are taken into account. Linear stochastic PDEs are analyzed through linearized Navier-Stokes equations with a random forcing. Stochastic equations for waves in random media as well as model equations in turbulent transport theory are considered. Markovian models in fully developed turbulence are discussed from a stochastic equation viewpoint.

Chow, P.-L.↗
NASA NTRS1982

Radiation and chemistry in the stratosphere - Sensitivity to O2 absorption cross sections in the Herzberg continuum

It is suggested that the discrepancies between observed and modeled vertical profiles of such halocarbons as CFCl3, as well as the problem of simultaneously fitting N2O, CH4, CF2Cl2 and CFCl3 profiles with a single eddy diffusion model, are due to an overestimation of the molecular oxygen absorption cross sections in the 200-220 nm spectral region. The replacement of current O2 cross sections in this range with values that are in better agreement with results for the compounds cited leads to N2O, CF2Cl2 and CFCl3 concentration reductions of factors 0.70, 0.62 and 0.19, respectively. Profiles of CH4, H2 and CO remain unchanged, and the predicted concentration of HNO3 above 30 km is reduced by about 50% for yet another improved fit with observations. It is noted that the correction proposed produces a 30% ozone increase near the 20-25 km peak.

Froidevaux, L.↗
NASA NTRS1985

Cosmic ray modulation in a random anisotropic magnetic field

Inhomogeneities of the interplanetary magnetic field can be divided into small scale and large scale ones as may be required by the character of the problem of cosmic ray (CR) propagation. CR propagation in stochastic magnetic fields is of diffusion character. The main contribution into the scattering of CR particles is made by their interaction with inhomogeneities of the magnetic field H which have characteristic dimensions 1 of the order of Larmor radius R=cp/eH of particle (p is the absolute value of particle momentum, e is particle charge, c is velocity of light). Scattering of particles on such inhomogeneities leads to their diffusion mostly along a magnetic field with characteristic dimensions of variation in space exceeding the mean free path.

Dorman, L. I.↗
NASA NTRS1985

Preliminary study: Moisture-polymer interaction. Stuby objectives

The problems associated with mathematically modeling water-module interaction phenomena, including sorption and desorption, diffusion, and permeation are discussed. With reliable analytical models, an extensive materials data base, and solar radiation surface meteorological observations (SOLMET) weather data, predicting module lifetimes in realistic environments can become a practical reality. The status of the present techniques of simulating the various transport mechanisms was reported. The Dent model (a modified Brunauer-Emmet-Teller) approach represented polyvinyl butyral (PVB) sorption data. A 100-layer material model and Fick's diffusion model gave diffusivity values exhibiting adequate agreement with those measured for PVB. Diffusivity of PVB is concentration dependent, decreasing as the water content in PVB increases. The temperature dependence of diffusion in PVB is well modeled by the Arrhenius rate equation. Equilibrium conductivity and leakage current data are well represented by Hearle's model for bulk ionic conductivity. A nodal network analysis using the Systems Improved Numerical Differencing Analyzer (SINDA) Thermal Analyzer gave reasonable correlation with measurable data. It is concluded that realistic lifetime predictions seem to be feasible.

Wen, L. C.↗
NASA NTRS1987

Particle acceleration at shocks - A Monte Carlo method

A Monte Carlo method is presented for the problem of acceleration of test particles at relativistic shocks. The particles are assumed to diffuse in pitch angle as a result of scattering off magnetic irregularities frozen into the fluid. Several tests are performed using the analytic results available for both relativistic and nonrelativistic shock speeds. The acceleration at relativistic shocks under the influence of radiation losses is investigated, including the effects of a momentum dependence in the diffusion coefficient. The results demonstrate the usefulness of the technique in those situations in which the diffusion approximation cannot be employed, such as when relativistic bulk motion is considered, when particles are permitted to escape at the boundaries, and when the effects of the finite length of the particle mean free path are important.

Kirk, J. G.↗
NASA NTRS1995

Non-local transport in turbulent MHD convection

The nonlocal non-diffusive transport of passive scalars in turbulent magnetohydrodynamic (MHD) convection is investigated using transilient matrices. These matrices describe the probability that a tracer particle beginning at one position in a flow will be advected to another position after some time. A method for the calculation of these matrices from simulation data which involves following the trajectories of passive tracer particles and calculating their transport statistics, is presented. The method is applied to study the transport in several simulations of turbulent, rotating, three dimensional compressible, penetrative MDH convection. Transport coefficients and other diagnostics are used to quantify the transport, which is found to resemble advection more closely than diffusion. Some of the results are found to have direct relevance to other physical problems, such as the light element depletion in sun-type stars. The large kurtosis found for downward moving particles at the base of the convection zone implies several extreme events.

Miesch, Mark↗
NASA NTRS2001

New Interstellar Dust Models Consistent with Interstellar Extinction, Emission and Abundances Constraints

We present new interstellar dust models that are consistent with both, the FUV to near-IR extinction and infrared (IR) emission measurements from the diffuse interstellar medium. The models are characterized by different dust compositions and abundances. The problem we solve consists of determining the size distribution of the various dust components of the model. This problem is a typical ill-posed inversion problem which we solve using the regularization approach. We reproduce the Li Draine (2001, ApJ, 554, 778) results, however their model requires an excessive amount of interstellar silicon (48 ppM of hydrogen compared to the 36 ppM available for an ISM of solar composition) to be locked up in dust. We found that dust models consisting of PAHs, amorphous silicate, graphite, and composite grains made up from silicates, organic refractory, and water ice, provide an improved fit to the extinction and IR emission measurements, while still requiring a subsolar amount of silicon to be in the dust. This research was supported by NASA Astrophysical Theory Program NRA 99-OSS-01.

Zubko, V.↗
NASA NTRS2004

Notes on Interface Growth Kinetics 50 Years after Burton, Cabrera and Frank

This overview is devoted to some unresolved basic problems in crystal growth kinetics. The density wave approach to propagation of a spatially diffuse interface between a growing crystal and its simple (e.g., metallic) melt is discussed is Section 2. This approach allows for the calculation of kinetic coefficients and is an alternative to the localized interface concept in which each atom belongs to either a solid or a liquid. Sections 3 and 4 deals mainly with layer growth from solution. Mutual retardation of the growth steps via their bulk and d a c e diffusion fields is the major subject. The influence of solution flow on step bunching (Section 4) suggests the essential influence of bulk diffusion on the surface morphology. The flow within the solution boundary layer enhances step-step interaction, influences the step bunching process and the resulting step pattern morphology on the growing surface. Recent experiments on the rates at which strongly polygonized steps on protein and small molecule crystals propagate during growth from solution are analyzed in Section 5 . We have shown that the step segments may be "singular" and that "one-dimensional nucleation" may be the rate limiting stage for the segments that are shorter or comparable in length to the thermodynamically equilibrium interlink distance. In this case, the reciprocal dependence of the segment propagation rate on the segment length that follow from the Gibbs-Thompson law, should be replaced by an abrupt switch from zero to a finite constant velocity. Until recently, the Kossel crystal remained the only model used in crystal growth theory. In such Kossel Gibbs-Thomson law, should be replaced by an abrupt switch &om zero to a finite constant velocity. crystals, all kinks at the steps are identical and the kink rate is a linear function of the supersaturation. In the non-Kossel crystals, there may be several kink configurations characterized by different geometries and energies. These configurations should appear in a specific sequence when each new lattice unit cell is filled. As a result of such a cooperative interaction within the unit cell, a non-linear dependence of the kink rate on the vapor pressure or solution concentration in excess over the equilibrium value should be expected.

Chernov, A. A.↗
NASA NTRS2004

Dust Accumulation and Solar Panel Array Performance on the Mars Exploration Rover (MER) Project

One of the most fundamental design considerations for any space vehicle is its power supply system. Many options exist, including batteries, fuel cells, nuclear reactors, radioisotopic thermal generators (RTGs), and solar panel arrays. Solar arrays have many advantages over other types of power generation. They are lightweight and relatively inexpensive, allowing more mass and funding to be allocated for other important devices, such as scientific instruments. For Mars applications, solar power is an excellent option, especially for long missions. One might think that dust storms would be a problem; however, while dust blocks some solar energy, it also scatters it, making it diffuse rather than beamed. Solar cells are still able to capture this diffuse energy and convert it into substantial electrical power. For these reasons, solar power was chosen to be used on the 1997 Mars Pathfinder mission. The success of this mission set a precedent, as NASA engineers have selected solar power as the energy system of choice for all future Mars missions, including the Mars Exploration Rover (MER) Project. Solar sells have their drawbacks, however. They are difficult to manufacture and are relatively fragile. In addition, solar cells are highly sensitive to different parts of the solar spectrum, and finding the correct balance is crucial to the success of space missions. Another drawback is that the power generated is not a constant with respect to time, but rather changes with the relative angle to the sun. On Mars, dust accumulation also becomes a factor. Over time, dust settles out of the atmosphere and onto solar panels. This dust blocks and shifts the frequency of the incoming light, degrading solar cell performance. My goal is to analyze solar panel telemetry data from the two MERs (Spirit and Opportunity) in an effort to accurately model the effect of dust accumulation on solar panels. This is no easy process due to the large number of factors involved. Changing solar flux (the amount of solar energy reaching the planet), solar spectrum, solar angle, rover tilt, and optical depth (the opacity of the atmosphere due to dust) were the most significant. Microsoft Excel and Visual Basic are used for data analysis. The results of this work will be used to improve the dust accumulation and atmosphere effects model that was first created after the Mars Pathfinder mission. This model will be utilized and applied when considering the design of solar panel array systems on future Mars projects. Based on this data, and depending upon the tenure and application of the mission, designers may also elect to employ special tools to abate dust accumulation, or decide that the expected level of accumulation is acceptable.

Turgay, Eren H.↗
DOE OSTI2020

Challenges in simulating ground interacting nuclear explosions

This paper summarizes recent above-ground nuclear explosion simulations as part of a broader effort to better characterize conditions within a fireball that may influence the chemical evolution of bomb materials and other materials entrained from the local explosion environment. A critical component of this work is validation against historic footage of atmospheric testing, requiring that we understand how the frequency-dependent sensitivity of the utilized film footage influences data captured in such images. We focus first on the early physics of a nuclear explosion in the atmosphere before discussing some of the technical challenges we seek to capture in late-time models that include more complex emplacement conditions and subsurface features. We discuss required physics packages (compressible hydrodynamics, radiation transport, as well as necessary ancillary tables such as equations of state (EOS) and opacities). Additionally, we note reasonable “shortcuts” one may make and their limitations, e.g., using ideal gas EOS, replacing spectrally resolved radiation with spectrally averaged radiation, and exchanging deterministic transport with diffusion. We then discuss an approach to achieving an equilibrated initial stress state for problems where buoyancy and subsurface lithostatic stress are important. Our methodology is presented in the context of LLNL’s ALE3D multiphysics code but may readily be implemented in other codes. In this paper, we start with a description of the challenges of NUDET simulations, followed by a presentation of the simulated intensity (flux) as it would appear on an analysis of the Dixie test. We then progressively introduce additional complexity in subsequent sections (near-surface burst and gravity initialization) before concluding.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
NASA NTRS1974

Pioneer 10 ultraviolet photometer observations at Jupiter encounter

A two-channel extreme ultraviolet photometer on Pioneer 10 was used to investigate hydrogen and helium emissions from the atmosphere of Jupiter and emissions associated with the Galilean satellites. The hydrogen Lyman alpha signal observed from Jupiter corresponded to 400 R in brightness. By using the results of Wallace and Hunten (1973), the eddy diffusion coefficient is found to be K = 3 x 10 to the (8 plus or minus 1) power. The He I 584-A emission rate was found to be 5.1 R. The radiative transfer problem for the resonantly scattered He I emissions was investigated in the coherent approximation. With these results, the observed brightness, and the derived eddy diffusion coefficient the He/H2 ratio in the mixing region of the atmosphere was found to be equal to 0.18 minus 0.12 or plus 0.46. Emissions attributed to H I Lyman alpha were found at the orbital radius of Io and appear to be due to resonance scattering by a toroidal cloud of H in orbit around Jupiter.

Carlson, R. W.↗
DOE OSTI2017

A conservative nonlocal convection–diffusion model and asymptotically compatible finite difference discretization

Here in this paper, we first propose a nonlocal convection–diffusion model, in which the convection term is constructed in a special upwind manner so that mass conservation and maximum principle are maintained in any space dimension. The well-posedness of the proposed nonlocal model and its convergence to the classical local convection–diffusion model are established. A quadrature-based finite difference discretization is then developed to numerically solve the nonlocal problem and it is shown to be consistent and unconditionally stable. We further demonstrate that the numerical scheme is asymptotically compatible, that is, the approximate solutions converge to the exact solution of the corresponding local problem when δ → 0 and h → 0. Numerical experiments are also performed to complement the theoretical analysis.

42 ENGINEERING↗
DOE OSTI2017

Extension of the DIF3D Code for Molten Salt Reactor Analysis

The molten salt reactor (MSR) with the fuel dissolved into the liquid salt has been selected as one of the six Generation-IV reactors due to its excellent characteristics in the aspects of sustainability, economy, passive safety, and resource utilization. In a MSR, the fuel salt is circulated throughout the whole system and thus some of delayed neutron precursors generated in the core decay in position of low importance or even out of the core. As a result, the multiplication factor (k-eff) of MSR is smaller than that of a reactor of stationary fuel when all the other conditions are same. Therefore, the neutronics code developed for stationary fuel cannot be applied directly to MSR analysis. In this paper, we describe the extension and application of the DIF3D code to MSR neutronics analysis. The DIF3D code system is a multi-group steady-state neutron diffusion and transport theory solver. It provides three flux solution options: finite-difference diffusion theory, nodal diffusion theory, and variational nodal transport theory methods. Eigenvalue, adjoint, fixed source and criticality (concentration) search problems are permitted. The DIF3D code has recently been modified to model the flowing fuel. To verify the new capability of DIF3D, the MSFR [4] core was analyzed with a wide range of velocity field of fuel salt and time spent outside of the core.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS2000

Vapor Transport Within the Thermal Diffusion Cloud Chamber

A review of the equations used to determine the 1-D vapor transport in the thermal diffusion cloud chamber (TDCC) is presented. These equations closely follow those of the classical Stefan tube problem in which there is transport of a volatile species through a noncondensible, carrier gas. In both cases, the very plausible assumption is made that the background gas is stagnant. Unfortunately, this assumption results in a convective flux which is inconsistent with the momentum and continuity equations for both systems. The approximation permits derivation of an analytical solution for the concentration profile in the Stefan tube, but there is no computational advantage in the case of the TDCC. Furthermore, the degree of supersaturation is a sensitive function of the concentration profile in the TD CC and the stagnant background gas approximation can make a dramatic difference in the calculated supersaturation. In this work, the equations typically used with a TDCC are compared with very general transport equations describing the 1-D diffusion of the volatile species. Whereas no pressure dependence is predicted with the typical equations, a strong pressure dependence is present with the more general equations given in this work. The predicted behavior is consistent with observations in diffusion cloud experiments. It appears that the new equations may account for much of the pressure dependence noted in TDCC experiments, but a comparison between the new equations and previously obtained experimental data are needed for verification.

Ferguson, Frank T.↗
DOE OSTI2021

Deep Learning Approaches to Surrogates for Solving the Diffusion Equation for Mechanistic Real-World Simulations

In many mechanistic medical, biological, physical, and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs), especially for diffusion, fluid flow and mechanical relaxation, can make simulations impractically slow. Biological models of tissues and organs often require the simultaneous calculation of the spatial variation of concentration of dozens of diffusing chemical species. One clinical example where rapid calculation of a diffusing field is of use is the estimation of oxygen gradients in the retina, based on imaging of the retinal vasculature, to guide surgical interventions in diabetic retinopathy. Furthermore, the ability to predict blood perfusion and oxygenation may one day guide clinical interventions in diverse settings, i.e., from stent placement in treating heart disease to BOLD fMRI interpretation in evaluating cognitive function (Xie et al., 2019; Lee et al., 2020). Since the quasi-steady-state solutions required for fast-diffusing chemical species like oxygen are particularly computationally costly, we consider the use of a neural network to provide an approximate solution to the steady-state diffusion equation. Machine learning surrogates, neural networks trained to provide approximate solutions to such complicated numerical problems, can often provide speed-ups of several orders of magnitude compared to direct calculation. Surrogates of PDEs could enable use of larger and more detailed models than are possible with direct calculation and can make including such simulations in real-time or near-real time workflows practical. Creating a surrogate requires running the direct calculation tens of thousands of times to generate training data and then training the neural network, both of which are computationally expensive. Often the practical applications of such models require thousands to millions of replica simulations, for example for parameter identification and uncertainty quantification, each of which gains speed from surrogate use and rapidly recovers the up-front costs of surrogate generation. We use a Convolutional Neural Network to approximate the stationary solution to the diffusion equation in the case of two equal-diameter, circular, constant-value sources located at random positions in a two-dimensional square domain with absorbing boundary conditions. Such a configuration caricatures the chemical concentration field of a fast-diffusing species like oxygen in a tissue with two parallel blood vessels in a cross section perpendicular to the two blood vessels. To improve convergence during training, we apply a training approach that uses roll-back to reject stochastic changes to the network that increase the loss function. The trained neural network approximation is about 1000 times faster than the direct calculation for individual replicas. Because different applications will have different criteria for acceptable approximation accuracy, we discuss a variety of loss functions and accuracy estimators that can help select the best network for a particular application. We briefly discuss some of the issues we encountered with overfitting, mismapping of the field values and the geometrical conditions that lead to large absolute and relative errors in the approximate solution.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

A quadratic programming flux correction method for high-order DG discretizations of S transport

In this work, we present a new flux-fixup approach for arbitrarily high-order discontinuous Galerkin (DG) discretizations of the S N transport equation, and we demonstrate the compatibility of this approach with the Variable Eddington Factor (VEF) method. The new fixup approach is sweep-compatible: during a transport sweep (block Gauss-Seidel iteration in which the scattering source is lagged), a local quadratic programming (QP) problem is solved in each spatial element to ensure that the solution satisfies certain physical constraints, including local particle balance. In this paper, we describe two choices of physical constraints, resulting in two variants of the method: QP Zero (QPZ) and QP Maximum Principle (QPMP). In QPZ, the finite element coefficients of the solution are constrained to be nonnegative. In QPMP, they are constrained to adhere to an approximate discrete maximum principle. There are two primary takeaways in this paper. First, when the positive Bernstein basis is used for DG discretization, the QPMP method eliminates negativities, preserves high-order accuracy for smooth problems, and significantly dampens unphysical oscillations in the solution. The latter feature – the dampening of unphysical oscillations – is an improvement upon standard, simpler fixup approaches such as the approach described in (denoted as the “zero and rescale” (ZR) method in this paper). This improvement comes at a moderate computational cost, but it is not prohibitive. Our results show that, even in an unrealistic worst-case scenario where 83% of the spatial elements require a fixup, the computational cost of performing a transport sweep with fixup is only ~31% greater than performing one without fixup. The second takeaway is that the VEF method can be used to accelerate the convergence of transport sweeps even when a fixup is applied. When optically thick regions are present, transport sweeps converge slowly, regardless of whether a fixup is applied, and acceleration is needed. However, attempting to apply standard diffusion synthetic acceleration (DSA) to fixed-up transport sweeps results in divergence for optically thick problems. Our results show that the same is not true for VEF. When VEF is combined with fixed-up transport sweeps, the result is a scheme that produces a nonnegative solution, converges independently of the mean free path, and, in the case of the QPMP fixup, adheres to an approximate discrete maximum principle.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1985

Advanced detectors and signal processing for bubble memories

The feasibility of combining silicon and magnetic bubble technologies is demonstrated. Results of bubble film annealing indicate that a low temperature silicon on garnet technology is the most likely one to succeed commercially. Annealing ambients are also shown to have a major effect on the magnetic properties of bubble films. Functional MOSFETs were fabricated on bubble films coated with thick (approximately 1 micron) SiO2 layers. The two main problems with these silicon on garnet MOSFETs are low electron mobilities and large gate leakage currents. Results indicate that the laser recrystallized silicon and gate oxide (SiO2) layers are contaminated. The data suggest that part of the contaminating ions originate in the sputtered oxide spacer layer and part originates in the bubble film itself. A diffusion barrier, such as silicon nitride, placed between the bubble film and the silicon layer should eliminate the contamination induced problem.

Kryder, M. H.↗
NASA NTRS2002

Laminar Soot Processes (LSP)

This is the final report of a research program considering the structure and the soot surface reaction properties of laminar nonpremixed (diffusion) flames. The study was limited to ground-based measurements of buoyant laminar jet diffusion flames at pressures of 0.1-1.0 atm. The motivation for the research is that soot formation in flames is a major unresolved problem of combustion science that influences the pollutant emissions, durability and performance of power and propulsion systems, as well as the potential for developing computational combustion. The investigation was divided into two phases considering the structure of laminar soot-containing diffusion flames and the soot surface reaction properties (soot surface growth and oxidation) of these flames, in turn. The first phase of the research addressed flame and soot structure properties of buoyant laminar jet diffusion flames at various pressures. The measurements showed that H, OH and O radical concentrations were generally in superequilibrium concentrations at atmospheric pressure but tended toward subequilibrium concentrations as pressures decreased. The measurements indicated that the original fuel decomposed into more robust compounds at elevated temperatures, such as acetylene (unless the original fuel was acetylene) and H, which are the major reactants for soot surface growth, and that the main effect of the parent fuel on soot surface growth involved its yield of acetylene and H for present test conditions. The second phase of the research addressed soot surface reaction properties, e.g., soot surface growth and surface oxidation. It was found that soot surface growth rates in both laminar premixed and diffusion flames were in good agreement, that these rates were relatively independent of fuel type, and that these rates could be correlated by the Hydrogen-Abstraction/Carbon-Addition (HACA) mechanisms of Colket and Hall (1994), Frenklach et al. (1990,1994), and Kazakov et al. (1995). It was also found that soot surface oxidation rates were relatively independent of fuel type, were not correlated with O2, CO2, H2O and O collision rates but were correlated with the collision rates of OH with a collision efficiency of 0.14, in agreement with the early measurements in premixed flames of Neoh et al. (1980), after allowing for oxidation by O2 via the classical rate expression of Nagle and Strickland-Constable (1962).

Dai, Z.↗