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At least 253 records · Page 14

All sources NASA NTRS DOE OSTI

DOE OSTI2020

Reduced Artifact Approach for Determining Diffusion Coefficients in Time-Resolved Microscopy

Ultrafast microscopy methods traditionally assume a Gaussian profile to extract excited state diffusivities from transport measurements. Although this fitting method recovers accurate diffusion coefficients when the point spread function is well-represented by a Gaussian, even minor spatial aberrations introduced by the imaging system cause significant errors in the determined value. To provide a more accurate measure of excited state transport in nano- and microscale materials systems, in this work an alternative analysis protocol is proposed that numerically convolves the Green’s function solution to the diffusion equation with the experimentally measured point spread function. In contrast to the Gaussian fitting approach, the numerical convolution is shown to be robust against artifacts caused by nonideal point spread functions. Furthermore, the numerical convolution approach is highly effective at resolving anisotropic diffusion in modeled data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks

One of the open problems in scientific computing is the long-time integration of nonlinear stochastic partial differential equations (SPDEs), especially with arbitrary initial data. We address this problem by taking advantage of recent advances in scientific machine learning and the spectral dynamically orthogonal (DO) and borthogonal (BO) methods for representing stochastic processes. The recently introduced DO/BO methods reduce the SPDE to solving a system of deterministic PDEs and a system of stochastic ordinary differential equations. Specifically, we propose two new physics-informed neural networks (PINNs) for solving time-dependent SPDEs, namely the neural network (NN)-DO/BO methods. The proposed methods incorporate the DO/BO constraints into the loss function (along with the modal decomposition of the SPDE) with an implicit form instead of generating explicit expressions for the temporal derivatives of the DO/BO modes. Hence, the NN-DO/BO methods can overcome some of the drawbacks of the original DO/BO methods. For example, we do not need the assumption that the covariance matrix of the random coefficients is invertible as in the original DO method, and we can remove the assumption of no eigenvalue crossing as in the original BO method. Moreover, the NN-DO/BO methods can be used to solve time-dependent stochastic inverse problems with the same formulation and same computational complexity as for forward problems. Furthermore, we demonstrate the capability of the proposed methods via several numerical examples, namely: (1) A linear stochastic advection equation with deterministic initial condition: we obtain good results with the proposed methods, while the original DO/BO methods cannot be applied directly in this case. (2) Long-time integration of the stochastic Burgers' equation: we show the good performance of NN-DO/BO methods, especially the effectiveness of the NN-BO approach for such problems with many eigenvalue crossings during the whole time evolution, while the original BO method fails. (3) Nonlinear reaction diffusion equation: we consider both the forward problem and the inverse problems, including very noisy initial point values, to investigate the flexibility of the NN-DO/BO methods in handling inverse and mixed type problems. Taken together, these simulation results demonstrate that the NN-DO/BO methods can be employed to effectively quantify uncertainty propagation in a wide range of physical problems, but future work should address the efficiency issue of PINNs for forward problems.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1984

Effect of growth parameters on compositional variations in directionally solidified HgCdTe alloys

A series of Hg(1-x)Cd(x)Te alloy crystals was grown by directional solidification with compositions ranging from x = 0.2 to x = 0.4. The measured axial compositional profiles were interpreted in terms of an exact numerical solution of the appropriate diffusion equation that takes into account both the variations of the segregation coefficient and solidification rate with composition. The solutions for all growth rates agree generally well with the experimental data, and confirm earlier observations that employed approximate analytical solutions. The effective mass diffusion coefficients showed no significant composition or melt temperature dependence. Slightly higher diffusion coefficients were obtained, however, for the highest growth rates.

Szofran, F. R.↗

NASA NTRS1975

Behaviour of nitric oxide trails deposited in the mesosphere and stratosphere

The transient behavior of a nitric oxide trail deposited at approximately 60 km altitude is studied by the solution of the appropriate multidimensional diffusion equation which includes terms representing the effects of wind shear. Similar analysis is then carried out for the situation in the stratosphere. Trail behavior is found to be relatively independent of altitude and background ozone, but strongly dependent on the magnitude of eddy diffusity and the initial nitric oxide concentration. The nitric oxide trail reacts with ambient ozone to form nitrogen dioxide. For a trail 100 m initial radius, an ozone hole will form to a maximum size in 4 to 6 hours and then decay. The overall recovery time of the atmosphere following the creation of the trail is less than 12 hours.

Eberstein, I. J.↗

NASA NTRS1980

The interplanetary transport of solar cosmic rays

Numerical solutions are presented for the propagation of solar cosmic rays in interplanetary space, including the effects of pitch-angle scattering and adiabatic focusing. The intensity-time profiles can be well fitted by a simple radial spatial diffusion equation with scattering mean-free path lambda(fit). The radial mean-free path so obtained is significantly larger than the true scattering mean-free path for low-rigidity particles due to both adiabatic focusing and the inapplicability of the diffusive approximation early in the event. The well-known discrepancy between lambda(fit) and the theoretical predictions may be resolved by these calculations.

Gombosi, T. I.↗

NASA NTRS2019

Permeation Rate Equations for Hydrogen and Deuterium in a Palladium-Silver Alloy

Mass transfer of a gas through a selective, solid membrane is an effective method for separation of desired species. This selective permeability is evident in the flow of hydrogen and the isotope deuterium through palladium-silver metal alloy media. In this study, based upon Sieverts’s law and the Arrhenius diffusion equation, an empirical correlation was developed to determine the steady-state permeation rate R, dependence on media temperature T, gas supply pressure p(sub S), and gas backpressure p(sub B) on the lower pressure side. Because of an extensive range of experimental conditions and complete reporting of raw data, the research by Ackerman and Koskinas was used as a source for data allowing empirical equation fitting. Unfortunately, those authors reported best-fit equations that poorly represented their own results. To improve the modeling of the original data and demonstrate the quality of the measurements, the current study develops improved hydrogen and deuterium permeation rate equations: P = 4.22×10(exp −6) A[exp(−704/T)](sq. root p(sub S) − sq. root p(sub B))/t for hydrogen P = 2.12×10(exp −6) A[exp(−468/T )](sq. root p(sub S) − sq. root p(sub B))/t for deuterium for values of cross-sectional area A (sq.cm), medium thickness t (cm), pressure p (psia), and temperature T (Kelvin), giving a permeation rate in mole/minute. These equations model permeation rate data more closely than do several other existing literature sources.

Smith, Phillip J.↗

DOE OSTI2026

Overlapping Schwarz Methods Are Not Anisotropy‐Robust Multigrid Smoothers

We analyze overlapping multiplicative Schwarz methods as smoothers in the geometric multigrid solution of two-dimensional anisotropic diffusion problems. For diffusion equations, it is well known that the smoothing properties of point-wise smoothers, such as Gauss Seidel, rapidly deteriorate as the strength of anisotropy increases. On the other hand, global smoothers based on line smoothing are known to generally provide good smoothing for diffusion problems, independent of the anisotropy strength. Here, a natural question is whether global methods are really necessary to achieve good smoothing in such problems, or whether it can be obtained with locally overlapping block smoothers using sufficiently large blocks and overlap. Through local Fourier analysis and careful numerical experimentation, we show that global methods are indeed necessary to achieve anisotropy-robust smoothing. Specifically, for any fixed block size bounded sufficiently far away from the global domain size, we find that the smoothing properties of overlapping multiplicative Schwarz rapidly deteriorate with increasing anisotropy, irrespective of the amount of overlap between blocks. Moreover, our results indicate that anisotropy-robust smoothing requires blocks of diameter 𝒪⁡(𝜖 −1/2 ) for anisotropy ratio 𝜖 ∈(0,1] .

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1984

On the acceleration of energetic ions in Jupiter's magnetosphere

Several aspects of the problem of high-energy ions in the Jovian magnetosphere are addressed. Voyager observations pertaining to the problem of high-energy ions in the magnetosphere are summarized, and the charge exchange emission of fast neutral sulfur and oxygen atoms and their subsequent recapture by electron impact, charge exchange, and photoionization is considered. Solutions are given to the diffusion equation assuming a source of ions injected with a gyroenergy corresponding to pickup in the middle and outer magnetosphere. It is concluded that no reasonable model parameters exist to produce the required steep spectra of the particle observations with only pickup and adiabatic radial diffusion included. A local acceleration mechanism based on nonadiabatic wave-particle interactions is needed. The assumptions and model predictions of stochastic acceleration by MHD turbulence for the Jovian magnetosphere are described. The model makes a specific correspondence between MHD wave spectrum properties and particle spectrum properties at energies above the Alfven energy.

Barbosa, D. D.↗

NASA NTRS1984

A spectral element method for fluid dynamics - Laminar flow in a channel expansion

A spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible Navier-Stokes equations. In the spectral element discretization, the computational domain is broken into a series of elements, and the velocity in each element is represented as a high-order Lagrangian interpolant through Chebyshev collocation points. The hyperbolic piece of the governing equations is then treated with an explicit collocation scheme, while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle. The implementation of the technique is demonstrated on a one-dimensional inflow-outflow advection-diffusion equation, and the method is then applied to laminar two-dimensional (separated) flow in a channel expansion. Comparisons are made with experiment and previous numerical work.

Patera, A. T.↗

NASA NTRS1995

The method of space-time and conservation element and solution element: A new approach for solving the Navier-Stokes and Euler equations

A new numerical framework for solving conservation laws is being developed. This new framework differs substantially in both concept and methodology from the well-established methods, i.e., finite difference, finite volume, finite element, and spectral methods. It is conceptually simple and designed to overcome several key limitations of the above traditional methods. A two-level scheme for solving the convection-diffusion equation is constructed and used to illuminate the major differences between the present method and those previously mentioned. This explicit scheme, referred to as the a-mu scheme, has two independent marching variables.

Chang, Sin-Chung↗

NASA NTRS1976

Lossy radial diffusion of relativistic Jovian electrons

The radial diffusion equation with synchrotron losses is solved by the Laplace-transform method for near equatorially mirroring relativistic electrons. The evolution of a power-law distribution function is found, and the characteristics of synchrotron burnoff are stated in terms of explicit parameters for an arbitrary diffusion coefficient of a specific form. The peaking of the 10.4-cm volume emissivity from Jupiter at an L shell of about 1.8 provides an estimate of the diffusion coefficient in the radiation belts; one value is suggested as the appropriate modification, for an equatorial field strength of 4.2 G, of the Birmingham et al. (1974) result. Nonsynchrotron losses are included phenomenologically; from the phase-space densities reported by McIlwain and Fillius (1975), the particle lifetime is estimated. Asymptotic forms for the distribution in the strong synchrotron loss regime are provided.

Barbosa, D. D.↗

NASA NTRS1976

Lossy radial diffusion of relativistic Jovian electrons

The radial diffusion equation with synchrotron losses was solved by the Laplace transform method for near-equatorially mirroring relativistic electrons. The evolution of a power law distribution function was found and the characteristics of synchrotron burn-off are stated in terms of explicit parameters for an arbitrary diffusion coefficient. Emissivity from the radiation belts of Jupiter was studied. Asymptotic forms for the distribution in the strong synchrotron loss regime are provided.

Barbosa, D. D.↗

NASA NTRS1993

Recent developments in high order K-exact reconstruction on unstructured meshes

This paper presents recent improvements in high-order K-exact reconstruction on unstructured meshes. The new reconstruction procedures are incorporated into a basic upwind finite-volume scheme suitable for solving scalar advection-diffusion equations as well as the Euler and Navier-Stokes equations. Numerical calculations are performed comparing the present method with lower order accurate reconstruction procedures (piecewise constant and piecewise linear) and various competing technologies such as the fluctuation splitting method of Roe (1987) and Deconinck et al. (1992) and a system-variant of the streamline diffusion Petrov-Galerkin method developed by Hansbo (1991) and Hansbo and Johnson (1991). Five test problems are used in the numerical comparisons: scalar circular advection, transonic and supersonic Euler flow, laminar boundary-layer flow, and general compressible Navier-Stokes flow.

Barth, Timothy J.↗

NASA NTRS1999

Efficient Multi-Stage Time Marching for Viscous Flows via Local Preconditioning

A new method has been developed to accelerate the convergence of explicit time-marching, laminar, Navier-Stokes codes through the combination of local preconditioning and multi-stage time marching optimization. Local preconditioning is a technique to modify the time-dependent equations so that all information moves or decays at nearly the same rate, thus relieving the stiffness for a system of equations. Multi-stage time marching can be optimized by modifying its coefficients to account for the presence of viscous terms, allowing larger time steps. We show it is possible to optimize the time marching scheme for a wide range of cell Reynolds numbers for the scalar advection-diffusion equation, and local preconditioning allows this optimization to be applied to the Navier-Stokes equations. Convergence acceleration of the new method is demonstrated through numerical experiments with circular advection and laminar boundary-layer flow over a flat plate.

Kleb, William L.↗

NASA NTRS1999

Efficient Multi-Stage Time Marching for Viscous Flows via Local Preconditioning

Kleb, William L.↗

DOE OSTI2023

Mass transfer in catalytic depolymerization: External effectiveness factors and serendipitous processivity in stagnant and stirred melts

Several heterogeneous catalysts are being developed to recycle plastics. Most operate in viscous polymer melts, where external mass transfer effects could limit the supply of co-reactants to active sites. External mass transfer can also impede the diffusion of long chain products away from the catalyst after each cut. Product egress limitations could potentially confer unintentional processivity to catalyst operation, i.e. a tendency for the catalyst to repeatedly cut the same chain after an initial encounter. We formulate reaction–diffusion equations to quantify mass transfer effects on the co-reactant transport to the catalyst and the degree of serendipitous processivity. Results are developed for catalysts in stagnant or stirred melts, with simple expressions involving Damkohler, Peclet, and Sherwood numbers, i.e. dimensionless combinations of rate constants, catalyst particle size, polymer diffusivities, and shear rates (where applicable). In conclusion, we estimate the impact of these effects for a spherical core–shell catalyst.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Quantifying heavy quark transport coefficients with an improved transport model

We report that the heavy-flavor transport coefficients contain important information on the strong interaction at finite temperatures. The extraction of these numbers from experimental data requires dynamical modeling of heavy-flavor transport that is coupled to realistic medium evolution. Furthermore, meaningful extractions necessitate both a faithful implementation of the physical inputs to be tested and the quantification of model uncertainty. For these purposes, we have developed a partonic transport model LIDO. It has an improved treatment of in-medium parton bremsstrahlung, which has been calibrated to theoretical calculations in a simple medium to reduce modeling uncertainty. Regarding the interaction between heavy quark and the medium, few-body perturbative scatterings are applied to large-momentum transfer (q) processes, while a diffusion equation models the dynamics of small-q processes. Such a separation restricts the explicit use of medium quasi-particles to large-q processes only. Another advantage is that deviations from the leading-order probe-medium coupling can be parametrized as an additional contribution to the diffusion constant. The heavy quark transport coefficients are then extracted with uncertainty estimation from a Bayesian analysis including both the RHIC and the LHC data. The results are found to be consistent with earlier extraction of the light-quark transport coefficients at high momentum and be comparable with lattice calculations of the heavy-flavor diffusion constant in the static limit at low momentum.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1989

Radial diffusion and losses of energetic protons in the 5 to 12 R(S) region of Saturn's magnetosphere

Phase space density profiles for nearly equatorial mirroring energetic protons, derived from Pioneer 11 measurements during the 1979 Saturn encounter, were analyzed using solutions of the time-averaged radial diffusion equation in a dipolar planetary magnetic field. Then, several loss models were considered, ranging from a model that takes into account satellite absorption only to the one that accounts for satellite plus ring-E absorption plus added distributed losses, and the corresponding form of the time-averaged radial diffusion coefficient was determined for each case by a minimum-variance fit to the data-derived phase space densiy profiles. The model comparisons clearly indicated the need for distributed losses, in addition to satellite absorption, in order to explain the smooth decline of the experimental energetic proton phase space density profiles in the 5-12-Saturn radius region of Saturn's magnetosphere.

Hood, L. L.↗