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At least 1,135 records · Page 63
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Symbolic regression development of empirical equations for diffusion in Lennard-Jones fluids

Symbolic regression (SR) with a multi-gene genetic program has been used to elucidate new empirical equations describing diffusion in Lennard-Jones (LJ) fluids. Some examples include equations to predict self-diffusion in pure LJ fluids and equations describing the finite-size correction for self-diffusion in binary LJ fluids. The performance of the SR-obtained equations was compared to that of both the existing empirical equations in the literature and to the results from artificial neural net (ANN) models recently reported. It is found that the SR equations have improved predictive performance in comparison to the existing empirical equations, even though employing a smaller number of adjustable parameters, but show an overall reduced performance in comparison to more extensive ANNs.

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

Atomistic models of In and Ga diffusion in Cu(In,Ga)Se 2

To improve the performance of Cu(In,Ga)Se 2 thin-film photovoltaic devices, a robust understanding of the dominant diffusion pathways of the alloy species In and Ga is needed. Here, the most probable defect complexes and mechanisms for In and Ga diffusion are identified with the aid of density functional theory. The binding energies and migration barriers for these complexes are calculated in bulk CuInSe 2 and CuGaSe 2 . Analytic models and kinetic lattice Monte Carlo simulations are employed to predict the diffusivity of In and Ga under variations in composition and temperature. Here, we find that a model based on coulombic interactions between group III antisites and vacancies on the Cu-sublattice produces results that match well with experiment.

14 SOLAR ENERGY↗
DOE OSTI2023

The Impact of Circumsolar Diffuse Radiation on the Numerical Computation and Forecasting of DNI

Weather Research and Forecasting model with solar extensions (WRF-Solar) uses the Fast All-sky Radiation Model for Solar applications (FARMS) to predict solar radiation from the forecasted atmospheric gases, aerosols, and clouds. The Beer-Bouguer-Lambert law utilized by FARMS as well as other radiative transfer models assumes Direct Normal Irradiance (DNI) is a narrow beam only covering the sun disk. This assumption is interpreted differently in solar observations by pyrheliometers where the circumsolar diffuse radiation is accounted. This study precisely computes circumsolar diffuse radiation in all-sky conditions using a radiative transfer model based on a parameterization of precomputed cloud transmittance and reflectance. The model is implemented in WRF-Solar to provide day-ahead DNI forecast in the north America. The computation and forecasting of DNI is compared with the Beer-Bouguer-Lambert law to understand the impact of circumsolar diffuse radiation.

aerosols↗
DOE OSTI2024

On-the-fly machine learned force fields for the study of warm dense matter: Application to diffusion and viscosity of CH

We develop a framework for on-the-fly machine learned force field (MLFF) molecular dynamics (MD) simulations of warm dense matter (WDM). In particular, we employ an MLFF scheme based on the kernel method and Bayesian linear regression, with the training data generated from the Kohn–Sham density functional theory (DFT) using the Gauss spectral quadrature method, within which we calculate energies, atomic forces, and stresses. We verify the accuracy of the formalism by comparing the predicted properties of warm dense carbon with recent Kohn–Sham DFT results in the literature. In so doing, we demonstrate that ab initio MD simulations of WDM can be accelerated by up to three orders of magnitude, while retaining ab initio accuracy. We apply this framework to calculate the diffusion coefficients and shear viscosity of CH at a density of 1 g/cm3 and temperatures in the range of 75 000–750 000 K. We find that the self- and inter-diffusion coefficients and the viscosity obey a power law with temperature, and that the diffusion coefficient results suggest a weak coupling between C and H in CH. In addition, we find agreement within standard deviation with previous results for C and CH but disagreement for H, demonstrating the need for ab initio calculations as presented here.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Diffusion-mediated passing of molecular species in linear nanopores constrained by orientational alignment

For diffusion-mediated catalytic conversion reactions in materials with narrow linear nanopores, e.g., mesoporous silica MCM-41, a key parameter is the propensity for product species to be able to pass reactant species and thus to efficiently exit the pore. For elongated species, this can require orientational alignment with the pore axis. In this work, we perform benchmark analyses for such solution-phase systems where one of these species is elongated in order to quantify the dependence of this passing propensity, P, on pore diameter and on the rotational diffusion coefficient, Dr, of the elongated species. In particular, we consider the passing of a spherical and an elongated spherocylindrical shaped species in a cylindrical pore in an implicit solvent, where these species cannot overlap. Passing is mediated by diffusive Brownian motion of these species as described by strongly damped Langevin dynamics. We quantify scaling of P for pore width just above the threshold where passing is sterically blocked, and also reveal a significant decrease in P for lower Dr. We also consider the dependence of P on the aspect ratio of the elongated species and obtain an exact result in the limiting regime of large aspect ratio.

Brownian motion↗
DOE OSTI2022

Observation of Weyl exceptional rings in thermal diffusion

A non-Hermitian Weyl equation indispensably requires a three-dimensional (3D) real/synthetic space, and it is thereby perceived that a Weyl exceptional ring (WER) will not be present in thermal diffusion given its purely dissipative nature. Here, we report a recipe for establishing a 3D parameter space to imitate thermal spinor field. Two orthogonal pairs of spatiotemporally modulated advections are employed to serve as two synthetic parameter dimensions, in addition to the inherent dimension corresponding to heat exchanges. We first predict the existence of WER in our hybrid conduction–advection system and experimentally observe the WER thermal signatures verifying our theoretical prediction. When coupling two WERs of opposite topological charges, the system further exhibits surface-like and bulk topological states, manifested as stationary and continuously changing thermal processes, respectively, with good robustness. Our findings reveal the long-ignored topological nature in thermal diffusion and may empower distinct paradigms for general diffusion and dissipation controls.

42 ENGINEERING↗
DOE OSTI2019

Nonlinear Diffusion Acceleration of the Least-Squares Transport Equation in Geometries with Voids

In this paper we show the extension of the Nonlinear-Diffusion Acceleration (NDA) to geometries containing small voids using a weighted least-squares (WLS) high order equation. Even though the WLS equation is well defined in voids, the low-order drift diffusion equation was not defined in materials with a zero cross section. This paper derives the necessary modifications to the NDA algorithm. We show that a small change to the NDA closure term and a non-local definition of the diffusion coefficient solve the problems for voids regions. These changes do not affect the algorithm for optical thick material regions, while making the algorithm well defined in optically thin ones. We use a Fourier analysis to perform an iterative analysis to confirm that the modifications result in a stable and efficient algorithm. Numerical results of our method will be presented in the second part of the paper. We test this formulation with a small, one-dimensional test problem. Additionally we present results for a modified version of the C5G7 benchmark containing voids as a more complex, reactor like problem. We compared our results to PDT, Texas A&M’s transport code, utilizing a first order discontinuous formulation as reference and the self-adjoint angular flux equation with void treatment (SAAFτ ), a different second order form. The results indicate, that the NDA WLS performed comparably or slightly worse then the asymmetric SAAFτ , while maintaining a symmetric discretization matrix.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Demonstrating Computational Equivalence Between Continuous and Discrete Adjoint Methods by Calculating Time-Dependent Adjoint Solutions with Neutron Diffusion Models

The continuous adjoint method and the discrete adjoint method are two alternative approaches used to calculate adjoint solutions for adjoint systems. The continuous adjoint method derives adjoint equations analytically from continuous forward equations and then solves the adjoint equations either analytically or numerically in a discretized form whereas the discrete adjoint method calculates the adjoint solutions directly from the discretized forward equations. With regard to the methodology development and calculation procedure, distinct differences are well recognized between the two methods. For certain reasons, both methods are exclusively preferred and commonly used by different computational communities, but limited studies clarify the connections between the two adjoint methods from either of the communities. Herein, this paper demonstrates the computational equivalence between the continuous and discrete adjoint methods by investigating time-dependent adjoint solutions to the two-group neutron diffusion model in nuclear reactor analysis problems using both methods. Adjoint solutions can be used to estimate system parameters for reactor safety analysis. Appropriate final state conditions for the adjoint systems are specified in both of the methods, and the conditions are clarified with proper physical explanations. With the help of an event-based case study on neutron diffusion models, the accuracy of the time-dependent adjoint fluxes obtained from both methods is verified, and the pros and cons of both adjoint methods are examined. More importantly, the computational equivalence of both methods is demonstrated when they are applied to multigroup neutron diffusion systems. The advantage of calculating time-dependent adjoint fluxes by directly solving time-dependent adjoint systems rather than taking steady-state approximations as in common practice is also demonstrated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

Lumping Techniques for Mixed Finite Element Diffusion Discretizations

We are interested in positivity preserving spatial discretizations applicable to arbitrary order mixed finite element spatial discretizations of the radiative diffusion equations. Though not guaranteed to yield strict positivity, matrix lumping is appealing as a method of increasing solution positivity because unlike ad hoc fixups or strictly non-negative, non-linear solution representations, matrix lumping keeps the mixed finite element diffusion equations as a linear system of equations. Self-lumping schemes have previously been shown to be a generalization of more traditional matrix lumping techniques. Self-lumping schemes restrict integration quadrature points to the interpolation points used to define interpolatory finite element basis functions. As shown previously, the positivity and order of accuracy of self-lumping schemes are directly related to the choice of finite element interpolation point. Here, we develop self-lumping schemes for arbitrary order, mixed finite element spatial discretizations of the diffusion equation in Cartesian geometry. After introducing several possible self-lumping schemes appropriate for mixed finite elements, we test the ability of each scheme to increase solution positivity relative to an unlumped discretization using a simple test problem designed to induce negative solutions, evaluating efficacy as a function of finite element order and finite element interpolation point type. The method of manufactured solutions is then used to evaluate order of convergence for promising self-lumping schemes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

DIFFUSIVE SHOCK ACCELERATION OF HIGH-ENERGY CHARGED PARTICLES AT FAST INTERPLANETARY SHOCKS: A PARAMETER SURVEY

We present results from numerical simulations of the acceleration of solar energetic particles (SEPs) associated with strong, fast, and radially propagating interplanetary shocks. We focus on the phase of the SEP event at the time of the shock passage at 1 AU, which is when the peak intensity at energies below a few MeV is the highest. The shocks in our study start between 2 and 10 solar radii and propagate beyond 1 AU. We study the effect of various shock and particle input parameters, such as the spatial diffusion coefficient, shock speed, solar wind speed, initial location of the shock, and shock deceleration rate, on the total integrated differential intensity, I, of SEPs with kinetic energies > 10 MeV. I is the integral over energy of the differential intensity spectrum at the time of the shock passage at 1 AU. We find that relatively small changes in the parameters can lead to significant event-to-event changes in I. For example, a factor of 2 increase in the diffusion coefficient at a given energy and spatial location, can lead to a decrease in I by as much as a factor of 50. This may help explain why there are fewer large SEP events seen during the current solar maximum compared to previous maxima. It is known that the magnitude of the interplanetary magnetic field is noticeably weaker this solar cycle than it was in the previous cycle and this will naturally lead to a somewhat larger diffusion coefficient of SEPs.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

A measurement of diffusion in 47 Tucanae

Using images from the Hubble Space Telescope Wide-Field Camera 3, we measure the rate of diffusion of stars through the core of the globular cluster 47 Tucanae (47 Tuc) using a sample of young white dwarfs that were identified in these observations. This is the first direct measurement of diffusion due to gravitational relaxation. We find that the diffusion rate κ≈10−13 arcsec{sup 2} Myr{sup −1} is consistent with theoretical estimates of the relaxation time in the core of 47 Tuc of about 70 Myr.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

SELF-GRAVITY, RESONANCES AND ORBITAL DIFFUSION IN STELLAR DISKS

Fluctuations in a stellar system's gravitational field cause the orbits of stars to evolve. The resulting evolution of the system can be computed with the orbit-averaged Fokker–Planck equation once the diffusion tensor is known. We present the formalism that enables one to compute the diffusion tensor from a given source of noise in the gravitational field when the system's dynamical response to that noise is included. In the case of a cool stellar disk we are able to reduce the computation of the diffusion tensor to a one-dimensional integral. We implement this formula for a tapered Mestel disk that is exposed to shot noise and find that we are able to explain analytically the principal features of a numerical simulation of such a disk. In particular the formation of narrow ridges of enhanced density in action space is recovered. As the disk's value of Toomre's Q is reduced and the disk becomes more responsive, there is a transition from a regime of heating in the inner regions of the disk through the inner Lindblad resonance to one of radial migration of near-circular orbits via the corotation resonance in the intermediate regions of the disk. The formalism developed here provides the ideal framework in which to study the long-term evolution of all kinds of stellar disks.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

On the averaging of cardiac diffusion tensor MRI data: the effect of distance function selection

Diffusion tensor magnetic resonance imaging (DT-MRI) allows a unique insight into the microstructure of highly-directional tissues. The selection of the most proper distance function for the space of diffusion tensors is crucial in enhancing the clinical application of this imaging modality. Both linear and nonlinear metrics have been proposed in the literature over the years. The debate on the most appropriate DT-MRI distance function is still ongoing. Here, in this paper, we presented a framework to compare the Euclidean, affine-invariant Riemannian and log-Euclidean metrics using actual high-resolution DT-MRI rat heart data. We employed temporal averaging at the diffusion tensor level of three consecutive and identically-acquired DT-MRI datasets from each of five rat hearts as a means to rectify the background noise-induced loss of myocyte directional regularity. This procedure is applied here for the first time in the context of tensor distance function selection. When compared with previous studies that used a different concrete application to juxtapose the various DT-MRI distance functions, this work is unique in that it combined the following: (i) metrics were judged by quantitative—rather than qualitative—criteria, (ii) the comparison tools were non-biased, (iii) a longitudinal comparison operation was used on a same-voxel basis. The statistical analyses of the comparison showed that the three DT-MRI distance functions tend to provide equivalent results. Hence, we came to the conclusion that the tensor manifold for cardiac DT-MRI studies is a curved space of almost zero curvature. The signal to noise ratio dependence of the operations was investigated through simulations. Finally, the 'swelling effect' occurrence following Euclidean averaging was found to be too unimportant to be worth consideration.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

Dynamics of the diffusive DM-DE interaction – Dynamical system approach

We discuss dynamics of a model of an energy transfer between dark energy (DE) and dark matter (DM) . The energy transfer is determined by a non-conservation law resulting from a diffusion of dark matter in an environment of dark energy. The relativistic invariance defines the diffusion in a unique way. The system can contain baryonic matter and radiation which do not interact with the dark sector. We treat the Friedman equation and the conservation laws as a closed dynamical system. The dynamics of the model is examined using the dynamical systems methods for demonstration how solutions depend on initial conditions. We also fit the model parameters using astronomical observation: SNIa, H ( z ), BAO and Alcock-Paczynski test. We show that the model with diffuse DM-DE is consistent with the data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Quantum diffusion during inflation and primordial black holes

We calculate the full probability density function (PDF) of inflationary curvature perturbations, even in the presence of large quantum backreaction. Making use of the stochastic-δ N formalism, two complementary methods are developed, one based on solving an ordinary differential equation for the characteristic function of the PDF, and the other based on solving a heat equation for the PDF directly. In the classical limit where quantum diffusion is small, we develop an expansion scheme that not only recovers the standard Gaussian PDF at leading order, but also allows us to calculate the first non-Gaussian corrections to the usual result. In the opposite limit where quantum diffusion is large, we find that the PDF is given by an elliptic theta function, which is fully characterised by the ratio between the squared width and height (in Planck mass units) of the region where stochastic effects dominate. We then apply these results to the calculation of the mass fraction of primordial black holes from inflation, and show that no more than ∼ 1 e -fold can be spent in regions of the potential dominated by quantum diffusion. We explain how this requirement constrains inflationary potentials with two examples.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Oxygen self-diffusion in ThO 2 under pressure: Connecting point defect parameters with bulk properties

ThO 2 is a candidate material for use in nuclear fuel applications and as such it is important to investigate its materials properties over a range of temperatures and pressures. In the present study molecular dynamics calculations are used to calculate elastic and expansivity data. These are used in the framework of a thermodynamic model, the cBΩ model, to calculate the oxygen self-diffusion coefficient in ThO 2 over a range of pressures (–10–10 GPa) and temperatures (300–1900 K). As a result, increasing the hydrostatic pressure leads to a significant reduction in oxygen self-diffusion. Conversely, negative hydrostatic pressure significantly enhances oxygen self-diffusion.

36 MATERIALS SCIENCE↗
DOE OSTI2022

A model of spatio-temporal regulation within biomaterials using DNA reaction–diffusion waveguides

In multi-cellular organisms, cells and tissues coordinate biochemical signal propagation across length scales spanning micrometres to metres. Designing synthetic materials with similar capacities for coordinated signal propagation could allow these systems to adaptively regulate themselves across space and over time. Here, we combine ideas from cell signalling and electronic circuitry to propose a biochemical waveguide that transmits information in the form of a concentration of a DNA species on a directed path. The waveguide could be seamlessly integrated into a soft material because there is virtually no difference between the chemical or physical properties of the waveguide and the material it is embedded within. We propose the design of DNA strand displacement reactions to construct the system and, using reaction–diffusion models, identify kinetic and diffusive parameters that enable super-diffusive transport of DNA species via autocatalysis. Finally, to support experimental waveguide implementation, we propose a sink reaction and spatially inhomogeneous DNA concentrations that could mitigate the spurious amplification of an autocatalyst within the waveguide, allowing for controlled waveguide triggering. Chemical waveguides could facilitate the design of synthetic biomaterials with distributed sensing machinery integrated throughout their structure and enable coordinated self-regulating programmes triggered by changing environmental conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Atomistic modeling of lanthanide diffusion in refractory body-centered cubic molybdenum

Lanthanide fission products can strongly interact with candidate cladding alloys, but their transport properties in refractory metals remain poorly understood. Here, in this work, we investigate the atomic-scale diffusion behavior of La, Ce, Pr, and Nd in body-centered cubic (bcc) molybdenum, a potential candidate for advanced nuclear cladding. Self-consistent mean-field transport modeling is performed to evaluate the fission product transport and vacancy mobility, informed by first-principles and nudged elastic band calculations of vacancy formation energies, migration barriers, and solute–vacancy binding characteristics. Compared with bcc Fe, lanthanide solutes in bcc Mo exhibit slower tracer diffusion due to higher vacancy formation and migration energies. Furthermore, the calculations reveal that the influence of fission products on migration barriers in bcc Mo are not as extensive in range compared to bcc Fe. Among the studied lanthanides, La exhibits the strongest vacancy binding while also being the fastest diffuser in Mo. These findings highlight how refractory bcc alloys can reduce fission product infiltration, offering valuable insight into the development of durable cladding systems for advanced reactors.

36 - MATERIALS SCIENCE↗