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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 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

A Numerical Study of Forbush Decreases with a 3D Cosmic-Ray Modulation Model Based on an SDE Approach

Based on the reduced diffusion mechanism for producing Forbush decreases (Fds) in the heliosphere, we constructed a three-dimensional (3D) diffusion barrier, and by incorporating it into a stochastic differential equation (SDE) based time-dependent, cosmic-ray transport model, a 3D numerical model for simulating Fds is built and applied to a period of relatively quiet solar activity. This SDE model generally corroborates previous Fd simulations concerning the effects of the solar magnetic polarity, the tilt angle of the heliospheric current sheet (HCS), and cosmic-ray particle energy. Because the modulation processes in this 3D model are multi-directional, the barrier’s geometrical features affect the intensity profiles of Fds differently. We find that both the latitudinal and longitudinal extent of the barrier have relatively fewer effects on these profiles than its radial extent and the level of decreased diffusion inside the disturbance. We find, with the 3D approach, that the HCS rotational motion causes the relative location from the observation point to the HCS to vary, so that a periodic pattern appears in the cosmic-ray intensity at the observing location. Correspondingly, the magnitude and recovery time of an Fd change, and the recovering intensity profile contains oscillation as well. Investigating the Fd magnitude variation with heliocentric radial distance, we find that the magnitude decreases overall and, additionally, that the Fd magnitude exhibits an oscillating pattern as the radial distance increases, which coincides well with the wavy profile of the HCS under quiet solar modulation conditions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

CRPropa 3.1—a low energy extension based on stochastic differential equations

The propagation of charged cosmic rays through the Galactic environment influences all aspects of the observation at Earth. Energy spectrum, composition and arrival directions are changed due to deflections in magnetic fields and interactions with the interstellar medium. Today the transport is simulated with different simulation methods either based on the solution of a transport equation (multi-particle picture) or a solution of an equation of motion (single-particle picture). We developed a new module for the publicly available propagation software CRPropa 3.1, where we implemented an algorithm to solve the transport equation using stochastic differential equations. This technique allows us to use a diffusion tensor which is anisotropic with respect to an arbitrary magnetic background field. The source code of CRPropa is written in C++ with python steering via SWIG which makes it easy to use and computationally fast. In this paper, we present the new low-energy propagation code together with validation procedures that are developed to proof the accuracy of the new implementation. Furthermore, we show first examples of the cosmic ray density evolution, which depends strongly on the ratio of the parallel κ{sub ∥} and perpendicular κ{sub ⊥} diffusion coefficients. This dependency is systematically examined as well the influence of the particle rigidity on the diffusion process.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Scalable domain decomposition solvers for stochastic PDEs in high performance computing

Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolution in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Stochastic and coarse-grained two-dimensional modeling of directional particle movement

In this work, we study the evolution of interacting groups of pedestrians in two-dimensional geometries. We introduce a microscopic stochastic model that includes floor fields modeling the global flow of individual groups as well as local interaction rules. From this microscopic model we derive an analytically-tractable system of conservation laws that governs the evolution of the macroscopic pedestrian densities. Numerical simulations show good agreement between the system of conservation laws and the microscopic model, though the latter is slightly more diffusive. We conclude by deriving second-order corrections to the system of conservation laws.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Pore diameter dependence of catalytic activity: p -nitrobenzaldehyde conversion to an aldol product in amine-functionalized mesoporous silica

The reaction yield for conversion of p-nitrobenzaldehyde (PNB) to an aldol product in amine-functionalized mesoporous silica nanoparticles (MSN) exhibits a 20-fold enhancement for a modest increase in pore diameter, d. This enhanced catalytic activity is shown to reflect a strong increase in the “passing propensity,” P, of reactant and product species inside the pores. We find that P ≈ 0, corresponding to single-file diffusion, applies for the smallest d which still significantly exceeds the linear dimensions of PNB and the aldol product. However, in this regime of narrow pores, these elongated species must align with each other and with the pore axis in order to pass. Thus, P reflects both translational and rotational diffusion. Langevin simulation accounting for these features is used to determine P versus d. The results are also augmented by analytic theory for small and large d where simulation is inefficient. The connection with the catalytic activity and yield is achieved by the incorporation of results for P into a multi-scale modeling framework. Specifically, we apply a spatially coarse-grained (CG) stochastic model for the overall catalytic reaction-diffusion process in MSN. Pores are treated as linear arrays of cells from the ends of which species adsorb and desorb, and between which species hop and exchange, with the exchange rate reflecting P. CG model predictions including yield are assessed by Kinetic Monte Carlo simulation.

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

Energetic electron transport in magnetic fields with island chains and stochastic regions

This paper investigates energetic electron transport in magnetized toroidal plasmas with magnetic fields characterized by island chains and regions of stochastic field lines produced by coil perturbations. We report on experiments performed in the DIII-D tokamak, which utilize electron cyclotron heating and current drive pulses to ‘tag’ electron populations within different locations across the discharge. The cross-field transport of these populations is then inferred from electron cyclotron emission measurements and gamma emission signals from scintillator detectors. Two types of energetic particles are distinguished and discussed: non-relativistic suprathermal electrons and relativistic runaway electrons. The magnetic field topology in each discharge is reconstructed with field-line tracing codes, which are also used to determine the location and scale of magnetic islands and stochastic regions. Comparison of simulations and experiments suggests that suprathermal transport is suppressed when the tagging is performed at a smaller radial location than the location of the $q = 1$ island chain and enhanced otherwise. Here q is the safety factor. We further demonstrate that increasing the width of the stochastic region within the edge plasma yields enhancement of the suprathermal electron transport.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Energy-momentum-conserving stochastic differential equations and algorithms for the nonlinear Landau-Fokker-Planck equation

Coulomb collision is a fundamental diffusion process in plasmas that can be described by the Landau-Fokker-Planck (LFP) equation or the stochastic differential equation (SDE). While energy and momentum are conserved exactly in the LFP equation, they are conserved only on average by the conventional corresponding SDEs, suggesting that the underlying stochastic process may not be well defined by such SDEs. Here, in this study, we derive new SDEs with exact energy-momentum conservation for the Coulomb collision by factorizing the collective effect of field particles into individual particles and enforcing Newton's third law. These SDEs, when interpreted in the Stratonovich sense, have a particularly simple form that represents pure diffusion between particles without drag. To demonstrate that the new SDEs correspond to the LFP equation, we develop numerical algorithms that converge to the SDEs and preserve discrete conservation laws. Simulation results are presented in a benchmark of various relaxation processes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Simultaneous Measurements of Noncommuting Observables: Positive Transformations and Instrumental Lie Groups

We formulate a general program for describing and analyzing continuous, differential weak, simultaneous measurements of noncommuting observables, which focuses on describing the measuring instrument autonomously, without states. The Kraus operators of such measuring processes are time-ordered products of fundamental differential positive transformations, which generate nonunitary transformation groups that we call instrumental Lie groups. The temporal evolution of the instrument is equivalent to the diffusion of a Kraus-operator distribution function, defined relative to the invariant measure of the instrumental Lie group. This diffusion can be analyzed using Wiener path integration, stochastic differential equations, or a Fokker-Planck-Kolmogorov equation. This way of considering instrument evolution we call the Instrument Manifold Program. We relate the Instrument Manifold Program to state-based stochastic master equations. We then explain how the Instrument Manifold Program can be used to describe instrument evolution in terms of a universal cover that we call the universal instrumental Lie group, which is independent not just of states, but also of Hilbert space. The universal instrument is generically infinite dimensional, in which case the instrument’s evolution is chaotic. Special simultaneous measurements have a finite-dimensional universal instrument, in which case the instrument is considered principal, and it can be analyzed within the differential geometry of the universal instrumental Lie group. Principal instruments belong at the foundation of quantum mechanics. We consider the three most fundamental examples: measurement of a single observable, position and momentum, and the three components of angular momentum. As these measurements are performed continuously, they converge to strong simultaneous measurements. For a single observable, this results in the standard decay of coherence between inequivalent irreducible representations. For the latter two cases, it leads to a collapse within each irreducible representation onto the classical or spherical phase space, with the phase space located at the boundary of these instrumental Lie groups.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Refined Sensitivity Estimates for Single-Molecule Magnet Dark Matter Detectors

We revisit the sensitivity of Single Molecule Magnet (SMM) crystals as detectors for low-mass dark matter. In previous work, we established the concept of the ``magnetic bubble chamber'', where energy deposited by dark matter triggers a magnetic avalanche in a metastable crystal. The original sensitivity estimates relied on a conservative criterion requiring the spin relaxation time to be strictly shorter than the thermal diffusion time. Here, we demonstrate that this criterion effectively ignores the stochastic nature of spin relaxation. We derive a refined analytic estimate which accounts for the fraction of spins that relax even when diffusion is fast. We show that the Zeeman energy released by this fraction contributes to local heating, significantly lowering the energy threshold for avalanche formation. We present simulation results confirming this effect and report on experimental verification of the assumed low-temperature thermal properties of two representative SMM crystals, Mn$_{12}$-acetate and Mn$_{32}$. Together, these efforts extend this pathfinder program toward the realization of SMM-based detectors with controlled material properties and enhanced dark matter sensitivity.

Eberhardt, Andrew [Tokyo U., IPMU]↗
DOE OSTI2021

Effect of diffusion constant on the morphology of dendrite growth in lithium metal batteries

Lithium dendrites can lead to a short circuit and battery failure, and developing strategies for their suppression is of considerable importance. In this work, we study the growth of dendrites in a simple model system where the solvent is a continuum and the lithium ions are hard spheres that can deposit by sticking to existing spheres or the electrode surface. Using stochastic dynamics simulations, we investigate the effect of applied voltage and diffusion constant on the growth of dendrites. We find that the diffusion constant is the most significant factor, and the inhomogeneity of the electric field does not play a significant role. Additionally, the growth is most pronounced when the applied voltage and diffusion constant are both low. We observe a structural change from broccoli to cauliflower shape as the diffusion constant is increased. The simulations suggest that a control of electrolyte parameters that impact lithium diffusion might be an attractive route to controlling dendrite growth.

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

A Probabilistic Scheme for Semilinear Nonlocal Diffusion Equations with Volume Constraints

This work presents a probabilistic scheme for solving semilinear nonlocal diffusion equations with volume constraints and integrable kernels. The nonlocal model of interest is defined by a time-dependent semilinear partial integro-differential equation (PIDE), in which the integro-differential operator consists of both local convection-diffusion and nonlocal diffusion operators. Here, our numerical scheme is based on the direct approximation of the nonlinear Feynman–Kac formula that establishes a link between nonlinear PIDEs and stochastic differential equations. The exploitation of the Feynman–Kac representation avoids solving dense linear systems arising from nonlocal operators. Compared with existing stochastic approaches, our method can achieve first-order convergence after balancing the temporal and spatial discretization errors, which is a significant improvement of existing probabilistic/stochastic methods for nonlocal diffusion problems. Error analysis of our numerical scheme is established. The effectiveness of our approach is shown in two numerical examples. The first example considers a three-dimensional nonlocal diffusion equation to numerically verify the error analysis results. The second example presents a physics problem motivated by the study of heat transport in magnetically confined fusion plasmas.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Irradiation-induced composition patterns in binary solid solutions

A theoretical/computational model for the irradiation-driven compositional instabilities in binary solid solutions has been developed. The model is suitable for investigating the behavior of structural alloys and metallic nuclear fuels in a reactor environment as well as the response of alloy thin films to ion beam irradiation. The model is based on a set of reaction-diffusion equations for the dynamics of vacancies, interstitials, and lattice atoms under irradiation. The dynamics of these species includes the stochastic generation of defects by collision cascades as well as the defect reactions and diffusion. The atomic fluxes in this model are derived based on the transitions of lattice defects. The set of reaction-diffusion equations are stiff, hence a stiffly stable method, also known as the Gear method, has been used to numerically approximate the equations. For the Cu-Au alloy in the solid solution regime, the model results demonstrate the formation of compositional patterns under high-temperature particle irradiation, with Fourier space properties (Fourier spectrum, average wavelength, and wavevector) depending on the cascade damage characteristics, average composition, and irradiation temperature.

36 MATERIALS SCIENCE↗
DOE OSTI2016

From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations

We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also show that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

A quantal diffusion approach for multinucleon transfer in heavy-ion collisions

The stochastic mean-field (SMF) approach beyond the time-dependent-Hartree-Fock theory is used to explore the primary production cross sections in 64 Ni + 130 Te at the bombarding energy E c.m. = 184.3 MeV and 206 Pb + 118 Sn at E c.m. = 436.8 MeV. Secondary production cross-sections in the same systems are calculated using a statistical de-excitation model with GEMINI++ code. Furthermore, the obtained results are compared with available experimental data. Analysis employing SMF and GEMINI++ exhibit a good agreement with the experimental data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

Modeling of Diffusivity for 2D Vacancy Nanopits and Comparison with 2D Adatom Nanoislands on Metal(100) Surfaces Including Analysis for Ag(100)

Diffusion coefficients, D N , for 2D vacancy nanopits are compared with those for 2D homoepitaxial adatom nanoislands on metal(100) surfaces, focusing on the variation of DN with size, N. Here, N is measured in missing atoms for pits and adatoms for islands. Analysis of D N is based on kinetic Monte Carlo simulations of a tailored stochastic lattice-gas model, where pit and island diffusion are mediated by periphery diffusion, i.e., by edge atom hopping. Precise determination of D N versus N for typical parameters reveals a cyclical variation with an overall decrease in magnitude for increasing moderate O(10 2 ) ≤ N ≤ O(10 3 ). Monotonic decay, D N ~ N -β , is found for N ≥ O(10 2 ) with effective exponents, β = β eff , for both pits and islands, both well below the macroscopic value of βmacro = 3/2. D N values for vacancy pits are significantly lower (higher) than for adatom islands for moderate N in the case of low (high) kink rounding barrier. However, D N values for pits and islands slowly merge, and β eff → 3/2 for sufficiently large N. The latter feature is expected from continuum Langevin formulations appropriate for large sizes. Finally, we compare predictions from our model incorporating appropriate energetic parameters for Ag(100) with different sets of experimental data for diffusivity at 300 K, including assessment of β eff , for experimentally observed sizes N from ~100 to ~1000.

36 MATERIALS SCIENCE↗
DOE OSTI2014

A stochastic extension of the explicit algebraic subgrid-scale models

The explicit algebraic subgrid-scale (SGS) stress model (EASM) of Marstorp et al. [“Explicit algebraic subgrid stress models with application to rotating channel flow,” J. Fluid Mech. 639, 403–432 (2009)] and explicit algebraic SGS scalar flux model (EASFM) of Rasam et al. [“An explicit algebraic model for the subgrid-scale passive scalar flux,” J. Fluid Mech. 721, 541–577 (2013)] are extended with stochastic terms based on the Langevin equation formalism for the subgrid-scales by Marstorp et al. [“A stochastic subgrid model with application to turbulent flow and scalar mixing,” Phys. Fluids 19, 035107 (2007)]. The EASM and EASFM are nonlinear mixed and tensor eddy-diffusivity models, which improve large eddy simulation (LES) predictions of the mean flow, Reynolds stresses, and scalar fluxes of wall-bounded flows compared to isotropic eddy-viscosity and eddy-diffusivity SGS models, especially at coarse resolutions. The purpose of the stochastic extension of the explicit algebraic SGS models is to further improve the characteristics of the kinetic energy and scalar variance SGS dissipation, which are key quantities that govern the small-scale mixing and dispersion dynamics. LES of turbulent channel flow with passive scalar transport shows that the stochastic terms enhance SGS dissipation statistics such as length scale, variance, and probability density functions and introduce a significant amount of backscatter of energy from the subgrid to the resolved scales without causing numerical stability problems. The improvements in the SGS dissipation predictions in turn enhances the predicted resolved statistics such as the mean scalar, scalar fluxes, Reynolds stresses, and correlation lengths. Moreover, the nonalignment between the SGS stress and resolved strain-rate tensors predicted by the EASM with stochastic extension is in much closer agreement with direct numerical simulation data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

N-particle irreducible actions for stochastic fluids

We construct one- and two-particle irreducible (1PI and 2PI) effective actions for the stochastic fluid dynamics of a conserved density undergoing diffusive motion. We compute the 1PI action in one-loop order and the 2PI action in two-loop approximation. We derive a set of Schwinger-Dyson equations and regularize the resulting equations using Pauli-Villars fields. We numerically solve the Schwinger-Dyson equations for a non-critical fluid. We find that higher-loop effects summed by the Schwinger-Dyson renormalize the non-linear coupling. We also find indications of a diffuson-cascade, the appearance of n-loop correction with smaller and smaller exponential suppression.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

The Multi-Plume Eddy-Diffusivity/Mass-Flux (EDMF) Unified Parameterization: Stratocumulus and the Transition to Cumulus Boundary Layers

The primary objective of this project is to mitigate inaccuracies and biases in subtropical boundary layer clouds, particularly in oceanic upwelling regions. Our approach began with developing a novel unified boundary layer and convection parameterization, utilizing the multi-plume Eddy-Diffusivity/Mass-Flux (EDMF) framework. We evaluated this advanced stochastic multi-plume EDMF parameterization in an independent single-column model (SCM), benchmarking it against Large-Eddy Simulation (LES) reference data and satellite observations. This version of the EDMF is designed to seamlessly represent a continuum of convective processes, from dry and cloudy boundary layer convection to deep moist convection. We progressed by integrating the stochastic multi-plume EDMF scheme into the Simple Cloud-Resolving E3SM (Energy Exascale Earth System Model) Atmosphere model (SCREAM), coupling it with the SHOC (Simplified Higher-Order Closure) turbulence and convection scheme. This combined approach was then evaluated against LES reference data for both maritime and continental shallow convection within the E3SM SCM.

54 ENVIRONMENTAL SCIENCES↗