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Results for “Diffuse fraction”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Intermittent cluster dynamics and temporal fractional diffusion in a bulk metallic glass

Glassy solids evolve towards lower-energy structural states by physical aging. This can be characterized by structural relaxation times, the assessment of which is essential for understanding the glass’ time-dependent property changes. Conducted over short times, a continuous increase of relaxation times with time is seen, suggesting a time-dependent dissipative transport mechanism. By focusing on micro-structural rearrangements at the atomic-scale, we demonstrate the emergence of sub-diffusive anomalous transport and therefore temporal fractional diffusion in a metallic glass, which we track via coherent x-ray scattering conducted over more than 300,000 s. At the longest probed decorrelation times, a transition from classical stretched exponential to a power-law behavior occurs, which in concert with atomistic simulations reveals collective and intermittent atomic motion. Our observations give a physical basis for classical stretched exponential relaxation behavior, uncover a new power-law governed collective transport regime for metallic glasses at long and practically relevant time-scales, and demonstrate a rich and highly non-monotonous aging response in a glassy solid, thereby challenging the common framework of homogeneous aging and atomic scale diffusion.

42 ENGINEERING↗
DOE OSTI2022

Fourier analysis of continuous fractional diffusion synthetic acceleration schemes in slab geometry

We propose two fractional extensions of continuous diffusion synthetic acceleration (DSA) with fractional derivative order α varying over the interval 2 ≥ α ≥ 1 . We investigate the spectral properties of the corresponding continuous families of fractional preconditioners by performing Fourier analysis for a model infinite homogeneous medium problem in slab geometry. The first family results in a fractional acceleration scheme, FrDSAo, that reduces to traditional DSA for .α = 2 and scattering ratio c limiting to a unit value (c → 1) but is otherwise optimized via the Fourier analysis, to obtain the smallest possible spectral radius, for c < 1 and 2 ≥ α ≥ 1. The second family corresponds to a fractional acceleration scheme, FrDSAs, that reduces to traditional DSA for α = 2 for all values of c. The latter scheme is not optimized but has the advantage of lending itself to a more straightforward implementation. For high values of c, the results of the Fourier analysis point to the existence of an interval 2 > α > ∼1.8 where both FrDSAo and FrDSAs can achieve a lower spectral radius than DSA. For example, DSA has a spectral radius of ∼0.2246 for c = 0.9999 while FrDSAo produces a value of ∼0.1616 at α = 1.92 and FrDSAs results in ∼0.2116 at α =1.93. (author)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Risk-Averse Control of Fractional Diffusion with Uncertain Exponent

In this paper, we introduce and analyze a new class of optimal control problems constrained by elliptic equations with uncertain fractional exponents. We utilize risk measures to formulate the resulting optimization problem. We develop a functional analytic framework, study the existence of solution and rigorously derive the first-order optimality conditions. Additionally, we employ a sample-based approximation for the uncertain exponent and the finite element method to discretize in space. Further, we prove the rate of convergence for the optimal risk neutral controls when using quadrature approximation for the uncertain exponent and conclude with illustrative examples.

finite element method↗
DOE OSTI2023

Control of Fractional Diffusion Problems via Dynamic Programming Equations

In this study, we explore the approximation of feedback control of integro-differential equations containing a fractional Laplacian term. To obtain feedback control for the state variable of this nonlocal equation, we use the Hamilton–Jacobi–Bellman equation. It is well known that this approach suffers from the curse of dimensionality, and to mitigate this problem we couple semi-Lagrangian schemes for the discretization of the dynamic programming principle with the use of Shepard approximation. This coupling enables approximation of high-dimensional problems. Numerical convergence toward the solution of the continuous problem is provided together with linear and nonlinear examples. The robustness of the method with respect to disturbances of the system is illustrated by comparisons with an open-loop control approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Data-driven learning of nonlocal physics from high-fidelity synthetic data

A key challenge to nonlocal models is the analytical complexity of deriving them from first principles, and frequently their use is justified a posteriori. Here, we extract nonlocal models from data, circumventing these challenges and providing data-driven justification for the resulting model form. Extracting data-driven surrogates is a major challenge for machine learning (ML) approaches, due to nonlinearities and lack of convexity — it is particularly challenging to extract surrogates which are provably well-posed and numerically stable. Our scheme not only yields a convex optimization problem, but also allows extraction of nonlocal models whose kernels may be partially negative while maintaining well-posedness even in small-data regimes. To achieve this, based on established nonlocal theory, we embed in our algorithm sufficient conditions on the non-positive part of the kernel that guarantee well-posedness of the learnt operator. These conditions are imposed as inequality constraints to meet the requisite conditions of the nonlocal theory. We demonstrate this workflow for a range of applications, including reproduction of manufactured nonlocal kernels; numerical homogenization of Darcy flow associated with a heterogeneous periodic microstructure; nonlocal approximation to high-order local transport phenomena; and approximation of globally supported fractional diffusion operators by truncated kernels.

42 ENGINEERING↗
DOE OSTI2022

Environmental controls on the light use efficiency of terrestrial gross primary production

Abstract Gross primary production (GPP) by terrestrial ecosystems is a key quantity in the global carbon cycle. The instantaneous controls of leaf‐level photosynthesis are well established, but there is still no consensus on the mechanisms by which canopy‐level GPP depends on spatial and temporal variation in the environment. The standard model of photosynthesis provides a robust mechanistic representation for C 3 species; however, additional assumptions are required to “scale up” from leaf to canopy. As a consequence, competing models make inconsistent predictions about how GPP will respond to continuing environmental change. This problem is addressed here by means of an empirical analysis of the light use efficiency (LUE) of GPP inferred from eddy covariance carbon dioxide flux measurements, in situ measurements of photosynthetically active radiation (PAR), and remotely sensed estimates of the fraction of PAR (fAPAR) absorbed by the vegetation canopy. Focusing on LUE allows potential drivers of GPP to be separated from its overriding dependence on light. GPP data from over 100 sites, collated over 20 years and located in a range of biomes and climate zones, were extracted from the FLUXNET2015 database and combined with remotely sensed fAPAR data to estimate daily LUE. Daytime air temperature, vapor pressure deficit, diffuse fraction of solar radiation, and soil moisture were shown to be salient predictors of LUE in a generalized linear mixed‐effects model. The same model design was fitted to site‐based LUE estimates generated by 16 terrestrial ecosystem models. The published models showed wide variation in the shape, the strength, and even the sign of the environmental effects on modeled LUE. These findings highlight important model deficiencies and suggest a need to progress beyond simple “goodness of fit” comparisons of inferred and predicted carbon fluxes toward an approach focused on the functional responses of the underlying dependencies.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Intermediate time sub-diffusion and stress relaxation in ring polymer melts

The slow dynamics of non-concatenated ring melts remains a frontier problem in polymer science with implications for many soft material environments including cellular biophysics. Here, in this work, we report large-scale simulations of model ring melts that analyze the monomer and center-of-mass (CM) mean square displacements (MSD) and stress relaxation function on intermediate time and length scales. The degree of dynamical slowing down is characterized by the maximally sub-diffusive fractional time scaling exponents. The data span an exceptionally wide range of ring degrees of polymerization and stiffnesses and are not successfully organized based on the classic measure linear chain entanglement, N/N e . Rather, we find that the crossover degree of polymerization, N D , based on ring macromolecular caging that successfully allows master curves to be constructed for the long-time CM self-diffusion constant also collapses these temporal dynamic scaling exponents. Different properties display different exponents and exhibit one or two regimes of linear variation with the logarithm of N D / N . A distinct crossover of the CM-MSD and stress relaxation exponents emerges at sufficiently large N or stiffness that is not found for the monomer MSD, indicating a novel form of dynamic decoupling. This crossover aligns with the predicted critical degree of polymerization for transitioning from a weak to strong caging regime, indicative of activated transport. The latter may reflect the emergence of an intermolecular collective contribution to stress in analogy with dense soft colloidal matter. Suggestions are made for future theoretical work to address the rich patterns of behavior discovered.

Anomalous diffusion↗
DOE OSTI2022

Learning functional priors and posteriors from data and physics

In this work, we develop a new Bayesian framework based on deep neural networks to be able to extrapolate in space-time using historical data and to quantify uncertainties arising from both noisy and gappy data in physical problems. Specifically, the proposed approach has two stages: (1) prior learning and (2) posterior estimation. At the first stage, we employ the physics-informed Generative Adversarial Networks (PI-GAN) to learn a functional prior either from a prescribed function distribution, e.g., Gaussian process, or from historical data and physics. At the second stage, we employ the Hamiltonian Monte Carlo (HMC) method to estimate the posterior in the latent space of PI-GANs. In addition, we use two different approaches to encode the physics: (1) automatic differentiation, used in the physicsinformed neural networks (PINNs) for scenarios with explicitly known partial differential equations (PDEs), and (2) operator regression using the deep operator network (DeepONet) for PDE-agnostic scenarios. We then test the proposed method for (1) meta-learning for one-dimensional regression, and forward/inverse PDE problems (combined with PINNs); (2) PDE-agnostic physical problems (combined with DeepONet), e.g., fractional diffusion as well as saturated stochastic (100-dimensional) flows in heterogeneous porous media; and (3) spatial-temporal regression problems, i.e., inference of a marine riser displacement field using experimental data from the Norwegian Deepwater Programme (NDP). The results demonstrate that the proposed approach can provide accurate predictions as well as uncertainty quantification given very limited scattered and noisy data, since historical data could be available to provide informative priors. In summary, the proposed method is capable of learning flexible functional priors, e.g., both Gaussian and non-Gaussian process, and can be readily extended to big data problems by enabling mini-batch training using stochastic HMC or normalizing flows since the latent space is generally characterized as low dimensional.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Diffuse Radiation Forcing Constraints on Gross Primary Productivity and Global Terrestrial Evapotranspiration

Abstract The diffuse radiation fertilization effect—the increase in plant productivity in the presence of higher diffuse radiation ( K ↓,d )—is an important yet understudied aspect of atmosphere‐biosphere interactions and can modify the terrestrial carbon, energy, and water budgets. The K ↓,d fertilization effect links the carbon cycle with clouds and aerosols, all of which are large sources of uncertainties for our current understanding of the Earth system and for future climate projections. Here we establish to what extent observational and modeling uncertainty in sunlight's diffuse fraction ( k d ) affects simulated gross primary productivity (GPP) and terrestrial evapotranspiration ( λE ). We find only 48 eddy covariance sites with simultaneous sufficient measurements of K ↓,d with none in the tropical climate zone, making it difficult to constrain this mechanism globally using observations. Using a land modeling framework based on the latest version of the Community Land Model, we find that global GPP ranges from 114 Pg C year −1 when using k d forcing from the Modern‐Era Retrospective analysis for Research and Applications, version 2 reanalysis to a ∼7% higher value of 122 Pg C year −1 when using the Clouds and the Earth's Radiant Energy System satellite product, with especially strong differences apparent over the tropical region (mean increase ∼9%). The differences in λE , although smaller (−0.4%) due to competing changes in shaded and sunlit leaf transpiration, can be greater than regional impacts of individual forcing agents like aerosols. Our results demonstrate the importance of comprehensively and systematically validating the simulated k d by atmosphere modules as well as the response to differences in k d within land modules across Earth System Models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Resistive drift wave turbulence and anomalous transport of multi-species plasma

Anomalous transport of multi-species plasma is considered with the generalized Hasegawa–Wakatani model. It is shown that the transport of all plasma species is described by fractional diffusion equations with the same effective diffusion coefficient. Strongly enhanced perturbations of heavy impurity density are found in long-living plasma flow vortices.

Physics↗
DOE OSTI2022

Advanced Isotope Separation Technology for Fusion Fuel

Deuterium-tritium fusion is the easiest nuclear fusion reaction among known fusion reactions. Since tritium is extremely rare, it is artificially produced by irradiating lithium metal. The separation, isolation, and storage of the tritium isotope has been a major focus of the Savannah River Site (SRS) for many decades. Thermal diffusion, fractional absorption, and cryogenic distillation have all been used in the past, and each has significant operational and safety challenges. A process known as the Thermal Cycling Absorption Process (TCAP) was invented at SRS, and because of its overwhelming advantages in safety, efficiency, size, and reduced tritium inventory, it has replaced all other hydrogen isotope separation processes at SRS. Here, the working principles and current development of hydrogen isotope separation using TCAP at SRS are explained as a potential advanced isotope separation process for the fusion fuel cycle.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Performance Improvements Through Advanced PV Backtracking on Uneven Terrain

The climatic sensitivity of new terrain-aware backtracking algorithms is evaluated across 800 locations in the continental USA on a representative synthetic rolling terrain. We find that a global optimization approach to backtracking results in climate-specific annual energy gains of 2.4%–3.2% relative to a traditional backtracking algorithm baseline. We identify a strong logarithmic correlation between local diffuse fraction and yield improvement, and highlight the effect of seasonal precipitation on performance gains. We also find that a backtracking approach, which approximates the terrain as constant, does not offer significant annual energy gains over the baseline on the synthetic terrain. Our findings suggest that specific yield from backtracking in the USA can be improved by as much as 88 kWh/kW by considering terrain when selecting a backtracking algorithm.

Backtracking↗
DOE OSTI2025

Virtual element approximations of the time-fractional nonlinear convection-diffusion equation on polygonal meshes

We extend the Virtual Element Method to a two-dimensional unsteady nonlinear convection-diffusion equation characterized by a fractional-order derivative with respect to the time variable. Our methodology is based on three fundamental technical components: a fractional version of the Grunwald-Letnikov approximation, discrete maximal regularity, and the regularity theory associated with non-linearity. We prove the method's well-posedness, i.e., the approximate solution's existence and uniqueness to the time-fractional convection-diffusion equation with a Lipschitz nonlinear source term. The fully discrete scheme inherently maintains stability and consistency by leveraging the discrete maximal regularity and the energy projection operator. The convergence in the L 2 -norm and H 1 -norm to various mesh configurations is validated by numerical results, underlining the practical effectiveness of the proposed method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A fractional model for anomalous diffusion with increased variability: Analysis, algorithms and applications to interface problems

Fractional equations have become the model of choice in several applications where heterogeneities at the microstructure result in anomalous diffusive behavior at the macroscale. Here, we introduce a new fractional operator characterized by a doubly-variable fractional order and possibly truncated interactions. Under certain conditions on the model parameters and on the regularity of the fractional order we show that the corresponding Poisson problem is well-posed. Additionally, we introduce a finite element discretization and describe an efficient implementation of the finite-element matrix assembly in the case of piecewise constant fractional order. Through several numerical tests, we illustrate the improved descriptive power of this new operator across media interfaces. Furthermore, we present one-dimensional and two-dimensional h-convergence results that show that the variable-order model has the same convergence behavior as the constant-order model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

The effect of ion pairing on speciation and transport in ion exchange membranes at varying hydration levels: A four-state model

Understanding ion pairing in ion exchange membranes (IEMs) is essential for advancing IEM applications in energy and environmental technologies. Here, this study introduces a four-state molecular dynamics model to quantify speciation and transport within Nafion-117, specifically examining the role of ion pairing in monovalent and divalent counterions (NaCl, Na 2 SO 4 , and MgSO 4 ). By analyzing radial distribution functions (RDFs) and molecular snapshots, we distinguish ion pairing modes and classify counterions into four states: condensed counterion, condensed ion pair, free ion pair, and free counterion. A key finding is that while divalent counterions (e. g., Mg 2+ ) maintain stable speciation across hydration levels, monovalent counterions (e.g., Na + ) show notable speciation shifts with hydration. Both monovalent and divalent counterions are not diffusive when condensed onto the polymer (sorbed to membrane functional groups). In contrast, free counterions are diffusive across all hydration levels. To evaluate the overall diffusivity of counterions, four-state fractions and diffusivities are computed, each contributing to counterion transport. The condensed/free ion speciation for multivalent sulfate salts aligns with previous revisions to the Donnan-Manning framework that include ion pairing, thereby validating its relevance to established membrane theories. The four-state model's diffusivity results support several current ion exchange assumptions, including that the condensed counterions are immobile, while uncondensed counterions are mobile. The four-state model offers insights into contact ion pairing within IEMs, highlighting its potential even when undetected in aqueous solution experiments. This work advances the theoretical understanding of counterion speciation in IEMs while identifying model limitations that suggest avenues for refinement, such as distinguishing water-mediated ion pairs between fully hydrated ions.

Ion exchange membranes↗
DOE OSTI2021

Error Estimates for the Optimal Control of a Parabolic Fractional PDE

In this work, we consider the integral definition of the fractional Laplacian and analyze a linear-quadratic optimal control problem for the so-called fractional heat equation; control constraints are also considered. We derive existence and uniqueness results, first order optimality conditions, and regularity estimates for the optimal variables. To discretize the state equation we propose a fully discrete scheme that relies on an implicit finite difference discretization in time combined with a piecewise linear finite element discretization in space. We derive stability results and a novel $L^2(0,T;L^2(\Omega))$ a priori error estimate. On the basis of the aforementioned solution technique, we propose a fully discrete scheme for our optimal control problem that discretizes the control variable with piecewise constant functions, and we derive a priori error estimates for it. We illustrate the theory with one- and two-dimensional numerical experiments.

97 MATHEMATICS AND COMPUTING↗