Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Diffusion models”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Leith diffusion model for homogeneous anisotropic turbulence

Here, a proposal for a spectral closure model for homogeneous anisotropic turbulence. The systematic development begins by closing the third-order correlation describing nonlinear interactions by an anisotropic generalization of the Leith diffusion model for isotropic turbulence. The correlation tensor is then decomposed into a tensorially isotropic part, or directional anisotropy, and a trace-free remainder, or polarization anisotropy. The directional and polarization components are then decomposed using irreducible representations of the SO(3) symmetry group. Under the ansatz that the decomposition is truncated at quadratic order, evolution equations are derived for the directional and polarization pieces of the correlation tensor. Here, numerical simulation of the model equations for a freely decaying anisotropic flow illustrate the non-trivial effects of spectral dependencies on the different return-to-isotropy rates of the directional and polarization contributions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A reaction–diffusion model for grayscale digital light processing 3D printing

We report that digital light processing (DLP) 3D printing is an additive manufacturing process that utilizes light patterns to photopolymerize a liquid resin into a solid. Due to the accuracy of modern digital micromirror devices (DMD) and recent advances in resin chemistry, it is now possible to create functionally graded structures using different light intensity values, also known as grayscale DLP (g-DLP). Different intensities of light lead to differences in the polymer crosslinking density after curing, which ultimately produces a part with gradients of material properties. However, g-DLP is a complicated process. First, the DLP printing is a highly coupled chemical and physical process that involves light propagation, chemical reactions, species diffusion, heat transfer, volume shrinkage, and changes in mechanical behaviors of the curing resin. Second, in g-DLP, light gradients create strong in plane gradients of chemical species concentrations in the curing liquid resin due to the strong dependence of light intensity on the rate of monomer crosslinking. Furthermore, light gradients through the depth create concentration gradients due to the degree of cure dependent light absorption and the use of photoabsorbers. These complex physical features of the printing process must be understood in order to properly control printing parameters such as light exposure time, printing speed, and grayscale variations to achieve accurate mechanical properties. In this paper, a photopolymerization reaction–diffusion model is developed and used in conjunction with experiments to investigate the coupled effects of light propagation, chemical reaction rates, and species diffusion during g-DLP 3D printing. The model is implemented numerically utilizing the finite difference method and simulation results are compared to experimental findings of simple printed structures. The agreement between experimental and model predictions of simple quantities of interest, such as geometric feature sizes, shows that the model can capture the overcure due to free-radical and other species diffusion during printing when grayscale patterns are employed. This model lays the groundwork for future extensions that can incorporate more complex coupled physics such as heat transfer, volume shrinkage, and material property evolution, which are critically important in utilizing g-DLP 3D printing for the fabrication of high-performance parts which excellent geometric and material property tolerances.

36 MATERIALS SCIENCE↗
DOE OSTI2013

Diffusion model of the non-stoichiometric uranium dioxide

Uranium dioxide (UO{sub 2}), which is used in light water reactors, exhibits a large range of non-stoichiometry over a wide temperature scale up to 2000 K. Understanding diffusion behavior of uranium oxides under such conditions is essential to ensure safe reactor operation. The current understanding of diffusion properties is largely limited by the stoichiometric deviations inherent to the fuel. The present DICTRA-based model considers diffusion across non-stoichiometric ranges described by experimentally available data. A vacancy and interstitial model of diffusion is applied to the U–O system as a function of its defect structure derived from CALPHAD-type thermodynamic descriptions. Oxygen and uranium self and tracer diffusion coefficients are assessed for the construction of a mobility database. Chemical diffusion coefficients of oxygen are derived with respect to the Darken relation and migration energies of defects are evaluated as a function of stoichiometric deviation. - Graphical abstract: Complete description of Oxygen–Uranium diffusion as a function of composition at various temperatures according to the developed Dictra model. - Highlights: • Assessment of a uranium–oxygen diffusion model with Dictra. • Complete description of U–O diffusion over wide temperature and composition range. • Oxygen model includes terms for interstitial and vacancy migration. • Interaction terms between defects help describe non-stoichiometric domain of UO{sub 2±x}. • Uranium model is separated into mobility terms for the cationic species.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Nonlinear Ensemble Filtering with Diffusion Models: Application to the Surface Quasigeostrophic Dynamics

The intersection between classical data assimilation methods and novel machine learning techniques has attracted significant interest in recent years. Here, we explore another promising solution in which diffusion models are used to formulate a robust nonlinear ensemble filter for sequential data assimilation. Unlike standard machine learning methods, the proposed ensemble score filter (EnSF) is completely training free and can efficiently generate a set of analysis ensemble members. Here, in this study, we apply the EnSF to a surface quasigeostrophic model and compare its performance against the popular local ensemble transform Kalman filter (LETKF), which makes Gaussian assumptions in the analysis step. Numerical tests demonstrate that EnSF maintains stable performance in the absence of localization and for a variety of experimental settings. We find that while LETKF maintains optimal performance in the case of linear observations of the entire state and a perfect model, EnSF shows improvements over LETKF when nonlinear observations are assimilated and the system is subject to unexpected model errors. A spectral decomposition of the analysis results in this nonlinear observation regime shows that the largest improvements over LETKF occur at large scales (small wavenumbers), where LETKF lacks sufficient ensemble spread. Overall, this initial application of EnSF to a geophysical model of intermediate complexity motivates further development of the algorithm for more realistic problems.

Artificial intelligence↗
DOE OSTI2016

THE B/C AND SUB-IRON/IRON COSMIC RAY RATIOS—FURTHER EVIDENCE IN FAVOR OF THE SPIRAL-ARM DIFFUSION MODEL

The boron to carbon (B/C) and sub-Fe/Fe ratios provide an important clue on cosmic ray (CR) propagation within the Galaxy. These ratios estimate the grammage that the CRs traverse as they propagate from their sources to Earth. Attempts to explain these ratios within the standard CR propagation models require ad hoc modifications and even with those these models necessitate inconsistent grammages to explain both ratios. As an alternative, physically motivated model, we have proposed that CRs originate preferably within the galactic spiral arms. CR propagation from dynamic spiral arms has important imprints on various secondary to primary ratios, such as the B/C ratio and the positron fraction. We use our spiral-arm diffusion model with the spallation network extended up to nickel to calculate the sub-Fe/Fe ratio. We show that without any additional parameters the spiral-arm model consistently explains both ratios with the same grammage, providing further evidence in favor of this model.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

A comparison between the fission matrix method, the diffusion model and the transport model

The fission matrix method may be used to solve the critical eigenvalue problem in a Monte Carlo simulation. This method gives us access to the different eigenvalues and eigenvectors of the transport or fission operator. We propose to compare the results obtained via the fission matrix method with those of the diffusion model, and an approximated transport model. To do so, we choose to analyse the mono-kinetic and continuous energy cases for a Godiva-inspired critical sphere. The first five eigenvalues are computed with TRIPOLI-4{sup R} and compared to the theoretical ones. An extension of the notion of the extrapolation distance is proposed for the modes other than the fundamental one. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Probabilistic Diffusion Models Advance Extreme Flood Forecasting

Extreme floods pose escalating risks in a changing climate, yet forecasting remains challenging due to peak flow underestimation and high uncertainty. We introduce diffusion-based runoff model (DRUM), a probabilistic deep learning (DL) approach that advances extreme flood forecasting across representative basins in the contiguous United States. DRUM outperforms state-of-the-art benchmarks, enhancing nowcasting skill for the top 1‰ of flows in 72.3% of studied basins. Under operational scenarios, DRUM extends reliable lead times by nearly a full day for 20- and 50-year floods. When evaluated with measured precipitation, an ideal condition, recall improves by 0.3–0.4 and the early warning window extends by 2.3 days for 50-year floods. The enhancement potential varies regionally, with precipitation-driven flood zones in the eastern and northwestern US benefiting most, gaining 3–7 days in lead time. These findings highlight the transformative potential of diffusion models as a cutting-edge generative AI technique for advancing hydrology and broader Earth system sciences.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Reaction Diffusion Modelling of 3D Pillar Electrodes in Single-Catalyst CO 2 Reduction Cascades

Effective electrochemical CO 2 reduction to liquid fuels requires that the local catalytic environment facilitates the desired reactivity, yet a microscopic understanding of this environment is difficult to achieve from experiment alone. In this work, a 3D reaction-diffusion model was developed to explore the effects of electrode surface area and local geometry on the performance of a heterogeneous catalyst that performs a two-step CO 2 reduction cascade reaction to CO and then CH 3 OH under aqueous conditions. Kinetic parameters for the model were inspired by experimental results using a cobalt phthalocyanine (CoPc) catalyst. Three-dimensional architectures composed of arrays of square pillars with varying dimensions and either smooth or periodically modulated surfaces were tested, revealing the extent to which geometry modulates the performance of the cascade reactions. Although structural variations modulate local concentration gradients, we find that electrochemically active surface area predominantly governs the overall cascade reaction. Moreover, the results suggest that supersaturation of CO, with concentrations up to ten-fold higher than the equilibrium solubility limit, might be critical for more efficient conversion to CH 3 OH. For any given geometry, the spatially averaged ratio of [CO] to [CO 2 ] is dictated by the electrochemically active surface area and determines the yield of CH 3 OH. For a fixed surface area, geometries that spatially confine the electrolyte yield moderate local [CO] to [CO 2 ] ratios within small volumes. In contrast, less confining geometries result in a broader distribution of local ratios spread over larger volumes, with both configurations yielding the same spatially averaged [CO] to [CO 2 ] ratio. These insights provide valuable design principles—highlighting the critical importance of surface area and possibly CO supersaturation—for engineering advanced electrode architectures that leverage intermediate trapping and CO supersaturation to enhance overall performance in tandem CO 2 reduction systems.

COMSOL↗
DOE OSTI2011

Nucleus-nucleus cold fusion reactions analyzed with the l-dependent 'fusion by diffusion' model

We present a modified version of the Fusion by Diffusion (FBD) model aimed at describing the synthesis of superheavy nuclei in cold fusion reactions, in which a low excited compound nucleus emits only one neutron. The modified FBD model accounts for the angular momentum dependence of three basic factors determining the evaporation residue cross section: the capture cross section {sigma}{sub cap}(l), the fusion probability P{sub fus}(l), and the survival probability P{sub surv}(l). The fusion hindrance factor, the inverse of P{sub fus}(l), is treated in terms of thermal fluctuations in the shape degrees of freedom and is expressed as a solution of the Smoluchowski diffusion equation. The l dependence of P{sub fus}(l) results from the l-dependent potential energy surface of the colliding system. A new parametrization of the distance of starting point of the diffusion process is introduced. An analysis of a complete set of 27 excitation functions for production of superheavy nuclei in cold fusion reactions, studied in experiments at GSI Darmstadt, RIKEN Tokyo, and LBNL Berkeley, is presented. The FBD model satisfactorily reproduces shapes and absolute cross sections of all the cold fusion excitation functions. It is shown that the peak position of the excitation function for a given 1n reaction is determined by the Q value of the reaction and the height of the fission barrier of the final nucleus. This fact could possibly be used in future experiments (with well-defined beam energy) for experimental determination of the fission barrier heights.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Relativistic diffusion model for hadron production in p -Pb collisions at energies available at the CERN Large Hadron Collider

We investigate charged-hadron production in relativistic heavy-ion collisions of asymmetric systems within a nonequilibrium-statistical framework. Calculated centrality-dependent pseudorapidity distributions for p-Pb collisions at s NN = 5.02 and 8.16 TeV are compared with data from the Large Hadron Collider. Our approach combines a relativistic diffusion model with formulations based on quantum chromodynamics while utilizing numerical solutions of a Fokker-Planck equation to account for the shift and broadening of the fragmentation sources for particle-production with respect to the stopping (net-baryon) rapidity distributions. To represent the centrality dependence of charged-hadron production in asymmetric systems over a broad region of pseudorapidities, the consideration and precise modeling of the fragmentation sources, along with the central gluon-gluon source, is found to be essential. Specifically, this results in an inversion of the particle-production amplitude from backward to forward dominance when transitioning from central to peripheral collisions, in agreement with recent ATLAS and ALICE p-Pb data at s NN = 5.02 T e V . Published by the American Physical Society 2024

Schulz, Philipp (ORCID:0009000266642148)↗
DOE OSTI2020

Pattern formation in a coupled membrane-bulk reaction-diffusion model for intracellular polarization and oscillations

Reaction-diffusion systems have been widely used to study spatio-temporal phenomena in cell biology, such as cell polarization. Coupled bulk-surface models naturally include compartmentalization of cytosolic and membrane-bound polarity molecules. Here we study the distribution of the polarity protein Cdc42 in a mass-conserved membrane-bulk model, and explore the effects of diffusion and spatial dimensionality on spatio-temporal pattern formation. We first analyze a one-dimensional (1-D) model for Cdc42 oscillations in fission yeast, consisting of two diffusion equations in the bulk domain coupled to nonlinear ODEs for binding kinetics at each end of the cell. In 1-D, our analysis reveals the existence of symmetric and asymmetric steady states, as well as anti-phase relaxation oscillations typical of slow-fast systems. We then extend our analysis to a two-dimensional (2-D) model with circular bulk geometry, for which species can either diffuse inside the cell or become bound to the membrane and undergo a nonlinear reaction-diffusion process. We also consider a nonlocal system of PDEs approximating the dynamics of the 2-D membrane-bulk model in the limit of fast bulk diffusion. In all three model variants we find that mass conservation selects perturbations of spatial modes that simply redistribute mass. In 1-D, only anti-phase oscillations between the two ends of the cell can occur, and in-phase oscillations are excluded. In higher dimensions, no radially symmetric oscillations are observed. Instead, the only instabilities are symmetry-breaking, either corresponding to stationary Turing instabilities, leading to the formation of stationary patterns, or to oscillatory Turing instabilities, leading to traveling and standing waves. Codimension-two Bogdanov—Takens bifurcations occur when the two distinct instabilities coincide, causing traveling waves to slow down and to eventually become stationary patterns. Our work clarifies the effect of geometry and dimensionality on behaviors observed in ma.ss-conserved cell polarity models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Reaction-diffusion modeling provides insights into biophysical carbon-concentrating mechanisms in land plants

Carbon-concentrating mechanisms (CCMs) have evolved numerous times in photosynthetic organisms. They elevate the concentration of CO 2 around the carbon-fixing enzyme rubisco, thereby increasing CO 2 assimilatory flux and reducing photorespiration. Biophysical CCMs, like the pyrenoid-based CCM (PCCM) of Chlamydomonas reinhardtii or carboxysome systems of cyanobacteria, are common in aquatic photosynthetic microbes, but in land plants appear only among the hornworts. To predict the likely efficiency of biophysical CCMs in C 3 plants, we used spatially resolved reaction-diffusion models to predict rubisco saturation and light use efficiency. We found that the energy efficiency of adding individual CCM components to a C 3 land plant is highly dependent on the permeability of lipid membranes to CO 2 , with values in the range reported in the literature that are higher than those used in previous modeling studies resulting in low light use efficiency. Adding a complete PCCM into the leaf cells of a C 3 land plant was predicted to boost net CO 2 fixation, but at higher energetic costs than those incurred by photorespiratory losses without a CCM. Two notable exceptions were when substomatal CO 2 levels are as low as those found in land plants that already use biochemical CCMs and when gas exchange is limited, such as with hornworts, making the use of a biophysical CCM necessary to achieve net positive CO 2 fixation under atmospheric CO 2 levels. This provides an explanation for the uniqueness of hornworts' CCM among land plants and the evolution of pyrenoids multiple times.

Kaste, Joshua A. M.↗
DOE OSTI2017

Aggregation-fragmentation-diffusion model for trail dynamics

We investigate statistical properties of trails formed by a random process incorporating aggregation, fragmentation, and diffusion. In this stochastic process, which takes place in one spatial dimension, two neighboring trails may combine to form a larger one, and also one trail may split into two. In addition, trails move diffusively. The model is defined by two parameters which quantify the fragmentation rate and the fragment size. In the long-time limit, the system reaches a steady state, and our focus is the limiting distribution of trail weights. We find that the density of trail weight has power-law tail P(w)~w –γ for small weight w. We obtain the exponent γ analytically and find that it varies continuously with the two model parameters. In conclusion, the exponent γ can be positive or negative, so that in one range of parameters small-weight trails are abundant and in the complementary range they are rare.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

A Mechanism-Based Reaction–Diffusion Model for Accelerated Discovery of Thermoset Resins Frontally Polymerized by Olefin Metathesis

Frontal ring-opening metathesis polymerization (FROMP) involves a self-perpetuating exothermic reaction, which enables the rapid and energy-efficient manufacturing of thermoset polymers and composites. Current state-of-the-art reaction–diffusion FROMP models rely on a phenomenological description of the olefin metathesis kinetics, limiting their ability to model the governing thermo-chemical FROMP processes. Furthermore, the existing models are unable to predict the variations in FROMP kinetics with changes in the resin composition and as a result are of limited utility toward accelerated discovery of new resin formulations. In this work, we formulate a chemically meaningful model grounded in the established mechanism of ring-opening metathesis polymerization (ROMP). Our study aims to validate the hypothesis that the ROMP mechanism, applicable to monomer-initiator solutions below 100 °C, remains valid under the nonideal conditions encountered in FROMP, including ambient to >200 °C temperatures, sharp temperature gradients, and neat monomer environments. Through extensive simulations, we demonstrate that our mechanism-based model accurately predicts the FROMP behavior across various resin compositions, including polymerization front velocities and thermal characteristics (e.g., T max ). Additionally, we introduce a semi-inverse workflow that predicts FROMP behavior from a single experimental data point. Notably, the physiochemical parameters utilized in our model can be obtained through DFT calculations and minimal experiments, highlighting the model’s potential for rapid screening of new FROMP chemistries in pursuit of thermoset polymers with superior thermo-chemo-mechanical properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

D$e^+e^-$ffusion: Capturing the Beam-Beam Physics of $e^+e^-$ Collisions with Diffusion Models

Beam-induced backgrounds at high-luminosity $e^+e^-$ colliders, such as the FCC-ee, are dominated by incoherent pair creation (IPC), and require computationally expensive simulations with dedicated Monte Carlo (MC) event generators. Reliable detector and machine-detector interface studies necessitate event samples that are several orders of magnitude larger than what is practically attainable with existing MC. To alleviate this bottleneck, we present D$e^+e^-$ffusion, a denoising diffusion probabilistic model that operates as a permutation-equivariant, set-valued surrogate for fast IPC simulation. Trained on a small GuineaPig++ sample, D$e^+e^-$ffusion faithfully reproduces the marginal and joint kinematic, angular, and positional distributions of all three IPC production processes. In addition, we assess the fidelity at the detector level by propagating both Geant4 and D$e^+e^-$ffusion events through a Geant4 simulation of the CLD vertex detector and by training a transformer-based two-sample classifier; the classifier achieves an area under the ROC curve of $0.553 \pm 0.016$. The trained model generates events nearly four orders of magnitude faster than Geant4, paving the way for a fast-simulation surrogate for FCC-ee design studies.

Chahine, Antonio [Imperial Coll., London]↗