Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Diffusion problems”

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 1,063 records · Page 59

MODELING THERMAL DUST EMISSION WITH TWO COMPONENTS: APPLICATION TO THE PLANCK HIGH FREQUENCY INSTRUMENT MAPS

We apply the Finkbeiner et al. two-component thermal dust emission model to the Planck High Frequency Instrument maps. This parameterization of the far-infrared dust spectrum as the sum of two modified blackbodies (MBBs) serves as an important alternative to the commonly adopted single-MBB dust emission model. Analyzing the joint Planck/DIRBE dust spectrum, we show that two-component models provide a better fit to the 100-3000 GHz emission than do single-MBB models, though by a lesser margin than found by Finkbeiner et al. based on FIRAS and DIRBE. We also derive full-sky 6.'1 resolution maps of dust optical depth and temperature by fitting the two-component model to Planck 217-857 GHz along with DIRBE/IRAS 100 μm data. Because our two-component model matches the dust spectrum near its peak, accounts for the spectrum's flattening at millimeter wavelengths, and specifies dust temperature at 6.'1 FWHM, our model provides reliable, high-resolution thermal dust emission foreground predictions from 100 to 3000 GHz. We find that, in diffuse sky regions, our two-component 100-217 GHz predictions are on average accurate to within 2.2%, while extrapolating the Planck Collaboration et al. single-MBB model systematically underpredicts emission by 18.8% at 100 GHz, 12.6% at 143 GHz, and 7.9% at 217 GHz. We calibrate our two-component optical depth to reddening, and compare with reddening estimates based on stellar spectra. We find the dominant systematic problems in our temperature/reddening maps to be zodiacal light on large angular scales and the cosmic infrared background anisotropy on small angular scales.

79 ASTRONOMY AND ASTROPHYSICS↗

Lattice Boltzmann method for diffusion-limited partial dissolution of fluids

A lattice Boltzmann model for two partially miscible fluids is developed. By partially miscible, we mean that although there is a definite interfacial region separating the two fluids with a surface tension force acting at all points of the transition region, each fluid can nonetheless accept molecules from the other fluid up to a set solubility limit. We allow each fluid to diffuse into the other with the solubility and diffusivity in each fluid being input parameters. The approach is to define two regions within the fluid. One interfacial region having finite width, across which most of the concentration change occurs, and in which a surface tension force and color separation step are allowed for. And one miscible fluid region where the concentration of the binary fluids follows an advection-diffusion equation and the mixture as a whole obeys the Navier-Stokes incompressible flow equations. Numerical examples are presented in which the algorithm produces results that are quantitatively compared to exact analytical results as well as qualitatively examined for their reasonableness. The model has the ability to simulate how bubbles of one fluid flow through another while dissolving their contents as well as to a range of practical invasion problems such as injecting supercritical CO 2 into a porous material saturated with water for sequestration purposes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Non-Galerkin Coarse Grids for Algebraic Multigrid

Algebraic multigrid (AMG) is a popular and effective solver for systems of linear equations that arise from discretized partial differential equations. And while AMG has been effectively implemented on large scale parallel machines, challenges remain, especially when moving to exascale. Particularly, stencil sizes (the number of nonzeros in a row) tend to increase further down in the coarse grid hierarchy, and this growth leads to more communication. Therefore, as problem size increases and the number of levels in the hierarchy grows, the overall efficiency of the parallel AMG method decreases, sometimes dramatically. This growth in stencil size is due to the standard Galerkin coarse grid operator, $P^T A P$, where $P$ is the prolongation (i.e., interpolation) operator. For example, the coarse grid stencil size for a simple three-dimensional (3D) seven-point finite differencing approximation to diffusion can increase into the thousands on present day machines, causing an associated increase in communication costs. We therefore consider algebraically truncating coarse grid stencils to obtain a non-Galerkin coarse grid. First, the sparsity pattern of the non-Galerkin coarse grid is determined by employing a heuristic minimal “safe” pattern together with strength-of-connection ideas. Second, the nonzero entries are determined by collapsing the stencils in the Galerkin operator using traditional AMG techniques. The result is a reduction in coarse grid stencil size, overall operator complexity, and parallel AMG solve phase times.

97 MATHEMATICS AND COMPUTING↗

Velocity-space Origins of the Pressure–Strain Interaction in Multipopulation Distributions and Its Application to Magnetic Reconnection

A forefront research question is how energy evolves in weakly collisional plasmas for which departures from local thermodynamic equilibrium (LTE) are significant. The standard approach is studying the terms in the non-LTE energy evolution equation derived by taking the second moment of the Boltzmann equation, but the resultant fluid metrics do not retain information about which particles at which velocities drive energy evolution. A widely studied channel for internal energy density evolution is the pressure–strain interaction. Here, we employ the kinetic pressure–strain, a phase-space diagnostic whose velocity-space integral recovers the pressure–strain interaction to disambiguate the contributions to the pressure–strain interaction from disparate particle populations in composite phase-space densities. We develop phase-space analogs of the pressure–strain interaction decompositions to provide the phase-space origins of normal versus sheared flow. We introduce the “kinetic strain-rate” tensor, the phase-space analog of the strain-rate tensor, which we argue is needed to interpret the phase-space origins of the pressure–strain interaction. To demonstrate the utility of these quantities, we investigate them for composite electron distributions near the electron diffusion region in two-dimensional particle-in-cell simulations of antiparallel symmetric magnetic reconnection. We find that the phase-space-based diagnostics isolate the roles of distinct populations. These results contribute to a growing body of work providing new methods for quantifying phase-space energy evolution for a broad array of processes, from magnetic reconnection to collisionless shocks and turbulence, opening new pathways for answering longstanding problems of particle energization in weakly collisional plasmas.

79 ASTRONOMY AND ASTROPHYSICS↗

Generative AI in Supply Chain Management: Applications, Challenges, and Future Directions

Supply chain management (SCM) is undergoing rapid transformation due to increasing global complexity, demand volatility, and operational disruptions. Generative Artificial Intelligence (GenAI) has emerged as a powerful paradigm capable of synthesizing data, simulating operational scenarios, and enabling adaptive decision-making across supply chain networks. This paper presents a survey of GenAI’s role in SCM, focusing on its applications in predictive analytics, autonomous logistics, and fraud detection. Unlike traditional AI systems that rely primarily on predictive analytics, GenAI models, including large language models, generative adversarial networks, and diffusion-based architectures, enable the creation of synthetic supply chain scenarios and autonomous optimization strategies. This survey provides (1) a taxonomy of GenAI techniques for supply chain applications, (2) a comparative analysis of generative AI approaches with traditional machine learning, reinforcement learning, and blockchain-based methods, and (3) a discussion of key challenges such as data privacy, interpretability, and integration with legacy enterprise systems. Furthermore, we outline open research problems and propose directions for future research toward autonomous, resilient, and sustainable AI-driven supply chains.

15 - GEOTHERMAL ENERGY↗

Evaluation of the toroidal torque driven by external non-resonant non-axisymmetric magnetic field perturbations in a tokamak

The toroidal torque driven by external non-resonant magnetic perturbations (neoclassical toroidal viscosity) is an important momentum source affecting the toroidal plasma rotation in tokamaks. The well-known force-flux relation directly links this torque to the non-ambipolar neoclassical particle fluxes arising due to the violation of the toroidal symmetry of the magnetic field. Here, a quasilinear approach for the numerical computation of these fluxes is described, which reduces the dimension of a standard neoclassical transport problem by one without model simplifications of the linearized drift kinetic equation. The only limiting condition is that the non-axisymmetric perturbation field is small enough such that the effect of the perturbation field on particle motion within the flux surface is negligible. Therefore, in addition to most of the transport regimes described by the banana (bounce averaged) kinetic equation also such regimes as, e.g., ripple-plateau and resonant diffusion regimes are naturally included in this approach. Based on this approach, a quasilinear version of the code NEO-2 [W. Kernbichler et al., Plasma Fusion Res. 3, S1061 (2008).] has been developed and benchmarked against a few analytical and numerical models. Results from NEO-2 stay in good agreement with results from these models in their pertinent range of validity.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Dynamics of metal-induced crystallization of ultrathin Ge films by rapid thermal annealing

Though Ge crystallization has been widely studied, few works investigate metal-induced crystallization of ultrathin Ge films. For 2 nm Ge films in oxide matrix, crystallization becomes challenging due to easy oxidation and low mobility of Ge atoms. Introducing metal atoms may alleviate these problems, but the functions and the behaviours of metal atoms need to be clarified. This paper investigates the crystallization dynamics of a multilayer structure 1.9 nm Ge/0.5 nm Al/1.5 nm Al{sub 2}O{sub 3} under rapid thermal annealing (RTA). The functions of metal atoms, like effective anti-oxidation, downshifting Raman peaks, and incapability to decrease crystallization temperature, are found and explained. The metal behaviours, such as inter-diffusion and defect generation, are supported with direct evidences, Al-Ge nanobicrystals, and Al cluster in Ge atoms. With these understandings, a two-step RTA process achieves high-quality 2 nm nanocrystal Ge films with Raman peak at 298 cm{sup −1} of FWHM 10.3 cm{sup −1} and atomic smooth interfaces.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Impact of parametric uncertainty on estimation of the energy deposition into an irradiated brain tumor

Predictions of the total energy deposited into a brain tumor through X-ray irradiation are notoriously error-prone. We investigate how this predictive uncertainty is affected by uncertainty in both the location of the region occupied by a dose-enhancing iodinated contrast agent and the agent's concentration. This is done within the probabilistic framework in which these uncertain parameters are modeled as random variables. We employ the stochastic collocation (SC) method to estimate statistical moments of the deposited energy in terms of statistical moments of the random inputs, and the global sensitivity analysis (GSA) to quantify the relative importance of uncertainty in these parameters on the overall predictive uncertainty. A nonlinear radiation–diffusion equation dramatically magnifies the coefficient of variation of the uncertain parameters, yielding a large coefficient of variation for the predicted energy deposition. This demonstrates that accurate prediction of the energy deposition requires a proper treatment of even small parametric uncertainty. Our analysis also reveals that SC outperforms standard Monte Carlo, but its relative efficiency decreases as the number of uncertain parameters increases from one to three. A robust GSA ameliorates this problem by reducing this number.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

How nanoscale protein interactions determine the mesoscale dynamic organisation of bacterial outer membrane proteins

The spatiotemporal organisation of membranes is often characterised by the formation of large protein clusters. In Escherichia coli, outer membrane protein (OMP) clustering leads to OMP islands, the formation of which underpins OMP turnover and drives organisation across the cell envelope. Modelling how OMP islands form in order to understand their origin and outer membrane behaviour has been confounded by the inherent difficulties of simulating large numbers of OMPs over meaningful timescales. Here, we overcome these problems by training a mesoscale model incorporating thousands of OMPs on coarse-grained molecular dynamics simulations. We achieve simulations over timescales that allow direct comparison to experimental data of OMP behaviour. Here, we show that specific interaction surfaces between OMPs are key to the formation of OMP clusters, that OMP clusters present a mesh of moving barriers that confine newly inserted proteins within islands, and that mesoscale simulations recapitulate the restricted diffusion characteristics of OMPs.

59 BASIC BIOLOGICAL SCIENCES↗

Collaborative Project: An Integrated Parameterization of Boundary Layer and Convective Mixing: The Eddy-Diffusivity/Mass-Flux (EDMF) Approach

The key goal of this project was to reduce cloud modeling deficiencies and biases by developing and implementing a new unified boundary layer and convection parameterization based on the multi-plume Eddy-Diffusivity/Mass-Flux (EDMF) approach. This is a turbulence and convection parameterization that can be considered fully unified, in the sense that it is able to represent convective processes from boundary layer convection to deep moist convection with one single parameterization. This project will ultimately lead to more accurate climate predictions, which have a significant societal impact. In general, turbulence and convection in the atmosphere are at the core of key climate prediction problems. For example: i) to reduce uncertainties in climate projections, it is essential to improve predictions of cloud feedbacks (how clouds respond to, and influence, climate change), which are controlled by the interactions between a turbulent flow with water phase transitions and radiation; (ii) to improve extreme weather prediction under climate change, it is essential to improve our understanding of how moist convection responds to a warmer world. A fully unified boundary layer and convection parameterization, such as EDMF, will help better represent and predict boundary layer, cloud and convection processes in the atmosphere during present and future climate. The following are the specific tasks that were completed and addressed the project’s objectives: i) Implementation and evaluation of the multi-plume EDMF parameterization into the Single Column Model (SCM) version of CESM; ii) Development of a fully unified multi-plume (shallow to deep convection) EDMF parameterization – that is also scale-aware; iii) Implementation and evaluation of the moist multi-plume EDMF scheme in the global version of WRF; iv) Extension and evaluation of the LES model to deep moist convection regimes; v) Implementation of EDMF in the SCM version of the LBL dynamical core.

54 ENVIRONMENTAL SCIENCES↗

Impurity transport in fractal media in the presence of a degrading diffusion barrier

We have analyzed the transport regimes and the asymptotic forms of the impurity concentration in a randomly inhomogeneous fractal medium in the case when an impurity source is surrounded by a weakly permeable degrading barrier. The systematization of transport regimes depends on the relation between the time t{sub 0} of emergence of impurity from the barrier and time t{sub *} corresponding to the beginning of degradation. For t{sub 0} < t{sub *}, degradation processes are immaterial. In the opposite situation, when t{sub 0} > t{sub *}, the results on time intervals t < t{sub *} can be formally reduced to the problem with a stationary barrier. The characteristics of regimes with t{sub *} < t < t{sub 0} depend on the scenario of barrier degradation. For an exponentially fast scenario, the interval t{sub *} < t < t{sub 0} is very narrow, and the transport regime occurring over time intervals t < t{sub *} passes almost jumpwise to the regime of the problem without a barrier. In the slow power-law scenario, the transport over long time interval t{sub *} < t < t{sub 0} occurs in a new regime, which is faster as compared to the problem with a stationary barrier, but slower than in the problem without a barrier. The asymptotic form of the concentration at large distances from the source over time intervals t < t{sub 0} has two steps, while for t > t{sub 0}, it has only one step. The more remote step for t < t{sub 0} and the single step for t > t{sub 0} coincide with the asymptotic form in the problem without a barrier.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Slip velocity boundary conditions for the lattice Boltzmann modeling of microchannel flows

Abstract Slip flows in ducts are important in numerous engineering applications, most notably in microchannel flows. Compared to the standard no‐slip Dirichlet condition, the case of slip formulates as a Robin‐type condition for the fluid tangential velocity. Such an increase in mathematical complexity is accompanied by a more challenging numerical transcription. The present work concerns with this topic, addressing the modeling of the slip velocity boundary condition in the lattice Boltzmann method (LBM) applied to steady slow viscous flows inside ducts of nontrivial shapes. As novelty, we extend the newly revised local second‐order boundary (LSOB) Dirichlet fluid flow method [ Philos. Trans. R. Soc. A 378, 20190404 (2020)] to implement the slip velocity condition within the two‐relaxation‐time (TRT) framework. The LSOB follows an in‐node philosophy where its operation principle seeks to explicitly reconstruct the unknown boundary populations in the form of a third‐order accurate Chapman–Enskog expansion, where the wall slip condition is built‐in as a normal Taylor‐type condition. The key point of this approach is that the required first‐ and second‐order momentum derivatives, rather than computed through nonlocal finite difference approximations, are locally determined through a simple local linear algebra procedure, whose formulation is particularly aided by the TRT symmetry argument. To express the obtained derivatives, two approaches are considered, called and , which operate with node and wall variables, respectively. These two formulations are developed to prescribe the physical slip condition over plane and curved walls, including the corners. Their consistency and accuracy characteristics are examined against alternative linkwise strategies to impose the wall slip velocity, such as the kinetic‐based diffusive bounce‐back scheme, the central linear interpolation slip scheme, and the multireflection slip scheme. The several slip schemes are tested over different 3D microchannel configurations, with walls not conforming with the LBM uniform mesh. Numerical tests confirm the advanced accuracy characteristics of the proposed LSOB slip boundary scheme, revealing the added challenge of the wall slip modeling, and that parabolic accuracy is a necessary requirement to reach second‐order accuracy within this problem class.

Silva, Goncalo↗

Correlation Function Approach for Diffusion in Confined Geometries

This paper describes a formalism for extracting spatially varying transport coefficients from simulations of a molecular fluid in a nano channel. This approach is applied to self-diffusion of a Lennard-Jones fluid confined between two parallel surfaces. A numerical grid is laid over the domain confining the fluid, and fluid properties are projected onto the grid cells. The time correlation functions between properties in different grid cells are calculated and can be used as the basis for a fitting procedure for extracting spatially varying diffusion coefficients from the simulation. Results for the Lennard-Jones system show that transport behavior varies sharply near the liquid-solid boundary and that the changes depend on the details of the liquid-solid interaction. A quantitative difference between the reduced and detailed models is discussed. It is found that the difference could be associated with assumptions about the form of the transport equations at molecular scales in lieu of problems with the method itself. The study suggests that this approach to fitting molecular simulations to continuum equations may guide the development of appropriate coarse-grained equations to model transport phenomena at nanometer scales.

Nanoscale flow, Transport, molecular simulation↗

Improving unfolding and systematic uncertainty estimation using generative diffusion networks (Final Technical Report)

This final technical report summarizes the key accomplishments on the unfolding using diffusion model project, a DOE award received by PI Pierre-Hugues Beauchemin at Tufts University. This project main goal was to investigate the potential of diffusion models for unfolding experimental High Energy Physics data from detector effects while controlling systematics uncertainties. The project accomplished its goals by completing the following objectives: 1) Performing an object-by-object, event-by-event unfolding of various kinematic distributions reconstructed from detector data in HEP in a way that keeps correlations between unfolded observables while demonstrating competitive performance compared to standard algorithms used in the field; 2) Address the generalization problem by developing an unfolding algorithm capable to correctly infer the underlying distributions of observables and processes never seen before, while controlling the dominant theoretical uncertainties affecting the process, therefore increasing the effectiveness, the precision, and the applicability of the developed algorithm; 3) Understand the theoretical foundations between the developed algorithm so to extend it to applications beyond experimental HEP, for broader benefits to the society. This report provides an overview of the accomplishments related to each of these key objectives.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Radiation Hydrodynamic Simulations of Dust-driven Winds

We study dusty winds driven by radiation pressure in the atmosphere of a rapidly star-forming environment. We apply the variable Eddington tensor algorithm to re-examine the two-dimensional radiation hydrodynamic problem of a column of gas that is accelerated by a constant infrared radiation flux. In the absence of gravity, the system is primarily characterized by the initial optical depth of the gas. We perform several runs with different initial optical depths and resolutions. We find that the gas spreads out along the vertical direction, as its mean velocity and velocity dispersion increase. In contrast to previous work using the flux-limited diffusion algorithm, we find little evolution in the trapping factor. The momentum coupling between radiation and gas in the absence of gravity is similar to that with gravity. For Eddington ratio increasing with the height in the system, the momentum transfer from the radiation to the gas is not merely ∼L/c, but amplified by a factor of 1+ητ{sub IR}, where τ{sub IR} is the integrated infrared optical depth through the system, and η∼0.5--0.9, decreasing with the optical depth. We apply our results to the atmosphere of galaxies and conclude that radiation pressure may be an important mechanism for driving winds in the most rapidly star-forming galaxies and starbursts.

79 ASTRONOMY AND ASTROPHYSICS↗

Simulations of ion acceleration at non-relativistic shocks. II. Magnetic field amplification

We use large hybrid simulations to study ion acceleration and generation of magnetic turbulence due to the streaming of particles that are self-consistently accelerated at non-relativistic shocks. When acceleration is efficient, we find that the upstream magnetic field is significantly amplified. The total amplification factor is larger than 10 for shocks with Alfvénic Mach number M = 100, and scales with the square root of M. The spectral energy density of excited magnetic turbulence is determined by the energy distribution of accelerated particles, and for moderately strong shocks (M ≲ 30) agrees well with the prediction of resonant streaming instability, in the framework of quasilinear theory of diffusive shock acceleration. For M ≳ 30, instead, Bell's non-resonant hybrid (NRH) instability is predicted and found to grow faster than resonant instability. NRH modes are excited far upstream by escaping particles, and initially grow without disrupting the current, their typical wavelengths being much shorter than the current ions' gyroradii. Then, in the nonlinear stage, most unstable modes migrate to larger and larger wavelengths, eventually becoming resonant in wavelength with the driving ions, which start diffuse. Ahead of strong shocks we distinguish two regions, separated by the free-escape boundary: the far upstream, where field amplification is provided by the current of escaping ions via NRH instability, and the shock precursor, where energetic particles are effectively magnetized, and field amplification is provided by the current in diffusing ions. The presented scalings of magnetic field amplification enable the inclusion of self-consistent microphysics into phenomenological models of ion acceleration at non-relativistic shocks.

79 ASTRONOMY AND ASTROPHYSICS↗

Water Saturation Relations and Their Diffusion-Limited Equilibration in Gas Shale: Implications for Gas Flow in Unconventional Reservoirs

Large volumes of water are used for hydraulic fracturing of low permeability shale reservoirs to stimulate gas production, with most of the water remaining unrecovered and distributed in a poorly understood manner within stimulated regions. Because water partitioning into shale pores controls gas release, we measured the water saturation dependence on relative humidity (rh) and capillary pressure (P c ) for imbibition (adsorption) as well as drainage (desorption) on samples of Woodford Shale. Experiments and modeling of water vapor adsorption into shale laminae at rh = 0.31 demonstrated that long times are needed to characterize equilibrium in larger (5 mm thick) pieces of shales, and yielded effective diffusion coefficients from 9 × 10 -9 to 3 × 10 -8 m 2 s -1 , similar in magnitude to the literature values for typical low porosity and low permeability rocks. Most of the experiments, conducted at 50°C on crushed shale grains in order to facilitate rapid equilibration, showed significant saturation hysteresis, and that very large P c (~1 MPa) are required to drain the shales. These results quantify the severity of the water blocking problem, and suggest that gas production from unconventional reservoirs is largely associated with stimulated regions that have had little or no exposure to injected water. Finally, gravity drainage of water from fractures residing above horizontal wells reconciles gas production in the presence of largely unrecovered injected water, and is discussed in the broader context of unsaturated flow in fractures.

58 GEOSCIENCES↗

FSISPH: An SPH formulation for impacts between dissimilar materials

Here, we present an SPH formulation with several new features designed to better model the fully-compressible interaction of dissimilar materials. We developed the new method to simulate the atmospheric entry and break-up of small celestial bodies in planetary atmospheres. The formulation uses a unity-based, density-energy discretization of the hydrodynamic conservation laws with linear-corrected kernel gradients. To account for variations in compressibility, we use an HLLC approximate Riemann solver to adjust the velocity gradient at material interfaces. To handle large transverse velocity discontinuities, we introduce a simple slip interface model that limits the artificial viscosity at material interfaces. Diffusion is optionally applied through the velocity gradient and this allows the density and specific thermal energy to evolve in a manner more consistent with the first law of thermodynamics in comparison to other more direct diffusion schemes. We also introduce a material-local second-order artificial conduction scheme used to smooth the specific thermal energy field. Material damage fits neatly under this framework by treating the damage front as a material interface. The method has been implemented as a solver, FSISPH, within the code, Spheral++, and is publicly available on github. We test our new solver on a number of classic shock, mixing, and multi-material problem. The components we outline can significantly improve accuracy of SPH for problems with sharp contact discontinuities.

79 ASTRONOMY AND ASTROPHYSICS↗