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 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Experimental test of a predicted dynamics–structure–thermodynamics connection in molecularly complex glass-forming liquids

Significance The physical origin of cooperative activated relaxation in glass-forming liquids, which underlies the huge growth of viscosity and suppression of diffusion with cooling, remains elusive. Understanding this problem is of fundamental scientific interest and can assist in the design of new materials. We combine experimental relaxation time and equation-of-state data of molecular liquids to provide strong evidence for the recent theoretical prediction that activated relaxation, though causally driven by dynamically coupled cage-scale hopping and nonlocal collective elasticity quantified by local structural correlations, is well captured based on a thermodynamic description with dimensionless compressibility as the key variable. A mechanistic deduction is the crossover from fragile to strong (e.g., inorganic networks) relaxation behavior arises from the irrelevance of long-range elasticity effects.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Hopping and crawling DNA-coated colloids

Understanding the motion of particles with multivalent ligand-receptors is important for biomedical applications and material design. Yet, even among a single design, the prototypical DNA-coated colloids, seemingly similar micrometric particles hop or roll, depending on the study. We shed light on this problem by observing DNA-coated colloids diffusing near surfaces coated with complementary strands for a wide array of coating designs. We find colloids rapidly switch between 2 modes: They hop—with long and fast steps—and crawl—with short and slow steps. Both modes occur at all temperatures around the melting point and over various designs. The particles become increasingly subdiffusive as temperature decreases, in line with subsequent velocity steps becoming increasingly anticorrelated, corresponding to switchbacks in the trajectories. Overall, crawling (or hopping) phases are more predominant at low (or high) temperatures; crawling is also more efficient at low temperatures than hopping to cover large distances. We rationalize this behavior within a simple model: At lower temperatures, the number of bound strands increases, and detachment of all bonds is unlikely, hence, hopping is prevented and crawling favored. We thus reveal the mechanism behind a common design rule relying on increased strand density for long-range self-assembly: Dense strands on surfaces are required to enable crawling, possibly facilitating particle rearrangements.

Science & Technology - Other Topics↗
DOE OSTI2014

A general hybrid radiation transport scheme for star formation simulations on an adaptive grid

Radiation feedback plays a crucial role in the process of star formation. In order to simulate the thermodynamic evolution of disks, filaments, and the molecular gas surrounding clusters of young stars, we require an efficient and accurate method for solving the radiation transfer problem. We describe the implementation of a hybrid radiation transport scheme in the adaptive grid-based FLASH general magnetohydrodyanmics code. The hybrid scheme splits the radiative transport problem into a raytracing step and a diffusion step. The raytracer captures the first absorption event, as stars irradiate their environments, while the evolution of the diffuse component of the radiation field is handled by a flux-limited diffusion solver. We demonstrate the accuracy of our method through a variety of benchmark tests including the irradiation of a static disk, subcritical and supercritical radiative shocks, and thermal energy equilibration. We also demonstrate the capability of our method for casting shadows and calculating gas and dust temperatures in the presence of multiple stellar sources. Our method enables radiation-hydrodynamic studies of young stellar objects, protostellar disks, and clustered star formation in magnetized, filamentary environments.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Long-Term Stability of PVD/Sputtered Au Electrical Contacts to Thermoelectric Bi 2 Te 2 : Re-evaluation of SAND2015-7203

The fabrication of long-lived electrical contacts to thermoelectric Bi 2 Te 3 -based modules is a challenging problem due to chemical incompatibilities and rapid diffusion rates. Previously, technical guidance from SAND report 2015-7203 selected electroplated Au as the preferred method for fabrication of long-lived contacts because of concerns that the grain structure of sputtered/physical vapor deposited (PVD) Au contacts can evolve during aging. We have re- evaluated PVD Au contacts and show that they are appropriate for long-life service. We measure grain size and morphology at different aging times under accelerated temperature gradient conditions, and we show that the PVD Au contacts are stable and remain relatively unchanged. The PVD Au fabricated here is not subject to the deterioration observed in the previous report.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Long-Term Stability of PVD/Sputtered Au Electrical Contacts to Thermoelectric Bi 2 Te 2 (Re-evaluation of SAND2015-7203)

The fabrication of long-lived electrical contacts to thermoelectric Bi 2 Te 3 -based modules is a challenging problem due to chemical incompatibilities and rapid diffusion rates. Previously, technical guidance from SAND report 2015-7203 selected electroplated Au as the preferred method for fabrication of long-lived contacts because of concerns that the grain structure of sputtered/physical vapor deposited (PVD) Au contacts can evolve during aging. We have re-evaluated PVD Au contacts and show that they are appropriate for long-life service. We measure grain size and morphology at different aging times under accelerated temperature gradient conditions, and we show that the PVD Au contacts are stable and remain relatively unchanged. The PVD Au fabricated here is not subject to the deterioration observed in the previous report.

36 MATERIALS SCIENCE↗
DOE OSTI2024

GAMPix: a novel fine-grained, low-noise and ultra-low power pixelated charge readout for TPCs

Here, we report on the development of a novel pixel charge readout system, Grid Activated Multi-scale pixel readout (GAMPix), which is under development for use in the GammaTPC gamma ray instrument concept. GammaTPC is being developed to optimize the use of liquid argon time projection chamber technology for gamma ray astrophysics, for which a fine grained low power charge readout is essential. GAMPix uses a new architecture with coarse and fine scale instrumented electrodes to solve the twin problems of loss of measured charge after diffusion, and high readout power. Fundamentally, it enables low noise and ultra low power charge readout at the spatial scale limited by diffusion in a time projection chamber, and has other possibly applications, including future DUNE modules.

Shutt, Tom↗
DOE OSTI2021

IMEX Runge-Kutta Parareal for Non-diffusive Equations

Parareal is a widely studied parallel-in-time method that can achieve meaningful speedup on certain problems. However, it is well known that the method typically performs poorly on non-diffusive equations. This paper analyzes linear stability and convergence for IMEX Runge-Kutta Parareal methods on non-diffusive equations. By combining standard linear stability analysis with a simple convergence analysis, we find that certain Parareal configurations can achieve parallel speedup on non-diffusive equations. These stable configurations all posses low iteration counts, large block sizes, and a large number of processors. Numerical examples using the nonlinear Schrodinger equation demonstrate the analytical conclusions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

On the value of the reconnection rate

Numerical simulations have consistently shown that the reconnection rate in certain collisionless regimes can be fast, of the order of $0.1v_{A}B_{u}$ , where $v_{A}$ and $B_{u}$ are the Alfven speed and the reconnecting magnetic field upstream of the ion diffusion region. This particular value has been reported in myriad numerical simulations under disparate conditions. But, despite decades of research, the reasons underpinning this specific value remain mysterious. We present an overview of this problem and discuss the conditions under which the '0.1 value' is attained. Finally, we explain why this problem should be interpreted in terms of the ion diffusion region length.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Screening Diffusion of Small Molecules in Flexible Zeolitic Imidazolate Frameworks Using a DFT-Parameterized Force Field

Quantitatively modeling adsorbate diffusion through zeolitic imidazolate frameworks (ZIFs) must account for the inherent flexibility of these materials. Here, the lack of a transferable intramolecular ZIF force field (FF) for use in classical simulations has previously made an accurate simulation of adsorbate diffusion in many ZIFs impossible. We resolve this problem by introducing a density functional theory parameterized force field (FF) for ZIFs named the intraZIF-FF, which includes perturbations to the class I force fields previously used to model ZIFs. This FF outperforms ad hoc force fields at predicting ab initio relative energies and atomic forces taken from fully periodic ab initio molecular dynamics simulations of SALEM-2, ZIF-7, ZIF-8, and ZIF-90. We use the intraZIF-FF to predict the infinite dilution self-diffusion coefficients of 30 adsorbates with molecular diameters ranging from 2.66 to 7.0 Å in these 4 ZIFs. These results greatly increase the number of adsorbates for which accurate information about molecular diffusion in ZIFs is available.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Absence of a charge diffusion pole at finite energies in an exactly solvable interacting flat-band model in $d$ dimensions

Motivated by recent bounds for charge diffusion in critical matter, we investigate the following question: What sets the scale for the velocity for diffusing degrees of freedom in a scale-invariant system? To make our statements precise, here we analyze the diffusion pole in an exactly solvable model for a Mott transition in the presence of a long-range interaction term. To achieve scale invariance, we limit our discussion to the flat-band regime. We find in this limit that the diffusion pole, which would normally obtain at finite energy, is pushed to zero energy, resulting in a vanishing of the diffusion constant. This occurs even in the presence of interactions in certain limits, indicating the robustness of this result to the inclusion of a scale in the problem. Consequently, scale invariance precludes any reasonable definition of the diffusion constant. Nonetheless, we do find that a scale can be defined, albeit irrelevant to diffusion, which is the product of the squared band velocity and the density of states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

A family of independent Variable Eddington Factor methods with efficient preconditioned iterative solvers

We present a family of discretizations for the Variable Eddington Factor (VEF) equations that have high-order accuracy on curved meshes and efficient preconditioned iterative solvers. The VEF discretizations are combined with the Discontinuous Galerkin transport discretization from to form effective high-order, linear transport methods. The VEF discretizations are derived by extending the unified analysis of Discontinuous Galerkin methods for elliptic problems presented by Arnold et al. to the VEF equations. This framework is used to define analogs of the interior penalty, second method of Bassi and Rebay, minimal dissipation local Discontinuous Galerkin, and continuous finite element methods. The analysis of subspace correction preconditioners, which use a continuous operator to iteratively precondition the discontinuous discretization, is extended to the case of the non-symmetric VEF system. Numerical results demonstrate that the VEF discretizations have arbitrary-order accuracy on curved meshes, preserve the thick diffusion limit, and are effective on a proxy problem from thermal radiative transfer in both outer transport iterations and inner preconditioned linear solver iterations. We demonstrate that the VEF solution converges to the S N transport solution as the mesh is refined on both problems with smooth and non-smooth behavior in angle. Parallel performance studies show that the interior penalty VEF discretization's linear solve weak scales out to 1024 processors and strong scales well on a single node. Particular attention is paid to the parallel performance of the VEF algorithm when used in combination with a parallel block Jacobi transport sweep.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

On the benefit of using both hand calculation methods and computer experiments algorithms to solve complex nuclear criticality safety problems - 14299

A companion paper shows the 'anomalies', and even the safety issues, that may be raised by the very usual problem of making safe a fissile mass inside a controlled geometry. These anomalies mainly come from the solving of such problems which belong to the mathematical family of 'robust inversion' including two inversion parameters (the fissile mass and the geometry) and one nuisance parameter (the moderation ratio of the fissile material). Since a 'brute force' method of resolution requires a lot of calculations and since a 'smart' method of resolution requires a lot of engineer time, it is tempting to solve these problems by a 'custom made' approach rather than to achieve a 'whole' resolution. The present paper shows how one can use a hand calculation method (derivation of the one-speed diffusion theory) to perform the whole resolution of such kind of problems with a minimum calculations and human efforts. The powerful capability of predicting the 'anomalies' highlighted in the companion paper is shown. Then the limitations of such a method are discussed: limitation in the geometry of the problem and bias in absolute values prediction. Finally, new algorithms of computer experiments design, dedicated to solve robust inversion problems and based on Kriging surrogates, are tested to solve these problems with limiting calculations and human efforts. The performance of these new algorithms may supplement the one-speed diffusion theory limitations. (authors)

42 ENGINEERING↗
DOE OSTI2020

The impact of nanoparticle softness on its tracer diffusion coefficient in all polymer nanocomposites

The diffusion of nanoparticles in a polymer matrix is an area of current interest. However, a complete understanding is still limited as it is often difficult to quantify the much slower motion of nanoparticles in a polymer matrix. To combat this problem, we have developed a protocol to measure the diffusion coefficient of soft nanoparticles in a linear polymer matrix. Recently developed synthetic control over soft nanoparticle structures combined with this protocol provides a pathway to separately elucidate the effects of the molecular weight and nanoparticle softness on its diffusive behavior. These results indicate that the nanoparticle softness and deformability dictate its motion. Increasing the cross-linking density of the nanoparticle for all molecular weights increases its hardness and suppresses its motion in the linear matrix. Additionally, the nanoparticle molecular weight dependence deviates from the exponential dependence for star polymers suggesting that these nanoparticles benefit from the cooperative motion of the matrix to open pathways for the nanoparticle. Finally, comparison of these experimentally determined values to the Stokes–Einstein theory demonstrates that the nanoparticles diffuse much slower than a hard sphere. This is interpreted to indicate that there exist additional interactions between the nanoparticle and polymer matrix that are not captured by Stokes–Einstein, including threading or entanglement of the linear chain with the nanoparticle.

Rostom, Sahar↗
DOE OSTI2018

Theoretical Analysis of the Entrainment–Mixing Process at Cloud Boundaries. Part I: Droplet Size Distributions and Humidity within the Interface Zone

Abstract The problem of a complex entrainment–mixing process is analyzed by solving a diffusion–evaporation equation for an open region in the vicinity of the cloud–dry air interface. Upon normalization the problem is reduced to a one-parametric one, the governing parameter being the potential evaporation parameter R proportional to the ratio of saturation deficit in the dry air to the available liquid water content in the cloud air. As distinct from previous multiple studies analyzing mixing within closed adiabatic volumes, we consider a principally nonstationary problem that never leads to a homogeneous equilibrium state. It is shown that at R < −1 the cloud edge shifts toward the cloud; that is, the cloud dissipates due to mixing with dry air, and the cloud volume decreases. If R > −1, the cloud edge shifts outside; that is, the mixing leads to an increase in the cloud volume. The time evolution of droplet size distribution and its moments, as well as the relative humidity within the expanding cloud–dry air interface, are calculated and analyzed. It is shown that the values of the mean volume radii rapidly decrease within the interface zone in the direction away from the cloud, indicating significant changes in the cloud edge microstructure. Scattering diagrams plotted for the cloud edge agree well with high-frequency in situ measurements, corroborating the reliability of the proposed approach. It is shown that the humidity front moves toward dry air faster than the front of liquid water content. As a result, the mixing leads to formation of a humid air shell around the cloud. The widths of the interface zone and humid shell are evaluated.

Pinsky, Mark↗
DOE OSTI2015

Submodels of model of nonlinear diffusion in the inhomogeneous medium involving absorption

We study the five-parameter model, describing the process of nonlinear diffusion in an inhomogeneous medium in the presence of absorption, for which the differential equation of the model admits a continuous Lie group of transformations, acting on the set of its solutions. We found six submodels of the original model of nonlinear diffusion, with different symmetry properties. Of these six submodels, the five submodels with transient absorption, for which the absorption coefficient depends on time according to a power law, represent the greatest interest with a mathematical point of view and with the point of view of physical applications. For each of these nonlinear submodels, we obtained formulas for producing new solutions that contain arbitrary constants, and we found all invariant submodels. All essentially distinct invariant solutions describing these invariant submodels are found in an explicit form or are reduced to finding the solution of nonlinear integral equations. The presence of the arbitrary constants in the integral equations that determine these solutions provide new opportunities for analytical and numerical study of boundary value problems for the received submodels and, thus, for the original model of nonlinear diffusion. For the received invariant submodels, we studied diffusion processes for which at the initial moment of the time at a fixed point is specified as a concentration and its gradient or as a concentration and its velocity. Solving of boundary value problems describing these processes is reduced to the solving of nonlinear integral equations. We established the existence and uniqueness of solutions of these boundary value problems under some additional conditions. The obtained results can be used to study the diffusion of substances, diffusion of conduction electrons and other particles, diffusion of physical fields and propagation of heat in inhomogeneous medium, and also to study a turbulence (Leith model, differential approximation to wave turbulence)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Manifold Learning-Based Polynomial Chaos Expansions for High-Dimensional Surrogate Models

In this work we introduce a manifold learning-based method for uncertainty quantification (UQ) in systems describing complex spatiotemporal processes. Our first objective is to identify the embedding of a set of high-dimensional data representing quantities of interest of the computational or analytical model. For this purpose, we employ Grassmannian diffusion maps, a two-step nonlinear dimension reduction technique which allows us to reduce the dimensionality of the data and identify meaningful geometric descriptions in a parsimonious and inexpensive manner. Polynomial chaos expansion is then used to construct a mapping between the stochastic input parameters and the diffusion coordinates of the reduced space. An adaptive clustering technique is proposed to identify an optimal number of clusters of points in the latent space. The similarity of points allows us to construct a number of geometric harmonic emulators which are finally utilized as a set of inexpensive pretrained models to perform an inverse map of realizations of latent features to the ambient space and thus perform accurate out-of-sample predictions. Thus, the proposed method acts as an encoder-decoder system which is able to automatically handle very high-dimensional data while simultaneously operating successfully in the small-data regime. The method is demonstrated on two benchmark problems and on a system of advection-diffusion-reaction equations which model a first-order chemical reaction between two species. In all test cases, the proposed method is able to achieve highly accurate approximations which ultimately lead to the significant acceleration of UQ tasks.

42 ENGINEERING↗
DOE OSTI2021

Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker--Planck Equation and Physics-Informed Neural Networks

The Fokker--Planck (FP) equation governing the evolution of the probability density function (PDF) is applicable to many disciplines, but it requires specification of the coefficients for each case, which can be functions of space-time and not just constants and hence require the development of a data-driven modeling approach. When the data available is directly on the PDF, there exist methods for inverse problems that can be employed to infer the coefficients and thus determine the FP equation and subsequently obtain its solution. Herein, we address a more realistic scenario, where only sparse data are given on the particles' positions at a few time instants, which are not sufficient to accurately construct directly the PDF even at those times from existing methods, e.g., kernel estimation algorithms. To this end, we develop a general framework based on physics-informed neural networks (PINNs) that introduces a new loss function using the Kullback--Leibler divergence to connect the stochastic samples with the FP equation to simultaneously learn the equation and infer the multidimensional PDF at all times. In particular, we consider two types of inverse problems, type I, where the FP equation is known but the initial PDF is unknown, and type II, in which, in addition to the unknown initial PDF, the drift and diffusion terms are also unknown. In both cases, we investigate problems with either Brownian or Lévy noise or a combination of both. Here, we demonstrate the new PINN framework in detail in the one-dimensional (1D) case, but we also provide results for up to five dimensions demonstrating that we can infer both the FP equation and dynamics simultaneously at all times with high accuracy using only very few discrete observations of the particles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

THE DECAY OF A WEAK LARGE-SCALE MAGNETIC FIELD IN TWO-DIMENSIONAL TURBULENCE

We investigate the decay of a large-scale magnetic field in the context of incompressible, two-dimensional magnetohydrodynamic turbulence. It is well established that a very weak mean field, of strength significantly below equipartition value, induces a small-scale field strong enough to inhibit the process of turbulent magnetic diffusion. In light of ever-increasing computer power, we revisit this problem to investigate fluids and magnetic Reynolds numbers that were previously inaccessible. Furthermore, by exploiting the relation between the turbulent diffusion of the magnetic potential and that of the magnetic field, we are able to calculate the turbulent magnetic diffusivity extremely accurately through the imposition of a uniform mean magnetic field. We confirm the strong dependence of the turbulent diffusivity on the product of the magnetic Reynolds number and the energy of the large-scale magnetic field. We compare our findings with various theoretical descriptions of this process.

79 ASTRONOMY AND ASTROPHYSICS↗