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At least 217 records · Page 12

A new approach to enforcing discrete maximum principles in continuous Galerkin methods for convection-dominated transport equations

This work introduces a set of design principles and new algorithmic tools for enforcing maximum principles and/or positivity preservation in continuous finite element approximations to convection-dominated transport problems. Enabling a linear first-order advection equation as a model problem, we address the design of first-order artificial diffusion operators and their higherorder counterparts at the element matrix level. The proposed methodology leads to a nonlinear high-resolution scheme capable of resolving moving fronts and internal/boundary layers as sharp localized nonoscillatory features. The amount of numerical dissipation depends on the difference between the solution value at a given node and a local maximum or minimum. The shockcapturing numerical diffusion coefficient is designed to vanish as the nodal values approach a mass-weighted or linearity-preserving average. The universal applicability and simplicity of the element-based limiting procedure makes it an attractive alternative to edge-based algebraic flux correction.

Kuzmin, D.↗

SUBSURFACE CHARACTERIZATION OF 67P/CHURYUMOV–GERASIMENKO’S ABYDOS SITE

On 2014 November 12, the ESA/ Rosetta descent module Philae landed on the Abydos site of comet 67P/Churyumov–Gerasimenko. Aboard this module, the Ptolemy mass spectrometer measured a CO/CO{sub 2} ratio of 0.07 ± 0.04, which differs substantially from the value obtained in the coma by the Rosetta /ROSINA instrument, suggesting a heterogeneity in the comet nucleus. To understand this difference, we investigated the physicochemical properties of the Abydos subsurface, leading to CO/CO{sub 2} ratios close to that observed by Ptolemy at the surface of this region. We used a comet nucleus model that takes into account different water ice phase changes (amorphous ice, crystalline ice, and clathrates) as well as diffusion of molecules throughout the pores of the matrix. The input parameters of the model were optimized for the Abydos site, and the ROSINA CO/CO{sub 2} measured ratio is assumed to correspond to the bulk value in the nucleus. We find that all considered structures of water ice are able to reproduce the Ptolemy observation with a time difference not exceeding ∼50 days, i.e., lower than ∼2% on 67P/Churyumov–Gerasimenko’s orbital period. The suspected heterogeneity of 67P/Churyumov–Gerasimenko’s nucleus is also found possible only if it is constituted of crystalline ices. If the icy phase is made of amorphous ice or clathrates, the difference between Ptolemy and ROSINA’s measurements would rather originate from the spatial variations in illumination on the nucleus surface. An eventual new measurement of the CO/CO{sub 2} ratio at Abydos by Ptolemy could be decisive to distinguish between the three water ice structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Apparent permeability prediction of organic shale with generalized lattice Boltzmann model considering surface diffusion effect

Gas flow in shale is associated with both organic matter (OM) and inorganic matter (IOM) which contain nano-pores ranging in size from a few to hundreds of nano-meters. In addition to the non-continuum effect which leads to an apparent permeability of gas higher than the intrinsic permeability, the surface diffusion of adsorbed gas in organic pores also can influence the apparent permeability through its own transport mechanism. In this study, a generalized lattice Boltzmann model (GLBM) is employed for gas flow through the reconstructed shale matrix consisting of OM and IOM. The Expectation–Maximization (EM) algorithm is used to assign the pore size distribution to each component, and the dusty gas model (DGM) and generalized Maxwell–Stefan model (GMS) are adopted to calculate the apparent permeability accounting for multiple transport mechanisms including viscous flow, Knudsen diffusion and surface diffusion. Effects of pore radius and pressure on permeability of both IOM and OM as well as effects of Langmuir parameters on OM are investigated. The effect of total organic content and distribution on the apparent permeability of the reconstructed shale matrix at different surface diffusivity is also studied. It is found that the influence of pore size and pressure on the apparent permeability of organic matter is affected by the surface diffusion of adsorbed gas. Furthermore, surface diffusion plays a significant role in determining apparent permeability and the velocity distribution of shale matrix.

02 PETROLEUM↗

An accurate and asymptotically compatible collocation scheme for nonlocal diffusion problems

Here, in this paper, we develop and analyze a collocation scheme for solving the linear nonlocal diffusion problem with general kernels. To approximate the nonlocal diffusion operator, we take a classic trapezoidal rule based on the linear interpolation as the starting point, and then carefully derive a new improved quadrature rule, which is not only more accurate but also could avoid the evaluations of singular integrals. We then use this rule to construct a collocation scheme for solving the nonlocal diffusion equations, that produces a symmetric positive definite stiffness matrix with Toeplitz structure. The proposed scheme is rigorously shown to be of second order accurate with respect to the mesh size for the nonlocal problem with fixed horizon, and in particular, it can achieve higher order accuracy for the commonly used kernels in the literature. Furthermore, we also prove that the scheme is asymptotically compatible, i.e., the approximate solution of the nonlocal diffusion problem converges to the exact solution of the corresponding local PDE problem when the horizon and the mesh size both go to zero. Finally, numerical experiments are presented to verify the theoretical results.

97 MATHEMATICS AND COMPUTING↗

Ag doped silicon nitride nanocomposites for embedded plasmonics

The localized surface plasmon-polariton resonance (LSPR) of noble metal nanoparticles (NPs) is widely exploited for enhanced optical spectroscopies of molecules, nonlinear optics, photothermal therapy, photovoltaics, or more recently in plasmoelectronics and photocatalysis. The LSPR frequency depends not only of the noble metal NP material, shape, and size but also of its environment, i.e., of the embedding matrix. In this paper, Ag-NPs have been fabricated by low energy ion beam synthesis in silicon nitride (SiN{sub x}) matrices. By coupling the high refractive index of SiN{sub x} to the relevant choice of dielectric thickness in a SiN{sub x}/Si bilayer for an optimum antireflective effect, a very sharp plasmonic optical interference is obtained in mid-range of the visible spectrum (2.6 eV). The diffusion barrier property of the host SiN{sub x} matrix allows for the introduction of a high amount of Ag and the formation of a high density of Ag-NPs that nucleate during the implantation process. Under specific implantation conditions, in-plane self-organization effects are obtained in this matrix that could be the result of a metastable coarsening regime.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Calcium carbonate formation on mica supported extracellular polymeric substance produced by Rhodococcus opacus

Extracellular polymeric substance (EPS) extracted from Rhodococcus opacus bacterial strain was used as a matrix for calcium carbonate precipitation using the vapour diffusion method. The total exopolymer and water-soluble exopolymer fraction of different concentrations were spread on the mica surface by the spin-coating method. The obtained layers were characterized using the atomic force microscopy measurement and XPS analysis. The effects of polymer concentration, initial pH of calcium chloride solution and precipitation time on the obtained crystals properties were investigated. Raman spectroscopy and scanning electron microscopy were used to characterize the precipitated minerals. It was found that the type of precipitated CaCO{sub 3} polymorph and the crystal size depend on the kind of EPS fraction. The obtained results indicates that the water soluble fraction favours vaterite dissolution and calcite growth, whereas the total EPS stabilizes vaterite and this effect is stronger at basic pH. It seems to be due to different contents of the functional group of EPS fractions. - Highlights: • CaCO{sub 3} crystal size and polymorph can be controlled by EPS substance obtained from R. opacus. • The water soluble fraction favours vaterite dissolution and calcite growth. • The total EPS stabilizes vaterite. • This effect is stronger at basic pH.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Nucleation and growth of α phase in a metastable β-Titanium Ti-5Al-5Mo-5V-3Cr alloy: Influence from the nano-scale, ordered-orthorhombic O" phase and α compositional evolution

We investigated the nucleation and growth of α precipitates in the presence of nano-scale, titanium-rich, ordered-orthorhombic O" precipitates formed during heating at 5 °C/min to 400 °C in a metastable β-Ti alloy, Ti-5Al-5Mo-5V-3Cr. The O" precipitates are found to assist α nucleation by serving as preferential nucleation sites. In the very initial stages of its precipitation, the α phase is found to have formed via a coupled diffusional-displacive mode as titanium-rich plates. At this stage, aluminum partitions equally between the β matrix and the growing α precipitates, but slowly diffuses up-hill into the α phase during isothermal aging at 400 °C for 15 h. The interplay between such pre-formed metastable phases and α can be exploited to tailor the microstructure, by refining the α distribution, and consequently improve the mechanical properties of β-Ti alloys. Finally, our work paves the way for exploiting this cascade of metastable phases for further microstructural engineering of β-Ti alloys.

36 MATERIALS SCIENCE↗

Lignin-Derived Methoxyterephthalates for Performance-Advantaged Polymers and Plasticizers

Lignin-derived aromatic carboxylic acids can be produced from oxidative catalytic processes and are promising building blocks for performance-advantaged bioproducts that leverage their inherent heteroatom functionalities. Here, we synthesize 2-methoxyterephthalate and 2,6-dimethoxyterephthalate derivatives by electrochemical carboxylation of guaiacyl- and syringyl-derived lignin monomers obtained from the oxidative deconstruction of lignin. These methoxylated terephthalates are evaluated as comonomers in poly(ethylene terephthalate) (PET) and as plasticizers that could replace petrochemically-derived isophthalate and phthalate, respectively. Specifically, we copolymerize 2-methoxy- and 2,6-dimethoxyterephthalate with dimethyl terephthalate to form several PET copolymers, both of which enable the properties of PET to be tuned, with an incorporation beyond 25% producing amorphous polyesters. At 10 mol % loading in the copolymers, we demonstrate that the bioderived comonomers exhibit comparable behavior to isophthalic acid, a commonly used comonomer in PET, by lowering the crystallinity and melting temperature. Moreover, methoxyterephthalate esters (2-ethylhexyl and butyl) are compared to phthalate and terephthalate ester counterparts used as poly(vinyl chloride) (PVC) plasticizers. The bioderived plasticizers are comparable to the petroleum-derived incumbents in reducing the glass transition temperature and increasing the thermal stability of PVC. Furthermore, the dimethoxyterephthalic esters are expected to have an extended lifetime in the polymer matrix due to their lower volatility and lower diffusion coefficients calculated by molecular dynamic simulations. These results demonstrate that the isophthalate and phthalate components in polyesters and plasticizers, respectively, could be substituted with biobased methoxyterephthalate derivatives.

09 BIOMASS FUELS↗

Enhanced Diffusive Transport in Fluctuating Porous Media

Mass transport within porous structures is a ubiquitous process in biological, geological, and technological systems. Despite the importance of these phenomena, there is no comprehensive theory that describes the complex and diverse transport behavior within porous environments. While the porous matrix itself is generally considered a static and passive participant, many porous environments are in fact dynamic, with fluctuating walls, pores that open and close, and dynamically changing cross-links. While diffusion has been measured in fluctuating structures, notably in model biological systems, it is rarely possible to isolate the effect of fluctuations because of the absence of control experiments involving an identical static counterpart, and it is generally impossible to observe the dynamics of the structure. In this paper, we present a direct comparison of the diffusion of nanoparticles of various sizes within a trackable, fluctuating porous matrix and a geometrically equivalent static matrix, in conditions spanning a range of regimes from obstructed to highly confined. The experimental system comprised a close-packed layer of colloidal spheres that were either immobilized to a planar surface or allowed to fluctuate locally, within the space defined by their nearest neighbors. Interestingly, the effective long-time diffusion coefficient was approximately 35–65% greater in the fluctuating porous matrix than in the static one (depending on the size of the nanoparticle probes), regardless of the geometric regime. This was explained by considering the enhancing effects of matrix fluctuations on the short-time diffusion coefficient and cooperative “gate-opening” motions of matrix particles and nanoparticle probes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Viscosities, diffusion coefficients, and mixing times of intrinsic fluorescent organic molecules in brown limonene secondary organic aerosol and tests of the Stokes–Einstein equation

Viscosities and diffusion rates of organics within secondary organic aerosol (SOA) remain uncertain. Using the bead-mobility technique, we measured viscosities as a function of water activity ( a w ) of SOA generated by the ozonolysis of limonene followed by browning by exposure to NH 3 (referred to as brown limonene SOA or brown LSOA). These measurements together with viscosity measurements reported in the literature show that the viscosity of brown LSOA increases by 3–5 orders of magnitude as the a w decreases from 0.9 to approximately 0.05. In addition, we measured diffusion coefficients of intrinsic fluorescent organic molecules within brown LSOA matrices using rectangular area fluorescence recovery after photobleaching. Based on the diffusion measurements, as the a w decreases from 0.9 to 0.33, the average diffusion coefficient of the intrinsic fluorescent organic molecules decreases from 5.5 × 10 - 9 to 7.1 × 10 - 13 cm 2 s -1 and the mixing times of intrinsic fluorescent organic molecules within 200 nm brown LSOA particles increases from 0.002 to 14 s. These results suggest that the mixing times of large organics in the brown LSOA studied here are short ( < 1 h) for a w and temperatures often found in the planetary boundary layer (PBL). Since the diffusion coefficients and mixing times reported here correspond to SOA generated using a high mass loading ( ~1000 µ g m -3 ), biogenic SOA particles found in the atmosphere with mass loadings ≤10 µ g m -3 are likely to have higher viscosities and longer mixing times (possibly 3 orders of magnitude longer). These new measurements of viscosity and diffusion were used to test the accuracy of the Stokes–Einstein relation for predicting diffusion rates of organics within brown LSOA matrices. The results show that the Stokes–Einstein equation gives accurate predictions of diffusion coefficients of large organics within brown LSOA matrices when the viscosity of the matrix is as high as 10 2 to 10 4 Pa s. These results have important implications for predicting diffusion and mixing within SOA particles in the atmosphere.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

First-principles study of migration and diffusion mechanisms of helium in α-Be

The behavior of interstitial helium in α-Be has been studied with first-principles method. It is found that the most favored position for helium is the basal octahedral (BO) site, closely followed by the basal tetrahedral (BT) site, in agreement with previous predictions. The interaction energy between the helium and the neighborhood Be atoms and the deformation energy of α-Be matrix are calculated. The feasible minimum-energy pathways (MEP) of interstitial helium atoms in α-Be matrix and the corresponding atomic structures of the saddle points associated with the each MEP are investigated. The temperature-dependent diffusion coefficients have also been predicted. It is confirmed that the interstitial helium diffuses two-dimensionally at low temperatures; however, it can diffuse three-dimensionally at higher temperatures. Besides, the microscopic parameters in the pre-factor and activation energy of the diffusion coefficients are obtained. Both diffusion coefficients are higher than the available experiment data, which may attribute to the fact that under real condition the diffusion is not free, i.e. the actual α-Be matric has various defects and impurities which heavily affect the diffusion of helium. Therefore, our theoretical prediction is the upper bound for helium diffusion in α-Be matrix.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Neutron, fluorescence, and optical imaging: An in situ combination of complementary techniques

An apparatus which enables the simultaneous combination of three complementary imaging techniques, optical imaging, fluorescence imaging, and neutron radiography, is presented. While each individual technique can provide information on certain aspects of the sample and their time evolution, a combination of the three techniques in one setup provides a more complete and consistent data set. The setup can be used in transmission and reflection modes and thus with optically transparent as well as opaque samples. Its capabilities are illustrated with two examples. A polymer hydrogel represents a transparent sample and the diffusion of fluorescent particles into and through this polymer matrix is followed. In reflection mode, the absorption of solvent by a nile red-functionalized mesoporous silica powder and the corresponding change in fluorescent signal are studied.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Accelerated coupled Monte Carlo-Thermal hydraulic calculations using a hybrid GTF-diffusion-based prediction block: first results

Accurate predictions of spatial power and temperature distributions require the coupling of a neutron transport solver with a thermal-hydraulic (TH) feedback. Nowadays, Monte Carlo (MC) codes are widely coupled to TH solvers, typically via a Picard iteration (PI) method, due to the higher fidelity that such frameworks can produce. To speed up a PI, a prediction step can produce an improved initial guess for a source distribution and feed it to the MC code. Recent work investigated a prediction step that uses generalized transfer functions (GTFs) to predict the macroscopic cross sections' variations following a perturbation in TH properties, such as coolant density. The previous method also relied on first order perturbation (FOP) theory to predict perturbed power profiles, rather than using an expensive MC iterate. The implemented FOP method relied on generating a fission matrix from which the forward and adjoint Eigenmodes were extracted and later used to for power calculations. The generation of the fission matrix can introduce a significant computational overhead, therefore undermining the performance of the proposed hybrid technique when applied to high-dimensional problems, e.g., full core calculations. This work attempts to improve the GTF-FOP prediction step by replacing the FOP solver with a nodal diffusion solver, thus eliminating the need to calculate a fission matrix. The GTF-diffusion step was tested for various moderator density perturbations. In each case, the predicted power distribution showed good agreement with the reference case. The latter is attributed to the generally good prediction of most spatially distributed macroscopic cross sections, except the transport cross section, which will become the focus of future work. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Accelerated Coupled Monte Carlo-Thermal Hydraulic Calculations using a Hybrid GTF-Diffusion-based Prediction Block: First Results

Accurate predictions of spatial power and temperature distributions require the coupling of a neutron transport solver with a thermal-hydraulic (TH) feedback. Nowadays, Monte Carlo (MC) codes are widely coupled to TH solvers, typically via a Picard iteration (PI) method, due to the higher fidelity that such frameworks can produce. To speed up a PI, a prediction step can produce an improved initial guess for a source distribution and feed it to the MC code. Recent work [1, 2] investigated a prediction step that uses generalized transfer functions (GTFs) to predict the macroscopic cross sections’ variations following a perturbation in TH properties, such as coolant density. The previous method also relied on first order perturbation (FOP) theory to predict perturbed power profiles, rather than using an expensive MC iterate. The implemented FOP method relied on generating a fission matrix from which the forward and adjoint eigenmodes were extracted and later used to for power calculations. The generation of the fission matrix can introduce a significant computational overhead, therefore undermining the performance of the proposed hybrid technique when applied to high-dimensional problems, e.g., full core calculations. This work attempts to improve the GTF-FOP prediction step by replacing the FOP solver with a nodal diffusion solver, thus eliminating the need to calculate a fission matrix. The GTF-diffusion step was tested for various moderator density perturbations. In each case, the predicted power distribution showed good agreement with the reference case. The latter is attributed to the generally good prediction of most spatially distributed macroscopic cross sections, except the transport cross section, which will become the focus of future work.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Matrix-Free High-Performance Saddle-Point Solvers for High-Order Problems in \(\boldsymbol{H}(\operatorname{\textbf{div}})\)

Here, this work describes the development of matrix-free GPU-accelerated solvers for high-order finite element problems in H(div). The solvers are applicable to grad-div and Darcy problems in saddle-point formulation, and have applications in radiation diffusion and porous media flow problems, among others. Using the interpolation–histopolation basis, efficient matrix-free preconditioners can be constructed for the (1, 1)-block and Schur complement of the block system. With these approximations, block-preconditioned MINRES converges in a number of iterations that is independent of the mesh size and polynomial degree. The approximate Schur complement takes the form of an M-matrix graph Laplacian and therefore can be well-preconditioned by highly scalable algebraic multigrid methods. High-performance GPU-accelerated algorithms for all components of the solution algorithm are developed, discussed, and benchmarked. Numerical results are presented on a number of challenging test cases, including the “crooked pipe” grad-div problem, the SPE10 reservoir modeling benchmark problem, and a nonlinear radiation diffusion test case.

97 MATHEMATICS AND COMPUTING↗

Thermal diffusivity and thermal conductivity of SiC composite tubes: the effects of microstructure and irradiation

Cladding thermal conductivity is an important physical property in assessing the performance of silicon carbide (SiC)-cladded fuels for nuclear reactors. However, there is a significant lack of reliable data, particularly for irradiated materials, because the geometry complicates the measurement. This study investigates the thermal diffusivity of coupons with a curvature, machined from SiC fiber–reinforced SiC matrix composite tubes, with and without neutron irradiation under light water reactor–relevant temperature and dose conditions. The tested materials included full composite and duplex SiC composite tubes. The measurements were conducted using a modern flash diffusivity apparatus. The analyzed area on the specimen during diffusivity testing was reduced for improved measurement accuracy due to sample curvature. Post-irradiation measurements showed that the effects of neutron irradiation on thermal conductivity (e.g. thermal defect resistivity) are different between SiC composite plates versus tubes. The difference was explained by higher matrix density of the tube than the plate. This study provides reliable thermal properties of prototypic SiC composite tubes useful for fuel performance modeling of SiC-based cladding.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Anomalous relaxation and the high-temperature structure factor of XXZ spin chains

We compute the spin-structure factor of XXZ spin chains in the Heisenberg and gapped (Ising) regimes in the high-temperature limit for nonzero magnetization, within the framework of generalized hydrodynamics, including diffusive corrections. The structure factor shows a hierarchy of timescales in the gapped phase, owing to s-spin magnon bound states (“strings”) of various sizes. Although short strings move ballistically, long strings move primarily diffusively as a result of their collisions with short strings. The interplay between these effects gives rise to anomalous power-law decay of the spin-structure factor, with continuously varying exponents, at any fixed separation in the late-time limit. We elucidate the cross-over to diffusion (in the gapped phase) and to superdiffusion (at the isotropic point) in the half-filling limit. We verify our results via extensive matrix product operator calculations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Connecting Hindered Transport in Porous Media across Length Scales: From Single-Pore to Macroscopic

Hindered mass transport is widely observed in various porous media, including filtration membranes and porous rocks. However, there is no universal model capable of predicting transport in porous media due to the heterogeneity of porous structures and the complexity of the underlying microscopic mechanisms, including electrostatic and hydrodynamic effects. Here, we used a highly ordered porous medium (i.e. a silica inverse opal film) as a model system to directly explore the effects of geometric parameters (i.e. pore size, pore throat size and tracer particle size) and microscopic interaction parameters (e.g. controlled by ionic strength) on nanoparticle transport in porous environments using three-dimensional single-particle tracking. We found a linear scaling relation between the macroscopic diffusion coefficient and microscopic diffusion behaviors and a combination of parameters associated with microscopic features and phenomena, including both geometric effects and particle-level interactions. The proportionality coefficient relating micro and macro behaviors was complex and related to the connectivity of the matrix and pore-size variation, which could lead to tortuous diffusion pathways, hindering macroscopic transport. Furthermore, these findings provide important insights into nanoparticles and macromolecules transport in various porous media.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗