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At least 235 records · Page 13

Testing and Modeling of Functionally Graded Aluminum-Doped Zinc Oxide Using Spark Plasma Sintering and Discrete Powder Layers of Varying Composition

Functionally graded material (FGM) ZnO is made via spark plasma sintering/field-assisted sintering technique (SPS/FAST) by varying the Al dopant content along the z-axis or pressing direction. A wide range of Al content (0–5 wt%) is used by adding Al powder to nanosized ZnO powder. Thermoelectric (TE) measurements are done on the FGM and individual layers made separately. X-ray diffraction (XRD) shows two phases, ZnO and spinel phase (ZnAl 2 O 4 ). High-resolution Raman spectroscopy reveals doped ZnO and spinel phase (ZnAl 2 O 4 ) spatially and shows segregation in the layer with highest Al content. Electron backscatter diffraction (EBSD) reveals noticeable grain growth with decreasing Al content, and there is a common, random preferred orientation in all layers. The tested properties are used to simulate efficiency curves for a discretely graded, five-layer FGM as well as a homogenous material, where both graded structures provide an opportunity to widen the current density ranges and therefore the temperature range of useful energy conversion.

36 MATERIALS SCIENCE↗

Entanglement Renormalization for Quantum Field Theories with Discrete Wavelet Transforms

We propose an adaptation of Entanglement Renormalization for quantum field theories that, through the use of discrete wavelet transforms, strongly parallels the tensor network architecture of the Multiscale Entanglement Renormalization Ansatz (a.k.a. MERA). Our approach, called wMERA, has several advantages of over previous attempts to adapt MERA to continuum systems. In particular, (i) wMERA is formulated directly in position space, hence preserving the quasi-locality and sparsity of entanglers; and (ii) it enables a built-in RG flow in the implementation of real-time evolution and in computations of correlation functions, which is key for efficient numerical implementations. As examples, we describe in detail two concrete implementations of our wMERA algorithm for free scalar and fermionic theories in (1+1) spacetime dimensions. Possible avenues for constructing wMERAs for interacting field theories are also discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Numerical analysis of a time discretized method for nonlinear filtering problem with Lévy process observations

Abstract In this paper, we consider a nonlinear filtering model with observations driven by correlated Wiener processes and point processes. We first derive a Zakai equation whose solution is an unnormalized probability density function of the filter solution. Then, we apply a splitting-up technique to decompose the Zakai equation into three stochastic differential equations, based on which we construct a splitting-up approximate solution and prove its half-order convergence. Furthermore, we apply a finite difference method to construct a time semi-discrete approximate solution to the splitting-up system and prove its half-order convergence to the exact solution of the Zakai equation. Finally, we present some numerical experiments to demonstrate the theoretical analysis.

Mathematics↗

A model for discrete fracture-clay rock interaction incorporating electrostatic effects on transport

Abstract A model based on the code CrunchClay is presented for a fracture-clay matrix system that takes electrostatic effects on transport into account. The electrostatic effects on transport include those associated with the development of a diffusion potential as captured by the Nernst-Planck equation, and the formation of a diffuse layer bordering negatively charged clay particles within which partial anion exclusion occurs. The model is based on a dual continuum formulation that accounts for diffuse layer and bulk water pore space, providing a more flexible framework than is found in the classical mean electrostatic potential models. The diffuse layer model is obtained by volume averaging ion concentrations in the Poisson-Boltzmann equation, but also includes the treatment of longitudinal transport within this continuum. The calculation of transport within the bulk and diffuse layer porosity is based on a new formulation for the Nernst-Planck equation that considers averaging of diffusion coefficients and accumulation factors at grid cell interfaces. Equations for function residuals and the associated Jacobian matrix are presented such that the system of nonlinear differential-algebraic equations can be solved with Newton’s method. As an example, we consider a 2D system with a single discrete fracture within which flow and advective transport occurs that is coupled to diffusion in the clay-rich matrix. The simulation results demonstrate the lack of retardation for anions (e.g., 36 Cl − ) of the contaminant plume within the fracture flow system because they are largely excluded from the charged clay rock, while the migration of cations (e.g., 90 Sr ++ ) is more strongly attenuated. The diffusive loss of divalent cations in particular from the fracture is accentuated by their accumulation in the diffuse layer within the clay-rich matrix.

58 GEOSCIENCES↗

Characterizing Reactive Transport Behavior in a Three-Dimensional Discrete Fracture Network

While several studies have linked network and in-fracture scale properties to conservative transport behavior in subsurface fractured media, studies on reactive transport cases remain relatively underdeveloped. In this study, we explore the behavior of an irreversible kinetic reaction during the interaction of two solute plumes, one consisting of species A and the other species B. When the plumes converge, these species react kinetically to form a new species C via A+B→kC. This reactive system is studied using a three-dimensional discrete fracture network (DFN) model coupled with reactive Lagrangian particle tracking. We find that the interplay of network topology and chemical properties of the reactive solutes controls reactive transport processes. The network topology drives species A and B together, and the chemical properties dictate whether and how quickly a reaction occurs. Results demonstrate that reactions are most likely to occur in high-velocity fractures that make up the network backbone. The interplay between species’ chemical properties and transport is characterized by a non-dimensional Damköhler (Da) number. We show that the spatial distribution of reactions is sensitive to Da, which subsequently influences late-time tailing behavior in outlet breakthrough time distributions. The results of this study provide initial insights into how an irreversible reaction occurs during transport in a fracture network, using a methodology that can be applied to study reactive transport in a wide range of fractured media environments and contexts.

58 GEOSCIENCES↗

Simulation of mixed-mode fracture using the combined finite–discrete element method

It has been shown experimentally that under mixed tensile and compressive stress states, a corresponding mixed-mode fracture will occur. Here, the formation of mixed-mode fractures is investigated using the combined finite–discrete element method. A series of simulations with confining pressures ranging from 7.5 to 150 MPa generate a spectrum of mixed-mode failure conditions. These stress states at failure span the transition from the tensile to compressive failure. The models reproduce previous experiments on Carrara marble using a dog-bone geometry, and a comparison shows good qualitative agreement with the experimental observations. This paper demonstrates that mixed-mode fracture can be captured via numerical simulations and identifies areas where further research is required to better understand mixed-mode fracture processes.

42 ENGINEERING↗

Direct interpolative construction of the discrete Fourier transform as a matrix product operator

The quantum Fourier transform (QFT), which can be viewed as a reindexing of the discrete Fourier transform (DFT), has been shown to be compressible as a low-rank matrix product operator (MPO) or quantized tensor train (QTT) operator. However, the original proof of this fact does not furnish a construction of the MPO with a guaranteed error bound. Meanwhile, the existing practical construction of this MPO, based on the compression of a quantum circuit, is not as efficient as possible. We present a simple closed-form construction of the QFT MPO using the interpolative decomposition, with guaranteed near-optimal compression error for a given rank. This construction can speed up the application of the QFT and the DFT, respectively, in quantum circuit simulations and QTT applications. We also connect our interpolative construction to the approximate quantum Fourier transform (AQFT) by demonstrating that the AQFT can be viewed as an MPO constructed using a different interpolation scheme.

97 MATHEMATICS AND COMPUTING↗

A Discrete Dendrite Dynamics Model for Epitaxial Columnar Grain Growth in Metal Additive Manufacturing with Application to Inconel

Epitaxial columnar grain growth is a prevalent microstructural feature in the additive manufacturing (AM) of metal components such as Inconel, with cubic unit cell crystal lattice structure (face centered cubic (FCC) or body centered cubic (BCC)). These columnar grains evolve from the partly molten grains in the substrate or the solidified metal. This work proposes an efficient model to simulate the competitive growth of epitaxial columnar dendritic grains. The proposed model tracks the dynamic changes in the dendrites emanating from discrete points along the solid/liquid interface of a quasi-steady melt pool (MP). These dynamic changes include convergence and divergence of growing dendrites. The model is extended to predict the microstructure of large 3D parts and experimentally validated by comparing the simulation results for laser powder bed fusion (L-PBF) and wire-arc additive manufacturing (WAAM) processes. The microstructure and pole figures are predicted for Inconel 718 samples produced by L-PBF and Inconel 740H samples produced by WAAM processes. Finally, the model predictions compare well with the observed microstructure and pole figures results for both the L-PBF and WAAM processes.

20 FOSSIL-FUELED POWER PLANTS↗

Transport Upscaling under Flow Heterogeneity and Matrix-Diffusion in Three-Dimensional Discrete Fracture Networks

For this work, we investigate the combined effects of network scale flow variability and retention due to matrix-diffusion on the scaling behavior of transport through fractured media. Two of the principal mechanisms controlling the transport of solutes through fractured low-permeability media are broad distributions of flow velocities and retention times in the solid matrix. We study the relative impact of these two processes under different initial conditions using a set of three-dimensional discrete fracture network simulations. We use these simulations to develop and calibrate an upscaled continuous time random walk (CTRW) approach for advective transport based on an Ornstein-Uhlenbeck model for the particle velocities that accounts for the fracture-matrix coupling using a compound Poisson process. This CTRW model can be conditioned on the initial solute distribution and allows to observe late-time scaling behavior at distances beyond what is feasible to observe using high-fidelity direct numerical simulations. We determine that the initial distribution of particles leads to marked differences in the persistent long-term scale behavior in the solute travel time distributions, even those undergoing retention due to matrix diffusion through implementation and analysis of the model.

54 ENVIRONMENTAL SCIENCES↗

Simulation of gas mixture dynamics in a pipeline network using explicit staggered-grid discretization

Here we develop an explicit staggered finite difference discretization scheme for simulating the transport of highly heterogeneous gas mixtures through pipeline networks. This study is motivated by the proposed blending of hydrogen into natural gas pipelines to reduce end use carbon emissions while using existing pipeline systems throughout their planned lifetimes. Our computational method accommodates an arbitrary number of constituent gases with very different physical properties that may be injected into a network with significant spatiotemporal variation. In this setting, the gas flow physics are highly location- and time- dependent, so that local composition and nodal mixing must be accounted for. The resulting conservation laws are formulated in terms of pressure, partial densities and flows, and volumetric and mass fractions of the constituents. We include non-ideal equations of state that employ linear approximations of gas compressibility factors, so that the pressure dynamics propagate locally according to a variable wave speed that depends on mixture composition and density. We derive compatibility relationships for network edge boundary values that are more complex than for a homogeneous gas. The simulation method is evaluated on initial boundary value problems for a single pipe and a small network, is cross-validated with a lumped element simulation, and used to demonstrate a local monitoring and control policy for maintaining allowable concentration levels.

97 MATHEMATICS AND COMPUTING↗

An experiment-informed discrete element modelling study of knife milling for flexural biomass feedstocks

A discrete element method (DEM) based approach is used to study the relationships between material attributes (MAs), processing parameters (PPs), and quality attributes (QAs) for the knife milling of maize stalks. An approximate DEM shape model was conceptualized based on real maize stalks and calibrated based on experimental bending test data for flexural properties (elastic bending stiffness, elastic bending angle limit, elastoplastic ratio, etc.). DEM simulations of maize stalk comminution in a Jordan Reduction Solutions (“JRS”) knife mill were performed to investigate the relationships between the MAs (maize stalk size and breakage stress limit), PPs (impeller rotational speed), and QAs (mass throughput and output particle size distribution (PSD)). The DEM results suggest that stalk length has little influence on mass throughput and PSD, whilst stalks with larger cross sections tend to generate larger sizes of milled particles given the same breakage stress limit. Both the DEM and experimental results show that faster impeller rotation (or higher power) does not necessarily generate higher throughput or smaller output PSD, especially for maize stalks of higher breakage stress limit. The correlations between these MAs, PPs and QAs are found highly stochastic, though breakage stress limit dictates mass throughput, regardless of stalk size. The DEM-predicted output particle size tended to match the experimental data with coarse PSDs based on sieve size but showed weakened fidelity with finer material, indicating the potential for further model improvement.

09 BIOMASS FUELS↗

A scalable domain decomposition method for FEM discretizations of nonlocal equations of integrable and fractional type

Nonlocal models allow for the description of phenomena which cannot be captured by classical partial differential equations. The availability of efficient solvers is one of the main concerns for the use of nonlocal models in real world engineering applications. Here, we present a domain decomposition solver that is inspired by substructuring methods for classical local equations. In numerical experiments involving finite element discretizations of scalar and vectorial nonlocal equations of integrable and fractional type, we observe improvements in solution time of up to 14.6x compared to commonly used solver strategies.

97 MATHEMATICS AND COMPUTING↗

Insights into the soft brittle-to-ductile transition from discrete dislocation dynamics

The Brittle-to-ductile transition (BDT) in body centered cubic metals exhibits a soft transition wherein the fracture toughness gradually rises to before the onset of ductility. The resultant brittle-to-ductile transition temperature can be described with an Arrhenius relationship whose activation energy is related to plasticity in the material. To provide further insight into the nature of the BDTT, in this work we utilized a discrete dislo- cation dynamics model with a crack to simulate the BDT and how it depends on the thermally activated nature of plasticity. The interrelationship between the BDT activation energy and the dislocation mobility parameters were determined via the calculation of first order sensitivity coefficients. This analysis allows us to demonstrate that the activation energy for the BDT is directly related to the activation energy for plasticity through an effective stress that defines this relationship. This effective stress physically is the average stress on the dislocations that move out of the crack. Lastly, we are able to show that this effective stress is dictated by the low temperature fracture toughness or cleave energy of the material and the source position, the latter of which can be affected by processing. Collectively, these results provide new insight into what controls the thermal activation of the BDT and what are the important parameters to control it.

36 MATERIALS SCIENCE↗

Modeling lattice rotation fields from discrete crystallographic slip bands in superalloys

Here in this work, we investigate the relationship between an intense slip band (ISB) and the zone of large lattice rotations that forms ahead of the tip of the ISB. We develop a crystal plasticity finite element model of a discrete ISB lying within an oligocrystalline assembly and calculate the local crystalline stress and lattice rotation fields generated by the ISB. The calculations demonstrate that, first, a region of severe lattice rotations, commonly referred to as a microvolume, does not form without the ISB, and second, large amounts of accumulated slip in the ISB are required to enlarge the microvolume to sizes and rotation magnitudes observed experimentally. Ahead of the ISB tip, the quintessential plastic zone always forms, but the atypical microvolume forms when non-concentrated and spatially diffuse slip is activated by the ISB-induced stress field. This result suggests that the detrimental ISB/microvolume pair will likely appear in pairs of crystals in which transmission of the slip from the ISB is severely blocked by the grain boundary, a hypothesis that we verify with a few target cases.

36 MATERIALS SCIENCE↗

A discrete dislocation dynamics study of precipitate bypass mechanisms in nickel-based superalloys

Order strengthening in nickel-based superalloys is associated with the extra stress required for dislocations to bypass the $\gamma'$ precipitates distributed in the $\gamma$ matrix. Depending on the operating conditions and microstructure, a rich variety of bypass mechanism has been identified, with various shearing and Orowan looping processes gradually giving way to climb bypass as the operating conditions change from the low/intermediate temperatures and high stress regime, to the high temperature and low stress regime. When anti phase boundary (APB) shearing and Orowan looping mechanisms operate, the classical picture is that, at for a given volume fraction, the bypass mechanism changes from shearing to looping with increased particle size and within a broad coexistence size window. Another possibility, which is supported by indirect experimental evidence, is that a third “hybrid” transition mechanism may operate. Here, in this paper we use discrete dislocation dynamics (DDD) simulations to study dislocation bypass mechanisms in Ni-based superalloys. We develop a new method to compute generalized stacking fault forces in DDD simulations, based on a concept borrowed from complex analysis and known as the winding number of a closed curve about a point. We use this method to study the mechanisms of bypass of a square lattice of spherical $\gamma'$ precipitates by $a/2\langle110\rangle$ {111} edge dislocations, as a function of the precipitates volume fraction and size. We show that not only the hybrid mechanism is possible, but also that it operates as the transition mechanism between the shearing and looping regimes over a wide range of precipitates volume fraction and radii. Based on our simulation results, we propose a simple model for the strength of this mechanism. We also consider the effects of a $\gamma$/$\gamma'$ lattice misfit on the bypass mechanisms, which we approximate by an additional precipitate stress computed according to Eshelby’s inclusion theory. We show that in the shearing and hybrid looping-shearing regimes, a lattice misfit generally results in an increased bypass stress. For sufficiently high lattice misfit, the critical bypass configuration in attractive dislocation-precipitates interactions changes dramatically, and the bypass stress is controlled by the pinning of the trailing dislocation on the exit side of the precipitates, similar to what has been reported in the high-temperature creep literature.

36 MATERIALS SCIENCE↗

Foundations for high-order, conservative cut-cell methods: Stable discretizations on degenerate meshes

Cut-cell methods for unsteady flow problems can greatly simplify the grid generation process and allow for high-fidelity simulations on complex geometries. However, cut-cell methods have been limited to low orders of accuracy. This is driven, largely, by the variety of procedures typically introduced to evaluate derivatives in a stable manner near the highly irregular embedded geometry. Here, a completely new approach, termed TEMO (truncation error matching and optimization), is taken to solve this problem. The approach is based on two simple and intuitive design principles. These principles directly allow for the construction of stable 8th To the best of the authors' knowledge, these are the highest orders ever achieved for a cut-cell discretization by a significant margin. This is done for both explicit and compact finite differences and is accomplished without any geometric transformations or artificial stabilization procedures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Discrete ordinates analysis of the forced-flight variance reduction technique in Monte Carlo neutral particle transport simulations

This paper presents mathematical formulations and methods to predict the effect of forced-flight variance reduction on Monte Carlo tally variance and calculation time. This includes deducing biasing operators that are then used to construct a history-score probability density function (HSPDF), which represents all possible Monte Carlo random walks and gives the probability of a Monte Carlo history scoring in a tally from a particular phase-space position. The history-score moment equations (HSMEs), the statistical moments of the HSPDF, are then derived to calculate the statistical behavior of the Monte Carlo tally when forced-flight variance reduction is applied. In addition, the future-time equation (FTE) is derived to predict the Monte Carlo computational time as a result of applying forced-flight variance reduction. The solutions of the HSMEs and FTE can be used to predict Monte Carlo computational cost. Furthermore, this work also describes a discrete ordinates method to solve the forced-flight HSMEs and FTE. Several 1-D and 2-D test problems verify that the derivations are performed and implemented correctly.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Agglomeration-based geometric multigrid solvers for compact discontinuous Galerkin discretizations on unstructured meshes

Here, we present a geometric multigrid solver for the Compact Discontinuous Galerkin method through building a hierarchy of coarser meshes using a simple agglomeration method which handles arbitrary element shapes and dimensions. The method is easily extendable to other discontinuous Galerkin discretizations, including the Local DG method and the Interior Penalty method. We demonstrate excellent solver performance for Poisson's equation, provided a flux formulation is used for the operator coarsening and a suitable switch function chosen for the numerical fluxes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗